Kyriakis, Sotirios A. (2016) Geothermal district heating networks: modelling novel operational strategies incorporating heat storage.

Transcription

1 Kyraks, Sotros A. (2016) Geothermal dstrct heatng networks: modellng novel operatonal strateges ncorporatng heat storage. PhD thess Copyrght and moral rghts for ths thess are retaned by the author A copy can be downloaded for personal non-commercal research or study, wthout pror permsson or charge Ths thess cannot be reproduced or quoted extensvely from wthout frst obtanng permsson n wrtng from the Author The content must not be changed n any way or sold commercally n any format or medum wthout the formal permsson of the Author When referrng to ths work, full bblographc detals ncludng the author, ttle, awardng nsttuton and date of the thess must be gven. Glasgow Theses Servce theses@gla.ac.uk

2 Geothermal dstrct heatng networks: modellng novel operatonal strateges ncorporatng heat storage SOTIRIOS A. KYRIAKIS Submtted n fulflment of the requrements for the degree of Doctor of Phlosophy at the Unversty of Glasgow School of Engneerng Unversty of Glasgow March 2016

3 Abstract The value of ntegratng a heat storage nto a geothermal dstrct heatng system has been nvestgated. The behavour of the system under a novel operatonal strategy has been smulated focusng on the energetc, economc and envronmental effects of the new strategy of ncorporaton of the heat storage wthn the system. A typcal geothermal dstrct heatng system conssts of several producton wells, a system of ppelnes for the transportaton of the hot water to end-users, one or more re-njecton wells and peak-up devces (usually fossl-fuel bolers). Tradtonally n these systems, the producton wells change ther producton rate throughout the day accordng to heat demand, and f ther maxmum capacty s exceeded the peak-up devces are used to meet the balance of the heat demand. In ths study, t s proposed to mantan a constant geothermal producton and add heat storage nto the network. Subsequently, hot water wll be stored when heat demand s lower than the producton and the stored hot water wll be released nto the system to cover the peak demands (or part of these). It s not ntended to totally phase-out the peak-up devces, but to decrease ther use, as these wll often be nstalled anyway for back-up purposes. Both the ntegraton of a heat storage n such a system as well as the novel operatonal strategy are the man noveltes of ths thess. A robust algorthm for the szng of these systems has been developed. The man nputs are the geothermal producton data, the heat demand data throughout one year or more and the topology of the nstallaton. The outputs are the szng of the whole system, ncludng the necessary number of producton wells, the sze of the heat storage and the dmensons of the ppelnes amongst others. The results provde several useful nsghts nto the ntal desgn consderatons for these systems, emphaszng partcularly the mportance of heat losses. Smulatons are carred out for three dfferent cases of szng of the nstallaton (small, medum and large) to examne the nfluence of system scale. In the second phase of work, two algorthms are developed whch study n detal the operaton of the nstallaton throughout a random day and a whole year, respectvely. The frst algorthm can be a potentally powerful tool for the operators of the nstallaton, who can know a pror how to operate the nstallaton on a random day gven the heat demand. The second algorthm s used to obtan the amount of electrcty used by the pumps as well as the amount of fuel used by the peak-up bolers over a whole year. These comprse the man operatonal costs of the nstallaton and are among the man nputs of the thrd part of the study. In the thrd part of the study, an ntegrated energetc, economc and envronmental analyss of the 1

4 studed nstallaton s carred out together wth a comparson wth the tradtonal case. The results show that by mplementng heat storage under the novel operatonal strategy, heat s generated more cheaply as all the fnancal ndces mprove, more geothermal energy s utlsed and less fuel s used n the peak-up bolers, wth subsequent envronmental benefts, when compared to the tradtonal case. Furthermore, t s shown that the most attractve case of szng s the large one, although the addton of the heat storage most greatly mpacts the medum case of szng. In other words, the geothermal component of the nstallaton should be szed as large as possble. Ths analyss ndcates that the proposed soluton s benefcal from energetc, economc, and envronmental perspectves. Therefore, t can be stated that the am of ths study s acheved n ts full potental. Furthermore, the new models for the szng, operaton and economc/energetc/envronmental analyses of these knd of systems can be used wth few adaptatons for real cases, makng the practcal applcablty of ths study evdent. Havng ths study as a startng pont, further work could nclude the ntegraton of these systems wth end-user demands, further analyss of component parts of the nstallaton (such as the heat exchangers) and the ntegraton of a heat pump to maxmse utlsaton of geothermal energy. Keywords: Geothermal, energy, dstrct, heatng, storage, operaton, strategy. 2

5 Acknowledgments Ths thess denotes the end of my doctoral studes. My sncere gratefulness and apprecaton goes to the followng people who helped me throughout these years wth many dfferent ways: My supervsor, Professor Paul Younger, for trustng me n ths poston and gvng me the chance to do a Ph.D. whch has always been a dream for me. Hs help and advce throughout my studes have been prceless. My second and thrd supervsors, Dr Manosh Paul and Dr Edryd W. Stephens, for ther useful comments and supervson. Many thanks also to Dr Zhbn Yu for gvng me the chance to assst hm wth hs courses. Cluff Geothermal Ltd., the Energy Technology Partnershp of Scotland (ETP) and the Unversty of Glasgow for fundng ths research project. A dstnct acknowledgment goes to Dr Mchael Felks of Cluff Geothermal, my ndustral supervsor, for the many frutful dscussons, the tmes that he hosted me n hs home and the general help and advce that he provded me. Mr Bert Young from the Estates and Buldngs offce of the Unversty of Glasgow for provdng me wth the heat demand data that I used n my thess, the Brtsh Atmospherc Data Centre (BADC) for gvng me access to the weather data that I used n a part of my thess as well as to Dr Rchard Coulton for the very useful nformaton on the storage tank costs. Mrs Elane McNamara and Mrs Heather Lambe of the Unversty of Glasgow for answerng my endless questons and beng always wllng to help. My Greek frends from Glasgow- Nkos, Maranna, Andreas, Ignatos and many othersfor ther wonderful company. Thanks a lot to all my foregn frends that I made n Glasgow- my Spansh frend and ex-flatmate Juan, my Mexcan frend Fernando, my Italan frends Alessandro and Ncola- and all the other wonderful people that I have met these 3.5 years. 3

6 My frends from Greece- Dmtrs, Chrstos, Kostas, Serafem, Anna, Stefanos and Thanass- for sufferng me all these years. Fnally, my most sncere grattude goes to my very own people: My parents- Anastasos and Mara- for ther endless support, love and values that they provded me snce I was born; My ssters- Eleana and Dmtra- for the very beautful moments; and the most mportant person for me- my grlfrend, Athna- for her endless love, support and for belevng n me and my capabltes. 4

7 Ths thess s dedcated to the memory of my frend, George Apostolou. 5

8 Declaratons Part of the work presented n ths thess has been publshed n the followng artcles: Kyraks, S.A., and Younger, P.L., Towards the ncreased utlsaton of geothermal energy n a dstrct heatng network through the use of a heat storage. Appled Thermal Engneerng, 94: Kyraks, S.A., Improvng the operaton of a geothermal dstrct heatng network through the use of a heat storage tank. In: Proceedngs of the 14 th UK Heat Transfer Conference, Ednburgh, UK, 7-8 September Kyraks, S.A., Effect of heat storage n geothermal dstrct heatng systems. In: Proceedngs of the 2015 ASME-ATI-UIT Conference, Naples, Italy, May (ISBN: ) Kyraks, S.A., Younger, P.L., Paul, M.C., and Stephens, W.E., Matchng producton and demand n geothermal dstrct heatng networks. Poster presentaton to the annual ETP Conference, Dundee, UK. Kyraks, S.A., Younger, P.L., Paul, M.C., and Stephens, W.E., Matchng producton and demand n geothermal dstrct heatng networks. In: Proceedngs of the 5 th European Geothermal Ph.D. Day, Darmstadt, Germany, 31 March-2 Aprl 2014, pp.: Kyraks, S.A., Younger, P.L., Paul, M.C., and Stephens, W.E., Advanced analyss of geothermal dstrct heatng systems. Poster presentaton to the annual ETP Conference, Ednburgh, UK. 6

9 I declare that, except when explct reference s made to the contrbuton of others, ths thess s my own work and t has not been submtted for any other degree at the Unversty of Glasgow or any other nsttuton. Sotros Kyraks Glasgow, March

10 Table of Contents Abstract... 1 Acknowledgments... 3 Declaratons... 6 Lst of Tables Lst of Fgures INTRODUCTION Motvaton, am, objectves and noveltes of ths thess Structure of the thess LITERATURE REVIEW Dstrct heatng Geothermal Energy Geothermal dstrct heatng General Examples of geothermal dstrct heatng systems Desgn aspects Basc thermodynamc evaluaton Addtonal parameters for the energetc evaluaton of geothermal dstrct heatng systems Economc analyss Thermal energy storage General Thermal energy storage n dstrct heatng systems Thermal energy storage n geothermal dstrct heatng systems Summary SIZING OF A GEOTHERMAL DISTRICT HEATING SYSTEM Introducton Mathematcal Modellng Inputs of the model

11 3.2.2 Frst calculaton of the basc parameters Szng of the geothermal nstallaton Szng of the hot water storage tank Energy balance n the hot water storage tank Szng of the ppelnes of the network Integrated model Possble sources of error Outputs of the model Results Dscusson Summary OPERATION OF A GEOTHERMAL DISTRICT HEATING SYSTEM Introducton Operaton over a randomly-selected day Input data Functons used n the model Output data Operaton over a year Results Operaton over random days Annual operaton Dscusson Summary ECONOMIC, ENVIRONMENTAL AND ENERGETIC ANALYSIS OF A GEOTHERMAL DISTRICT HEATING SYSTEM Introducton Methodology Economc analyss Envronmental analyss

12 5.2.3 Energetc ndces of the nstallaton Results Dscusson Further nvestgaton on the fnancal vablty of the nvestment Summary CONCLUSION Achevement of am and objectves Summary of contrbutons of the thess Recommendatons for future work APPENDICES Appendx A Senstvty analyss of two basc parameters of the system Appendx B Relatonshp between the heat demand and the weather condtons B1) Introducton B2) Methodology B3) Results B4) Concluson Appendx C Calculaton of the cost of the storage tanks Appendx D Hstorc electrcty and gas prces for non-domestc users n the U.K REFERENCES

13 Lst of Tables Table 2.1 Indcatve results of several studes conducted on energetc and exergetc analyses of geothermal dstrct heatng systems Table 3.1 Man nput data Table 3.2 Man results of the szng of the nstallaton Table 3.3 Desgn temperatures of the transmsson network (K) Table 3.4 Optmum dmensons of the transmsson network's ppelnes (cm) Table 3.5 Desgn temperatures of the dstrbuton network (K) Table 3.6 Optmum dmensons of the dstrbuton network (cm) Table 3.7 Temperature drop per length for the ppelnes of the network (K/km) Table 3.8 Captal Cost and length of each par of ppelnes (Costs n, lengths n m) Table 3.9 Senstvty analyss of the storage tank heat losses Table 3.10 Proporton of each part of the cost durng the szng of the transmsson ppelnes (75%le case) Table 4.1 Daly heat demands of the desgn-day for each case of szng as calculated n Chapter Table 4.2 Daly heat demands of the random days chosen for study n ths secton Table 4.3 Total mass of fuel (kg) used over the day for each case Table 4.4 Necessary geothermal flow rate (kg/s) for each case Table 4.5 Man results of the studed case Table 4.6 Man results of the tradtonal operaton of the nstallaton Table 5.1 Unt prces of fuel and electrcty for each case of szng Table 5.2 Average annual ncrease of the prce of fuel and electrcty for each case of szng Table 5.3 Man ntal captal costs of the studed and the tradtonal case for each case of szng Table 5.4 Man ntal runnng costs of the studed and the tradtonal case for each case of szng Table 5.5 Fnancal ndces of the studed and the tradtonal case (RHI ncluded) Table 5.6 Fnancal ndces of the studed and the tradtonal case (RHI not ncluded) Table 5.7 Results of the envronmental and energetc analyss of the nstallaton

14 Lst of Fgures Fgure 1.1 Total U.K. end energy use n 2013 (DECC, 2014) Fgure 1.2 Typcal layout of a Geothermal Dstrct Heatng System (P.W. = Producton Well, R.W. = Re-njecton Well, G.H.E. = Geothermal Heat Exchanger, SS = Substaton) Fgure 1.3 Fluctuaton of the heat demand for a set of houses (Bosman et al., 2012).. 19 Fgure 1.4 Layout of the proposed system (H.S.T. = Hot Water Storage Tank, C.S.T. = Cold Water Storage Tank, the other abbrevatons are as n Fg. 1.2) Fgure 2.1 Smplfed schematc flow-chart for a geothermal dstrct heatng energy system (from Hepbasl, 2010) Fgure 2.2 Installed geothermal drect-use capacty n MWth n European countres at the end of 2012 (GeoDH, 2013) Fgure 2.3. Classfcaton of geothermal felds on the bass of enthalpy (Younger, 2015) Fgure 3.1 Smplfed scheme ndcatng the temperatures across the transmsson ppelnes (G.H.E. = Geothermal Heat Exchanger, D.N. = Dstrbuton network, P.W. = Producton Well, R.W. = Re-njecton Well, H.S.T. = Hot water storage tank, C.S.T. = Cold water storage tank) Fgure 3.2 Heat flows and temperatures through the sdes of the tank Fgure 3.3 A schematc llustraton of the mass balances and temperatures assocated wth the hot water storage tank Fgure 3.4 Cross-sectonal area of a ppelne wth the assocated dmensons Fgure 3.5 Studed system of double pre-nsulated underground ppes Fgure 3.6 Inlet and outlet temperatures n each spatal element of the ppelnes Fgure 3.7 Heat demand data for the year of study Fgure 3.8 Sorted daly heat demands on a percentage bass Fgure 3.9 Volume of stored water over tme (25%le szng) Fgure 3.10 Volume of stored water over tme (50%le szng) Fgure 3.11 Volume of stored water over tme (75%le szng) Fgure 3.12 Temperature evoluton of stored water over tme (25%le szng) Fgure 3.13 Temperature evoluton of stored water over tme (50%le szng) Fgure 3.14 Temperature evoluton of stored water over tme (75%le szng) Fgure 3.15 Heat losses of the ppelnes aganst ther bural depth (75-C case) Fgure 3.16 Heat losses of the ppelnes aganst ther between dstance (75-C case)

15 Fgure 3.17 Heat losses of the ppelnes aganst the nlet temperature (75-C case) Fgure 3.18 Heat losses of the ppelnes aganst ther nternal dameter (75-C case) Fgure 3.19 Heat losses of the ppelnes aganst the mass flow rate (75-C case) Fgure 3.20 Schematc llustraton of the process Fgure 4.1 Herarchy of functons used n the developed model Fgure 4.2 Mass of stored water for Day 1 (25%le szng) Fgure 4.3 Mass of stored water for Day 1 (50%le szng) Fgure 4.4 Mass of stored water for Day 1 (75%le szng) Fgure 4.5 Mass of stored water for Day 2 (25%le szng) Fgure 4.6 Mass of stored water for Day 2 (50%le szng) Fgure 4.7 Mass of stored water for Day 2 (75%le szng) Fgure 4.8 Mass of stored water for Day 3 (25%le szng) Fgure 4.9 Mass of stored water for Day 3 (50%le szng) Fgure 4.10 Mass of stored water for Day 3 (75%le szng) Fgure 4.11 Mass of stored water for Day 4 (25%le szng) Fgure 4.12 Mass of stored water for Day 4 (50%le szng) Fgure 4.13 Mass of stored water for Day 4 (75%le szng) Fgure 4.14 Volume of stored water over the year (25%le szng) Fgure 4.15 Volume of stored water over the year (50%le szng) Fgure 4.16 Volume of stored water over the year (75%le szng) Fgure 5.1 Cash flow of the nvestment wth the RHI subsdy (25%le szng) Fgure 5.2 Cash flow of the nvestment wthout the RHI subsdy (25%le szng) Fgure 5.3 Cash flow of the nvestment wth the RHI subsdy (50%le szng) Fgure 5.4 Cash flow of the nvestment wthout the RHI subsdy (50%le szng) Fgure 5.5 Cash flow of the nvestment wth the RHI subsdy (75%le szng) Fgure 5.6 Cash flow of the nvestment wthout the RHI subsdy (75%le szng) Fgure 5.7 Influence of the varable cost of heatng on the cash flow of the nvestment (RHI ncluded-25%le szng) Fgure 5.8 Influence of the varable cost of heatng on the cash flow of the nvestment (RHI not ncluded-25%le szng) Fgure 5.9 Cash flow of the nvestment wth the RHI subsdy (25T-50D szng) Fgure 5.10 Cash flow of the nvestment wthout the RHI subsdy (25T-50D szng) 217 Fgure 5.11 Cash flow of the nvestment wth the RHI subsdy (25T-75D szng) Fgure 5.12 Cash flow of the nvestment wthout the RHI subsdy (25T-75D szng)

16 Fgure 6.1 Layout of the proposed system (G.H.E. = Geothermal Heat Exchanger, SS = Substaton, P.W. = Producton Well, R.W. = Re-njecton Well, H.S.T. = Hot Water Storage Tank, C.S.T. = Cold Water Storage Tank, Pel = Electrcal Power)

17 1 INTRODUCTION Worldwde concerns about the envronment grow day by day. The need for change to our energy polcy and behavour seems more necessary than ever as ther mpacts on the envronment worsen. Nowadays, the man concerns n energy polcy are sustanablty, securty of supply, as well as reducton of fossl fuels consumpton. So, ncreasng the share of renewable energy sources on the supply sde and mprovng the effcency on the demand sde are necessary for sustanable growth (Hepbasl, 2010; Parr, 2007). Over the last two decades, a lot of research has been carred out on renewable energy technologes whch can be a crucal soluton to the aforementoned problems. Renewable energy sources have many advantages, such as the neglgble envronmental polluton and the fact that these are an ndgenous source, ncreasng the energy ndependence from expensve energy mports and provdng jobs and growth to the local communtes. The mportance of energy ndependence can be seen by the data publshed n DECC (2015), where t s shown that a bg fracton of the fossl resources used for energy producton n the U.K. are mported. It s easly understood that ths energy mport s also dependent on the poltcal relatons between the nvolved countres. Ths fact becomes even more mportant when takng nto account the fragle contemporary poltcal scene, whch hghly endangers the relatonshps between countres that can stop the fossl fuel supply to each other at any tme. Ths scenaro could potentally be catastrophc for a bg mporter, lke the U.K. Therefore, the need for local, ndgenous and, f possbly, envronmentallyfrendly energy resources s even more necessary. All these crtera are fulflled by the renewable energy sources, such as wnd, solar, geothermal, and bomass energy amongst others. A basc dsadvantage of the majorty of renewable energy sources s ther ntermttent producton whch leads to unstable producton. The latter together wth the ntermttent, and often unpredctable, pattern of energy demand (heat, electrcty, and transportaton) poses a clear problem for matchng supply and demand. Ths problem can be solved by geothermal energy, whch s the only renewable energy source other than bomass whch offers constant producton and reaches avalablty factors close to 100%. Geothermal energy also has the prevously mentoned advantages of the other renewable energy sources. 15

18 In general, heatng accounts for a large proporton of our energy demands. More specfcally, n the U.K. the use of heat accounts for 48% of the total end energy use as can be seen n Fg Ths means that almost half of the energy produced s used n the fnal form of heat and thus heatng s a bg contrbutor to overall carbon emssons. Ths ndcates that usng renewable energy sources for heatng applcatons should be prortsed. In ths pont a paradox arses, as the majorty of the fundng and the research s focused on the ncreased use of renewable energy sources for electrcty producton (manly wnd and solar energy). Ths paradox s hghlghted even more by the fact that wth current technology (manly n the electrcal networks), there s a huge gap to acheve 100% penetraton of renewable energy sources n electrcty consumpton. Furthermore, even f ths s acheved sometme, for several countres t s qute dffcult to fulfl ther energy targets only by decarbonsng electrcty. All these facts pont out the necessty of developng or mprovng exstng technologes that can support heat provson by renewables. Ths thess ntends to show that decarbonsng the heatng sector by means of geothermal energy s not only possble, but can also be very effectve and attractve. Fgure 1.1 Total U.K. end energy use n 2013 (DECC, 2014) Our focus n ths study wll be on heat provson n domestc buldngs, but the methods and the results can be appled n any case of heatng f the temperature level of the source s adequate for the end-user needs. The focus s on domestc buldngs as the typcal range of temperatures needed s physcally close to that of geothermal energy, as wll be seen later. Typcally, heatng s provded n buldngs by two dfferent means. Frstly, t can be provded by local bolers, stoves, electrc heatng and, n general, by equpment whch produces heat wthn the buldng. A second opton s to be provded by a dstrct heatng 16

19 system, n whch the heat s produced n a central plant and dstrbuted to the end-users by means of a ppelne network. As wll be seen n the lterature revew, dstrct heatng systems are generally cheaper, more effcent and more envronmentally frendly than local heatng systems. Addtonally, geothermal energy (apart from ground-source heat pumps) s usually produced at scales larger than those of a sngle buldng and a sngle well can provde heat to numerous buldngs. For these two reasons, ths study s focused on geothermal dstrct heatng systems for heat provson n buldngs. A pont that should be mentoned here s that t s assumed that the studed systems are heat-only producton unts and not CHP unts. Usually, n the latter the heat producton s a by-product of the electrcty producton and, therefore, t s strongly coupled wth t. A heat-only producton unt s obvously more flexble as ts producton s ndependent of any electrcty producton. Ths s true for many geothermal systems, as outsde of volcanc regons ther temperatures n the majorty of the cases are not hgh enough for effcent electrcty producton usng current technology, but t s hgh enough for heatng provson. So, n the studed systems t s assumed that the pumped geothermal water s utlsed drectly for heatng purposes. Geothermal dstrct heatng, whch s the topc of ths research, addresses all of the above aspects of energy polcy as t s a green and ndgenous energy resource, whch decreases the use of fossl-fuels and can be a poneerng technology for sustanable growth. 1.1 Motvaton, am, objectves and noveltes of ths thess As mentoned before, the topc of ths thess s the study of geothermal dstrct heatng systems (GDHSs) as these combne the advantages of geothermal energy and dstrct heatng systems and can provde an affordable, effcent and envronmentally-frendly soluton for heatng purposes and can be a potental soluton to the energetc problem. In the next Chapter, an exhaustve lterature revew has been carred out on GDHSs and t wll be observed that the man gap s on ther operaton. To the author s knowledge, there has been no publshed research whch studes n detal the operaton of GDHSs. For that purpose, ths thess wll be focused on the operaton of GDHSs. Frstly, a bref explanaton of a GDHS should be gven. A typcal geothermal dstrct heatng system can be seen n Fg In these systems, the geothermal water s pumped 17

20 from the underground through one or more producton wells. The geothermal water s usually corrosve and n order to mnmse these effects and the possble scalng due to ts dssolved mnerals, ts heat s transferred to fresh water through a geothermal heat exchanger. It should be mentoned that a geothermal heat exchanger s a typcal heat exchanger (usually plate heat exchanger), but the word geothermal s used to dstngush t from any other heat exchangers that mght exst n the nstallaton, such as n the substaton or n the end-users. Subsequently, the heated fresh water s dstrbuted to the end-users through a system of ppelnes whch typcally ncludes a transmsson and dstrbuton network. The connecton between the transmsson and dstrbuton network often happens wth a substaton. After the heated water provdes ts heat to the end-users, t returns to the geothermal heat exchanger n order to be re-heated and contnue the cycle. At the same tme, the cooled geothermal water s ether re-njected to the underground or used n other purposes (such as agrculture) whch requre lower temperatures. These are the socalled ndrect GDHSs and these wll be studed throughout ths thess as the case of drect GDHSs s qute rare. Fgure 1.2 Typcal layout of a Geothermal Dstrct Heatng System (P.W. = Producton Well, R.W. = Re-njecton Well, G.H.E. = Geothermal Heat Exchanger, SS = Substaton) In practse, a GDHS s szed so that t can cover up to a specfc amount of heat demand whch s equal to ts capacty and ts typcal operaton s as follows: The mass flow rate from the geothermal wells s fluctuatng throughout the day, accordng to heat demand, up to ts maxmum capacty and f the heat demand cannot be covered by geothermal energy solely, peak-up devces (usually fossl-fred bolers) are used to cover the excess heat demand. On the other hand, the heat demand throughout the day s usually far from constant and fluctuates a lot throughout the day. As an ndcator, Fgure 1.3 shows the fluctuaton of the heat demand for a set of houses that was used n another study. Ths 18

21 fgure shows the average heat demand and ts devaton throughout the day for a set of 10 and 100 houses. It should be noted that the values of ths fgure have no relaton wth ths thess and ths fgure s only used to depct the fluctuaton of the heat demand. Fgure 1.3 Fluctuaton of the heat demand for a set of houses (Bosman et al., 2012) It can be easly understood that accordng to the fluctuaton of the heat demand and the capacty of the GDHS, the geothermal feld can be under-utlsed several tmes (.e. producng less geothermal energy than the avalable one), whle at other tmes t mght not be enough to cover the heat demand. In the latter case, expensve and pollutng peak-up bolers are used. Furthermore, n renewable energy sources t s desrable to maxmse ther utlsaton and to produce as much energy from these sources as possble. Intutvely, the bass of the man dea of ths study arses, whch s to the ncrease geothermal producton when the feld s under-utlsed n order to use ths energy later when needed. The latter together wth the lack of publshed research on the operaton of geothermal dstrct heatng systems gave rse to the man dea explored n ths thess, as follows: Instead of changng ts producton throughout the day the geothermal system wll operate at a constant producton rate. More detals on how to calculate ths constant producton rate wll be gven n Chapter 3. Furthermore, the 19

22 nstallaton wll be planned to operate on a daly bass, so each day may have a dfferent constant producton. When the geothermal producton s hgher than the heat demand, the excess geothermal energy wll be stored n a heat storage. On the other hand, the stored energy wll be released to the network when the geothermal producton s not enough to cover the heat demand, thus smoothng the overall operaton of the nstallaton and decreasng the use of the peak-up bolers. The layout of the proposed system can be seen n Fg It should be noted n ths pont that t s not ntended to totally phase-out the use of the peak-up bolers, as ths would probably lead to over-dmensonng of the geothermal nstallaton whch would lkely render the nvestment unfeasble, but to mnmse ther use. After all, there wll always be some peak-up bolers n ths knd of nstallatons for back-up purposes, so phasng them out would not remove ther captal cost n realty. Fgure 1.4 Layout of the proposed system (H.S.T. = Hot Water Storage Tank, C.S.T. = Cold Water Storage Tank, the other abbrevatons are as n Fg. 1.2) So, the am of ths thess s to study the effect of ncludng a heat storage n a GDHS under the proposed novel operatonal strategy. In other words, ths thess wll examne whether t s benefcal to nclude a heat storage under the proposed strategy n a GDHS from energetc, envronmental and economc perspectves. Ths s acheved by developng the followng three core models whch are the objectves of ths thess: 20

23 Model for the szng of a GDHS. Ths s a robust model for the szng of a GDHS that operates under the proposed strategy. The results of ths model wll also provde useful nsghts about the operaton of the prncpal components of a GDHS and dentfy where mprovements can be made. Model for the operaton of a GDHS. Ths model wll nvolve two sub-models, where the frst wll study the operatonal strategy of the nstallaton over a random day wth a gven heat demand and the second wll smulate the annual operaton of the nstallaton. The frst sub-model wll be a useful tool for the operators of the nstallaton as they wll know n advance how to schedule the operaton of the nstallaton. The second sub-model wll smulate how the nstallaton operates over an annual cycle and wll use ths to dentfy the basc operatonal costs of t. Model for the energetc, economc and envronmental analyss of a GDHS. In ths model, the man energetc, economc and envronmental ndces of the nstallaton wll be calculated and a comparson wth the tradtonal case,.e. the geothermal dstrct heatng system that operates wthout a heat storage and as mentoned n the begnnng of ths secton, wll be carred out. By dong ths comparson, the man queston whch s posed n the end of ths secton wll be answered and the am of ths thess wll have been acheved. The frst two of the above models are necessary for the thrd model as ths s a novel operaton of a GDHS so both ts szng and detaled operaton should be fully understandable. Both of these models are qute practcally-orented as wll be seen n the correspondent Chapters, and can be used n real nstallatons as tools for ther correspondng use. So, these models are also an mportant outcome of ths thess and can be a powerful tool for geothermal companes and planners. The man novelty of ths study s not only the ncluson of the heat storage n the system, but also the operaton n a novel way. Another novelty of ths thess s the approach to the modellng of the heat storage. Usually n dstrct heatng systems, stratfed hot water storage tanks are used as the heat storage. More detals on ths are gven n Chapter 2. In ths case, as there s no publshed research on ths aspect too n a GDHS and by takng nto account that the flow rates are qute bg n these systems (as wll be shown n Chapter 3), t s consdered dffcult to mantan the stratfcaton wthn the tank and, therefore, fully mxed storage tanks wll be used. Furthermore, there wll be no sngle 21

24 storage tank for the hot and cold streams, but, two dfferent storage tanks, one to store hot water and one to store cold water. The proposed confguraton can be seen n Fg In contrast wth the stratfed tanks whch are always full wth water (only the proporton of hot and cold water changes throughout the day), n our case both tanks wll operate n a fll-release mode. Ths means that the amount of water that s stored n each tank wll change throughout the day and t wll depend on the mass balance of the whole system. All these wll be more understandable n Chapter 3 of the thess. In the proposed approach, the mass flow rate to the left of the hot water storage tank (see Fg. 3.1) wll be constant throughout the day, whle the flow rate to the rght of the storage tank wll change accordng to the heat demand. It s assumed that the hot water storage tank wll be placed as close as possble to the substaton n order to obtan a qucker response n the change of the heat demand. The cold water storage tank wll ensure that the flow rate to the geothermal heat exchanger wll reman constant and can be placed anywhere between the heat exchanger and the substaton. The mportant component that has to be modelled s the hot water storage tank as ths s the man regulator between the producton and the demand. The mass fluxes between ths tank and the network as well as ts heat losses wll be studed n detal. As wll be seen n Chapter 3, the heat losses of the hot storage tank wll be neglgble, so the heat losses of the cold storage tank wll be even smaller as the temperature gradent between the envronment and the tank wll be smaller. Therefore, the cold water storage tank wll not be studed further as ts operaton can be ensured by the use of a control-valve and ths s out of the scope of ths thess. So, n the followng, the word tank wll refer to the hot water storage tank unless otherwse stated. Ths thess ntends to study manly f for a gven nstallaton, the ncluson of the heat storage and the novel operaton can cover economcally a hgher fracton of the heat demand wth geothermal energy. From another pont of vew, ths could ndcate the possble downszng of the nstallaton for the same heat demand coverage by geothermal energy. In concluson, the am of ths thess s to study the effect of ncludng a heat storage n a GDHS under a novel operatonal strategy from an energetc, economc and envronmental pont of vew. The man queston that wll be addressed s the followng: Is t worthwhle ncludng a heat store wthn the proposed operaton of a geothermal dstrct heatng system or not? 22

25 1.2 Structure of the thess In ths Chapter, a bref ntroducton n GDHSs, whch are the topc of ths thess was gven. Through a clear logcal path t was explaned why these systems are worth to study and what these can offer to a sustanable future socety. Furthermore, the man dea of ths study was explaned brefly and the objectves were clearly defned. In Chapter 2, the lterature revew of ths topc s provded. More specfcally, the lterature revew commences wth several detals on geothermal energy and dstrct heatng, ther advantages and dsadvantages, several hstorcal data on them as well as some lmts on ther expanson. Then, an exhaustve revew of geothermal dstrct heatng systems follows wth the majorty of the revew concernng the desgn aspects of the systems and ther energetc as well as ther economc analyss. Through ths revew the gap that was explaned above and set the objectves of ths thess s dentfed. Fnally, some detals are presented on the use of heat storage n dstrct heatng systems, n general, an n geothermal dstrct heatng systems n specfc. In Chapter 3, a model for the ntegrated and robust szng of a GDHS s developed. The mathematcal model s explaned n detal accompaned by all the governng equatons of the nvolved phenomena, such as mass conservaton equatons, heat and frcton losses etc. The whole study s carred out for three dfferent cases of szng whch are also explaned n detal, whle the only data that are real data are the heat demand data. The rest of the data are arbtrary realstc nputs selected by the author to make the whole model as realstc as possble. Ths s the case for the other Chapters too. Thereafter, the results of ths model are presented whch provde many useful conclusons, through an extensve dscusson, on the desgn of GDHSs and wll be qute useful durng the prelmnary desgn of these systems. In Chapter 4, the outcome of the prevous model (.e. the szed nstallaton) s used as nput n order to study the operaton of ths nstallaton n detal. Theoretcally, the nstallaton whch s the result of Chapter 3 wll have been bult and the model of ths Chapter wll be used to study ts operaton. Intally, a model that provdes the operatonal strategy of the nstallaton over a random day wth a known (or predcted) heat demand s presented. By operatonal strategy s meant the complete knowledge of the operaton of the nstallaton,.e. the necessary geothermal flow rate, when and by how much should the 23

26 storage tank be charged or dscharged etc. In realty, ths model could be a powerful tool for the operators of the nstallaton as they would know a pror how to operate the nstallaton when the heat demand s known. Then, ths model s extended for the study of the operaton of the nstallaton over a whole year. Although ths model uses the daly model as a bass, t has qute dfferent outputs. Its outputs are the man operatonal costs of the nstallaton whch are among the man nputs of the next Chapter. The results of the frst model are shown for dfferent random days wth varous daly heat demands whch provde useful knowledge on the operaton of the nstallaton for a range of heat demands. Fnally, the results of the annual operaton are also presented followed by an extensve dscusson for both models. In Chapter 5, the operatonal costs of the nstallaton as well as the other outputs of the second part of Chapter 4 are used as nputs together wth the captal costs of the nstallaton n order to carry out a comprehensve economc, energetc and envronmental analyss of the studed case. More specfcally, several fnancal ndces are calculated and the cash flows are presented for the nvestment, whle two energetc ndces are used for the energetc analyss together wth the calculaton of the emssons of the nstallaton for the envronmental part. All these calculatons are carred out both for the studed as well as for the tradtonal case of operaton of a GDHS. Through the analyss of the results and the comparson of the two cases, a clear answer s gven to the most mportant queston of ths thess on whether the ncluson of a heat storage n a GDHS s eventually benefcal or not. Fnally, n Chapter 6 a synopss of the man fndngs of the thess s provded together wth ts contrbutons to the feld. The thess ends wth some propostons about further work that could be carred out on the bass of ths study and for dfferent approaches that could be potentally used to maxmse the use of geothermal energy n the future energy system. 24

27 2 LITERATURE REVIEW 2.1 Dstrct heatng In general, dstrct heatng refers to the producton of heat n a central plant and ts dstrbuton to the consumers va a network of ppelnes. An mportant factor for the early development of dstrct heatng was the avalablty of ndustral waste heat, especally from power plants (Cassto, 1990). Dstrct heatng can use many heat sources, such as combned heat and power plants (CHP; coal-, gas- or bomass-fred), whch s the most common source; conventonal bolers; waste ncnerators; ndustral waste heat sources; solar collectors; heat pumps and geothermal energy (Lund and Lenau, 2009). The man advantages of dstrct heatng, as opposed to prvate heatng provson n each buldng, are well summarsed by Rosada (1988) and Rezae and Rosen (2012) as: the hgher effcency of the whole procedure, wth subsequent reducton of emssons; the faclty of waste-heat recovery; the ablty to utlze heat sources whch would be dffcult to utlze n sngledwellng nstallatons, such as heat from waste; the hgh level of relablty etc. The economc vablty of dstrct heatng depends a lot on the heat demand densty of the examned area. As the heat demand densty ncreases, the vablty of dstrct heatng ncreases (see Dalla Rosa et al., 2012, amongst others). The advantage of relablty was studed by Lauenburg et al. (2010). More specfcally, those authors examned what happens n a dstrct heatng network n the case of power falure. They found that usually natural crculaton occurs, so heat s stll beng provded to houses (usually about 80% of the nomnal heat) despte the power falure. A basc prerequste for that s the mantenance of dstrct heatng producton,.e. the heat producton must not be nterrupted by the power falure as would happen for example wth heat pumps. Dstrct heatng also has some dsadvantages, manly from an economc pont of vew. Usually t s not vable n areas of low populaton densty and t s necessary to provde some ncentves. Dstrct heatng also has hgh captal costs, so most of the tme subsdes are necessary. In addton, due to the hgh captal costs, t usually becomes the monopoly of the owner, whch s counter to the desre to have lberalsaton of energy markets (Grohnhet and Mortensen, 2003). Furthermore, t s dffcult to retroft exstng buldngs from a techncal and an economcal pont of vew. Fnally, dstrct heatng s usually 25

28 produced n CHP statons, and the heat producton s coupled wth, or lmted by, the electrcty producton. The latter reduces the flexblty of the heatng nstallaton. The development of dstrct heatng was faster n countres wth cold clmates, such as Iceland, Germany, Fnland, Sweden (Gustavsson, 1994a, b; amongst others), Denmark (Moller and Lund, 2010, amongst others), Latva (Lund et al., 1999), Lthuana (Rezae and Rosen, 2012), Belgum, Romana (Iacobescu and Badescu, 2011), Poland (Zgoda, 1986) etc. In the UK, the penetraton of dstrct heatng s stll qute low, about 1%, apparently due to short/md-term hgh rsks and regulatory uncertantes (Kelly and Polltt, 2010). However, the UK together wth Germany and France hosts 50% of the short-term market expanson potental for dstrct heatng wthn the European Unon (Persson and Werner, 2011). In the last 20 years, a lot of research has been carred out on varous aspects of dstrct heatng. A few examples are gven below for the nterested reader. Gustavsson (1994a, b) analysed possble energy conservaton measures for buldngs. The results showed that wth typcal conservaton measures a decrease of 30-50% n buldng energy consumpton can be acheved. Dalla Rosa and Chrstensen (2011) studed the concept of low energy dstrct heatng for buldngs. Ths concept s based on low-temperature operaton of the nstallaton. In any case, the lowest possble return temperature s needed for maxmum utlzaton of thermal energy. Noro and Lazzarn (2006) compared local heatng by natural gas wth dstrct heatng. Concernng emssons and energy effcency, the modern local heatng systems turn out to be more effcent than dstrct heatng. In contrast, ths s not the case from an economc pont of vew. The latter depends a lot on the taxaton of the fuel n local and dstrct heatng systems. Torcho et al. (2009) undertook envronmental research nto dstrct heatng systems, fndng that dstrct heatng s advantageous concernng CO2 emssons, but concernng the other pollutants the postve effect of dstrct heatng s not always so clear. The authors also menton that a dstncton between global and local emssons should always be made. Moller and Lund (2010) examned the potental expanson of dstrct heatng n areas prevously suppled by domestc bolers n the Dansh dstrct heatng system. The results showed that t s worth expandng the exstng network around ctes and towns and replacng natural gas bolers. In more remote areas, ndvdual heat pumps seem to be the optmum soluton. 26

29 Dotzauer (2003) appled an optmzaton algorthm to a dstrct heatng network whch ncluded the energy producton unt, energy storage and energy snks. The objectve was to mnmze the operatonal cost and to fnd the optmum producton plan, satsfyng the condton of fulfllng the heat demand on the md-term horzon,.e days. Verda et al. (2012) studed another optmzaton problem, whch examned whch users n an urban area should be connected to the dstrct heatng network and whch ones should not, n favour of beng served wth a ground-source heat-pump system. Concludng, t can be sad that he future of dstrct heatng depends manly on the prces of alternatves, the prce of electrcty and the dstance from the nearest network. In hgh heat densty areas dstrct heatng seems a better soluton, whle as heat densty decreases, heat pumps become more favorable. Of course, clear and precse legslaton s necessary for the constructon, adopton and expanson of dstrct heatng networks. In some cases, the change of the legslatve framework mght also be necessary. 2.2 Geothermal Energy Geothermal energy s the energy contaned n the Earth s crust as heat and ts orgn s manly from the processes that occur n Earth s nteror and heat conducton takng place to the upper layers. Ths energy can be used for electrcty producton and / or for drect uses. Typcally, temperatures above 15 o C can be utlzed and even lower f heat pumps are used (Banks, 2012). More detals on the use of heat pumps for geothermal applcatons can be found n the work of Underwood (2014). Dependng on the temperature of the source, dfferent utlzatons of geothermal energy can be acheved. Temperatures above 150 o C are usually used for electrcty generaton, but n recent years the development of new technologes,.e. bnary cycles, has made t possble to produce electrcty from water wth temperatures of only 120 o C. Lower temperatures stll are used for drect uses, such as space heatng, dstrct heatng, agrculture, aquaculture, balneology, dryng, snow meltng, ndustral processes, heatng of pools and spa, dstllaton etc. (e.g. Kecebas, 2011, amongst many others). Geothermal wells are categorsed nto: hydrothermal wells, whch are the most common wells; geo-pressured wells; shallow wells; and enhanced geothermal systems (EGS) or hot dry rocks (D Pppo, 2007). The latter are an emergng technology whch are beleved to ncrease geothermal potental by a large factor, compared to the currently 27

30 proven potental. For example, the potental of EGS systems s estmated to be ten tmes hgher than the potental of hydrothermal systems. In EGS systems, reservor propertes are developed n deep strata by means of physcal stmulaton processes, and then water s njected through a frst well, heated n the enhanced reservor, and pumped to surface by a second well (Thorstensson and Tester, 2010, amongst many others). Hstorcally, the expanson of geothermal energy has been slow compared to other renewable energy sources, such as wnd energy, for many reasons, such as the low fosslfuel prces, the hstorc lack of ecologcal concerns and the hgh upfront captal expendture requrements, partcularly those consdered rsky n the early years of development of a gven geothermal feld. For example as stated by Rybach (2014), the average annual geothermal growth between 1995 and 2013 s around 5%, whle for wnd and solar PV systems the growth rate exceeds 25-30% from 2004 onwards. Nowadays, ths stuaton has changed and new, cleaner, more effcent local energy sources are enthusastcally nvestgated. Another mportant reason for the delay of development of geothermal energy was that local authortes and socetes were, and mght stll be n some cases, unaware of geothermal energy and ts benefts, snce t was perceved as a complex and rsky energy source. So, educaton s necessary for the benefts of geothermal energy, as well as for the other renewable energy sources, to be fully realsed. Fnally, a lack of the necessary knowledge to develop geothermal systems, especally geothermal dstrct heatng systems, was an mportant reason for ths delay (Thorstensson and Tester, 2010). Accordng to Lund et al. (2005), 71 countres reported geothermal energy utlzaton for drect uses n 2005, showng a sgnfcant rse over the correspondng values n 2000 (.e. 58) and 1995 (.e. 28). These drect uses comprsed: 20% for drect space heatng, 33% for space heatng usng heat pumps, 29% for bathng and swmmng, 7.5% for greenhouse uses, 4% for aquaculture, 1% for agrcultural uses etc. Dstrct heatng accounts for 75-77% of space heatng from geothermal energy. Kecebas (2013) states that n 2013 at least 76 countres were usng geothermal energy for drect use purposes, wth 24 countres producng electrcty. The USA, Phlppnes, Mexco, Italy, Indonesa, Japan and New Zealand are the leadng countres n electrcty producton, whle Iceland, Turkey, Japan, Chna and France are the leaders n heat producton from geothermal energy. Iceland, Turkey, Chna and France are the leaders n geothermal dstrct heatng, whle Russa, Japan, Italy and USA are the leaders n ndvdual home heatng by geothermal energy (Lund et al., 2005). 28

31 2.3 Geothermal dstrct heatng General Geothermal dstrct heatng systems are a combnaton of geothermal energy wth dstrct heatng systems. More specfcally, heat s extracted from the ground usng one or more wells and s dstrbuted (ether drectly or va a secondary workng flud) through a dstrct heatng network to many consumers, such as ndvdual and commercal buldngs or ndustres. The subsurface formaton n whch heat s stored s called a reservor. Dependng on the combnaton of pressure and temperature wthn the reservor, heat can be extracted ether n the form of hot water or as a steam-water mxture, or even n the form of saturated or dry steam. Most common are the wells that produce hot water (Kanoglu and Cengel, 1999). A geothermal dstrct heatng system manly conssts of a heat producton unt, a transmsson-dstrbuton system and the n-buldng equpment. More specfcally, heat s extracted from the producton wells, then s dstrbuted to the consumers and fnally s renjected n another well, called a re-njecton well or otherwse dsposed of nto the envronment. Often, the geothermal flud has corrosve propertes, so a prmary heat exchanger s used to extract heat from the geothermal flud, and a secondary flud dstrbutes the heat to the consumers through a transmsson and dstrbuton network. Addtonally, there are usually conventonal bolers, whch operate as back-up unts and for the coverage of peak load. In some occasons, storage tanks are mplemented for the same purpose. A smplfed scheme of a geothermal dstrct heatng system s shown on Fg It should be mentoned that a geothermal source can have multple uses. In general, maxmsaton of the temperature drop of the geothermal flud across the user nfrastructure s desrable n order to extract the maxmum amount of thermal energy. So, f there s more than one use for the geothermal flud, they wll be mplemented smultaneously or n seres (so-called cascadng use, wth each process usng water cooler than the last) n order to acheve maxmum effcency. For example, n Iceland, the geothermal flud s frst used for electrcty and heat producton, and subsequently s used for snow meltng, achevng hgh utlzaton effcences (Bjornsson, 2010). 29

32 Fgure 2.1 Smplfed schematc flow-chart for a geothermal dstrct heatng energy system (from Hepbasl, 2010) Another example of ntegrated use of geothermal energy s gven by Bellache et al. (2000), where the heat extracted from the geothermal flud s used n order to heat hotels and a spa. Arslan and Kose (2010) studed the ntegrated use of geothermal energy n Kutahya, Turkey. In ths regon, geothermal energy was used for multple purposes, but not n an ntegrated way. A more complex system s proposed to acheve hgher utlzaton. More specfcally, t s proposed to buld a bnary cycle for electrcty producton, wth the waste heat of the electrcty plant then beng used for dstrct heatng, and subsequently for greenhouse heatng and spa heatng. The basc servces that can be provded by geothermal dstrct heatng are the same as n any other dstrct heatng scheme,.e. space heatng, domestc hot water delvery, agrculture, balneology, ndustral uses, etc. Indeed, the ntegraton wth ndustral uses s very desrable n a geothermal dstrct heatng system because the demand profle s qute stable n the latter, so the fluctuaton of the total heat demand s flattened a lot. The mportance of the penetraton of ndustral uses n dstrct heatng systems s hghlghted n the work of Dfs et al. (2009). In general, the fluctuaton of the heat demand n dwellngs throughout the day s qute large. Hence, flattenng of the demand s hghly benefcal for the nstallaton. Addtonally, the ndustral users usually have a stable demand throughout the year, makng the nstallaton more feasble to operate all year round. 30

33 A new, emergng technology s dstrct coolng. In ths technology, the heat s provded to an absorpton chller, whch operates usually wth a LBr/water mxture and provdes coolng. A basc dsadvantage of these nstallatons s that they need slghtly hgher temperatures than heatng systems n order to operate,.e. at least o C (Ncol, 2009) for sngle stage absorpton chllers. But, wth the mplementaton of ths technology, the annual demand rses a lot. It can be sad that the reducton of heat demand durng the summer can go hand n hand wth the ncrease of the coolng demand over the same perod. So, n that way the total demand wll be much more constant throughout the year, whle prevously n summer the demand decreased a lot, snce t comprsed solely of the hot water preparaton load, whch usually was not enough to make the nstallaton feasble for ths perod. The mportance of the development of dstrct coolng s obvous (Bloomqust, 2003; Hederman and Cohen, 1981). The ablty to provde a contnuous and adequate flow at the requred temperature s a basc prerequste for a geothermal heatng system (Ozgener et al., 2006a). Other prerequstes are an area wth hgh heat demand densty, and a hgh load factor (.e. the proporton of the total hours n a year over whch the system s used). Geothermal dstrct heatng systems provde numerous advantages both to ndvdual customers and the socety, such as (Lund and Lenau, 2009): Reduced fossl fuel consumpton, snce fuel s needed only for the peak demands. Consequently, a major reducton n emssons s acheved. Reduced heatng cost: geothermal energy usually provdes heatng at lower cost than conventonal fuels. Reduced fre hazard n buldngs, because no combuston takes place n them. Possblty of cogeneraton,.e. utlzaton of the geothermal flud for multple uses. Provson of contnuous base load, n contrast wth the other renewable energy sources. Indeed, geothermal energy has a hgh capacty factor, due to hgh avalablty. Smple, safe and adaptable systems and electromechancal equpment. A geothermal resource usually has a lfetme of years, but n some cases can be mantaned even for years. But, n order to do that a proper management of the reservor has to be mplemented n order to avod depleton. 31

34 In most cases, re-njecton of the geothermal flud s necessary. So, geothermal energy can be consdered as a sustanable energy source. Geothermal energy has huge potental. As stated by L et al. (2011), n Chna alone the geothermal energy that s stored n the subsurface (wthn 2000m) of the sedmentary basns s equvalent to 250 mllon tons of standard coal. Geothermal energy does not depend on weather condtons (Kecebas et al. 2011). Low operatng costs. Geothermal energy wll probably have a stable prce n the future, n contrast wth combustble fuel prces. Because low-grade geothermal energy s wdespread, t s nvarably a domestc source of energy, thus contrbutng to securty of supply and energy ndependence, as well as enhancement of local economes. Concernng the latter, many new jobs are also created (Hepbasl and Canakc, 2003). In purely heat producton statons, the heat producton s ndependent of any electrcty producton. As was mentoned before, concernng CHP plants, the dependence of heat producton on electrcty producton was a bg dsadvantage. Very weak dependence on electrcty prces, snce the only electrcty needed s for the pump systems Accordng to Lund et al. (2005), up to 2005 the usage of 25.4 mllon tonnes of fuel-ol had been avoded due to geothermal energy use. The envronmental mpact of geothermal energy s qute low, snce the emssons of a geothermal plant are just a fracton of the emssons of fossl fuel plants, and of the same magntude as the other renewable energy sources. Durng the constructon and the decommssonng of the plant, there are some emssons, but the lfe-cycle emssons of a geothermal nstallaton stll reman qute low. Indeed, the emssons from low temperature resources are even smaller. If careful renjecton of the geothermal flud takes place and the leaks are prevented, then polluton s mnmsed. A study whch hghlghts the advantages of geothermal energy for local economes was carred out by Karytsas et al. (2003). More specfcally, a soco-economc study was carred out about the utlzaton of low enthalpy geothermal resources n a regon n north Greece. The geothermal flud would be utlzed n a dstrct heatng network as well as for greenhouses uses. The benefts for the local socety would be numerous, such as: reducton 32

35 n annual fuel consumpton of up to 2325 tonnes of ol equvalent; subsequent reducton n CO2 emssons of up to 7440 tonnes per year; annual savngs of up to US$1,250,000; and 60 new jobs n the regon. A governmental subsdy would defntely enhance the feasblty of the nvestment. Inevtably geothermal energy, and subsequently geothermal dstrct heatng, has some dsadvantages. Geothermal energy s ste dependent,.e. geothermal energy of hgher enthalpes cannot be found everywhere. Addtonally, n the case of dstrct heatng the producton plant must be relatvely near to the consumers n order to be feasble, whereas geothermal felds may exst n areas far away from nhabted dstrcts (Sommer et al., 2003). A specfc heat load densty s also necessary, as has been prevously mentoned for dstrct heatng n general. So, t s benefcal to fnd consumers wth constant and hgh loads throughout the year, such as ndustres, hotels, hosptals etc., whch are also close to the producton area. Intal captal costs are qute hgh for these nstalments, for ths reason a large part of them are of publc ownershp. Fnally, t must be hghlghted that the drllng of the geothermal wells s qute rsky, because there s always an uncertanty about the temperature, the flow rate and the pressures of the underground water, at least durng the early stages of feld development. Takng nto account that geothermal dstrct heatng networks are a captal ntensve nvestment, t s obvous that ntal engneerng decsons are crucal both from a techncal and an economcal pont of vew. A wrong ntal decson n the techncal desgn of the system can lead to hgh fnancal losses as shown by Krstmannsdottr and Bjornsson (2012). It can be concluded that geothermal dstrct heatng seems a potental soluton for many current energy and envronmental problems and that t can play an mportant role n the future energy target n the bult envronment sector. As noted by Ostergaard and Lund (2011), the ntegrated use of renewable energy sources, such as geothermal energy, waste ncneraton, heat pumps etc., can enhance the way to a sustanable future. In the latter study, the role of low temperature geothermal energy n a 100% renewable energy system was also analysed. The case of a small town n Denmark was examned, and the results showed that low temperature geothermal energy, combned wth an absorpton heat pump, could cover more than 40% of the total heat needs. 33

36 2.3.2 Examples of geothermal dstrct heatng systems In ths secton, a few examples of geothermal dstrct heatng systems n several areas (from specfc systems up to whole countres) wll be gven n order to hghlght ther dfference n sze and operaton as well as ther potental. For example, n Pars 100,000 resdences are provded wth heat by geothermal energy, whle n Iceland, 22 geothermal dstrct heatng systems have been constructed. The system n Reykjavk whch s one of the bggest n the world has a total nstalled capacty of 1,070MWth. Almost 90% of the space heatng n Iceland s provded by geothermal energy. The huge development of geothermal energy n Iceland has occurred manly due to the rch physcal resources of the country, as well as the postve atttude of people towards geothermal energy, whch s seen as a relable and clean source that has mproved qualty of lfe. It s worth mentonng that the fuel saved between through swtchng to geothermal energy had a value of some 8.2M,.e. three tmes the 2000 budget of the country (Loftsdottr and Thorarnsdottr, 2006; Bjornsson, 2010). Turkey, on the other hand, has around 12% of the worldwde geothermal potental, but 95% s sutable for drect uses only. More specfcally, drect use potental s estmated to be 31,500MWth, but by the turn of the Mllennum only 2-3% of ths potental had been utlzed (Hepbasl and Canakc, 2003, amongst many others). In the USA, 18 geothermal dstrct heatng networks have been constructed, but the dentfed potental s capable of provdng heat to more than 271 ctes (Sommer et al., 2003). Fnally, as stated by the European Geothermal Energy Assocaton, 216 geothermal dstrct heatng systems exsted n Europe by 2012, wth a total nstalled capacty of 4900MWth,and 157 of these systems exst n the EU27 states. Fgure 2.2 ndcates the nstalled capacty of geothermal dstrct heatng systems at the end of 2012 (GeoDH, 2013). 34

37 Fgure 2.2 Installed geothermal drect-use capacty n MW th n European countres at the end of 2012 (GeoDH, 2013) The frst geothermal dstrct heatng nstallaton was constructed at Chaudes-Agues Cantal, France, n the 14 th century. The frst muncpal nstallatons were constructed n Bose, Idaho, USA n 1893 and n Reykjavk n 1930 (Lttle and Bssell, 1980). Geothermal dstrct heatng systems can dffer greatly n sze: for nstance, the system n Reykjavk provdes heat to 150,000 houses, wth over 60 mllon cubc meters of geothermal flud used annually. At the other end of the range, n Klamath Falls, Oregon, USA, a mn dstrct heatng system s used to heat 11 buldngs on a Unversty campus as mentoned n the work of Thorstensson and Tester (2010). Harrson (1994) hghlghts the range of dfferent operatonal strateges of geothermal dstrct heatng networks, through two extremely dfferent examples. In Iceland, the hot sprngs of Deldartunga heat the nearby town of Akranes. The water s produced from a shallow depth almost free of pumpng costs, at a hgh flow rate of almost 180kg/s, and s transported over a dstance of 62km to the town of Akranes. The water s potable, so t s used drectly to heat the houses. After heatng the houses the water s dscharged to the sea. In ths case, even the peaks are met by those sprngs. In Beauvas, France, the water s produced from great depths and at smaller flow rates. The water s salne, so a heat 35

38 exchanger s used to extract heat from the geothermal flud. The geothermal flud s then re-njected nto the reservor to prevent head depleton and polluton of the envronment. In ths case, the heat producton s much lower than n the case of Akranes. In some extreme cases, such as Akranes, geothermal energy provdes almost all the necessary heat. But, ths s usually not economcally vable, because the dstrct heatng network s overszed for most of the tme and the feld s underutlzed. Hence geothermal energy usually provdes base load, and the peaks are covered by auxlary bolers or storage tanks. It must be emphassed that Iceland s a country wth unusually hgh potental for geothermal energy, whch can be produced at a very cheap prce, and the danger of depleton of the wells s almost non-exstent. Hence re-njecton does not always take place there Desgn aspects In ths secton, the basc desgn prncples of a geothermal dstrct heatng system wll be analysed. More specfcally, detals wll be provded about the basc confguraton of the network, the heat load estmaton, the selecton and the desgn of the approprate heat exchangers, the basc aspects of the ppelne system and the n-house system, and fnally a few detals wll be provded on the necessty of havng a re-njecton system. Dependng on the qualty of the underground water, a geothermal dstrct heatng system can be a drect cycle (as n Reykjavk), wth the geothermal flud beng crculated drectly to the end-users, or an ndrect cycle, provdng the geothermal heat to a secondary flud whch s then dstrbuted to the consumers. Indrect systems are more common, although they contan three extra costs compared to drect systems,.e. the cost of a heat exchanger, the cost of crculatng pumps and the cost of heat losses n the heat exchanger. Obvously, drect systems are cheaper than ndrect systems, manly because of avodng the cost of the heat exchanger. Indrect cycles are used n order to mnmze the corrosve acton of the geothermal flud and they are the most common case. Further nformaton about corroson problems n geothermal systems can be found n the work of Rchter et al. (2006). However, njecton of ant-corrosve as well as ant-freezng addtves may take place n the dstrbuton network (Chuanshan, 1997). An extra reason whch may lead to the adaptaton of ndrect systems s the scalng problem whch may occur due to the dssolved salts n the geothermal water. As stated by Krstmannsdottr and Bjornsson 36

39 (2012) scalng and corroson can cause bg problems n the operaton of the system. So, careful research about the composton of geothermal water must be carred out durng the prelmnary study of the nstallaton. Desgn components for geothermal dstrct heatng systems are generally smple, safe and adaptable electromechancal devces. However, careful desgn s necessary due to the large scale of the nvestment. In general, t s found that the ppelne network, the heat exchanger and the re-njecton system need the most careful desgn (Kecebas, 2011, amongst others). Fnally, f the temperature of the geothermal flud s not adequate for heatng purposes, ntegraton wth a heat pump may be mplemented (Harrson, 1994). In the prelmnary research of a new well, the sustanable flow rate, the temperature and the qualty of the water have to be dentfed (as noted by Lund and Lenau, 2009, amongst many others). Of course, the fnal verfcaton wll be based on drllng tests. Avalable areas wth geothermal potental can be dentfed by constructng sotherms for dfferent depths. Addtonally, n the prelmnary desgn, f there s more than one producton well, a lot of attenton has to be pad to the mnmzaton of the nteracton between these wells. 1999): To summarse, a geothermal dstrct heatng system conssts of (Kanoglu and Cengel The producton system,.e. the producton wells, the well pumps and the prmary heat exchanger. The transmsson-dstrbuton system, whch comprses of the ppelne system and the crculatng pumps. The end-user systems. A secondary heat exchanger may be used n the buldngs crcut, n order to avod hgh values of pressure n the dstrbuton network (Harrson, 1987). In many cases, two heat exchangers are used n each buldng, one for space heatng and one for domestc hot water preparaton. Dsposal and re-njecton system. Peakng and back-up systems, such as bolers or storage tanks. Of course, at many ponts n the network, there are varous meters and valves to ensure the correct operaton of the network (Bloomqust, 2003). Addtonally, t s shown n 37

40 numerous studes that automatc control wll reduce the human nvolvement and ncrease the effcency of the system. A crucal ntal factor for the proper desgn of a dstrct heatng network s an adequate estmaton of the heat load. Domestc heat load conssts manly of the space heatng load and the load of domestc hot water. The latter s qute stable throughout the year and can be easly estmated (see Oktay et al., 2008). However, t s not usually suffcent to justfy the nvestment feasble for the summer perod, so addtonal loads, such as dstrct coolng, ndustral processes, pool heatng are usually necessary n order to enhance the economc vablty of the system (Popovsk et al., 2000). The most common method to estmate the space heatng demand s the degree-day or degree-hour method whch s summarsed n the work of Heller (2002). In ths method, the amount of observatons where the ambent temperature s lower than a specfc threshold are metered. The extent of the observaton s usually an hour or a day as the aforementoned names ndcate. Ths process s done for a normal or representatve day for whch the heat load s also known. Then for any other day or hour, the degree-days or hours are calculated based on the predcted meteorologcal data and the heat demand s then calculated as: HL = DD HL n DD n (2.1) Where: HL = Heat load (W) HL n = Nomnal heat load (W) DD = Degree-day or hour (Dmensonless) DD n = Nomnal degree-day or hour (Dmensonless) Yetemen and Yalcn (2009) proposed a predcton model, whch predcts the demand the next day when knowng the weather condtons on the present day plus the consumpton the prevous day. It s consdered to be a relable model, snce weather predcton for the next day s qute relable. Of course, the heat load duraton curve s of huge mportance n order to estmate the optmum sze of the geothermal plant and the ntegraton of peak-up devces. The nterested reader can fnd further nformaton about heat load predcton n the works of Barell et al. (2006), Nelsen and Madsen (2006) and Popescu et al. (2009). 38

41 Gelegens (2005) proposed an algorthm for the quck estmaton of the coverage of total heat load n a dstrct heatng system by geothermal energy. Geothermal systems of all knds were examned,.e. drect system; prmary heat exchange system; heat pump asssted system; heat pump only system. In general, t was concluded that maxmum supply temperature and mnmum return temperature n the dstrbuton network are desrable, n order to maxmze the coverage acheved by geothermal energy. The proposed algorthm shows very good agreement wth actual data. Accordng to Mlanovc et al. (2004), the overall heat transfer coeffcent of the buldng can be consdered stable throughout the heatng season. So, f the heat load s known for a specfc set of ndoor and outdoor temperature, then the heat load for any other set of these temperatures can be calculated usng the followng equaton: HL HL n = T nd T outd T nd,n T outd.n (2.2) Where: T nd, T outd = Indoor and outdoor temperatures, respectvely (K) T nd,n, T outd,n = Nomnal ndoor and outdoor temperatures, respectvely (K) The above equaton s very smlar to Eq. (2.1) and the ndex nomnal also refers to a representatve case of ndoor and outdoor temperatures for whch the heat load s known. Usually, each system s desgned for a set of nlet and outlet temperatures and the demand fluctuatons are met by varatons n flow rate. The supply temperature of the geothermal network s usually constant, whle the supply temperature of the secondary network s usually also kept constant because certan servces, such as domestc hot water, need partcular temperatures. The prmary desgn of the network s made n such a way that the re-njecton temperature of the geothermal flud s mnmsed,.e. maxmum thermal energy s extracted. So, by varyng the flow rate, the fluctuaton of heat demand s met. In order to meet very hgh demands, usually peak-up bolers or storage tanks are used. Harrson (1987) studed the basc desgn prncples of ndrect geothermal dstrct heatng systems. A fundamental prncple s that the flow rate of the dstrbuton network has to be hgher than the flow rate of the geothermal flud n order to obtan optmum heat 39

42 transfer and maxmum utlzaton of the geothermal heat. The locaton of the peak-up bolers can be ether centrally, after the prmary heat exchanger, or ndvdually n each buldng. It has been found that the latter approach s worthwhle only n buldngs that prevously had an ndvdual boler. Storage tanks operate to meet peaks and keep the flow constant through the heat exchanger. Ths means that for the small varatons of the load through the day the flow rate n each buldng changes to meet the demand and peak-up bolers or storage tanks are used for the peak demands. However, the total flow rate through the prmary heat exchanger does not usually change wth the fluctuaton of demand. A change n the return temperature of the dstrbuton network, and consequently n the return temperature of the geothermal flud may occur due to the demand varaton. The vablty of heat storage depends a lot on the fluctuaton of the heat demand. In most geothermal dstrct heatng networks usually counter-flow plate heat exchangers are used. Accordng to Ozsk (1985), plate type heat exchangers have better corroson resstance, requre less space, are cheaper and can cope better wth the changes of the heat demand than can shell-and-tube heat exchangers. Coated carbon steel heat exchangers seem a good soluton to meet corroson problems of geothermal fluds (Chuanshan, 1997), whle n some cases ttanum plates are also used, though those are much more expensve. Obvously, the latter s an extreme stuaton used at very hgh corrosvty rates. In the prmary heat exchanger the mnmum dfference between the hot temperatures of the two flows s desrable n order to maxmze the effcency of the heat exchanger. The heat extracted from the geothermal flud s gven by the followng equaton: Q G = m G Cp G (T G,h T G,c ) (2.3) Where: Q G = Heat extracted from the geothermal flud (W) m G = Mass flow rate of the geothermal flud ( kg s ) Cp G = Specfc heat capacty of the geothermal flud ( J kg K ) T G,h, T G,c = Hot and cold temperature of the geothermal flud, respectvely (K) 40

43 The heat provded to the secondary flow s gven by the followng equaton: Q sf = m sf Cp sf (T sf,h T sf,c ) (2.4) All the terms are defned as for equaton (2.3), though here referrng to the secondary flud nstead of the geothermal flud. The suffx w denotes the secondary workng flud, whch flows through the transmsson and dstrbuton network. The equaton of heat exchange between the two flows s as follows: Q trans = A HE K t T lm = A HE K t (T G,h T sf,h ) (T G,c T sf,c ) (2.5) ln T G,h T sf,h T G,c T sf,c Where: A HE = Actve surface area of the heat exchanger (m 2 ) In the above equaton K t ( W ) the overall heat transfer coeffcent of the heat m 2 K exchanger gven by the followng equaton (Jalng and We, 2003, amongst many others): K t = 1 1 h c,h +R f,h + δ plate k plate +R f,c + 1 hc,c (2.6) Where: K t = Overall heat transfer coeffcent ( W m 2 K ) h c,h, h c,c = Convectve heat transfer coeffcent of the hot (geothermal) and cold (dstrbuton network) water stream, respectvely ( W m 2 K ) R f,h, R f,c = Foulng factor of the hot and cold water stream, respectvely ( m2 K W ) δ plate = Thckness of each plate of the heat exchanger (m) k plate = Conductve heat transfer coeffcent of each plate of the heat exchanger ( W m K ) 41

44 The convectve heat transfer (h) coeffcent for both sdes can be calculated by the followng equaton: h c = Nu k f d h (2.7) Where: Nu = Nusselt number (Dmensonless) k f = Conductve heat transfer coeffcent of the correspondng flud ( W ) m K d h = Hydraulc dameter (m) In the above equaton, the Nusselt number can be calculated usng the approprate equaton accordng to the prevalent condtons. Addtonally, the foulng factor can be consdered equal for both the hot and the cold sdes, as Rf,h=Rf,c= The conductve heat transfer coeffcent of the plate can be consdered to be equal to 50 W, whle the thckness of the plate can be consdered to be m 2 K equal to m (Arslan et al., 2009). Of course, all these values are just ndcatve. Usually, the propertes of the geothermal flud are consdered to be those of pure water, snce the effects of salts and non-condensable gases are consdered neglgble (Kanoglu, 2002). So, n the rest of the study there wll be no dstncton between the propertes of the geothermal flud and those of pure water and the ndex w (water) wll be used for that purpose. On the other hand, durng the heat exchange process some heat losses wll occur, whch have to be taken nto account. In an deal analyss, the above heat transfer rates (Eqs. (2.3)- (2.5)) are consdered equal to each other. Further analyss of counter flow heat exchangers can be found n the work of Dagdas (2007), who states that an optmum heat exchange surface area of the heat exchanger can be found, takng nto account the nvestment cost of the heat exchanger as an expendture, as well as the fuel savng due to geothermal energy as an ncome. 42

45 Accordng to Stoecker (1989) amongst many others, the effectveness of a plate type heat exchanger, assumng no losses, s equal to the rato of the heat transferred to the maxmum avalable heat, and can be calculated by the followng equaton: η HE = Q trans Q max = m sf Cp w (T sf,h T sf,c ) m G Cp w (T G,h T sf,c ) (2.8) Where all the terms are defned as prevously. In the transmsson and dstrbuton networks, pre-nsulated ppes are usually used. Kanoglu and Cengel (1999), amongst others, mentoned that a temperature drop of about 1 o C occurs n every 3-4 km of ppelne. The most mportant steps n the desgn of the ppelne system are the selecton of the proper materal and the determnaton of target pressure losses. Carbon steel ppes are 13-35% cheaper than composte ppes, but they are not usually sutable for geothermal loops, because of the corrosve effects. So, carbon steel ppes are usually used n secondary loops, and composte materals are used for geothermal loops. Accordng to Bloomqust (2003), jacketed welded steel ppes can also be used, and n the return lnes plastc ppes can also been used. The ppes are usually bured underground n order to mnmze heat losses and to avod vsual dsturbance. Usually, they are bured drectly nto the sol because t s cheaper, but the constructon of an underground tunnel can provde other advantages, such as easy access for mantenance, easer future expanson and an avalable corrdor for other uses. However, the cost of the latter s typcally double that of the drect buryng of ppes and s thus usually not preferred. Typcally, n order to determne the optmum dameter of the ppes two aspects must be taken nto account. These are the cost of materal of the ppelne and the pressure losses. Obvously, the smaller the dameter, the lower the materal costs of the ppelne. However, the smaller the dameter, the hgher are the pressure (.e. frctonal head) losses, whch leads to ncreased power consumpton by the pumps, whch consequently means hgher electrcal energy costs. So, an optmum dameter of the ppelnes exsts and has to be determned. Furthermore, great attenton has to be pad to any leakage from the ppelne system, snce ths s an energy loss, and as wll be made clear n the followng secton, t can be a 43

46 huge component of loss (Kecebas, 2013, amongst many others). Fnally, Brown (2006) stated that great attenton has to be pad n the mosture on the external surface of the ppelnes, whch can also lead to corroson. Consequently, he proposes that sometmes a concrete tunnel wth a ventlaton system mght be necessary. Chuanshan (1997) provdes a summary of the basc equatons for the heat exchange process wthn a buldng. The heat needed to mantan a stable ndoor temperature T nd when the outdoor temperature s T outd can be calculated by the followng equaton: Q 1 = C q,b V b (T nd T outd ) (2.9) Where: C q,b = Specfc volumetrc heat load capacty of the buldng ( W m 3 K ) V b = Internal volume of the buldng (m 3 ) The same amount of heat can also be estmated by the followng equaton accordng to Yldrm et al. (2005): Q 1 = U b A b (T nd T outd ) (2.10) Where: U b = Overall heatng coeffcent between the buldng and the envronment ( W m 2 K ) A b = External area of the buldng (m 2 ) The latter wll have to be calculated separately for dfferent parts of the buldngs, such as walls, glasses etc. The heat transferred through the radator can by calculated by the followng equaton: Q 2 = K rad A rad T lm (2.11) In the above equaton all the terms are defned as n equatons (2.5)-(2.6)-(2.7), though here they refer to the radator nstead of the heat exchanger. ΔTlm (K) s the mean logarthmc temperature dfference whch s typcally calculated as shown n the second and thrd part of Eq. (2.5), but n ths case, t can also be calculated as follows: 44

47 T lm = T rad,n+t rad,out 2 T rad,n (2.12) Where: T rad,n, T rad,out = Input and output water temperatures, respectvely, of the radator (K) Tradtonally, heatng crcuts operated n the range 90 to70 o C. The crcuts n geothermal dstrct heatng systems can operate at temperatures as low as 60 to 45 o C or even lower. Wth the development of buldng nsulaton and other technologes, lower temperature systems are becomng more and more popular. Low-temperature systems also mprove ndoor-ar qualty (Myhren and Holberg, 2008). A common technque s the use of an ar velocty component, whch forces the ar to move through the radator wth ncreased velocty, causng that way ncreased heat transfer. (Myhren and Holberg, 2007). Szta (2010) descrbed a three-ppe geothermal dstrct heatng system n a town n Hungary, whch utlzes geothermal energy at dfferent levels of temperature accordng to the enduser technology of each buldng, e.g. radator, under floor heatng etc. The mportance of the end-user system s hghlghted n ths study. In ths connecton, t should be noted that there s no unque confguraton or operatonal strategy for geothermal dstrct heatng networks. No general conclusons about the operatonal strategy and the economc feasblty can be made. Everythng depends on the condtons of each case,.e. the flow rate, temperature and qualty of geothermal water, the heat densty, the dstance of the producton well to the buldngs etc. In most cases the re-njecton of the geothermal flud s necessary manly for the followng reasons (Stens and Zarrouk, 2012): Prevents reservor depleton, whch would otherwse result n declnng reservor pressures and thus a gradually ncreasng pumpng cost. It s more envronmentally frendly to dspose the brne n the well. Indeed n hgh temperature reservors, t s sometmes necessary to add addtonal water to replace that lost to evaporaton n coolng towers, so that the reservor wll not get depressurzed. 45

48 In general, t can be concluded that the desgn of a geothermal dstrct heatng system depends greatly on the condtons of the selected area and that there s no sngle desgn and operatonal strategy. Hence few general conclusons can be reached. The most mportant nfluences on the desgn of a geothermal dstrct heatng system are the maxmum utlzaton of the geothermal feld, and the securty of supply of the consumers. To the best of the author s knowledge no studes about the optmzaton and smulaton of geothermal dstrct heatng systems have been carred out to date. Concernng the optmzaton and smulaton of non-geothermal dstrct heatng systems, the nterested author can fnd the descrpton and mplementaton of many dfferent models n the lterature such as: MODEST (Hennng, 1997, amongst many others): It s an optmsaton algorthm of dynamc energy system wth tme dependent components and boundary condtons. In general, MODEST fnds the nvestment and operaton decsons that satsfy the energy demand at mnmum overall cost n local, regonal and natonal energy systems. DESDOP (Weber and Shah, 2011): Ths algorthm s a mxed nteger lnear optmsaton tool whch provdes the optmum mx of technologes n order to mnmze the emssons. Mxed nteger lnear optmzaton technques have also been used by other researches, such as Gustafsson and Ronnqvst (2008) etc. DEECO (Lndenberger et al., 2000): Ths model whch smplex algorthm optmzaton technques, n order to examne the maxmum ntegraton of solar energy n a dstrct heatng system. SAFARI (Dotzauer, 2003): Ths s a mxed nteger program used for the mdterm plannng of dstrct heatng systems. GATE/CYCLE (Krause et al., 1999) and TERMIS (Gabrelatene et al., 2007): These are commercally avalable software for the smulaton of thermal systems and dstrct heatng networks. TRNSYS (Heller, 2002, amongst others): It s a commercally avalable software for the smulaton of transent systems. 46

49 2.3.4 Basc thermodynamc evaluaton Overvew In ths secton, a bref revew of the lterature concernng the energetc and exergetc evaluaton of geothermal dstrct heatng networks wll be presented, emphaszng the advantages of exergy analyss. In general, energy analyss alone s not enough to understand the whole system (Hepbasl, 2010, amongst others). For ths reason, exergy analyss s necessary n order to get a more complete vew of the system energy flows. It can be brefly sad that exergy s the maxmum avalable energy, or n other words the maxmum work that can be produced from the system when t s nteractng wth ts surroundngs. Energy s based on the 1 st law of thermodynamcs, whle exergy s based on the 2 nd law of thermodynamcs. In other words, exergy s the optmal use of energy and takes nto account all the energy losses that occur due to rreversbltes of the process, as summarsed by Ozgener et al. (2005a), amongst many others. Unlke energy, exergy s not subject to a conservaton law; t s ether consumed or destroyed. Ths happens due to rreversbltes that take place n any real process. Entropy s generated due to these rreversbltes, whch consequently leads to exergy consumpton. By mplementng exergy analyss, t s possble to determne f (and by how much) t s possble to desgn more effcent systems. In general, exergy analyss s accepted as the most approprate way to evaluate a geothermal dstrct heatng system, because t can pont out the real magntude of losses, and the parts of the nstallaton that can be mproved and t can show how effcently the system operates. Parr (2007) states that the use of fossl fuels for heatng purposes,.e. for a desred temperature smaller than 60 o C, s a huge waste from an energetc and exergetc pont of vew. It s far more effcent to use low enthalpy (and thus low exergy fluds), rather than hgh enthalpy ones. From that pont of vew, geothermal energy has much to offer n the sustanable development agenda, and the effcent utlzaton of energy sources. It s also noteworthy that for space heatng at about 20 o C, a flud wth slghtly hgher temperature s theoretcally usable. But, n that case the effectve surface area of the radator has to be ncreased consderably. If new, more effcent, radators are desgned n the future, then a temperature of 35 o C wll be feasble for space heatng, ncreasng the geothermal felds that 47

50 are vable for space heatng purposes. At the moment, a mnmum temperature of 50 o C s stll necessary for even the best radators, wth many stll requrng temperatures n excess of 70 o C. An excepton to that s the use of underfloor heatng systems n the newly bult houses, whch can operate wth temperatures as low as 35 o C. Fnally, great attenton has to be pad to the domestc hot water load, for whch a temperature of 60 o C s necessary anyway. So, t should be nvestgated n detal f the latter should be ncluded n the general thermal load of the dwellngs or f t should be provded by other means, e.g. electrc heatng. Very lttle research has been carred out nto the energetc and exergetc analyss of geothermal dstrct heatng systems. As mentoned also before, Turkey has among the hghest potentals for geothermal dstrct heatng systems worldwde and s an emergng market snce 170 geothermal felds have been dscovered n the country as stated by Smsek (2001) Basc equatons Summares of the man equatons used for energetc and exergetc evaluaton have been gven by many authors (Ozgener et al., 2005a,b; Ozgener et al., 2006a,b; Ozgener et al., 2007a,b; Oktay et al., 2008; Kecebas et al., 2011 etc.) and these form the bass of the followng lstng. These equatons can be used to evaluate any geothermal dstrct heatng system. Thermal and hydraulc steady-state condtons were assumed n formulatng these equatons. Mass balance: m m m m m (2.13) n out well r ds wells Where: m well = Mass flow rate of one geothermal well ( kg ) s m r = Re-njecton mass flow rate ( kg ) s m ds = Dscharge mass flow rate whch takes nto account the amount of water that t s not re-njected ( kg ) s 48

51 The latter takes nto account both the mass flow rate of the water that s naturally dscharged and any leakage, although t s dffcult to quantfy the latter. In the majorty of the studes, Eq. (2.13) s used to calculate the dscharge mass flow rate. It should be noted that, dependng on the partcular case, one of the values of re-njecton or dscharge may be equal to zero. For example, n Akranes, Iceland, the entre amount of geothermal water s dscharged, so the re-njecton mass flow rate s equal to zero. Energy balance n a control volume: Q CV W CV = m (h + v2 2 g z) net (2.14) Where: Q CV, W CV = Heat and work transfer rate through the control volume, respectvely (W) h = Specfc enthalpy ( J kg ) v = velocty ( m s ) g = gravtatonal acceleraton ( m s 2) z = heght (m) The suffx net denotes the dfference between the nput and output values. If there s no heat transfer and work nput/output through the boundares of the network, the above equaton reduces to the followng: m (h + v2 2 + g z) net = 0 (2.15) Usually, knetc energy s consdered neglgble n these systems. So, f there s no change n the potental energy of the system, the above equaton can be smplfed to the followng form: m n h n = m out h out (2.16) The above equaton s the one most commonly used n analysng geothermal dstrct heatng systems. 49

52 Exergy balance nto a control volume: k T (2.17) 0 (1 ) Qk W mn n mout out Exdest. system Tk Where: T 0 = Temperature n the dead-state condtons (K) T k = Temperature n the kth process (K) ψ = Specfc exergy ( J kg ) Ex dest,system = Rate of the exergy destructon through the system (W) Smlarly to the energy balance, f there s no heat or work transfer through the boundares of the system, the above equaton reduces to the followng: m n ψ n m out ψ out = Ex dest,system (2.18) In geothermal dstrct heatng systems, physcal exergy s predomnant, so eventually the specfc exergy wll be gven by the followng equaton: ψ = (h h 0 ) T 0 (s s 0 ) (2.19) Where: s = Specfc entropy ( J kg K ) h 0 = Specfc enthalpy n the dead-state condtons ( J kg ) s 0 = Specfc entropy n the dead=state condtons ( J kg K ) In the above equaton the suffx 0 denotes the dead-state condtons. At dead-state, the mechancal, thermal and chemcal equlbra between the system and the envronment are satsfed. No further nteracton between them s possble. The exergy s by defnton equal to zero at that pont. The exergy destructon of a geothermal dstrct heatng system s equal to the sum of the exergy destructon of ts parts. For a typcal system, ths s equal to the sum of the 50

53 exergy destructon of the heat exchangers, the pumps and the ppelnes. All these are defned by the followng equatons: Ex dest,system = Ex dest,he + Ex dest,pump + Ex dest,ppe (2.20) Ex dest,he = Ex n Ex out (2.21) Ex dest,pump = W pump + Ex n Ex out (2.22) Ex dest,ppe = Ex n Ex out (2.23) Where: Ex n, Ex out = Input and output exergy rate on each of the aforementoned equpment (W) Ex dest = Exergy destructon rate on each of the above equpment (W) W pump = Electrcal power provded by the pumps (W) In energetc and exergetc analyses t s crucal to defne the boundares of the system. Thus t must be noted that n these studes, the system studed was from the producton well to the prmary heat exchanger: hence only the performance of the geothermal heat extracton was studed. Of course, the above equatons are the same for the equpment of the secondary network and can be used n the same way. If there are any other devces n the equpment that cause exergy destructon, these devces also have to be taken nto account. Effcences of the whole system: Bearng n mnd that the prevously-studed systems only analysed the prmary heat exchanger, the thermal energy effcency of the whole system wll be provded by the followng set of equatons: η th = Q out Q n = Q sf Q brne (2.24) 51

54 Q brne = m G (h brne h 0 ) (2.25) Where: η = Energetc effcency (dmensonless) Q sf = Provded by Eq. (2.4) Q brne = Energy rate of the geothermal brne (W) h brne = Specfc enthalpy of the brne ( J kg ) In the denomnator of the above equaton, the suffx brne s used n order to dstngush ths energy rate from the energy rate provded by Eq. (2.3), whch denotes the actual energy provded by the geothermal flud. Ths energy rate wll be used n ths thess, whle the energy rate used n Eq. (2.24) s closer to the concept of exergy as t provdes roughly the maxmum energy that can be provded by the geothermal flud and not the actual energy provded. In the same way, the total exergetc effcency of the system wll be gven by the followng set of equatons: ε = Ex useful,he Ex G = 1 Ex dest,system+ex r+ex ds Ex G (2.26) Ex useful,he = m sf (ψ out ψ n ) (2.27) Ex G = m G [(h G h 0 ) T 0 (s G s 0 )] (2.28) Where: Ex, Ex = Exergy rates of the re-njected and dscharged water, respectvely (W) r d The exergy rates of the re-njected and dscharged water can be calculated by an equaton smlar to (2.28) f the propertes of these flows are known. The rest of the exergy rates have been calculated n prevous equatons. Fnally, the exergetc effcency of the heat exchanger can be calculated usng the followng equaton: 52

55 ε HE = m w (ψ w,out ψ w,n ) m G (ψ G,n ψ G,out ) (2.29) Where: ψ w,n, ψ w,out = Input and output exergy rate of the secondary flud (pure water), respectvely ( J kg ) ψ G,n, ψ G,out = Input and output exergy rate of the geothermal flud ( J kg ) Indcatve results and dscusson A short revew of the above studes and ther results wll be provded n the table below. All of these studes were based on actual data. Addtonally, the pressure and heat losses n the ppelnes were not taken nto account, although ther ndrect effects were observed n the real data. For the calculaton of water propertes the engneerng equaton solver tool (EES) was used (Kecebas et al., 2011). Table 2.1 Indcatve results of several studes conducted on energetc and exergetc analyses of geothermal dstrct heatng systems GDHS Date of data used Energetc effcency (%) Exergetc effcency (%) Reference Gonen 1 st February Ozgener et al. (2005b) Balcova 1 st December Ozgener et al. (2006b, 2007b) Salhl 1 st December Ozgener et al. (2006b, 2007b) Balcova 1 st February Ozgener et al. (2005a) Afyon 8 th January Kecebas et al. (2011) Bgadc November Oktay et al. (2008) Bgadc December Oktay et al. (2008) Balcova 2 nd January Ozgener et al. (2006a) 53

56 More ndcatve results can be found n Table 1 of the study of Hepbasl (2010). As already mentoned, the effects of salts and non-condensable gases n the geothermal flud are neglected (Kanoglu, 2002). The man exergy losses take place n the heat exchanger, the re-njecton of geothermal water and the natural dscharge. It has to be mentoned that the re-njected water s not a real loss, snce t returns to the reservor, but t s consdered as a loss wth the logc that snce t was pumped over-ground t delvered a specfc amount of energy that could be utlzed. The exergy losses n the ppelnes and the pumps of the system are much smaller. The man energy losses of the system occur due to re-njecton and natural dscharge. The dfference between energy and exergy analyss s hghlghted through these studes. Though the losses of re-njecton are somethng that cannot be avoded, the losses of natural dscharge can be mnmzed through good desgn and mantenance of the ppelne system. In most of these systems, a lot of leakages occur due to bad mantenance. In order to mprove effcency, leakage should be mnmsed. In many of these nstallatons, carbon steel ppes should be replaced by glass renforced plastc ppes (GRP) for that very reason, as stated by Ozgener et al. (2005a). As can be seen n Table 2.1, n geothermal systems the exergy effcency s usually hgher than the energy effcency n comparson wth conventonal thermal systems. Exergy analyss s known to depend a lot on the surroundngs of the system,.e. the deadstate condtons. In geothermal systems, the operatng temperatures are near dead-state condtons, so the magntude of losses s smaller. For example, n a thermal power plant, the boler reaches a temperature of about 2000 o C, whle n a geothermal dstrct heatng system the maxmum temperature s about o C. It s obvous that n the frst system the exergy losses wll be much hgher. The hgher the temperature dfference between two streams, the hgher are the exergy losses for ths process (Oktay et al., 2008). Of course, the lower the re-njecton temperature, the hgher are the effcences of the nstallaton. Ozgener et al. (2007a) produced correlatons of the effcences wth the ambent temperature. In geothermal dstrct heatng systems, both the numerator and the denomnator depend a lot on the ambent condtons, n comparson to the conventonal thermal systems where the dependency of the denomnator on ambent condtons s weak snce t s usually a fuel stream. So, n most cases the effcences ncrease wth an ncrease of ambent condtons. But t has to be borne n mnd that ths s not always the case. For 54

57 example, Kecebas and Yabanova (2012) found through ther model that the energy effcency ncreases wth ncreasng ambent temperature, whle exergy effcency decreases. These correlatons refer to a specfc day of the year. Yuksel et al. (2012) nvestgated the seasonal performance of a geothermal dstrct heatng system. Energetc and exergetc analyses were mplemented n wnter, summer and transton perod, where heat loads dffer. Hghest effcences are found n the transton perod Addtonal parameters for the energetc evaluaton of geothermal dstrct heatng systems Specfc exergy ndex Geothermal felds can be classfed accordng to ther temperature as: hgh enthalpy felds f the reservor temperature s hgher than 150 o C; medum enthalpy felds f the reservor temperature s between 90 o C and 150 o C; and low enthalpy felds f the reservor temperature s lower than 90 o C (D Pppo, 2007). In general, ths classfcaton s very generc and s not completely agreed between scentsts. Furthermore, no nformaton about the qualty of the reservor s provded by ths classfcaton. Lee (2001) classfed the geothermal felds accordng to ther exergy content. More specfcally, the specfc exergy ndex (SExI) parameter was proposed. Ths parameter, whch s dmensonless, can be calculated by the followng equaton: SExI = h G s G 1192 (2.30) Where: h G = Specfc enthalpy of geothermal flud ( J kg ) s G = Specfc entropy of geothermal flud ( J kg K ) The constant value of the denomnator denotes the maxmum value of exergy n the wet-steam regon of a Moller dagram,.e. for saturated steam at 90 bar absolute pressure wth trple-pont snk, and actually normalzes all the exergy values wthn the water-steam regon (Lee,2001). These exergy values vary between 0 and 1 wthn the water-steam regon. In ths way, the values of SExI are almost ndependent of the snk condtons. Accordng to Lee (2001), f the specfc exergy ndex of a reservor s hgher than 0.5, then 55

58 t s a hgh qualty reservor. If ths value s between 0.05 and 0.5, then t s medum qualty reservor. Fnally, f ths value s lower than 0.05, then the reservor s of low qualty. Ozgener et al. (2005a, b; 2007b) appled ths equaton to ther studes, and n most cases the reservors were found to be low qualty. A later study by Younger (2015) attempted the classfcaton of geothermal felds accordng to ther enthalpy, whch s a more comprehensve and realstc approach compared to the classfcaton accordng to the temperature of the feld. The results of ths study are represented graphcally n Fg. 2.3, n whch the numbers on the lnes dvdng the dfferent enthalpy categores are approxmate values of enthalpes n KJ kg. Fgure 2.3. Classfcaton of geothermal felds on the bass of enthalpy (Younger, 2015) Improvement potental The followng equaton can be mplemented n order to calculate the maxmum exergetc mprovement that can be obtaned by each process of the network (Hammond and Stapleton, 2001): IP = (1 ε pr ) (Ex n Ex out) (2.31) 56

59 Where: IP = Improvement potental (W) ε pr = Exergetc effcency of the process (Dmensonless) Ozgener et al. (2005a) found that the hghest mprovement potental exsts n the heat exchangers of the system. Ths hghlghts the mportance of the careful desgn and selecton of the heat exchangers Other parameters Very few studes have been carred out concernng other parameters of geothermal dstrct heatng systems. Hepbasl (2010), amongst few others, summarzes the concept of energy generaton due to frcton and heat losses n a system. Ozgener et al. (2005b) state the parameters of fuel depleton rato; relatve rreversblty; and productvty lack, whch were orgnally mplemented for conventonal systems. Coskun et al. (2009) ntroduced four new parameters whch ndcate how much the system s renewable and sustanable. These parameters, whch were mplemented to the Edremt, Turkey, geothermal dstrct heatng system are the followng: Energetc renewablty rato; exergetc renewablty rato; energetc re-njecton rato; and exergetc re-njecton rato. The frst two are defned as the rato of the renewable energy or exergy, respectvely, obtaned from the system to the total energy or exergy nput (renewable and non-renewable). The latter two are defned as the rato of renewable energy or exergy, respectvely, dscharged to envronment or re-njected to the well from the system to the total geothermal energy or exergy suppled to the system. Ozgener and Ozgener (2009) analysed three parameters whch descrbe the total avalablty of the system. These are the average techncal avalablty; the real avalablty; and the capacty factor. Techncal avalablty s defned as the rato of operaton hours to total machne hours avalable n the heatng season and takes nto account the machne faults of the system. The techncal avalablty of a geothermal system s usually hgher than 90%. Real avalablty s defned as the rato of generaton hours to total machne hours and depends manly on the non-avalablty of the system due to possble leakages. If a system s well mantaned the real avalablty can be almost 100%. Fnally, the capacty factor s defned as the rato of the desred actual useful producton to the maxmum 57

60 theoretcal producton of the system. As shown n ths study, the average value of the capacty factor s around 40-42%. Ozgener (2012) defned the coeffcent of performance of a geothermal dstrct heatng system as the rato of the useful energy provded to the summary of all the electrcal energy consumed by the pumps of the system. COP E pumps useful G th W E pumps W (2.32) Fnally, Hepbasl (2010) ntroduced four new parameters whch take nto account the buldng s crcut. These are: the dstrbuton cycle exergetc rato; the energy consumpton crcut exergetc rato; the reservor specfc exergy utlzaton ndex; and the geothermal brne specfc exergy utlzaton ndex. Defnng further these parameters s out of the scope of ths study Further studes Sahn and Yazc (2012) and Kecebas et al. (2012) studed Afyon, Turkey, geothermal dstrct heatng system usng artfcal neural network (ANN) and adaptve neuro-fuzzy (ANFIS) models. An artfcal neural network s a computatonal tool that mmcs the way nformaton s learned by bologcal neural systems. It conssts of an nput layer, an output layer and some hdden layers whch usually have stored nformaton from some prevous data, the so-called tranng. The use of ANNs has some benefts such as nonlnearty, flexblty, speed, smplcty and adaptve learnng as noted by Kecebas and Yabanova (2012) amongst others. Artfcal neural networks are more approprate for systems for whch no physcal model exsts, but they can also be used for systems wth physcal models. An artfcal neural network needs some sets of nputs-outputs to determne the connectng weghts n the hdden layers. After that, for any gven nput t s able to provde the output. Aksoy et al. (2011) state that It has been demonstrated that f there s suffcent number of neurons n the hdden layer of a feedforward ANN, wth three layers, then the network can approxmate any contnuous functon at the desred accuracy. A feedforward ANN s an ANN that the transmsson from a layer occurs only to layers followng that layer. ANFIS s a hybrd scheme of neural networks and fuzzy logc technques. It analyses the relaton between nputs and outputs and fnds the optmal 58

61 dstrbuton of membershp functons usng ether a back-propagaton gradent descent algorthm or the latter n combnaton wth the least-squares method. Results are compared and t s shown that the ANN models are slghtly better n determnng energy and exergy rates. Addtonally, the correlaton factors are very satsfactory. It s shown that ANN and ANFIS can provde a practcal and fast soluton for the estmaton of energy and exergy rates. Coskun et al. (2012) studed a new hybrd system for Edremt, Turkey, geothermal dstrct heatng system. The waste heat s re-njected at almost 40 o C, whch s a very satsfactory temperature for feedng a heat pump and a bogas power plant, as s proposed. The electrcty producton of the bogas plant s proposed to be used for the heat pump, the dstrct heatng system pumps and all the auxlary equpment. A bogas power plant needs a constant temperature of about 38 o C to operate. On the other hand, the coeffcent of performance of a heat pump rses as the feedng temperature rses. Addtonally, heat pumps depend a lot on the prce of electrcty. In ths model, the electrcty wll be produced effectvely for free. Results show that the energetc effcency ncreases by 7.5% and the exergetc effcency by 13%. So, by mplementng ths hybrd nstallaton several advantages are realsed,.e. ncrease of effcences; ncreased number of heated resdences; reducton of fuel consumpton; reducton of emssons; and ncrease of the system s sustanablty. Fnally, a basc prerequste for such a system s that hgh amounts of agrcultural and ndustral waste are necessary for the bogas plant to operate Economc analyss Conventonal economc analyss After a resource has been found to be vable from an energetc and techncal pont of vew, the last barrer for mplementaton s the economc feasblty. As already mentoned, a geothermal dstrct heatng system s a captal ntensve nvestment (Erdogmus et al., 2006, amongst many others). Addtonally, the cost of drllng mght render an nvestment nfeasble. In contrast, operatonal and mantenance costs are qute low. The total cost can be estmated as the sum of the nvestment cost, the operatonal cost and the mantenance cost. Possbly, the salvage cost of the equpment may decrease the total captal cost. 59

62 The nvestment cost conssts of the cost of drllng, the cost of electromechancal equpment,.e. ppelne system; heat exchangers; pumps; end user systems etc., and the cost of nfrastructure,.e. substatons; storage tanks; control systems; ppelne bural costs etc. The nvestment cost can be separated nto surface costs, whch are easly predcted, and subsurface costs, whch contan a lot of rsk. The nvestment cost manly depends of the followng (Erdogmus et al., 2006): Depth of resource. Dstance between resource and consumers. Well flow rate and temperature. Load factor. Composton of geothermal flud. Ease of dsposal and re-njecton. Heat densty. The man operatonal costs of a geothermal dstrct heatng system are the followng (Harrson, 1994; Erdogmus et al., 2006): Cost of personnel. Cost of electrcty for the pumps and auxlary equpment. Cost of fuel for peak-up and back-up bolers. Cost of tap and make-up water. Cost of ant-corrosve and ant-freezng chemcals. Cost of marketng. Cost of rentng facltes. Vorum and Petterson (1981) ndcate that the dstrbuton cost accounts usually more than 25% of the ntal nvestment cost, whle the mantenance costs mght be even less than 1% of the nvestment cost. It has to be hghlghted at ths pont that no general conclusons can be made about geothermal dstrct heatng systems costs. Dependng on each case, allocaton of costs mght be qute dfferent. In some cases the cost of drllng mght be a large porton of the nvestment cost, e.g. EGS deep systems, whle n other cases t mght be neglgble, e.g. shallow wells. A case study from Dlugosz (2003), for example, shows that the cost of wells s about 8% of the total cost, whle transmsson and 60

63 dstrbuton costs account for more than 66% of the total cost. In other stuatons the relatve costs of these components mght be very dfferent. The man ncomes for geothermal dstrct heatng systems are usually smlar to tradtonal heatng systems and consst of a fxed cost whch s used as a mnmum guaranteed ncome and n order to re-pay the ntal nvestment costs and a varable heatng cost whch s varable and s prced accordng to the real use of heat. In the latter, the cost s usually calculated by specfc meters whch count the flow rate through the buldng, and the temperature of the dstrbuton water before and after the buldng. These are called Btu-meters or just heat meters and can provde the actual use of heat wthn each end-user (Bloomqust, 2003). Based on ths value, the varable cost of heatng s calculated and then s summed wth the fxed cost, to form the total ncome of the nvestment. Fnally, there s the possblty of the extra ncome due to a fnancal subsdy that can be provded. Ths s the case n many countres worldwde whch provde subsdes for the promoton and faster commssonng of renewable technologes. Usually, n the economc analyss of geothermal dstrct heatng systems, a comparson wth conventonal systems s carred out. Ths comparson s carred out usng some economc ndcators. Of course, as Hederman and Cohen (1981) state, all the comparsons must be made on a common bass. Consstency must be acheved for taxes, nterest rates etc. The man economc ndcators are descrbed shortly below and summarsed n the works of Erdogmus et al. (2006) and Hederman and Cohen (1981). Net present value (NPV) Ths s the sum of all the future ncomes and expendtures at present-day monetary values. The transformaton of future values (-years from now) nto present values can be done usng the nterest rate and the followng equaton: PV = FV (1 + DR) (2.33) Where: PV = Present value ( ) FV = Future value ( ) DR = Dscount rate (Dmensonless) 61

64 Therefore, the net present value of an nvestment wth N years nvestment perod can be calculated as: NPV N PV (2.34) 0 The hgher the net present value, the more economcally feasble s a gven nvestment as t denotes a hgher net total ncome throughout the whole nvestment perod. Internal rate of return method (IRR) The IRR s defned as the dscount rate whch equates the net present value to zero. Ths can be calculated by solvng the followng equaton for the dscount rate: N PV 0 (2.35) (1 DR) 0 In general, the present value of the nvestment n any year can be calculated as the dfference between the nflows and the outflows of the nvestment the specfc year,.e. the net cash flow of the nvestment. For an nvestment to be feasble, the IRR has to be hgher than the current nterest rate. On the other hand, when comparng nvestments, the one wth the hgher value of IRR s more feasble as t denotes hgher fnancal securty. It should be noted that f the nstallaton s a publc nvestment, the net present value can be very close to zero, snce there may be no strong nterest n makng a proft. Unt cost of energy Ths s smply the cost of producng one unt of energy. Ths s the mnmum heatng fee that the producer could accept n order to have sutable revenues. It s calculated, n general, by the followng equatons through the annuty method (Krajacc et al., 2011): UCE = CC tot CRF+C O&M +C msc E annual (2.36) CRF = IR 1 (1+IR) N (2.37) 62

65 Where: UCE = Unt cost of energy ( kwh ) CC tot = Total captal cost ( ) C O&M = Cost of operaton and mantenance of the nstallaton ( year ) C msc = Mscellaneous costs of the nstallaton ( year ) CRF = Cost recovery factor (Dmensonless) E annual = Annual energy produced (kwh) IR = Interest rate (Dmensonless) Other possble costs, such as salvage cost f avalable, should be also taken nto account. Typcal assumed values of nterest and dscount rate are 6% and 5%, respectvely (Sommer et al., 2003), although n many countres, such as UK, the central bank sets n advance the base nterest rate to a specfc value, whch s used as a startng pont n any analyss. Atknson and Huxtable (1984) hghlght the mportance of two crucal factors of geothermal dstrct heatng systems. These two factors, as mentoned earler, are the dstance between the well and the energy consumpton centre and the heat load densty. These factors can render an nvestment nfeasble f they are not examned thoroughly. Erdogmus et al. (2006) evaluated the geothermal dstrct heatng of Balcova, Turkey, from an economc pont of vew. The proftablty was nvestgated wth the nternal rate of return method. Many dfferent scenaros for operatng costs and utlzed energy prce were examned. It was found n that case that the proper monthly utlzaton prce for a 100m 2 buldng was US$55.5 (equal to 37.95). It s also shown that IRR ncreases when the heatng fee ncreases and when the operatonal costs decrease. Hederman and Cohen (1981) examned the cost of geothermal commercal-scale drect heat applcatons and compared them wth fuel alternatves. Fve dfferent projects concernng the well depth and the use of geothermal heat were examned. In general, lfecycle costs of a geothermal nstallaton are much dfferent from those of a conventonal unt. A geothermal nstallaton has large ntal captal nvestment costs but low recurrent 63

66 operatonal costs. In contrast, a conventonal unt has lower nvestment costs but qute hgh operatonal costs, due to the cost of conventonal fuels. For ths reason, the lfe-cycle costs must be taken nto account when mplementng a comparson between renewable and conventonal unts. Geothermal energy s found to be cheaper than ol n all crcumstances, and cheaper than natural gas n many cases. So, t s shown that geothermal energy can provde a cheap alternatve to conventonal fuels. Kanoglu and Cengel (1999) carred out a feasblty study for the combned generaton of power and heatng or coolng from hgh enthalpy geothermal resources. They state that n hgh enthalpy geothermal felds, electrcty produced from geothermal energy s about 1/13 th of the heat power that can be produced from the same source. But, from a thermodynamc pont of vew, t s not wse to produce heat solely from hgh enthalpy resources. As prevously mentoned, the best soluton s the combned generaton of heatng or coolng and power. Kanoglu and Cengel (1999) also verfy the latter from an economc pont of vew. It s found that heatng can provde 3.1 tmes and coolng 2.9 tmes the revenue of power alone generaton. Addtonally, combned heat and power generaton can provde 2.1 tmes the revenue of power alone generaton, whle combned coolng and power generaton can provde 1.2 the revenue of power alone generaton. In any case, the ntegrated use of geothermal energy s more feasble than the use for a sngle purpose, especally f there s a hgh enthalpy resource. Sommer et al. (2003) studed the spatal economcs of geothermal dstrct heatng systems. The commercal software HEATMAP (Bloomqust et al., 2004) was used to examne the feasblty for a low densty town n the USA. HEATMAP s a very useful tool whch has varous nputs, such as: buldng uses and szes; a supply source; the source locaton; the ppelne confguraton etc. The outputs that HEATMAP provdes are the followng: thermal densty; szng of ppelnes; total cost estmate; revenues; estmaton of vablty of the nvestment; unt cost of energy. In general, costs of geothermal energy vary a lot accordng to many factors already dscussed. Sommer et al. (2003) stated the followng: An mportant factor for the economcs of geothermal dstrct heatng s the trade-off between economes of scale and transportaton costs. There s an optmum where the expandng of the network to capture more customers s not worth anymore. The latter s manly not worthwhle from the customers pont of vew, because they wll have to pay a very hgh prce for heatng. Sommer et al. (2003), show that the rate of partcpaton,.e. the proporton of customers n the area that adopts geothermal dstrct heatng, s a crucal factor for the vablty of the nvestment. As already dscussed, n order to acheve hgh a 64

67 rate of partcpaton, educaton of the ctzens about the benefts of geothermal energy s necessary. A senstvty analyss on the rate of partcpaton was carred out. It was found that even n the pessmstc case, geothermal energy s compettve at least n the core buldng dstrct area. But the economes of scale by larger servce areas do not necessarly outwegh the hgher development costs. The further we get from the core buldng dstrct, the less feasble s the nvestment. In general, t s found that no general concluson can be reached on that aspect. It depends on each case, and careful study s necessary. Vorum and Petterson (1981) carred out a feasblty analyss of geothermal dstrct heatng systems, whch ndcated that they are compettve wth other energy sources, such as fossl fuels, bomass etc. More specfcally, two servce areas were examned and the unt cost of energy was found to be equal to US$10.3 and US$8.2 per mllon Btu (roughly equal to 0.024/kWh and 0.019/kWh), respectvely. These prces were compared wth the prces of electrcty, propane and fuel ol, whch were respectvely US$8.76, US$13.65 and US$11.71 (roughly equal to /kWh, /kWh and /kWh). It was also estmated that an annual savng of about US$480 (c. 330) could be acheved f fuel ol was used before. The compettveness of geothermal dstrct heatng s made clear through ths study. It can be concluded that geothermal dstrct heatng s a cheap, or at least compettve, alternatve to tradtonal fossl-fuelled heatng systems. The cost of geothermal dstrct heatng depends on many factors and can vary wdely, but n general geothermal dstrct heatng s a cheap soluton whch together wth ts low emssons could be a crucal contrbutor to meetng future energy targets and sustanable development, thus provdng many benefts both to the customers and to the socety Exergoeconomc analyss Exergy analyss s provng to be a powerful tool for fndng where mprovements can be made. But, only economc analyss can determne the feasblty of such an mprovement. For ths reason, they are usually mplemented together. Exergoeconomc analyss s the combnaton of exergy and economcs for long term operatonal condtons (Ozgener et al., 2007c, amongst others). Ozgener et al. (2007c) conducted an exergoeconomc study of the Salhl, Turkey, geothermal dstrct heatng system mplementng mass, energy, exergy and cost analyss. 65

68 The relaton between thermodynamc losses and captal cost of the whole system and ts components s examned wth the followng equatons: L en = E loss (2.38) L ex = Ex dest (2.39) R en = L en CC tot (2.40) R ex = L ex CC tot (2.41) Where: L en = Energy losses rato (W) E loss = Energy losses (W) L ex = Exergy losses-destructon rato (W) R en, R ex = Rato of energy and exergy losses to captal cost, respectvely ( W ) It s shown that a correlaton between captal cost and nternal or total exergy losses exsts. Internal exergy losses are the losses whch occur due to rreversbltes of the process, whle external losses are the losses whch occur due to nteracton of the system wth ts surroundngs. Obvously, the total exergy losses are the sum of nternal and external exergy losses. So, usually the total exergy losses are taken nto account. No correlaton between energy losses and captal cost exsts. In general, the prces of the rato of exergy loss to captal cost of each component tend to be close to each other. So, t seems to be a systematc correlaton between exergy losses and captal cost. It s shown that a successful desgn must balance the thermodynamc and economc characterstcs of the system. As Ozgener et al. (2005c) state n ther study The results suggest that a good desgn, n terms of balancng effcency wth cost, occurs when the loss-to-captal cost ratos based on exergy for the devces comprsng the geothermal dstrct heatng system approach the loss-to-captal cost rato based on exergy for the overall system. Hence, n a successful desgn the value of loss to captal cost rato based on exergy for the components comprsng the system must approach an approprate value, whch s usually the loss to captal cost rato based on exergy for the whole system. 66

69 However, the components whch need mprovement can stll be ndcated by exergy analyss. Exergoeconomc analyss s very useful to ndcate f balance exsts between thermodynamc and economc characterstcs of the system. 2.4 Thermal energy storage General An mportant parameter for the sustanable development s the maxmum utlsaton of the avalable energy sources. Tradtonally, f the energy producton was hgher than the energy consumpton, the energy surplus was smply wasted n the envronment. On the other hand, n the opposte case expensve equpment and energy sources were used to cover the energy shortages. Ths msmatch between the producton and the demand occurs due to ther ntermttent nature. For example, n a solar system the energy producton s qute changeable throughout the day and t depends on the solar radaton, the cloudness etc. In contrast, the energy requrements can fluctuate a lot throughout the day dependng on the habts of the end-users, amongst many other factors. Lately, the concept of energy storage has been studed extensvely as a means of matchng the producton wth the demand. The man dea s to store energy when n excess producton and release t when n shortage (Han et al., 2009). The energy storage systems are, n general, dvded n the followng categores accordng to the knd of energy stored: Mechancal, electrcal, thermal and chemcal energy storage, whle less developed are the magnetc and bologc energy storage methods (Dncer and Rosen, 2011). For the sake of smplcty, the thermal energy storage systems wll be examned n ths secton, as well as n the overall thess, as the studed systems are dealng only wth thermal energy both n the producton and the demand sde. Therefore, the thermal energy storage systems are consdered to be the most approprate for these systems. The thermal energy storage systems (TES) are further dvded n the followng categores (Artecon et al., 2012): Sensble TES: In these systems, the energy s stored through the temperature change of the storage medum. The most common storage medum n these 67

70 systems s water. A basc advantage of the sensble TES s that the storage medum s safe, cheap, abundant and easy to handle. Furthermore, these are the best establshed storage systems. In contrast, the basc dsadvantage of these systems s that ther operaton s typcally lmted by the bolng pont of the storage medum, whch for water s 100 o C. In some cases, sold meda, such as concrete, are used for storage, but requre generally large storage volumes and are not preferred. Latent TES: As ts name ndcates, n a latent TES the energy s stored through the phase change of the storage medum. The storage meda n these systems are called PCMs (Phase Change Materals). Typcally, the storage medum s n sold form and when the energy s stored t lquefes. Durng the dscharge phase, the opposte process occurs. A basc advantage s that the system operates n a constant temperature, and the range of the storage temperature s much hgher compared to a sensble TES. On the other hand, these systems are more expensve and requre better mantenance. The most typcal storage meda, are water/ce, salt hydrates and polymers. Cold TES: Ths s a specal category of the two aforementoned TES and t refers to the thermal energy storage for cold applcatons. The typcal materals that are used are ce, chlled water and some PCMs. Thermochemcal TES: These systems could also be ncluded n the chemcal storage systems and, therefore, wll be explaned brefly. A reversble chemcal reacton s utlsed n these systems. Typcally, the energy s stored through an endothermc reacton, and the energy s released by performng the reacton n the opposte way. The envronmental concerns around these systems have manly slowed down ther development. Apart from the aforementoned detals, when comparng these systems two man parameters are taken nto account. These are the energy densty of the storage medum and ts cost. Concernng the energy densty, the thermochemcal TES are by far the best opton followed by the latent TES and, then, the sensble TES. In contrast, the costs of these systems follow exactly the reverse trend. So, t s a matter of engneerng decson whch of the prevously mentoned TES wll be used. Other factors that should be taken nto account are the operatng temperature, the safety and the avalable storage volume. 68

71 2.4.2 Thermal energy storage n dstrct heatng systems As mentoned earler, the typcal temperatures of the water n a dstrct heatng system (ncludng GDHSs) s well below 100 o C. Takng ths nto account together wth the fact that water s the workng flud anyway, the use of a sensble TES s an obvous soluton. For ths purpose, water storage tanks are mplemented for the matchng between the producton and the demand. In a dstrct heatng system fed by a CHP unt, the msmatch between the producton and the demand can be ntensfed when the CHP unt s operatng n an electrcally-drven mode, when the heat producton s lmted by the electrcty producton. Water by ts nature dsplays a natural phenomenon, called stratfcaton, whch can nfluence the operaton and effectveness of the storage. When water s stored n a storage tank, t tends to develop a thermoclne and be separated vertcally nto two dfferent temperature zones. In practce, stratfcaton occurs manly due to the heat losses to the envronment, whch creates a zone of colder flud close to the walls of the tank whch tends to move downwards. For the modellng of storage tanks, two man approaches are used: stratfed and fully-mxed storage tanks. In practce, stratfcaton not only occurs naturally but can also be desrable. As mentoned before, the majorty of dstrct heatng systems are fed by CHP unts, n whch the temperature of the water provded to the network can be varable (Kostowsk and Skorek, 2005; Haeseldonckx et al., 2007). The supply temperature to the end-users should have a specfc value accordng to the end-users needs. On the other hand, the return temperature to the producton unt should be mnmsed n order to optmse the whole process. So, stratfed tanks wth a hgh degree of stratfcaton are used n many cases. Furthermore, the stratfcaton can be enhanced n many dfferent ways on whch a lot of research has been carred out (e.g. Verda and Colella, 2011; Garca-Mar et al., 2013; Kenjo et al., 2007; Jordan and Furbo, 2005). The majorty of the studes have shown that stratfed storage tanks can provde numerous advantages when coupled wth a CHP unt. For example, Verda and Colella (2011) found that the prmary energy consumpton can be reduced by 12%, whle the total costs can be decreased by 5%. Ghaddar (1994) states that a stratfed storage tank works more effcently under a varable temperature, whch comes n contrast wth the logc of a GDHS. A basc dsadvantage of ths knd of tank s that the 69

72 stratfcaton can be easly destroyed and low flow rates are generally requred. Ths also contrasts wth GDHS n whch the flow rates are farly hgh. Fully mxed storage tanks have not been studed as extensvely as stratfed tanks. Paglarn and Raner (2010) studed the effect of a fully mxed storage tank when coupled wth a CHP unt for the heatng needs of a Unversty campus. The results hghlght the energetc and economc benefts of ntegratng a heat storage n ths system. Subsequently, Campos Celador et al. (2011) compared the dfferent approaches to modellng of water storage tanks n a CHP plant. More specfcally, they used the fully mxed, the actual stratfed and the deal stratfed models to smulate the storage tank. It was found that from an energetc pont of vew, the effectveness of all the smulatons are roughly the same, but from an economc pont of vew, the stratfed approach s more desrable. These results agree partally wth the results of Ghaddar (1994) who stated that the stratfed approach also substantally mproves the results from an energetc pont of vew Thermal energy storage n geothermal dstrct heatng systems As mentoned before, the majorty of the studes of hot water storage tanks concerned CHP or solar unts, whch have a varable feedng temperature whch makes the use of stratfed tanks unavodable. To the best of the author s knowledge, there are no publshed studes whch ntegrate a heat storage nto a geothermal dstrct heatng system. In contrast wth the aforementoned studes, the temperatures across a GDHS and, subsequently, the feedng temperature nto the tank, are roughly constant. Furthermore, n these systems the mass flow rates are usually very hgh (as wll also be seen n the followng Chapters), whch makes the mantenance of stratfcaton qute dffcult and costly. Another reason for usng a stratfed tank s the lack of avalable area for buldng a fully mxed tank. In a GDHS, ths should not be a problem. Therefore, for all these reasons and n order to ncrease the knowledge base on fully mxed tanks, n ths thess, a fully mxed storage tank wll be used to store hot water and a second fully mxed tank wll be used to store cold water. Although t s not very clear, n the studes where fully mxed tanks are used t s assumed that there s only one tank where hot and cold water are stored together. A novelty of ths study s that two separate tanks wll be used for storng the hot and cold water. As wll be seen later, throughout ths study the hot water storage tank (HST) wll be studed n detal as ths wll be the man buffer between the heat producton and the heat demand. The 70

73 cold water storage tank wll be used manly n order to keep the flow rate headng to the geothermal heat exchanger to a constant value. All ths wll be made clear n the followng Chapters. 2.5 Summary In ths Chapter, dstrct heatng systems that utlze geothermal energy were revewed. Heat s extracted from a flud n the Earth s crust, the so-called geothermal flud (usually brne), and t s dstrbuted to consumers through a dstrbuton network. The geothermal flud can be dstrbuted drectly to the consumers, or ts heat can be provded to a secondary clean water closed system. Usually the latter s the case, because the majorty of geothermal fluds have corrosve propertes and t s not possble to securely dstrbute them over large dstances. Hence, usually, plate-type counter flow heat exchangers are used for ths purpose. Addtonally, n most cases, each buldng has ts own secondary heat exchanger, n order to avod hgh pressures n the dstrbuton network. The basc prerequstes for a successful geothermal dstrct heatng system are an avalable resource near to the heat consumpton centre and a satsfactory heat densty. An adequate temperature of the resource s crucal n order to meet the specfc demands of the process n whch the geothermal heat wll be utlzed. As already mentoned, the man processes are space heatng and domestc hot water preparaton. Developments n the technology of space heatng can render many more geothermal wells sutable for space heatng. Other uses, ether separately or n an ntegrated way, can be for agrcultural purposes, ndustral processes, greenhouse heatng, balneology, aquaculture, dstllaton, snow meltng etc. Apart from the well temperature, an adequate contnuous flow rate s a basc prerequste. Estmaton of these values can be undertaken n many ways, but both of these can only be assured when the drllng takes place, so a hgh rsk s contaned n these projects. The rsk gets even hgher as the cost of drllng ncreases. As noted n the correspondng secton, the drllng s usually a large part of the nvestment cost. So, a careful estmaton of the mass flow rate and the temperature of the well must be done n advance, n order to mnmze the drllng rsk. Addtonally, subsdes are necessary n some cases n order to mnmse that rsk. An avalable geothermal resource, wth an adequate temperature and mass flow rate, s not useful f t s far away from the consumers. The transmsson and dstrbuton costs are 71

74 a large part of the nvestment cost, sometmes over 50%, so the less dstance that the geothermal heat has to be transferred the better. Addtonally, a hgh heat densty area s desrable to maxmze the ncome from the nvestment. The hgher the heat densty of the area, the hgher the amount of heat sold. Addtonally, a hgh rate of partcpaton n the proposed area s also desrable. Hgh partcpaton can be acheved through educaton, so that people fully apprecate the advantages of geothermal energy. Of course, geothermal expertse s necessary to develop and promote geothermal dstrct heatng systems (Luns, 1985). As already mentoned, ntal choces are crucal for these systems. Maxmzaton of heat sold together wth maxmzaton of ncome and maxmzaton of geothermal energy utlzed all need to be acheved for a successful geothermal dstrct heatng scheme. Numerous studes have shown the advantages of geothermal energy. It can be concluded that geothermal energy, and therefore geothermal dstrct heatng systems, are cleaner than fossl fuels and n most cases cheaper or at least compettve. They result n better ndoor ar qualty, and n countres wth hgh penetraton of geothermal energy use, e.g. Iceland, the consumers state that ther qualty of lfe has also ncreased snce swtchng to geothermal energy (Jonasson and Thordarson, 2007). Geothermal energy s also a local energy source, whch provdes benefts to the local socety, and also enhances energy ndependence. Fnally, wth the development and mplementaton of EGS systems, many new felds are lkely to become explotable, thus substantally ncrease the geothermal resource base. The refurbshment of old buldngs and the constructon of new energy-effcent buldng can go hand n hand wth the development of geothermal dstrct heatng networks, provdng elegant means of achevng targets set to address envronmental and energy supply problems. 72

75 3 SIZING OF A GEOTHERMAL DISTRICT HEATING SYSTEM 3.1 Introducton In ths Chapter, an ntegrated model for the szng of a GDHS s developed. For ths purpose, the geothermal data, the heat demand data throughout a whole year and the topology of the studed area are used as the basc nputs. The heat demand data should have a fne tme dscretzaton n order to get more accurate results. The output of ths model s the complete szng or dmensonng of the nstallaton, ncludng the number of geothermal wells, the szng of the storage tank and the szng of the ppelnes amongst others. It should be noted that two components of the nstallaton,.e. the peak-up bolers and the cold storage tank, wll be szed n Chapter 4 as some data from that algorthm are necessary for that purpose. Detals on the other data used n ths model are gven n the next secton. The analyss of the nstallaton s carred out on a daly bass. Therefore, a specfc day has to be chosen as the desgn-day on whch the szng of the nstallaton wll be based. The bass of ths selecton as well as the detals of all the mathematcal modellng are gven n secton 3.2. Then, the results of ths model are shown n secton 3.3. The results are gven for real heat demand data, but for arbtrary geothermal data and topology. Ths s because as the developed model, as well as the others descrbed n ths thess, are generc models and t was not logcal to study a geographcally specfc test-case. The heat demand data are real data however, rather than formulated or arbtrary data, as t was consdered that only by usng real data could realstc fluctuatons be hghlghted, and thus the model s advantages and dsadvantages made clear. Furthermore, all the results n ths thess are gven for three dfferent cases of the desgn-day. More detals on these cases are gven n the results secton. Fnally, n secton 3.4 a detaled dscusson on the results s provded and n secton 3.5 the hghlghts of ths Chapter are summarsed. 73

76 3.2 Mathematcal Modellng Inputs of the model As mentoned before, the majorty of the nputs of the model wll be arbtrary numbers as the developed model s generc. Some of these nputs are ntal estmatons of some basc values of the nstallaton and wll be updated by the algorthm, whle the rest are characterstcs of the nstallaton and reman constant. The nputs that are updated by the algorthm are the followng: The rato of the mass flow rate of workng flud (water) passng through the geothermal heat exchanger to the geothermal flow rate comng from the well (Rm nt ). The thermal effcency of the hot water storage tank (η HST,nt ). Temperature drop n the substaton (ΔT sub,nt ). Temperature drop per km of the hot transmsson ppelne (ΔT tr.h,nt ). It should be noted that where the ndex nt s used, ths refers to ntal estmatons and later n the algorthm the exact values wll be calculated. On the other hand, the nputs that reman constant are the followng: Heat demand data. Geothermal, ambent and sol temperatures. Mass flow rate of one geothermal well. Thcknesses, thermal and physcal characterstcs of the materals used for the hot water storage tank and the ppelnes. Length of the transmsson and dstrbuton ppelnes. Bural depth and dstance between the ppelnes. Maxmum pressure and tensle strength of the ppelnes. Absolute roughness of the ppelne. Thermal effcency of the geothermal heat exchanger. Thermal effcency of the substaton (η sub ). Ths effcency takes nto account the heat losses of the dstrbuton network as well as the end-user nstallatons. Mnmum temperature dfferences on the hot and the cold sde of the geothermal heat exchanger. 74

77 Mechancal effcency of the pumps. Ar velocty. Unt prces of heatng and electrcty as well as prces of the materals used. Interest rate Lfespan of the nvestment. Operatng hours per year. Furthermore, the temperature drop n the end of each dstrbuton branch s also used as nput. These temperature drops are consdered constant throughout the whole study and t s assumed that the heat demand varatons wll be covered solely by the varaton of the mass flow rate. Ths s one of the basc assumptons of ths study. Addtonally, for desgn purposes only, t s consdered that the mass flow rate n each branch of the dstrbuton network s equal to a specfc proporton of the total mass flow rate on the transmsson network. In Chapter 4, where the operaton of the nstallaton s studed, the real-tme mass flow rates of each branch are taken nto account. Fnally, the necessary propertes of ar and water are wrtten as functons of temperature as the data used are pont-data 1. These data are wrtten n an excel fle n order to fnd the optmum knd of the fttng functon. Then, the data are nserted n the algorthm and the best ft functon s calculated wthn the algorthm. The calculated functons have a fttng coeffcent of almost 100% and refer to temperatures between o C, whch s the man temperature range n the studed cases. Concernng ar, the vscosty s found to be a second order polynomal aganst the temperature, whle the Prandtl number and the thermal conductvty are found to be frst order polynomals. Concernng the water, the densty and the vscosty are found to be thrd order polynomals aganst the temperature, whle the specfc heat capacty s consdered to be constant throughout the studed temperature range and equal to 4190 J. kg K It has to be made clear at ths pont that some varables are pont values, whle others refer to a whole tme nterval. In the frst category, the temperatures and masses of stored water are ncluded, whle n the latter all the other mass exchanges are ncluded. Obvously, the parameters n the frst category have one more value than the latter, snce the last pont of the day s also ncluded. For example, f the tme dscretzaton s 1 hour,

78 then the frst category of varables wll have 25 values, whle the latter wll have just 24 tme ntervals. In the followng, both varables wll have the superscrpt, but for the frst knd of varables t wll mean the pont-value whle for the second knd of varables t wll mean the contnuous value throughout the tme nterval -+1. The frst knd of varables wll be called ponts whle the latter are called tme-ntervals. Ths dstncton wll be made clearer n Chapter Frst calculaton of the basc parameters In ths secton, a frst calculaton of some basc parameters of the network s carred out. Intally, some values of the temperatures of the transmsson network have to be calculated. Ths s done by applyng some of the nputs descrbed prevously as ntal estmatons. The ponts of these temperatures on the transmsson network are shown n Fg. 3.1 together wth the assocated masses. Snce the temperature of the geothermal flud s known, the nlet temperature of the transmsson supply ppelne s calculated as: T tr,s, = T G,h T h,ghe.,mn (3.1) Where: T tr,s, = Temperature n the nlet of the transmsson supply ppelne (K) T G,h = Temperature (hot) of the geothermal flud (K) T h,ghe.,mn = Mnmum temperature dfference n the hot sde of the G.H.E. (K) Then, the temperature n the nlet of the hot water storage tank s calculated by the followng equaton, whch takes nto account the heat losses n the supply ppelne: T HST, = T tr,s, L tr,s,1 T tr,s,nt (3.2) Where: T HST, = Inlet temperature n the hot water storage tank (K) L tr,s,1 = Length of the transmsson supply ppelne between the G.H.E. and the hot water storage tank (km) T tr,s,nt = Intal estmaton of the temperature drop per unt of ppe length n the supply ppelne ( K km ) 76

79 Fgure 3.1 Smplfed scheme ndcatng the temperatures across the transmsson ppelnes (G.H.E. = Geothermal Heat Exchanger, D.N. = Dstrbuton network, P.W. = Producton Well, R.W. = Re-njecton Well, H.S.T. = Hot water storage tank, C.S.T. = Cold water storage tank) The thermal effcency of the hot water storage tank s calculated as the proporton of the energy extng the tank to the energy enterng the tank. These energes consst of the thermal energy of the water due to ts temperature, and any other forms of energy, such as knetc energy, are consdered neglgble. At ths stage, the ntal estmaton of the effcency wll be used, and only the correspondng temperatures wll be taken nto account snce the mass flow rates are not known yet. It should be noted that all these values of the temperatures across the transmsson network wll be later checked and re-calculated, f necessary, n an teratve loop. So, the temperature at the ext of the hot water storage tank s calculated as: T HST,o = η HST,nt (T HST, T a ) + T a (3.3) Where: T HST,o = Outlet temperature from the hot water storage tank (K) η HST,nt = Intal estmaton of the thermal effcency of the hot water storage tank (Dmensonless) T a = Ambent temperature (K) The outlet temperature of the transmsson supply ppelne can be calculated by an equaton smlar to Eq. (3.2), but, t s proposed the hot water storage tank to be as close as 77

80 possble to the substaton, so that the response n any change of the demand to be as quck as possble. Therefore, we get: T tr,s,o = T HST,o (3.4) Where: T tr,s,o = Outlet temperature from the supply transmsson ppelne (K) Afterwards, the nlet temperature of the transmsson return ppelne s calculated through the temperature drop n the substaton as: T tr,r, = T tr,s,o ΔT sub,nt (3.5) Where: T tr,r, = Inlet temperature of the return transmsson ppelne (K) ΔT sub,nt = Intal estmaton of the temperature drop n the substaton (K) The rest of the temperatures n the transmsson return ppelne are calculated wth smlar equatons to those for temperatures n the transmsson supply ppelne. More specfcally, the followng equatons are used: T CST, = T tr,r, (3.6) T CST,o = η CST,nt (T CST, T a ) + T a (3.7) T tr,r,o = T CST,o L tr,r,2 T tr,r,nt (3.8) Where: T CST, = Inlet temperature n the cold water storage tank (K) T CST,o = Outlet temperature from the cold water storage tank (K) η CST,nt = Intal estmaton of the thermal effcency of the cold water storage tank (Dmensonless) T tr,r,o = Outlet temperature from the return transmsson ppelne (K) L tr,r,2 = Length of the return transmsson ppelne between the cold water storage tank and the G.H.E. (km) 78

81 T tr,r,nt = Intal estmaton of the temperature drop per unt of ppe length for the return transmsson ppelne ( K km ) The cold water storage tank s also proposed to be as close as possble to the substaton, so that the mass flow rate n both ppelnes of the transmsson network wll be the same. Equaton (3.6) arses from ths proposton. Furthermore, there are two basc dfferences n the calculatons of the transmsson return ppelne compared to the transmsson supply ppelne. Frstly, the heat losses of the return ppelne are assumed, at ths stage, to be half of the heat losses of the supply ppelne. As wll be seen n secton 3.2.6, the heat losses of the ppelnes are proportonal to the temperature dfference between the water and the ambent. So, t s qute sensble to assume that the temperature n the return ppelne wll be around the mddle between the supply and the ambent temperatures and, therefore, the heat losses of the return ppelne to be half of the supply ppelne. Secondly, the heat losses of the cold storage tank are assumed to be half those of the hot storage tank. Ths s assumed on the same bass as the heat losses of the ppelnes. As wll also be seen n the results secton, both the losses of the ppelnes and of the hot water storage tank are qute small, so any wrong estmatons n these factors wll not cause an mportant general error. Nevertheless, f these assumptons are not very precse, the only problem that wll arse s that the algorthm wll need more tme to converge (see secton also). So, these two assumptons are defntely acceptable from an engneerng pont of vew. Concernng the storage tanks, consderng that ther thermal effcency can also be defned as (1 Losses), then the thermal effcency of the cold storage tank s easly calculated as: η CST,nt = 1 1 η HST,nt 2 (3.9) Snce all the temperatures of the transmsson network are known, the temperature drop of the geothermal water and ts temperature at the ext of the geothermal heat exchanger can be, respectvely, calculated as: ΔT G = R m,nt T tr,s, T tr,r,o η GHE (3.10) T G,c = T G,h ΔT G (3.11) 79

82 Where: ΔT G = Temperature drop of the geothermal flud (K) R m,nt = Intal estmaton of the rato of the mass flow rate on the transmsson network on the rght of the G.H.E. (or left of the hot water storage tank, whch wll be constant throughout the day as seen on the next) to the geothermal flow rate (Dmensonless) η GHE = Thermal effcency of the G.H.E. (Dmensonless) T G,c = Outlet (cold/ re-njecton) temperature of the geothermal flud (K) Fnally, the total thermal effcency of the nstallaton s calculated as: η tot = η sub,nt R m T tr,s,o T tr,r, T G (3.12) Where: η tot = Total thermal effcency of the nstallaton (Dmensonless) So, through Eqs. (3.1)-(3.12), a frst calculaton of the basc parameters of the network s carred out. All these values wll be checked and updated, f necessary, n later stages of the algorthm. By knowng these ntal values, the calculatons n the followng sectons are now possble Szng of the geothermal nstallaton A basc nput of ths model s the detaled heat demand over a year. The daly heat demand of each day can be easly calculated as the summary of the separate heat demands over ths day. DHD HD (3.13) Day Where: HD = Heat demand per tme nterval of the studed day (kwh or J) DHD = Daly heat demand of the studed day (kwh or J) 80

83 So, a lst of the daly heat demands over the year of study can be calculated. Then, a specfc day s chosen by the user as the desgn-day. In the desgn-day, all the heat demand wll be covered by geothermal energy only wth the assstance of the heat storage and no peak-up bolers wll be used. Therefore, the total geothermal energy harvested throughout the day can be calculated by the followng equaton: E G,D,D = DHD D η tot (3.14) Where: E G,D,D = Geothermal energy harvested throughout the desgn-day (kwh or J) DHD D = Daly heat demand of the desgn-day (kwh or J) In the above equaton, the total effcency calculated n Eq. (3.12) s used. Then, the above energy term has to be converted n the equvalent power term. Ths converson depends on the unts of the energy terms whch depend on the unts of the heat demand data. Commonly, these data are provded n kwh, and therefore the converson n power terms (n W) s done by dvdng the energy term by the hours of the day. For the sake of smplcty, n the rest of ths study t s assumed that the heat demand data wll be used n kwh. Q G,D = E G,D,D (3.15) Where: Q G,D = Geothermal power of the desgn-day (W) The term 1000 n the above equaton s used to turn the unts from kw to W. Snce the geothermal power of the desgn-day s known, the necessary geothermal mass flow rate can be easly calculated as: m G,D = Q G,D Cp w T G (3.16) Where: m G,D = Geothermal mass flow rate on the desgn-day ( kg s ) 81

84 Cp w = Specfc heat capacty of the geothermal flud ( J kg K ) The temperature of the geothermal flud s known from Eq. (3.10) and ts specfc heat capacty s also a known value. As mentoned n Chapter 2, the propertes of the geothermal flud are the same as those of pure water as the effect of mnerals and noncondensable gases s neglgble. Then, the necessary number of geothermal wells s calculated by dvdng the geothermal mass flow rate by the mass flow rate of one well, whch s a known value: N wells = m G,D m well (3.17) Where: N wells = Number of geothermal wells m well = Mass flow rate of each geothermal well ( kg s ) Most probably, the above result wll be a decmal number whch, of course, does not have a physcal meanng snce t refers to the number of geothermal wells. Therefore, ths result has to be rounded. The knd of roundng (floor, bottom or closest nteger) depends on the user. In our case, t s selected to round ths result to the closest nteger, unless for the case where the result s less than 1 where t s rounded to 1. The fnal number of wells s gven by the followng equaton: If N wells < 1: Then: N wells = 1 } (3.18) Else: N wells = round(n wells ) So, the fnal value of the geothermal mass flow rate and the geothermal power are calculated by Eqs. (3.16) and (3.17) properly re-arranged by takng nto account the fnal value of the number of geothermal wells. Therefore, by applyng Eqs. (3.13)-(3.18), the geothermal nstallaton s szed and the geothermal power of the desgn-day are known. The geothermal power of the desgn-day, s also the maxmum geothermal power that can be delvered at any tme, snce the maxmum mass flow rate s used. For that reason, ths value s also the geothermal capacty of the nstallaton. 82

85 3.2.4 Szng of the hot water storage tank The szng of the hot water storage tank as well as of the rest of the nstallaton wll be carred out for the desgn-day. In our approach, the mass flow rate to the left of the storage tank wll be constant throughout the day, whle the mass flow rate to the rght of the storage tank wll be varable accordng to the heat demand of each tme nterval (see Fg. 3.1). Snce the heat demand s known per tme nterval, n the followng all the calculatons wll be done for masses per nterval (symbolsed wth M), nstead of mass flow rates. So, the masses to the left and the rght of the storage tank are calculated, respectvely, as: M tr,g = M G,D R m,nt (3.19) For each tme nterval : HD M tr,s = } (3.20) Cp w (T tr,s,o T tr,r, ) η sub Where: M tr,g = Mass of water per tme nterval n the left of the storage tank (kg) M tr,s = Mass of water per tme nterval n the rght of the storage tank (kg) Then, by the dfference of these values, the masses of charged and dscharged water n the storage tank can be calculated, respectvely, as: For each tme nterval : If M tr,g M tr,s 0: Then: M ch = M tr,g M tr,s Else: M ch = 0 } (3.21) For each tme nterval : If M tr,g M tr,s 0: Then: M ds = 0 Else: M ds = M tr,s M tr,g } (3.22) Where: M ch = Mass of charged water n the storage tank per tme nterval (kg) M ds = Mass of dscharged water from the storage tank per tme nterval (kg) 83

86 Afterwards, the mass of stored water can be easly calculated by the followng equaton: M st For 1: = M ch M ds M 1} (3.23) st Where: M st = Mass of stored water per tme nterval (kg) As a boundary condton n the above equaton, t s consdered that ntally there s no stored water n the hot water storage tank. M 0 st = 0 (3.24) Fnally, the volume of the hot water storage tank wll be calculated through the maxmum value of stored water durng the desgn-day as: V HST = max (M st ) SF (3.25) ρ w (T HST. ) Where: V HST = Volume of the hot water storage tank (m 3 ) ρ w = Densty of water ( kg m 3) SF = Securty factor (Dmensonless) In the above equaton, the densty of water s calculated for the temperature n the nlet of the water tank. Ths happens because the densty of water decreases wth ncreasng temperature. Therefore, the maxmum temperature s used, n order to get the mnmum densty and, subsequently, the maxmum storage volume. A securty factor SF s also used n the above equaton, whch n our case s consdered to be equal to 1.1. Ths allows errors of up to 10% durng the szng of the hot water storage tank. Fnally, the thckness of the materal of the storage tank, whch s stanless steel n our case, s calculated through the API Standard 650 (Baker, 2009). Ths Standard has been orgnally produced for the szng of ol storage tanks, but, t s assumed that the same methodology can be appled for water storage tanks wthout mportant errors. 84

87 In concluson, by applyng Eqs. (3.19)-(3.25), all the mass balances across the transmsson network as well as the volume of the hot water storage tank are calculated Energy balance n the hot water storage tank In ths secton, the methodology for the calculaton of the temperature evoluton wthn the hot water storage tank s developed. Furthermore, the calculaton of the heat losses from the tank are explaned and a defnton of the thermal effcency of the tank s gven n order to get a more precse value of t. For the calculaton of the temperature evoluton of the stored water, the energy conservaton equaton n the storage tank s appled wthn one tme nterval (smlar equaton appled by Kostowsk and Skorek, 2005): d(ρ w Cp w V w,st T st ) dt = Q + Q Q loss (3.26) Where: V w,st = Volume of stored water between ponts and +1 (m 3 ) T st = Temperature of stored water n pont (K) Q +, Q, Q loss = Heat surplus due to chargng, heat shortage due to dschargng and heat losses rate of the storage tank, respectvely (W) In the above equaton, the left hand sde denotes the accumulaton term balanced by the heat surplus due to chargng, the heat shortage due to dschargng and the heat losses, respectvely, n the rght hand sde. Furthermore, V w,st s the volume of stored water whch changes wthn the tme nterval. As the specfc heat capacty of water has been consdered constant, and by replacng the densty-tmes the volume of stored water equal to the mass of stored water, the left hand sde of the above equaton can be dscretsed as: d(ρ w Cp w V w,st T st ) dt = Cp w d(ρ w V w,st T st ) dt = Cp w d(m st T st ) dt = Cp w M st +1 T +1 st M st T st t (3.27) Then, both sdes of the above equaton are multpled by the tme nterval (dt) n order to convert the power terms n energy terms whch are easer to mplement snce, as mentoned before, the masses across the network are known and not the mass flow rates. 85

88 So, the heat surplus and shortage terms can be calculated by the followng equatons, respectvely: Q + = M ch Cp w (T HST, T a ) (3.28) Q = M ds Cp w ( T st +1 +T st T 2 a ) (3.29) The heat losses of the storage tank nclude the heat losses from the top, sdes and base. Therefore, t s calculated by the followng equaton: Q loss = Q loss,top + Q loss,sde + Q loss,base (3.30) Where: Q loss,top storage tank (W), Q loss,sde, Q loss,base = Heat losses rate from the top, sdes and base of the A basc assumpton of ths thess s that the storage tank s consdered to be fully mxed. Ths means that the temperature wll be unform wthn the tank and equal to the storage temperature (T st ). So, the nner surface of the tank wll have a temperature equal to the storage temperature at each tme-step. The heat losses from the top and sdes of the tank occur due to conducton wthn the dfferent layers of the tank and convecton together wth radaton to the ambent envronment. On the other hand, the heat losses from the base occur due to conducton through the dfferent layers of the tank and the underlyng sol. The layers of the storage tank consst of stanless steel, nsulaton and a cover for the top and sdes, and of stanless steel, nsulaton and a concrete base for the base. For the calculaton of the convectve heat transfer coeffcent n the top part of the tank, the equatons for flow parallel to a horzontal body are used, whle for the sde part the equatons for flow perpendcular to a cylndrcal body are used. Therefore, the heat losses n the three parts of the tank can be calculated by the followng sets of equatons (Kakatsos, 2006), n whch all the equatons for each part of the tank are referred here as one equaton (equaton numberng n parentheses below): 86

89 Top (3.31): Q loss,top = K top A top ( T st +1 +T st T 2 a ) t A top = π D st t 1 1 K k h h j top j j c, top r,top h c,top = Nu k ar D st Re = u ar D st ν ar If Re < : Then: Nu = Pr 1/3 Re 1/2 Else-f < Re < : Then: Nu = Pr 0.43 Re 0.8 Else: Nu = Pr 1/3 Re 0.8 h r,top 2 = ε cv σ (T sur + 2 Ta ) (T sur + T a ) Sdes (3.32): Q loss,sde = K sde A sde ( T st +1 +T st T 2 a ) t A sde = π D st H st 1 t 1 1 K k h h j sde j j c,sde r,sde h c,sde = Nu k ar D st 87

90 Re = u ar D st ν ar If < Re < : Then: Nu = Re1/2 Pr 1/3 [1 + ( [1+( 0.4 Pr ) 2 3 ] 1/4 Else: Nu = Re1/2 Pr 1/3 [1 + ( [1+( 0.4 Pr ) 2 3 ] 1/4 Re 1 ) 2 ] Re 5 ) 8 ] 4/ h r,sde 2 = ε cv σ (T sur + 2 Ta ) (T sur + T a ) Base (3.33): Q loss,base = K base A base ( T st +1 +T st T 2 sol ) t A base = π D st = t j K j base k j Where: Q loss,top, Q loss,sde, Q loss,base = Heat losses from the top, sde and base of the storage tank durng tme nterval (J) K top, K sde, K base = Overall heat transfer coeffcent of the top, sde and base of the storage tank durng tme nterval ( W m 2 K ) A top, A sde, A base = Top, sde and base area of the storage tank (m 2 ) D st, H st = Dameter and heght of the storage tank (m) t j = Thckness of each materal j of the storage tank (m) k j = Thermal conductvty of each materal j of the storage tank ( W m K ) h c,top, h c,sde = Convectve heat transfer coeffcent of the top and sdes of the storage tank for each tme nterval ( W m 2 K ) h r,top, h r,sde = Radatve heat transfer coeffcent of the top and sdes of the storage tank for each tme nterval I ( W m 2 K ) Nu, Re, Pr = Nusselt, Reynolds and Prandtl numbers, respectvely (Dmensonless) 88

91 k ar = Thermal conductvty of ar ( W m K ) u ar = Velocty of ar ( m s ) ν ar = Knematc vscosty of ar ( m2 s ) ε cv = Emssvty of the cover of the storage tank (Dmensonless) σ = Stefan-Boltzmann constant for radatve heat transfer whch s equal to W m 2 K 4 T sur = Temperature of the surface of the storage tank for each tme nterval (K) It can be seen from the above sets of equatons that the average storage temperature between two tme ntervals s used n each case. In the cases of the top and sdes of the tank, the calculatons depend on the temperature of the stored water each tme and on the outer surface temperature of the tank. Therefore, a temporal superscrpt s assgned n these calculatons. In the case of the base of the tank, the heat transfer coeffcent depends only on the materals of the tank and, therefore, t s constant all the tme. Furthermore, some of the parameters used n the calculaton of the convectve heat transfer coeffcents are temperature dependent. These parameters,.e. the Prandtl number and the knematc vscosty of ar, are calculated for the average temperature between the ambent temperature and the outer surface temperature. The latter s also an unknown varable n the problem. For the soluton of ths problem, t s consdered that the heat transfer due to conducton n the dfferent layers of the tank s equal to the heat transfer due to convecton and the radaton to the ambent envronment. Ths s schematcally llustrated n Fgure 3.2, where a cross-sectonal area of the sde of the tank s shown together wth the assocated temperatures and heat flows. 89

92 Fgure 3.2 Heat flows and temperatures through the sdes of the tank By the equalty between the heat flows, and by assumng that these are onedmensonal only, we get the followng equaton: Q cond j = Q conv + Q rad k (3.34) t j 4 4 ( Tst Tsur ) hconv ( Tsur Ta ) cv ( Tsur Ta ) j Where: Q cond, Q conv respectvely (W), Q rad = Conductve, convectve and radatve heat transfer rates, As already mentoned, the convectve heat transfer coeffcent s dependent on the surface temperature, so n order to solve the above equaton an teratve method has to be appled. The above equaton s vald both for the top and the sdes of the tank. For the calculaton of the convectve heat transfer coeffcent, the correspondng equatons to (3.31) and (3.33) have to be used. So, for each tme nterval, the followng steps are carred out for the calculaton of the storage temperature: 1. An ntal estmate for the surface temperature s made. 2. Equaton (3.34) s solved teratvely tll the real surface temperature s found. 3. The total heat transfer coeffcents (K) for each part of the storage tank are calculated through the correspondng equatons from the (3.31)-(3.33) sets of equatons. 90

93 4. Fnally, Eqs. (3.26)-(3.30) are appled for the calculaton of the heat storage temperature n the next tme step. As a boundary condton for the above process, t s consdered that the storage temperature at the begnnng of the day s equal to the temperature of the water enterng the tank. T st 0 = T HST, (3.35) So, the evoluton of the stored temperature wthn the desgn-day can be calculated. Then, a new value of the thermal effcency of the storage tank can also be calculated. For that purpose, a new defnton whch takes nto account the mass and temperature varatons s defned. The new defnton of the thermal effcency of the storage tank s as follows: HST Mtr, S Cpw ( THST, o Ta ) Ew, out, total E M Cp ( T T ) w,n,total tr, G w HST, a (3.36) Where: E w,n,total, E w,out,total = Total energy of water enterng and leavng the storage tank, respectvely (J) η HST = Effcency of the hot water storage tank (Dmensonless) Fgure 3.3 s provded for the better understandng of the above equaton and the masses as well as the temperatures that are taken nto account n t. As can be seen, the mass and the temperature that are used n the numerator are those after the mxng pont wth the water comng from the geothermal producton, whle the mass and the temperature used n the denomnator are those before the splttng of the flow to the storage tank. In other words, the energy before the splttng and after the mxng of the flows are taken nto account. The temperature of the water after the mxng pont has been calculated ntally n secton 3.2.2, but n ths pont a more detaled calculaton that takes nto account the mxng wth the water comng from the tank on each tme nterval can be carred out. 91

94 Therefore, by assumng no heat losses at the mxng pont, the followng energy conservaton equaton can be appled: (M tr,g M ch 1 +M ch 2 (M tr,g M ch 1 +M ch 2 ) T HST, + M ds + M ds 1 +M ds 2 1 +M ds 2 ) T HST,o T st = (3.37) The above equaton was mplemented from the mddle of each tme nterval to the mddle of the next tme nterval as the masses are contnuous values, whle the temperatures are pont values as explaned earler. So, for each tme nterval, all the masses are known by Eqs. (3.19)-(3.22), whle the stored temperature s known by the process explaned prevously. Therefore, by Eq. (3.37) the temperature after the mxng pont can be calculated and, fnally, by Eq. (3.36) the thermal effcency of the hot water storage tank can also be calculated. Fgure 3.3 A schematc llustraton of the mass balances and temperatures assocated wth the hot water storage tank Concernng the cold water storage tank, t s stll assumed that ts losses wll be stll the half of those of the hot water storage tank, and therefore, ts value wll be calculated through Eq. (3.9), but now takng nto account the new value of the thermal effcency of the hot water storage tank. 92

95 3.2.6 Szng of the ppelnes of the network For the szng of the ppelnes of the network, an optmzaton algorthm s assembled. The objectve functon s the total cost of the ppelnes whch conssts of the captal cost, the cost of electrcty used by the pumps to overcome the frcton losses and the cost of the heat losses. The latter s not a drect cost, but an ndrect monetary loss, so t s also taken nto account n the total cost. The optmzaton parameters are the nternal dameter of the ppelne and the thckness of the nsulaton. As a general approach, a system of double prensulated underground ppelnes wll be used. More detals on ths wll be gven on the calculaton of the heat losses. F mn (D p,ex, t ns ) = CC p + C p.el + C p,hl (3.38) Where: CC p = Captal cost of ppelnes ( ) C p.el = Cost of the electrcty used by the pumps of the network to overcome the frcton losses of the ppelnes ( ) C p,hl = Cost of the heat losses of the ppelnes ( ) Captal cost calculaton The captal cost of the ppelnes conssts of the cost of the materals, whch are selected to be carbon steel and nsulaton, and the cost of weldng. Knowng the dmensons of the ppelnes, the total volume of each materal can easly be calculated and, then, by multplyng the volume of each materal wth ts unt cost, the cost of each materal s calculated. Fgure 3.4 shows a cross sectonal area of one ppelne for the better understandng of the geometry. The cost of weldng s usually a specfc cost provded by the manufacturer of the ppelnes. In our case, t s consdered to have a specfc prce per weld and meter of dameter. Therefore, the captal cost of the ppelnes s calculated by the followng equatons: V c.steel = π D p,o 2 2 D p, L 4 p (3.39) V ns = π (D p.o+2 t p,ns ) 2 D2 p.o 4 L p (3.40) 93

96 CC mat = CC c,steel + CC ns = V c,steel C u,c,steel + V ns C u,ns (3.41) CC p = 2 (CC mat + CC weld ) (3.42) Fgure 3.4 Cross-sectonal area of a ppelne wth the assocated dmensons (m 3 ) Where: V c.steel, V ns = Volume of carbon steel and nsulaton used n the ppelnes, respectvely D p,, D p,o = Inner and outer (not ncludng the nsulaton) dameter of the ppelnes, respectvely (m) L p = Length of the ppelnes (m) t p,ns = Thckness of the nsulaton of the ppelnes (m) C u,c,steel, C u,ns = Unt cost of carbon steel and nsulaton, respectvely ( m 3) CC c,steel, CC ns = Captal cost of carbon steel and nsulaton, respectvely ( ) CC mat, CC weld = Captal cost of materal and weldng, respectvely ( ) CC p = Total captal cost of ppelnes ( ) In Eq. (3.42), the factor 2 s used n order to take nto account both the supply and the return ppelnes. In the prevous equatons, the only parameter that cannot be used n the optmzaton algorthm s the external dameter of the ppelne. Ths s calculated through the necessary thckness of the ppelne n order to sustan the nternal pressure of the water. For the calculaton of the mnmum thckness of the ppelne, the followng equaton s used (Papantons, 2006): 94

97 e mn = P max D p,o σ SF + e 1 (3.43) Where: P max = Maxmum pressure wthn the ppelne (Bar). Usually, t s equal to 5.5Bar. D p,o = D p + 2 e mn σ = Tensle strength of the materal. For carbon steel t s 1500 kp SF = Securty factor. In ths case, t s set equal to 1.7. e 1 = Corroson allowance. It s set equal to 1mm. cm 2 Furthermore, for the szng of the ppelnes the standardzed dmensons are used accordng to EN10220 (Brtsh Standards Insttuton, 2002). So, after the mnmum thckness of the ppelne s calculated by Eq. (3.43), then the result s ncreased to the next hgher value of standardsed thckness. It should be noted that only standardsed values of external dameters wll be used throughout these calculatons. Fnally, by combnng and replacng Eqs. (3.39)-(3.41) and (3.43) nto Eq. (3.42), the latter can be wrtten as a functon of the nternal dameter and the thckness of the nsulaton, whch are the parameters of the ntal optmzaton functon Electrcal cost calculaton For the calculaton of the electrcal cost used by the pumps to overcome the frcton losses, t s necessary to calculate the frcton losses frst. The frcton losses are assumed to consst of the lnear losses only, whch are calculated by the Darcy-Wesbach equaton as follows: δh l = λ L p u 2 w D p 2 g (3.44) Where: δh l = Frcton losses (m) λ = Frcton losses coeffcent (Dmensonless) u w = Velocty of water ( m ) s In the above equaton, λ s the frcton losses coeffcent whch s calculated through teratons by the Colebrook equaton: 95

98 1 λ = 2 log ( 2.51 Re λ + ε r 3.71 ) (3.45) The unknown varables n Eqs. (3.44)- (3.45) can be easly calculated by the followng equatons: u w = 4 m ρ w π D p, 2 (3.46) Re = u w D p, ν w (3.47) ε r = ε a D p, (3.48) Where: ε r = Relatve roughness of the ppelne (Dmensonless) ε a = Absolute roughness of the ppelne (m) In Eq. (3.48), ε a s the absolute nternal roughness of the ppelne, whch s assumed to be equal to 0.1mm. The densty and the knematc vscosty of water are calculated for the average temperature of water wthn the ppelne. These temperatures wll be known after the heat losses are calculated. Therefore, ths part has to be combned wth the next one also. But, snce these temperatures are defned, then the frcton losses can be wrtten as a functon of the nternal dameter only through Eqs. (3.45)-(3.48). Afterwards, the electrcal power that has to be provded to the pumps s gven by the followng equaton: P el = m g δh l η pump (3.49) Where: P el = Electrcal power of the pump (W) η pump = Mechancal effcency of the pump (Dmensonless) The mechancal effcency of the pump (η pump ) s assumed to be equal to 70%. So, the cost of the electrcty can be easly found by multplyng the electrcal power of the pumps by the operatng hours per year and by the unt cost of electrcty. Addtonally, snce the captal cost refers to all the years of the nvestment, then the electrcal cost has to be taken 96

99 nto account for all the years of operaton too. Eventually, the electrcal cost used n the objectve functon s calculated as: C p, el P AOH C N el u, el (3.50) 1 (1 IR) Where: C p,el = Total cost of electrcty used by the pumps ( ) C u,el = Unt cost of electrcty ( kwh ) AOH = Annual operatng hours of the nstallaton IR = Interest rate (Dmensonless) In the above equaton, the factor 2 s not used as t s n Eq. (3.42) because the electrcal cost s not the same between the two ppelnes. Ths happens because the temperatures wthn the ppelnes are dfferent and, subsequently, the propertes of water are dfferent and, fnally, the electrcal cost s dfferent. So, n the fnal objectve functon, the electrcal cost of each ppelne has to be taken nto account separately. Wth the process explaned n ths secton, t was shown that through Eqs. (3.44)-(3.49), the electrcal cost of the pumps can be expressed as a functon of the nternal dameter only. Therefore, ths part of the total cost can be replaced n the ntal objectve functon Cost of heat losses In order to calculate the cost of the heat losses, frst the heat losses have to be calculated. For ths purpose, a system of double pre-nsulated underground ppelnes s consdered (see Fg. 3.5). As a begnnng, the equatons summarsed by Bohm (2000) wll be used. 97

100 Fgure 3.5 Studed system of double pre-nsulated underground ppes These equatons are the followng: q s = (U 1 U 2 ) ( T s+t r 2 T sol ) + (U 1 + U 2 ) ( T s T r 2 ) (3.51) q r = (U 1 U 2 ) ( T s+t r 2 T sol ) (U 1 + U 2 ) ( T s T r 2 ) (3.52) U 1 = R g+r (R g +R ) 2 R n 2 (3.53) U 2 = R n (R g +R ) 2 R n 2 (3.54) R = 1 2 π k ns ln ( D ns D p,o ) π k p ln ( D p,o D p. ) (3.55) R g = 1 2 π k sol [ln ( 4 H D ns ) S n S d ] (3.56) R n = 1 4 π k sol ln [1 + ( 2 H E )2 ] (3.57) S n = ( D ns 2 E )2 + ( D ns 4 H ) D ns 4 (4 H 2 +E 2 ) (3.58) S d = 1+β 1 β (D ns 2 E )2 (3.59) 98

101 β = k sol k ns ln ( D ns D p,o ) (3.60) D ns = D p,o + 2 t p,ns (3.61) D p,o = D p, + 2 e p (3.62) H = H + k sol h gs (3.63) Where: q s, q r = Heat losses rate of the supply and return ppelnes, respectvely (W) k ns, k p, k sol = Thermal conductvtes of the nsulaton, the materal of the ppelnes and the sol, respectvely ( W ) m K T sol = Sol temperature (K) D ns = Total dameter of the ppelnes, ncludng the nsulaton (m) e p = Thckness of the materal of the ppelne (m) E, H = Dstance between the ppelnes and ther bural depth, respectvely (m) Equaton (3.63) s used to take nto account the convecton and radaton occurrng due to the ground surface. In ths equaton, H s the equvalent depth and h gs s the convectve heat transfer coeffcent n the ground surface whch also takes nto account the radaton. Accordng to Kvsgaard and Hadvg (1980, as cted n Bohm, 2000), the value of h gs can be consdered constant and equal to 14.6 W. m 2 K In general, Eqs. (3.51)-(3.63) are defned for a system of double pre-nsulated underground ppelnes wth a unque temperature across ther length (T s for the supply ppelne and T r for the return ppelne). But, n our case the temperature drop has to be taken nto account. For ths purpose, each ppelne wll be dscretsed n space and n each element the temperature wll be consdered to decrease lnearly (see Fg. 3.6). Then, the average temperature n each element of each ppelne wll be used n Eqs. (3.51)-(3.63). For each spatal element: T s = T j j+1 s +Ts 2 (3.64) 99

102 T r = T j j+1 r +Tr 2 (3.65) It should be noted that Eqs. (3.55)-(3.57) refer to 1 meter of ppelne, therefore n order to take nto account the space dscretzaton each of these varables has to be dvded by the value of the space dscretzaton n meters. Then, the followng defnton of the heat losses wll also be used n each spatal element of the ppelnes: q s = m p Cp w (T s j T s j+1 ) (3.66) q r = m p Cp w (T r j+1 T r j ) (3.67) Fgure 3.6 Inlet and outlet temperatures n each spatal element of the ppelnes Therefore, by combnng Eqs. (3.51)-(3.65) wth Eqs. (3.66) and (3.67), we end up n the followng two equatons for each spatal element: A 1 T s j + A 2 T s j+1 + A 3 T r j + A 3 T r j+1 = A 4 (3.68) A 3 T s j + A 3 T s j+1 + A 2 T r j + A 1 T r j+1 = A 4 (3.69) Where: A 1 = A 5 A 6 A 3 A 2 = A 5 A 6 A 3 A 3 = U

103 A 4 = A 7 T sol A 5 = m p Cp w A 6 = U 1 U 2 2 A 7 = U 1 U 2 Where all the varables have been defned prevously. If the ppelnes are dscretsed n N spatal elements, then the unknown varables are 2N + 2 n total. Furthermore, by wrtng down the Eqs. (3.68) and (3.69) for each element, we get 2N equatons. In order to solve ths problem the followng two consderatons are made: The nlet temperature n the supply lne (T s 0 ) wll be a known value. The temperature dfference n the boundary of the ppelnes (T s N T r N ) wll also be a known value. So, wth these consderatons the prevous system of 2N equatons wth 2N + 2 varables, s transformed n a system of 2N + 1 equatons wth 2N + 1 varables. Therefore, ths system can be solved n order to provde the temperatures along the lengths of both ppelnes. It should be noted that the process developed up to now n ths secton can provde the temperature dstrbuton over a system of double pre-nsulated underground ppelnes f the nlet temperature of the supply ppelne and the temperature dfference between the ends of the ppelnes are known. In the studed system, the temperatures over the transmsson network have been estmated up to now, whle the temperature drops between the ends of the dstrbuton network are known. In the next secton, the method for applyng ntegraton of ths algorthm to the whole system wll be explaned. The heat losses of each par of ppelnes can, then, be easly calculated as the summary of the heat losses of the supply and return ppelne: (3.70) q q m Cp ( T T ) hl, pp hl, p p w p, n p, out s, r s, r 101

104 Where: q hl,pp = Heat losses of a par of ppelnes (J) q hl,p = Heat losses of one ppelne (J) m p = Mass flow rate through one ppelne ( kg ) s T p,n, T p,out = Inlet and outlet temperature n one ppelne, respectvely (K) In the above equaton, the ndexes s and r denote the supply and return ppelnes. Fnally, the cost of the heat losses can be easly calculated by multplyng the total heat losses wth the unt cost of heatng. Smlarly, all the years of operaton have to be taken nto account before the heat losses cost can be used n the objectve functon. Therefore, the fnal equaton for the heat losses cost s the followng: C p, hl qhl, pp C N h, u ppes (3.71) 1 (1 IR) Where: C p,hl = Total cost of heat losses ( ) C u.h = Unt cost of heat losses ( kwh ) In concluson, by applyng Eqs. (3.68) and (3.69) together wth the boundary condtons and the process explaned n ths secton, the temperatures across a par of ppelnes can be calculated. Then, by applyng Eqs. (3.70) and (3.71) the cost of the heat losses of the ppelnes are calculated for a gven set of dmensons Integrated algorthm for the szng of the ppelnes As mentoned earler, standardsed values of nternal dameters of the ppelne wll be used accordng to EN Concernng the thckness of the nsulaton, dscrete values of the thckness from 1 to 30cm wll be used wth a dscretzaton of 1cm. Therefore, both the nternal dameter and the thckness of the nsulaton (whch are the optmzaton parameters) wll get only dscrete values. For the optmum szng of all the ppelnes of the network, the followng process s followed: 102

105 a) For each branch of the dstrbuton network t s consdered that the nlet temperature n the supply ppelne s equal to the outlet temperature of the j transmsson supply ppelne (T d,s, = T tr,h,o ). The latter s calculated n secton b) For each combnaton of dscrete szes of nternal dameter (D p, ) and thckness of nsulaton (t p,ns ) and for each branch of the dstrbuton network: 1. Equaton (3.43) s used to calculate the thckness of the ppelnes or ther external dameter (D p,o ). 2. The process of secton s appled for the calculaton of the temperatures and the cost of the heat losses of each branch of the dstrbuton network. 3. Snce the temperatures along the ppelnes are known, the process explaned n secton s appled to calculate the electrcal cost of each ppelne. 4. The captal cost s calculated through the process explaned n secton These costs are added together. c) The dmensons for whch the total cost s mnmzed are dentfed. These are the optmum dmenson for each branch of the dstrbuton network. The temperatures across each branch of the dstrbuton network are also known. d) Snce the outlet temperature from each return ppelne of the dstrbuton network s known, an energy conservaton equaton s appled n the mxng pont connectng the end of the cold dstrbuton ppelne wth the begnnng of the cold transmsson ppelne n order to fnd a new value of the nlet temperature of the return transmsson ppelne (T tr,c, ). e) Eqs. (3.3) and (3.4) are appled usng the new value of the thermal effcency of the hot water storage tank (Eq. 3.36), n order to fnd a new value of the temperature at the nlet of the hot water storage tank (T st,h, ). In the same way, a new value of the temperature at the ext of the cold water storage tank (T st,c,o ) s calculated through Eqs. (3.6)-(3.7) and (3.9). f) As mentoned n secton 3.2.2, both the storage tanks are n the boundary of the transmsson network. Therefore, t can be consdered that the temperature drop n the boundary of the transmsson network s equal to T st,h, T st,c,o. The nlet temperature of the supply lne of the transmsson network (T tr,h, ) s calculated n secton and wll reman constant throughout the calculatons as t depends only on the temperature dfference n the hot sde of the geothermal heat exchanger. 103

106 g) The process explaned n step b s now appled n the transmsson network. Its optmum dmensons as well as new values of T st,h, and T st,c,o are now known. h) Equatons (3.26)-(3.37) are appled n order to determne a new value of the outlet temperature of the transmsson supply ppelne (T tr,h,o ). ) If ths value s dfferent that the value calculated n secton 3.2.2, then steps a-h are repeated tll convergence s acheved. Eventually, through ths process the optmum dmensons of both the transmsson and dstrbuton network wll be known. Furthermore, the captal cost of each par of ppelnes wll be known as well as new values of the temperatures across the network. So, all the temperatures of the transmsson network wll have updated values compared to those calculated n secton 3.2.2, apart from the nlet temperature n the supply ppelne (T tr,h, ), whch s constant, as mentoned before Integrated model By applyng the methodology explaned n sectons , the szng of the nstallaton can be carred out f some ntal estmatons are done. But, n the end of secton 3.2.6, the temperatures across the transmsson network have an updated value. On the other hand, these temperatures have been calculated through the ntal estmatons n secton and based on these values the rest of the calculatons, ncludng those on secton 3.2.6, were carred out. Therefore, all the calculatons have to be done agan tll convergence acheved. All the values that had the suffx nt (ntal estmatons) and a renewed value was calculated, the renewed value wll be used n the new calculatons. For better supervson of the process, the parts of the methodology are separated n dfferent functons n whch one uses the results from the prevous and feeds the next functon. The whole programmng n Python (Python Software Foundaton, 2016) was also carred out n ths way. Each functon wll contan several equatons of those shown up to now. In the followng, the short name of each functon s shown n bold letters, the equatons used n the parenthess and the use of each functon n brackets. So, the functons used are the followng: TFC ( ) Frst calculatons of the temperatures of the transmsson network 104

107 TFF ( ) Thermal effcency of the nstallaton GS ( ) Szng of the geothermal nstallaton HST ( ) Szng of the hot water storage tank THL ( ) Hot storage tank heat losses PS ( ) Szng of the ppelnes So, the steps that are followed n the ntegrated model for the szng of the nstallaton are the followng: 1. TFC functon s used for the frst calculaton of the temperatures of the transmsson network. 2. Snce the temperatures of the network are known, TFF functon s used for the calculaton of the thermal effcency of the nstallaton as well as of the thermal effcency of the hot water storage tank. 3. By havng calculated a frst value of the thermal effcency of the nstallaton, then GS functon s appled for the szng of the geothermal nstallaton. 4. The mass flow rates across the network are known through step 3, therefore HST functon s mplemented for the szng of the hot water storage tank. 5. THL functon s appled for the calculaton of the heat losses of the storage tank. A new thermal effcency of the hot water storage tank s found. 6. PS functon s used for the optmum szng of all the ppelnes of the network. New values of the temperatures across the whole network are found. 7. If the thermal effcency of the hot water storage tank found n step 5 and the temperatures of the transmsson network found n step 6 are dfferent from those n steps 2 and 1, respectvely, then the new values are mplemented and steps 2-6 are repeated tll convergence of the problem. The convergence lmts used are for the thermal effcency and 10 6 for the temperatures. Eventually, when the problem converges, the whole szng of the nstallaton wll be known. More detals on the outputs of the algorthm wll be gven n secton

108 3.2.8 Possble sources of error Three man sources of error can arse from the results of the above explaned algorthm. Frstly, the mass of stored water n the hot water storage tank can get negatve values. Ths s unphyscal, and t bascally means that more hot water s needed n the network, whch subsequently leads to the use of the peak-up bolers. Ths also comes n contrast wth the ntal concept of the desgn-day for whch t was stated that all the heat demand wll be covered by geothermal energy only. Secondly, the outlet temperature of the return transmsson ppelne (T tr,r,o ) can get hgher values than the re-njecton temperature of the geothermal water (T G,c ). In other words, the temperature dfference on the cold sde of the geothermal heat exchanger ( T c,ghe ) can get negatve values. Ths s of course somethng unacceptable as n a heat exchanger the temperatures of the heatng flud n the nlet and the outlet have to be hgher than the correspondng temperatures of the heated flud. Thrdly, the temperature that arrves n the end-users mght have a temperature lower than the needs of the end-users. For the sake of smplcty, a mnmum value of the outlet temperature of the supply transmsson ppelne (T tr,s,o,mn ) s defned, whch s estmated through the mnmum end-users requrements and the estmated heat losses. So, the thrd source of error s defned as the case n whch the value of the outlet temperature of the return transmsson ppelne s found to be lower than the mnmum acceptable value. The frst source of error cannot be solved automatcally n the developed code as ths error s due to the fluctuaton of the heat demand wthn the specfc day. For example, two days can have the same daly heat demand, yet dffer greatly n the degree of varaton of the heat demand wthn the day. So, n one case the mass of stored water can be always postve or zero whle n the other case negatve values can occur. If ths problem arses, the only soluton s to select the day wth the closest daly heat demand to that of the ntally selected desgn-day as the new desgn-day. If ths does not work, then ths process has to be repeated. It was shown that, n the worst case, three selectons of the desgn-day are enough. Therefore, ths source of error can be relatvely easly solved. The only dsadvantage s the hgher computatonal tme needed, but ths s neglgble for the tmescale of the plannng or research for ths type of nstallaton. The second and the thrd sources of error occur due to the physcs of the problem. Two varables of the problem that are ntally estmated and kept constant throughout the whole algorthm can have a bg effect on ts physcs. These varables are the temperature 106

109 dfference on the hot sde of the geothermal heat exchanger ( T h,ghe ) and the rato of the mass flow rate on the left of the storage tank to the geothermal mass flow rate (R m ). For the frst varable, ts mnmum value whch s provded by the manufacturer, whle for the second varable an estmaton of the user are used n the developed algorthm. The temperature dfference can ncrease above ths mnmum value and the rato of the mass flow rates can ether ncrease or decrease compared to the ntal estmaton. In general, t s desred to keep the rato of the mass flow rates n the maxmum possble value as, n ths way, more geothermal energy s harvested (see Eq. 3.10). A loop that checks f any of these two sources of error arse n the end of the algorthm was bult. The man scope of ths loop was to fx the values of the varables that mght present an error by adjustng the aforementoned varables that affect them. Furthermore, the cost of the ppelnes and the number of wells should be kept n the mnmum possble value. A prelmnary analyss (Appendx A) has shown the followng: As the temperature dfference n the hot sde of the geothermal heat exchanger ( T h,ghe ) ncreases, the temperature dfference n the cold sde of the geothermal heat exchanged ( T c,ghe ) ncreases, the outlet temperature of the supply transmsson ppelne (T tr,s,o ) decreases, the captal cost of the ppelne s varable and manly decreases after a steep ntal ncrease, and fnally, the number of wells s not affected sgnfcantly. As the rato of the mass flow rates (R m ) ncreases, the temperature dfference on the cold sde of the geothermal heat exchanger ( T c,ghe ) decreases, the outlet temperature of the supply transmsson ppelne (T tr,s,o ) s almost constant, the captal cost of the ppelnes presents small and stochastc varatons and the number of wells decreases. Intally, the algorthm s run wth the ntal estmatons of the temperature dfference and the rato of the mass flow rates. If any of the errors arse, then by takng nto account the above observatons, the followng f-loop of four dfferent cases s used for the soluton of the errors runnng the algorthm as many tmes as requred by the followng condtons: 107

110 If T c,ghe < T c,ghe,mn and T tr,s,o > T tr,s,o,mn : Then: Whle T tr,s,o > T tr,s,o,mn : T h,ghe If (stll) T c,ghe < T c,ghe,mn : Then: Whle T c,ghe < T c,ghe,mn : R m If T c,ghe < T c,ghe,mn and T tr,s,o < T tr,s,o,mn : Then: Assstance by a heat pump s needed If T c,ghe > T c,ghe,mn and T tr,s,o < T tr,s,o,mn : Then: Whle T c,ghe > T c,ghe,mn : T h,ghe If (stll) T tr,s,o < T tr,s,o,mn : Then: Assstance by a heat pump s needed If T c,ghe > T c,ghe,mn and T tr,s,o > T tr,s,o,mn : Then: Whle T c,ghe > T c,ghe,mn and T tr,s,o > T tr,s,o,mn : R m It should be mentoned that the fourth case of the above f-loop s not an error of the algorthm, but by ncreasng the rato of the mass flow rates, then the economcally optmum soluton s found. Ths happens because by ncreasng the rato of the mass flow rates the number of wells, on the one hand, decreases wth a subsequent bg decrease of the total cost, and the cost of the ppelnes changes stochastcally. But, t can be defntely sad that the reducton n the cost due to less wells beng needed s much greater than any change caused by the cost of the ppelnes. It s assumed that the other costs of the nstallaton are not affected mportantly by ths change. Therefore, the last case represents a knd of economcal optmzaton when there are no errors caused by the ntal estmatons. By observng the above four-case f-loop, t can be observed that n some cases the use of a heat pump s needed. Ths denotes manly that the specfc geothermal potental s unavalable to provde wth heat the specfc end-users. Consequently, the use of a heat pump to lft of the temperature to the desred level s needed. Ths case s out of the scope of ths thess and wll not be studed further. 108

111 In general, t can be ntutvely stated that f the temperature of the geothermal flud s some degrees hgher than the needs of the end-users, then by the proper adjustment of the two varables shown above, the algorthm can work and the nstallaton can be properly szed. Ths was also shown n the studed case. More detals on ths wll be gven n the results secton. An aspect that requres careful consderaton s the case where some endusers requre a much hgher temperature than the others. In a case lke that, then these users ether cannot be provded wth heat or a heat pump should be mplemented only for them. So, the above f-loop could be appled wth the condton of the temperature for the average users and, then, a heat pump could be appled to those users whch requre a hgher temperature. Fnally, another soluton would be the rejecton of a part of the load as an error would also ndcate that the whole load cannot be covered n ths way. The latter s a rare case as, normally, ths would have been dentfed n the very early stages of the desgn of the nstallaton. To summarse, n ths secton some possble sources of errors that can arse durng the applcaton of the developed algorthm have been dentfed. Then, a soluton for each of these errors was presented and t was shown that, n most of the cases, ether wth the selecton of a day wth a very smlar heat demand as the desgn-day or wth the proper adjustment of some nput varables the problem can be solved. Usually, the problem wll not be solved when the temperature of the geothermal flud s lower or just a bt hgher than the needs of the end-users or when some end-users have much hgher temperature needs. In these cases, the use of a heat pump s requred ether for a part or for all the users, but normally, ths problem wll have been dentfed n the very frst desgn stages, so the developed algorthm would provde a soluton n the vast majorty of the cases Outputs of the model In ths secton, a collectve mappng of the outputs of ths model wll be gven. In secton 3.2.1, the nputs of the model were explaned and n sectons , the developed algorthm was explaned n detal. For better understandng, the outputs dvded n the followng groups: Man results: Necessary number of geothermal wells; Volume and dmensons of the hot water storage tank; Temperature drop of the geothermal flud; Total thermal effcency of the nstallaton; Geothermal capacty; Mass flow rate on 109

112 the left of the storage tanks; and Rato of the mass flow rate on the left of the storage tank to the geothermal mass flow rate. Transmsson network data: Desgn temperatures (Inlet/outlet of supply and return ppelnes); Inner dameter; Outer dameter; Thckness of nsulaton; Captal Cost. Dstrbuton network data: For each branch of the dstrbuton network, the same data as for the transmsson network are provded. Plots of the evoluton of the mass and temperature of the stored water. Desgn-day heat demand. 3.3 Results In ths secton, the results of the above explaned algorthm are presented. As mentoned earler, the heat demand data used are real data, whle the rest of the nputs are arbtrary data. The heat demand data were provded by the Estates and Buldngs offce of the Unversty of Glasgow and refer to some buldngs managed by the Unversty. The annual heat demand s around 38500MWh wth an average and a peak demand of around 4.4 and 14MW, respectvely. The tme dscretzaton of the data s 30 mnutes. A plot of the data for the year of study can be seen n Fg Some other basc nput data are shown n Table 3.1. As already mentoned, throughout the developed model a specfc day s chosen as the desgn-day and based on ths day, the szng of the whole nstallaton wll be carred out. In our case, three dfferent and very dscrete days have been chosen as the desgn-day. More specfcally, the chosen days are those that ther daly heat demand corresponds to the 25 th -, 50 th - and 75 th - centle of the daly heat demands of the whole year. For the sake of smplcty, these cases wll be called 25%le, 50%le and 75%le n the rest of ths study, respectvely. In Fg. 3.8, the curve that sorts the daly heat demands from the lower to the hgher n a percentage base s shown. The chosen days are those whch ther daly heat demand corresponds to the 25, 50 and 75% of ths fgure. So, three very dfferent cases of szng have been selected and wll be studed. 110

113 Fgure 3.7 Heat demand data for the year of study Table 3.1 Man nput data Data Value Mass flow rate of each geothermal well ( kg s) Temperature of the geothermal flud (K) Mnmum temperature dfference on the hot sde of the G.H.E. (K) 5 Ambent desgn temperature (K) Sol temperature (K) Mnmum temperature at the outlet of the supply transmsson ppelne (K) Lfespan of the nvestment (Years) As the daly heat demand for the day based on whch the szng s done ncreases, the total fracton of heat demand that s covered by geothermal energy ncreases wth the sze of the geothermal nstallaton. Therefore, by applyng the model n three dfferent cases, the effect of szng the geothermal nstallaton wll be made clear both from an energetc, economc and envronmental pont of vew. Addtonally, the algorthm s not appled for a hgher szng of the geothermal nstallaton as, n ths case, the nstallaton wll work at partal load the majorty of tme and ths wll lkely make the nvestment unfeasble. 111

114 Daly Heat Demand (kwh) The man results of the model are shown n Table 3.2 and refer to the desgn-day for each case. It should be noted that the heght-to-dameter rato of the hot water storage tank was selected to be equal to 1. Therefore, snce ts volume s known for each case, then, ts heght and dameter can also be easly calculated. The volume of stored water n the hot water storage tank throughout the desgn day can be seen for each case n Fgs , whle ts temperature evoluton can be seen n Fgs Concernng the ppelnes of the transmsson network, the desgn temperatures can be seen n Table 3.3, whle the dmensons can be seen n Table 3.4. Smlarly, the desgn temperatures and the dmensons for each branch of the dstrbuton network are shown n Tables 3.5 and 3.6, respectvely. In our case, t was assumed that the dstrbuton network conssts of 5 branches. Furthermore, the temperature drop per length for each ppelne of the network s shown on Table 3.7 and the captal cost of each par of ppelnes, together wth ther lengths, are shown on Table ,50E+05 Sorted Daly Heat Demands 2,00E+05 1,50E+05 1,00E+05 5,00E+04 0,00E Tme percentage over the year (%) Fgure 3.8 Sorted daly heat demands on a percentage bass 112

115 Table 3.2 Man results of the szng of the nstallaton Case 25%le 50%le 75%le No of wells Geothermal mass flow rate, m G (kg/s) Mass flow rate on the left of the storage tank, m tr,s (kg/s) Geothermal capacty, Q G,D (kw) Temperature drop of the geothermal flud, dt G (K) Total thermal effcency, η tot (%) Volume of the hot water storage tank, V HST (m 3 ) Dameter and heght of the hot water storage tank, D HST, H HST (m) Fgure 3.9 Volume of stored water over tme (25%le szng) 113

116 Fgure 3.10 Volume of stored water over tme (50%le szng) Fgure 3.11 Volume of stored water over tme (75%le szng) 114

117 Fgure 3.12 Temperature evoluton of stored water over tme (25%le szng) Fgure 3.13 Temperature evoluton of stored water over tme (50%le szng) 115

118 Fgure 3.14 Temperature evoluton of stored water over tme (75%le szng) Table 3.3 Desgn temperatures of the transmsson network (K) Case 25%le 50%le 75%le Supply-Inlet Supply-Outlet Return-Inlet Return-Outlet Table 3.4 Optmum dmensons of the transmsson network's ppelnes (cm) Case 25%le 50%le 75%le Inner dameter Outer dameter Thckness of nsulaton

119 Table 3.5 Desgn temperatures of the dstrbuton network (K) Case 25%le 50%le 75%le Branch 1 Supply-Inlet Supply-Outlet Return-Inlet Return-Outlet Branch 2 Supply-Inlet Supply-Outlet Return-Inlet Return-Outlet Branch 3 Supply-Inlet Supply-Outlet Return-Inlet Return-Outlet Branch 4 Supply-Inlet Supply-Outlet Return-Inlet Return-Outlet Branch 5 Supply-Inlet Supply-Outlet Return-Inlet Return-Outlet

120 Table 3.6 Optmum dmensons of the dstrbuton network (cm) Case 25%le 50%le 75%le Branch 1 Inner dameter Outer dameter Thckness of nsulaton Branch 2 Inner dameter Outer dameter Thckness of nsulaton Branch 3 Inner dameter Outer dameter Thckness of nsulaton Branch 4 Inner dameter Outer dameter Thckness of nsulaton Branch 5 Inner dameter Outer dameter Thckness of nsulaton

121 Table 3.7 Temperature drop per length for the ppelnes of the network (K/km) Case 25%le 50%le 75%le Transmsson Network Supply ppelne Return Ppelne Dstrbuton Network Branch 1 Supply ppelne Return Ppelne Branch 2 Supply ppelne Return Ppelne Branch 3 Supply ppelne Return Ppelne Branch 4 Supply ppelne Return Ppelne Branch 5 Supply ppelne Return Ppelne

122 Table 3.8 Captal Cost and length of each par of ppelnes (Costs n, lengths n m) Case CC (25%le) CC (50%le) CC (75%le) Length Transmsson Network Dstrbuton Network Branch Branch Branch Branch Branch Fnally, a senstvty analyss was carred out for the heat losses of the ppelnes aganst some basc parameters of ths process. The analyss was carred out for the transmsson ppelne of the 75-C case. The results are shown n Fgs , where the heat losses of the ppelnes are presented aganst ther bural depth, the dstance between them, the nlet water temperature, ther nternal dameter and the mass flow rate through them, respectvely. Fgure 3.15 Heat losses of the ppelnes aganst ther bural depth (75-C case) 120

123 Fgure 3.16 Heat losses of the ppelnes aganst ther between dstance (75-C case) Fgure 3.17 Heat losses of the ppelnes aganst the nlet temperature (75-C case) 121

124 Fgure 3.18 Heat losses of the ppelnes aganst ther nternal dameter (75-C case) Fgure 3.19 Heat losses of the ppelnes aganst the mass flow rate (75-C case) 122

125 3.4 Dscusson A frst mportant observaton whch s not vsble drectly s that the algorthm was able to produce results and there was no need to use a heat pump. As can be seen n Table 3.1, the temperature of the geothermal flud s roughly 19K hgher than the needs of the endusers. Although ths temperature dfference s not that bg, t s beleved that even f t was smaller, then the algorthm would also be able to provde results. Therefore, the earler ntutve clam that a temperature somehow hgher than the needs of the end-users can be functonal s, at least, partally verfed. The man results of the developed model were shown on Table 3.2 and refer to the desgn-day for each case of szng. As can be seen n ths table, the number of wells and, subsequently, the geothermal flow rate ncrease as the szng of the nstallaton (.e. the heat demand coverage by geothermal energy) ncreases. Ths s totally expected, as n order to cover a hgher fracton of the heat demand by geothermal energy, hgher geothermal flow rate s necessary. Subsequently, ths s also depcted n the number of the necessary geothermal wells. Addtonally, t s observed that the temperature drop of the geothermal flud s almost the same n each case and s roughly equal to 30K degrees. Therefore, and by takng nto account Eq. (3.16) properly re-arranged, the geothermal capacty ncreases almost proportonally wth the number of wells. Ths s normal, as the geothermal capacty depends on the geothermal flow rate and the temperature drop of the geothermal flud. Snce, the latter s almost constant, then, t can be sad that the geothermal capacty s roughly proportonal to the geothermal flow rate or to the number of wells. Another mportant fndng s that the total thermal effcency of the nstallaton ncreases as the szng also ncreases. So, t can be sad that as more geothermal energy s harvested the whole process becomes more effcent. The volume of the hot water storage tank, on the other hand, ncreases wth the ncrease of the coverage by geothermal energy as expected, but not proportonally. Ths happens because the mass or volume of stored water, and the volume of storage tank subsequently, depend strongly on the fluctuaton of the heat demand wthn the specfc desgn-day. Two days mght have the same daly heat demand, but the fluctuaton wthn the day can be very dfferent. For example, one day can have a very peaky heat demand whle the other day can have a rather constant heat demand. Intutvely, t s understood that n the frst case the volume of the storage tank wll be bgger as hgher storage capacty wll be needed n order 123

126 to accommodate the sharp changes of the heat demand wthn the day. But, n general, t can be defntely stated that the volume of the storage tank wll ncrease wth the sze of the nstallaton. Furthermore, t can be seen that the rato of the mass flow rate on the left of the storage tank to the geothermal flow rate (m tr,s/m G) s almost the same n all three cases and s equal to around 1.5, but these not exactly equal as ths value, whch s symbolsed as R m n the model, s a value provded as output of the model. An ntal estmaton of ths value s gven as nput, but as mentoned n secton 3.2.9, ths value mght be changed f the physcs of the problem requre ths. Snce these values are slghtly dfferent, t means that the algorthm has changed the ntally provded value n some or all the cases. Ths result s n accordance wth the lterature: Harrson (1987) states that ths value has to be hgher than 1. It can also be observed that the mass flow rate s qute large as wll be the mass exchanges between the network and the storage tank. Ths would make the conservaton of the stratfcaton of the tank qute dffcult. Ths fact justfes the choce of a fully mxed storage tank as a logcal selecton for ths knd of process. In Fgs , the volume of stored water n the hot water storage tank throughout the desgn-day was presented for each case. It s observed that all the graphs represent a smlar trend, n whch the maxmum amount of stored water s acheved n almost the same, early mornng, hours. Ths s somethng expected as the heat demand s generally low over the nght, so n ths perod of tme the majorty of produced water would be stored for later use. Then, a relatvely sharp decrease occurs between hours, and subsequently the decrease of the amount of stored water s smoother. Of course, ths varaton depends a lot on the end-users. In our case, the end-users are buldngs managed by the Unversty, so the heat demand s expected to be hgh n the aforementoned hours. If the heat demand referred to typcal dwellngs, then an even sharper decrease of the amount of stored water would be expected durng the early mornng hours (typcally 06:00-08:00), n whch there s usually the peak demand, then the stored water would ncrease tll the evenng hours (typcally 19:00-22:00), where there s a second peak demand whch s typcally lower than the mornng peak demand. Ths statement makes clear why the case of geothermal dstrct heatng s very case-specfc by ts own nature and, therefore, t s qute dffcult to extract completely generalsed conclusons n many aspects. 124

127 The temperature evoluton of the stored water s shown n Fgs It can be seen that the hgher temperature decreases occur durng the frst and, manly, the last hours of the day n whch the storage tank s almost empty. Durng the rest of the day the temperature s almost constant, ndcatng neglgble heat losses. The only excepton s the graph that depcts the temperature evoluton for the lower szng (Fg. 3.12), where especally n the early hours there s a much steeper decrease n the temperature of stored water. Ths happens because, as can be seen n Fg. 3.9, there s no stored water for many hours and the mathematcal model shows some nstablty. These fgures hghlght the effect of the nsulaton thckness, whch s equal to 20cm n our case, showng that the heat losses n a well-nsulated tank can be mnmsed. The thckness of the nsulaton s also n agreement wth publshed values (Chan et al., 2013). In order to further quantfy the effect of the nsulaton, a senstvty analyss was carred out for the smple coolng of the storage tank. More specfcally, the storage tank of the 75%le case was consdered to be full of water at 350K degrees and the tme needed to cool down the water by 10K degrees was calculated for dfferent nsulaton thcknesses. The results of ths senstvty analyss are shown on Table 3.9. It can be seen that when nsulaton s used a very long perod of tme s requred to cool down the water, ndcatng that the heat losses are qute small. In ths case, the storage tank s consdered to be always full, so stratfcaton phenomena wll occur whch are not taken nto account n ths senstvty analyss. These phenomena mght affect the fnal results, but the general trend and scale of the results wll be the same. It s also seen that the coolng tme ncreases almost lnearly wth the thckness of the nsulaton. So, both from Table 3.9 and from Fgs , the effect of the nsulaton on the mnmzaton of the heat losses s hghlghted and t s consdered that the process followed s approprate. Table 3.9 Senstvty analyss of the storage tank heat losses Thckness of the nsulaton (cm) Tme (h) needed to cool the water by T = 10K

128 Concernng the szng of the ppelnes, the desgn temperatures of the transmsson and dstrbuton network are shown on Tables 3.3 and 3.5, respectvely. The correspondng temperature drop per km of ppelne, whch depcts the heat losses of the ppelne, s shown on Table 3.7. A frst mportant observaton s that the calculated values of the heat losses are rather lower than publshed values (see Kanoglu and Cengel, 1999, for example). In many cases, the heat losses are even a scale of magntude lower than smlar publshed values. Ths s because n the developed algorthm, the heat losses of the ppelnes are taken nto account n the objectve functon and qute thck nsulaton s used. Ths can also be verfed by Tables 3.4 and 3.6, where the dmensons of the ppelnes of the transmsson and dstrbuton network are presented, respectvely. In order to further verfy ths argument, the proporton of each cost for the transmsson ppelne of the 75%le case of szng s shown n Table It can be seen that, ndeed, the heat losses cost account for a bg fracton of the total cost and ths justfes the thck nsulaton used. Probably n practce, the heat losses would not be taken nto account as much as they should be and a thnner nsulaton would be used. Addtonally, the fact that these are smulaton results and not real data mght be partally a reason for ths dscrepancy. Table 3.10 Proporton of each part of the cost durng the szng of the transmsson ppelnes (75%le case) Part of the total Cost Proporton (%) Captal cost Electrcal cost Heat losses cost 30.2 On the other hand, although the heat losses are lower than the publshed values, t can be observed that there are some mportant dfferences between them. Ths happens because the optmzaton algorthm does not take nto account only the heat losses, but also the captal and electrcal costs. For example, by combnng the results of Tables 3.4, 3.6 and 3.7, t can be observed that the smaller ppelnes have ncreased heat losses compared to the bgger ones. Ths happens because as the dameter of the ppelne decreases, the frcton losses ncrease (see Eq. 3.44) and, therefore, the electrcal cost ncreases. So, for smaller ppelnes, the heat losses are a smaller fracton of the total cost, as the electrcal cost becomes much more mportant. Therefore, the heat losses wll be hgher n ths case. 126

129 Another mportant fndng from the results s that the sze of the ppelnes ncreases as the overall sze of the nstallaton ncreases. Ths s to be expected, as larger szng entals hgher flow rates and, therefore, larger ppelnes wll be needed to deal wth these hgher flow rates. In Table 3.8, the captal cost for each par of ppelnes s shown. Two mportant observatons can be drawn from ths table. Frstly, the captal cost of the ppelnes ncreases as the szng ncreases. Ths s also to be expected because, as mentoned above, larger szng means hgher flow rates and, subsequently, larger ppelnes. Secondly, t can be observed that the captal cost ncreases wth the length of the ppelne, but not proportonally. Ths happens because each component of the total cost s affected dfferently wth the change n the length and ths s taken nto account explctly n the objectve functon. So, t can be stated that all the above observatons ndcate the power and usefulness of the developed algorthm for the optmum szng of the ppelnes of the network. Fnally, n Fgs , the heat losses of the ppelnes are shown aganst some basc parameters that nfluence the phenomenon of heat loss. Some mportant observatons can be made on these fgures whch can be useful for the ntal desgn stages of the ppelne system. These observatons can also be generalsed for any system of ppelnes whch transfer a hot flud, as the governng equatons wll be the same. Frstly, t s observed from Fg that the heat losses of the ppelnes decrease as the bural depth ncreases. Ths means that the ppelnes should be bured as deeply as possble. Ths, on the other hand, can sgnfcantly ncrease the cost, so an optmum soluton should be found takng ths nto account. Secondly, n Fg t s seen that the heat losses decrease as the ppelnes are lad closer to each other. Ths ndcates that the ppelnes should be lad as close to each other as possble. Then, n Fg s t shown that the heat losses ncrease proportonally wth the nlet temperature. Ths s somethng expected as wth the ncrease of the nlet temperature, the temperature gradent between the ppelnes and the surroundng sol ncreases and, therefore, the heat losses wll ncrease. Almost the same trend s presented n Fg. 3.18, n whch t s shown that the heat losses ncrease almost proportonally wth the ncrease of the nternal dameter of the ppelnes. The latter s also expected as an ncrease n the dameter of the ppelne ndcates an ncrease n the heat transfer area whch, subsequently leads to hgher heat losses. Eventually, Fg shows an ncrease of the heat losses wth the ncrease of the mass flow rate through the ppelnes. Ths s expected ntutvely, but also through Eqs. (3.66)-(3.67). An nterestng observaton s that 127

130 the heat losses ncrease more rapdly at lower flow rates, but after a pont the rate of the ncrease levels off. 3.5 Summary Ths Chapter presented the frst developed model of ths thess, whch concerns to the szng of a geothermal dstrct heatng system. Frst, the mathematcal modellng was presented n detal together wth a synoptc revew of the nputs and outputs. Subsequently, the results for three dfferent cases of szng were provded, followed by an extended dscusson on these whch hghlght some mportant observatons that can be qute useful n the desgn of such systems. The developed model manly uses as nputs the geothermal data, the heat demand data throughout at least one year, and the topology of the nstallaton. Other case-specfc data, such as the ambent desgn and sol temperatures or the physcal propertes of water, are used as nputs also. The model was desgned to be as generc as possble and, therefore, the majorty of the data are user-defned nputs. In our case, only the heat demand data were real data whle the rest of the data were arbtrary nputs by the author. By applyng the mathematcal model developed n secton 3.2, the szng of the nstallaton wll be acheved. More specfcally, the man outputs of the model wll be the necessary number of wells, the szng of the hot water storage tank and the szng of the ppelnes. A smplstc llustraton of the process s presented n Fg Fgure 3.20 Schematc llustraton of the process 128

131 The developed model was then appled for three dfferent cases of desgn-day, whch affects the szng of the whole nstallaton. More specfcally, the szng was carred out for those days that ther daly heat demand s equal to the 25 th -, 50 th - and 75 th centle of the daly heat demands of the whole year. The most mportant conclusons that were drawn by the results and dscusson sectons were the followng: The total thermal effcency s qute hgh for any case of szng and s about %, and t also ncreases wth the overall szng. The temperature drop of the geothermal flud s around 30K degrees for any case. The mass flow rates across the network are qute hgh, justfyng the selecton of a fully mxed storage tank nstead of a stratfed tank. The heat losses of the storage tank are neglgble when a thck nsulaton s used. Only n the tmes when the storage tank s almost empty s the temperature drop notceable, but agan the heat losses, n total, are qute small. The mportance of the heat losses of the ppelnes at the ntal desgn stage was hghlghted. It was shown that by usng the developed optmzaton algorthm for the szng of the ppelnes, the heat losses are much smaller than prevously publshed values. Ths ndcates that the heat losses were probably underestmated n the past, but ths s nadvsable as t was shown that these are a bg fracton of the total cost. Therefore, the power of ths algorthm was hghlghted. The heat losses of the ppelnes ncrease as the szng gets smaller because there s a trade-off between the heat losses and the electrcal cost, whch are both taken nto account n the szng of the ppelnes. The captal cost of the ppelnes ncreases wth the ncrease n the szng, as bgger ppelnes are needed to deal wth the hgher flow rates of the bgger szng. In concluson, t can be sad that there seem to be two controversal trends concernng the szng of the nstallaton. On the one hand, as the szng of the nstallaton ncreases the cost of the nstallaton wll ncrease as bgger ppelnes, bgger storage tanks, and more geothermal wells (amongst other thngs) wll be needed, whch of course, wll ncrease the ntal captal cost. On the other hand, the total thermal effcency ncreases (however slghtly) as the szng ncreases and together wth the decrease of the heat losses, ths s an 129

132 ndcator that the whole process mproves wth the ncrease n sze. Ths can potentally lead to lower operatonal costs whch mght level-off the dfference n the captal cost. All these wll be studed n detal on Chapter 5, where a detaled economc, energetc and envronmental comparson between the proposed and the tradtonal case of operaton as well as between the dfferent cases of szng, wll be carred out. 130

133 4 OPERATION OF A GEOTHERMAL DISTRICT HEATING SYSTEM 4.1 Introducton In ths Chapter, the operaton of a geothermal dstrct heatng system wll be studed n detal. More specfcally, two dfferent models have been developed for ths purpose that ther man nput s the output of the model of Chapter 3,.e. the szng of the nstallaton. In other words, the operaton of the nstallaton that can theoretcally be bult based on the outcome of Chapter 3 s now studed. Frstly, a model that provdes the operatonal strategy of the nstallaton over a random day has been bult. By operatonal strategy s defned the complete knowledge of the operaton of the nstallaton wthn one day, snce the nstallaton s scheduled on a daly bass. The nputs of ths model are the szng of the nstallaton and the heat demand over a random day. The frst set of nputs wll be the same for every day, whle the heat demand wll obvously be changeable from day to day. So, wth ths model the operatonal strategy of the szed nstallaton wll be known for a gven heat demand. In general, the man outputs of ths model wll be the necessary geothermal mass flow rate; when and by how much should the storage tank be charged or dscharged; when and by how much should the peak-up bolers used; all the mass flow rates across the nstallaton; the cost of electrcty for the pumps; the cost of the fuel needed for the peak-up bolers; and the temperature n the crtcal ponts of the nstallaton. The concept of crtcal ponts n a dstrct heatng system was frst ntroduced by Pnson et al. (2009). It s stated that n a dstrct heatng system, t s usually not mportant to know what happens at every sngle pont of the network, but only at some specfc ponts, whch are called the crtcal ponts of the network. In ths work, the crtcal ponts of the network are the nlet and the outlet of each ppelne of each branch of the dstrbuton network, the nlet and the outlet of each ppelne of the transmsson network, the ponts before and after the storage tank as well as the pont after the peak-up bolers. Ths algorthm would be qute useful for the operators of the nstallaton as they would know n advance how they should operate the nstallaton the next day or days f the heat demand of ths day s known or can be predcted. Secondly, a model that studes the operaton of the nstallaton over a whole year has been bult. For ths purpose, the model of a random day has been extended over a whole 131

134 year. In the model of the random day, some nputs from the prevous day are necessary to run the algorthm and some of the outputs are data for the next day. More detals on ths wll be gven below. So, n ths case the model of the random day wll be run serally for all the days of the year and each day wll provde the necessary data for the next day and wll be fed wth the necessary data from the prevous day. The outputs of ths model are the same as of those of the random day, but some of them are those of nterest for further study. More specfcally, those are the total cost of electrcty to run the pumps and the total fuel used over the year. These two comprse the man operatonal costs of the nstallaton and wll be used n the economc analyss n Chapter 5. Furthermore, through ths model, the cold water storage tank and the peak-up bolers wll be szed as shown on the correspondng secton. In ths secton, a bref ntroducton on the developed models was provded. In secton 4.2, the mathematcal modellng for both models wll be presented n detal, whle n secton 4.3 ndcatve results wll be gven for random days together wth the results of the annual operaton of the nstallaton. Afterwards, these results wll be dscussed n secton 4.4 and a bref concluson of ths Chapter wll be provded n secton Operaton over a randomly-selected day Input data In ths secton, all the nput data used n the developed algorthm wll be presented. As mentoned before, there wll be some data that are ndependent of the day of study, and thus constant (such as the sze of the system), and some other data that change day-by-day, such as the heat demand data. These two knds of data wll be clearly separated below. All the nput, as well as the output data of all the models are n txt fles, whch s the smplest way to store data, but at the same tme t s qute easy to handle them for postprocessng, such as mportng nto an Excel fle. The only matter that the user of the model wll have to be careful of s to wrte the varables n each txt fle n the correct order, because wthn the Python code each lne of the txt fle refers to a dfferent and specfc varable. So, the code knows that a specfc lne of a specfc txt fle wll be a specfc varable and never anythng else. So, the user wll have to be very careful on wrtng the varables n the correct order otherwse the model wll provde completely wrong results. 132

135 In order to be better understandable, the nput data wll be separated n dfferent groups accordng to ther orgn or purpose. The nput data that are ndependent of the day of study are the followng: Installaton data: Temperature of the geothermal flud (T G,h ); temperature n the nlet of the supply transmsson ppelne (T tr,s, ); rato of the mass flow rate on the left of the storage tank to the geothermal mass flow rate (R m ); thermal effcency of the geothermal heat exchanger (η GHE ); thermal effcency of the n-house nstallatons (η dw ); tme dscretzaton of heat demand data. Szng data: Number of wells (N wells ); mass flow rate of each well (m well); mnmum mass flow rate of each well (m well,mn); volume and heght to dameter rato of the hot water storage tank. Desgn day approxmatons: Outlet temperature of the supply transmsson ppelne (T tr,s,o,nt ); nlet temperature of the return transmsson ppelne (T tr,r,,nt ); outlet temperature of the return transmsson ppelne (T tr,r,o,nt ); total thermal effcency of the nstallaton (η tot,nt ); temperature drop of the geothermal flud (ΔT G,nt ). Transmsson network data: Length of the transmsson ppelne (L tr ); dmensons of the ppelnes as calculated n Chapter 3. Dstrbuton network data: Length of each branch of the dstrbuton ppelnes; dmensons of the ppelnes (as calculated n Chapter 3) and temperature drop on ther boundares. Ppelne data: Data referrng to the heat transfer phenomenon of the ppelnes of the system as presented n secton Hot storage tank data: Data referrng to the calculaton of the heat losses of the hot water storage tank as presented n secton Boler data: Thermal effcency of the peak-up bolers (η b ), lower heatng value of the fuel used (LHV f ) and temperature of the water provded by the boler (T b,out ). Ambent data: Ar temperature (T a ); Sol temperature (T sol ); ar velocty (u ar ). It should be noted that the temperature n the nlet of the supply transmsson ppelne wll be the same every day and equal to the value calculated for the desgn day. Ths value wll also reman constant throughout the algorthm. On the other hand, the values ncluded 133

136 n the desgn-day approxmatons are those calculated n the desgn-day, but are used only as ntal approxmatons and ther values wll change through the calculatons. Addtonally, the nputs of the algorthm that change for each day are the followng: Total heat demand: Heat demand for each tme nterval (HD ) Dscretsed heat demand: Heat demand for each branch of the network and for each tme nterval (HD j ) Prevous day storage data: Mass and temperature of the stored water n the last pont of the prevous day (M 0 0 st,t st respectvely). These are used as the values of the frst pont of the studed day. As mentoned before, the mass and temperature of stored water are pont data, n contrast wth the next varables whch are contnuous values. Prevous day masses: Masses n the left and rght of the storage tank, masses of charged and dscharged water and mass of water provded by the boler durng the last tme nterval of the prevous day (M P tr,g respectvely).,m P tr,s,m P ch, M P ds and M P b, Prevous day dstrbuton mass flow rates: Mass flow rates of each branch of the dstrbuton network over the last tme nterval of the prevous day (m d,j P ). As n the model explaned n Chapter 3, the Python language has been used to develop ths model too. Ths model s based on a functonal logc of code developng. Ths means that the code s broken nto some functons, whch work lke the subroutnes of classcal programmng, and each functon may call other functons. Usng ths logc, the code s more readable and understandable, and so s the logc of the calculatons. Each functon has some nputs and outputs and wthn the functon there are all the necessary calculatons. So, n the next secton each functon wll be explaned separately and n the end the general logc and herarchy between the functons wll be explaned. The model of Chapter 3 was also developed usng the functonal logc, but t was not explaned n that Chapter because the calculatons were more straghtforward. In ths case, the calculatons and the logc are more complex, so t s consdered that n ths way the whole logc wll be better understood. 134

137 4.2.2 Functons used n the model In ths secton, the functons used n ths model wll be descrbed. In the case where functons from the model of Chapter 3 are used, these wll be brefly presented. In each case, the nput values, the man equatons used as well as the output values wll be specfed. It should be noted that the functons wll be presented n the same order as they are wrtten n the code. Some functons whch are wrtten later on the code wll call earler functons whch wll often provde as nput a value whch s frst calculated by them. So, some nputs on the early functons wll not be fully understandable ntally, snce some of ther nputs wll be calculated by later functons whch are then callng them. Ths wll be totally clear n the next sesson, where the herarchy of the functons wll be presented Water mass balances functon The nputs used n ths functon are the followng: M 0 st : Mass of stored water n the frst pont. M tr,s : Mass on the transmsson network on the rght of the storage tank n each tme nterval. Ths wll be calculated wthn a followng functon. m G,1: Frst estmaton of the geothermal mass flow rate. Ths wll also be calculated wthn a followng functon. Frst, a more accurate value of the geothermal mass flow rate has to be calculated. The exact value wll be calculated n a followng functon. At the moment, t has to be checked f the value of the frst estmaton les wthn the lmts of avalable geothermal mass flow rate. So, the followng loop s used for ths purpose and addtonally n order to calculate the number of wells whch should operate at ths day: If m G,1 m G,max = m well N wells : Then: m G = m well N wells N wells,oper = N wells Else f m G,1 < m mn,well: Then: m G = m mn,well N wells.oper = 1 Else: m G = m G,1 N wells,oper = a + 1 } (4.1) 135

138 Where: N wells,oper = Operatng wells at the specfc day of study In the above loop, a s the dvson remander of the dvson of m G,1 wth m well. The frst and the second cases of the loop refer to the ntal estmaton of the geothermal flow rate beng hgher than the maxmum or lower than the mnmum avalable flow rate, respectvely. In these cases, the geothermal flow rate wll be set to be equal to the maxmum or mnmum avalable value, respectvely. The thrd case refers to the ntal estmaton beng between the maxmum and mnmum avalable flow rates and, therefore, remans the same. Therefore, a more accurate geothermal mass flow rate as well as the number of operatng wells have been calculated. Then, the mass flow rate on the transmsson network n the left of the storage tank as well as the correspondent mass durng a tme nterval can be calculated, respectvely, as: m tr,g = R m m G (4.2) M tr,g = m tr,g 60 TmeMesh (4.3) It s reterated that the above values are constant throughout the whole day. Snce the mass of water on the transmsson network n the rght of the storage tank s known as an nput, then the masses of charged and dscharged water can be calculated as: For each tme nterval : If M tr,g M tr,s : Then: M ch = M tr,g M tr,s M ds,1 M ds,1 = 0 Else: M ch = 0 = M tr,s M tr,g } (4.4) The terms n Eqs. (4.2)-(4.4) have been explaned n Chapter 3. The above loop s smlar to Eqs. (3.21)-(3.22) wth the dfference beng n the mass of dscharged water. The above calculated value s not the fnal one as t does not take nto account the case that the storage tank s empty. Therefore, the number 1 s n ts suffx. In ths case, t s mpossble to dscharge water from the tank. The exact mass of dscharged water wll be calculated n the end of ths functon. 136

139 Afterwards, the mass of stored water as well as the mass provded by the boler wll be calculated. It s assumed that the tme nterval are quet small, so that wthn one tme nterval t won t be needed to dscharge both the storage tank and put the boler n operaton. The mass of stored water n the begnnng of the day s an nput to the functon and n order to proceed to the next tme ntervals, a smple mass conservaton law, smlar to Eq. (3.23) has to be appled as follows: For each tme nterval : A = M st + M ch M ds If A < 0: Then: M +1 st = 0 M b = abs(a) Else: M +1 st = A M b = 0 } (4.5) Where: M b = Mass of water provded by the boler to the network n each tme nterval (kg) In the above loop, the frst case refers to when the boler has to be used to cover a part of the demand, whle the second case refers to when the boler does not have to be used. Fnally, snce the mass of stored water s known, the accurate value of dscharged water can be calculated wth the followng loop: For each tme nterval : If M st = 0: Then: M ds = 0 Else f M st > 0 and M +1 st = 0: Then: M ds = M st Else: M ds = M ds,1 } (4.6) The second case of the above loop refers to the case when the storage tank gets dscharged wthn the specfc tme nterval, and therefore only the mass of the prevously stored water can be dscharged from the storage tank. So, by applyng expressons (4.1)-(4.6), all the masses across the transmsson network wll be known. More specfcally, the outputs of ths functon are the followng: 137

140 Geothermal flow rate (m G). Mass flow rate on the left of the storage tank (m tr,g) Masses of charged and dscharged water for each tme nterval (M ch and M ds, respectvely. Mass of stored water throughout the day (M st ). Mass provded by the boler n each tme nterval (M b ). Necessary operatng wells (N wells ) Dmensonng of the hot water storage tank functon In ths functon the basc dmensons of the hot water storage tanks are calculated. The calculatons ncluded n ths functon were also used and explaned n Chapter 3. So, a smple reference wll be made here. The nputs of ths functon are the volume of the hot water storage tank (V) and ts heght-to-dameter rato (hdr), whle the outputs wll be the followng: Heght of the storage tank (H HST ). Dameter of the storage tank (D HST ). Thckness of the materal of the storage tank (t st ). The area of the sde, base and top surface, respectvely, of the hot water storage tank (A sde, A base and A top ). It should be noted that the above values could be calculated separately and used as nputs n ths model, but t was decded to have them calculated wthn ths functon n order to mnmze the nput values of the code Hot water storage tank heat balance functon Ths case s not actually one functon but a number of smaller functons feedng a bgger one whch calculates the heat losses of the storage tank. The majorty of these functons has also been explaned n Chapter 3 and more specfcally n secton So, n ths secton the man dfferences from the functon of the prevous model wll be explaned. 138

141 The man dea behnd ths functon s to apply the energy conservaton equaton to the storage tank for each tme nterval and through ths equaton to fnd the evoluton of the temperature wthn the storage tank, as well as the temperature at the ext of the storage tank. The smaller functons are used to calculate the heat losses coeffcents of the base, top and sde parts of the storage tank (see Eqs. ( )). The man nputs of ths functon are the followng: Temperature n the nlet of the storage tank (T HST, ). The basc dfference wth the prevous model s that ths temperature s not constant throughout the day, but t s varable at each pont. Ths temperature wll be calculated wthn a later functon n order to be used as nput n ths functon. Temperature of stored water at the frst pont (T st 0 ). Mass of stored water at each pont (M st ). Mass of water on the transmsson network on the left of the storage tank durng one tme nterval (M tr,g ). Ths value s constant throughout the day. Mass of water on the rght of the storage tank throughout the day (M tr,s ). Masses of charged and dscharged water from the storage tank throughout the day (M ch and M ds, respectvely). Mass of water provded by the peak-up bolers throughout the day (M b ). All these masses are calculated and provded as an nput by the functon explaned n secton The basc dmensons of the storage tank as calculated n secton Intally, the temperature evoluton of the water stored n the hot water storage tank wll be calculated. For ths purpose, the methodology explaned n secton wll be appled. The only dfference compared to ths secton s that the temperature of the water at the nlet of the storage tank wll be varable, and not constant as n Chapter 3, and ths has to be taken nto account. Therefore, nstead of calculatng the heat surplus to the tank due to chargng by Eq. (3.28), t s calculated by the followng equaton: Q + = M ch Cp w (T HST, T a ) (4.7) So, the temperature evoluton of the stored water can be easly calculated and, afterwards, the temperature evoluton at the ext of the storage tank and after the mxng pont (see Fg. 3.3) can be calculated. In order to do ths calculaton an equaton smlar to 139

142 (3.37) s used, but n ths case the varaton of the temperature at the nlet of the storage tank has to be taken nto account agan. So, the correspondng equaton as follows: (M tr,g M ch 1 +M ch ) T 2 HST, (M tr,g M ch 1 +M ch 2 + M ds 1 +M ds 2 + M 1 ds+m ds T 2 st = ) T HST,o (4.8) By applyng the above equaton the temperature after the mxng pont of the storage tank s calculated. Several notes that dfferentate further the calculatons n ths case compared to those of Chapter 3 have to be made: At the frst tme nterval, the term of the mass on the transmsson network on G.H.E. s sde (M tr,g ) should be replaced by M P tr,g +Mtr,G 2, snce the energy equaton takes nto account the second half of the last perod of the prevous day. Ths s the frst tme that the data of the prevous day are needed. At the last tme nterval, under the same logc the mass data of the frst nterval of the next day are needed. Snce these are unknown, t s assumed that they are equal to the data of the last perod of the studed day. So, n ths case, the temperature at the last pont of the studed day may not be totally accurate. But, ths pont wll be the frst pont of the next day, and t wll be calculated very accurately. So, from an engneerng pont of vew ths assumpton and the possble subsequent error s not mportant. For each tme nterval, f the water provded by the boler s postve, whch means that there s no water dscharge, then the temperature after the mxng pont s set drectly equal to the temperature of the water before the mxng pont (T HST, ), snce the above equaton can cause some nstabltes and the results are not accurate. The outputs of ths functon wll be the followng: Temperature evoluton of the stored water throughout the day (T st ). Temperature of the water after the mxng pont throughout the day (T HST,o ). 140

143 Ppelne temperatures functon In ths functon, the temperature dstrbuton across the ppelnes s calculated. As mentoned earler, the calculaton of the temperature n the crtcal ponts of the network s adequate. Ths functon s the bass of the next two functons and uses the method explaned n secton and, more specfcally, Eqs. (3.51)-(3.69). As explaned n the aforementoned secton, n order to calculate the temperature dstrbuton across a set of double pre-nsulated underground ppes, the temperature n the nlet of the supply ppelne as well as the temperature drop n the boundary of the ppelne has to be known. These two values have to be provded as an nput to ths functon together wth the geometrcal characterstcs (Dmensons, bural depth and dstance between the ppelnes) of the ppelnes. The outputs of ths functon are the temperatures n the crtcal ponts of the par of ppelnes,.e. the temperatures at the nlet and outlet of each ppelne Sngle teraton temperatures functon The functon of ths secton together wth the next one are the basc functons of ths model. In ths functon the frst calculaton of the temperatures of the network for each pont throughout the day wll be carred out, whle wth the next functon, as wll be explaned later, the complete calculaton of all the varables of the network wll be done. Ths functon wll be called by the next one, and wll get some nputs that wll be calculated at the begnnng of the next functon. The calculatons are qute smlar to those of secton , but are lmted only n the calculaton of the heat losses or temperatures of the ppelnes. These wll be explaned brefly here. The nputs of ths functon are as follows: Temperature at the nlet of the storage tank for each pont (T HST, ). Intal temperature of the stored water (T st 0 ). The temperature of the water provded by the boler (T b,out ). The mass provded by the boler n each tme nterval (M b ). The mass of charged and dscharged water of the storage tank n each tme nterval (M ch and M ds, respectvely). The mass of stored water n each pont (M st ). 141

144 The mass of water n the transmsson network n the left and the rght of the storage tank, as well as the correspondent mass flow rates (M tr,g, m tr,g, M tr,s and m tr,s, respectvely). The mass flow rate on each branch of the dstrbuton network for each tme nterval (m d.j). The temperature drop n the boundares of each branch of the dstrbuton network ( T d,j ). The dmensons of the transmsson network. The dmensons of all the branches of the dstrbuton network. The dmensons of the storage tank. It should be noted that most of the nputs of ths functon are calculated n the next functon. Actually, ths functon operates as an ntermedate step for the complete calculaton of the varables of the network. Some mportant assumptons made n Chapter 3 are recalled n ths pont. More specfcally, t was assumed that the peak-up boler s rght after the storage tank and that both of these devces are very close to the substaton. Ths s qute realstc, snce wth ths approach a qucker response to the peak demands can be acheved. So, the heat losses between the storage tank and the peak-up boler as well as the substaton wll be neglected. Addtonally, t can be assumed that the hot transmsson ppelne s up to the nlet of the storage tank. The cold storage tank wll be at the begnnng of the cold transmsson ppelne. So, t can be sad that both the ppelnes of the transmsson network have the same mass flow rate (M tr,g ). Fnally, the total length of the transmsson network wll be used for the calculaton of the heat losses, wthout causng an mportant error to the calculatons. The general method for the calculaton of the temperatures of the whole network s as follows: Gven the temperature at the nlet of the storage tank, by callng the functon of hot storage tank heat balance, the temperature evoluton at the outlet of the storage tank (T HST,o ) wll be known. 142

145 In order to calculate the temperature at the ext of the hot transmsson ppelne,.e. takng nto account the possble nfluence of the ncomng water by the boler, the followng energy conservaton equaton wll be used: (M tr,g M ch + M ds ) Cp w (T HST,o T a ) + M b Cp w (T b,out T a ) = M tr,s Cp w (T tr,s,o T a ) By applyng the same dscretzaton method as n secton for the calculaton of the temperature after the mxng pont of the storage tank, the temperature at the ext of the hot transmsson ppelne wll be known for each pont (T tr,s,o ). Then, t s assumed that the outlet temperature of the hot transmsson ppelne, calculated above, wll be equal to the nlet temperature of all the hot ppelnes of the transmsson branches: Ttrho T,. dho j For each branch of the dstrbuton network, the nlet temperature of the hot ppelne s known as well as the temperature drop on ts boundares. So, for each branch and for each tme-pont, the functon of the ppelne temperatures can be appled n order to fnd the temperatures n the crtcal ponts of the branches of the dstrbuton network. These are T d,s,o,j, T d,r,,j respectvely. and T d,r,o,j, The mass flow rates of the return ppelnes of the branches of the dstrbuton network are mxed before they pass to the return ppelne of the transmsson network. The heat losses n the mxng pont are neglected and by applyng the energy conservaton equaton n the mxng pont, the nlet temperature n the cold transmsson ppelne s calculated for each pont (T tr,s, ). The energy equaton that s appled s the followng: j m d,j T d,r,o,j = m tr,s T tr,r, Then, for each pont the temperature at the nlet of the storage tank ( T the nlet of the cold transmsson ppelne ( T trc sth ) are known. So, takng nto account the assumpton made prevously about what s consdered as the transmsson ppelne and by neglectng the thermal nterference of the cold water storage tank, the temperature drop at the boundary of the transmsson network can be calculated for each pont as T tr = T HST, T tr,s,. ) and The nlet temperature of the hot transmsson ppelne s also known, as t s a basc nput of the model. So, for each pont the ppelne temperature functon can be appled for the transmsson network n order to fnd the temperatures at 143

146 the crtcal ponts of the transmsson network. These are T HST,, T tr,s, and T tr,s,o. It should be noted that the frst of the above calculated temperatures s used as an nput also. The outputs of ths functon, as mentoned earler, are the temperatures n the crtcal ponts of the whole network throughout the day. It should be noted that wthn ths functon only one calculaton or one teraton of the temperatures s carred out. The name of ths functon comes from ths fact. In the next functon, a bg loop for the accurate calculaton of the temperatures of the network wll be created and ths functon wll be used wthn the loop Network calculaton functon As mentoned before, the complete calculaton of the varables of the network wll be carred out wthn ths functon. The functon descrbed n secton wll be used as a bass for that purpose. The nputs of ths functon are the followng: Total heat demand data throughout the day (HD ). Dscretzed heat demand data throughout the day (HD j ). The temperature at the nlet of the hot transmsson ppelne, whch s known and constant throughout the day (T tr,s, ). The frst approxmaton for the temperatures at the outlet of the supply transmsson ppelne as well as the nlet and the outlet of the return transmsson ppelne (T tr,s,o,nt, T tr,r,,nt and T tr,r,o,nt, respectvely). The frst approxmaton of the temperature drop of the geothermal flud ( T G,nt ). The frst approxmaton of the thermal effcency of the nstallaton (η tot,nt ). The temperature of the water provded by the peak-up boler (T b,out ). The prevous day storage data,.e. the mass and temperature of the stored water 0 at the begnnng of the day (M st and T 0 st, respectvely). Dmensons of both the transmsson and dstrbuton network. The temperature drop along the boundares of each branch of the dstrbuton network ( T d,j ). The thermal effcency of the n-house nstallaton (η dw ). 144

147 It should be noted that the last two nputs wll be calculated accurately n subsequent functons, and teratve processes wll be used n order to fnd ther precse values. So, actually, ths functon has as nput a temperature drop and an effcency and t does not matter f t s a precse or an estmated value. But, wthn ths functon all the other varables wll be calculated precsely. For the sake of smplcty, n ths secton the symbol of ntal estmaton wll be neglected for all the varables. It should also be noted, that t cannot be known n advance f the peak-up bolers wll be used or not durng the day, so t s assumed that the nput of the effcency equals to the total thermal effcency of the nstallaton. If the peak-up bolers are used, then ths effcency should be equal to the thermal effcency of the geothermal part of the nstallaton. Ths dstncton wll be made clear n the followng functons. A few equatons used n Chapter 3 wll also be used here n a very smlar way. These equatons wll be wrtten n full for reasons of completeness. Frstly, the daly heat demand of the studed day s calculated as: DHD HD (4.9) Day Subsequently, the geothermal energy and the correspondng geothermal power needed to cover the above demand can be calculated by: E G,D = DHD η tot (4.10) Q G = E G,D (4.11) Where: E G,D = Daly energy provded by geothermal energy n the studed day (kwh) Q G = Geothermal power provded n the studed day (W) In ths case, there s some stored water at the begnnng of the day. The thermal power of ths stored water has to be taken nto account and s provded by the followng equaton: Q st 0 = M st 0 Cp w (T 0 st mn(t tr,r,o )) (4.12) 145

148 Where: Q st 0 = Thermal power of ntally stored water n the hot water storage tank (W) It should be mentoned that the mnmum outlet temperature of the return transmsson ppelne s used as the reference temperature, snce ths s the lowest temperature n the network. The above value s necessary for the calculaton of the mass flow rate of geothermal water snce t s an amount of energy/power that can also cover a part of the daly heat demand. So, the above value should be reduced from the necessary geothermal power for the cover of the heat demand. Ths mass flow rate wll be the frst estmaton that s used as an nput n the Water mass balances functon (1.3.1). The mass flow rate of geothermal water wll then be equal to: Q G Q st 0 = m G,1 Cp w T G m G,1 = Q G Q st 0 (4.13) Cp w T G Ths mass flow rate wll be the frst estmaton that s used as an nput n the Water mass balances functon ( ). Snce the characterstcs of the dstrbuton network together wth the dscretsed heat demand are nputs of ths functon, the mass flow rate n each branch of the network s calculated wth the followng loop: For each branch j of the network and for each tme nterval : HD m d,j = j } (4.14) Cp w η dw T d,j In the above expresson, probably some transformatons should be made n the numerator or the denomnator n order to obtan the same unts n both cases. Subsequently, the mass flow rate on the transmsson network on the rght of the storage tank can be easly calculated as the summaton of the mass flow rates of the branches of the dstrbuton network. m m (4.15) tr, S d, j j 146

149 The correspondent value for the whole tme nterval s then calculated as: M tr,s = m tr,s TmeMesh 60 (4.16) In the above equaton, TmeMesh denotes the tme dscretzaton of the heat demand data n mnutes. As a next step, the water mass balances functon s called. Some nputs of that functon have already been calculated wthn the studed functon. By callng the water mass balances functon, and usng the above calculatons, all the mass flow rates and mass exchanges of the network wll be determned. Then, dependng on the fluctuaton of the heat demand throughout the day, t can be possble to use the peak-up boler when t s not necessary,.e. when there s more geothermal energy that can be provded. So, n order to mnmze the use of the peak-up boler and maxmze the utlzaton of geothermal energy, the followng loop s used: For each tme nterval : Whle M b > 0 and m G,1 < m well N wells : Then: m G,1 = m G, Call Water Masses Functon New values of M b and of all the other outputs} (4.17) The second crteron n the above loop was set so that the geothermal flow rate wll not become hgher than the maxmum avalable one. So, wth the above calculatons, the mnmzaton of peak-up boler use s acheved. Of course, the peak-up bolers are not necessarly phased out as the maxmum geothermal flow rate mght not be enough to cover the load. Then, another condton that should be satsfed s that the stored water volume must not exceed the capacty of the storage tank. For that purpose, the followng loop s used: For each tme nterval : Whle M st > V ρ HST : w Then: m G,1 = m G, Call Water Masses Functon New values of M st and of all the other outputs} (4.18) (m 3 ) Where: V HST = Volume of the hot water storage tank, whch s a general nput n the algorthm 147

150 In the above loop, the crteron for the maxmum geothermal flow rate s not used, snce the geothermal flow rate s decreased only, so t cannot be hgher than the maxmum avalable flow rate. Therefore, now, all the fnal mass flow rates and mass exchanges of the network are known for each tme nterval. The dmensonng of the hot storage tank functon wll then be called, so that the dmensons of the storage tank wll be known. All the necessary nputs for the functon explaned n secton are now avalable, so, n order to calculate the temperatures of the whole network the followng steps are carred out: Frst, the followng ntal estmatons are made: T HST, =T tr,s,o,nt, T tr,r, = T tr,r,,nt and T tr,r,o = T tr,r,o,nt. Call One Iteraton Temperatures functon New values of T HST,, T tr,r, and T tr,r,o are now known together wth the other results of ths functon. For the fnal calculaton of all the temperatures of the network a correcton of the estmated temperatures should be made. Ths s done by the followng teratve loop: For each pont: Whle abs(t HST,,new or abs(t tr.r.o.new Then: T HST, T HST, ) > 10 6 or abs(t tr,r,,new T tr,r,o ) > 10 6 : T tr,r, ) > 10 6 = T HST,,new, T tr,r, = T tr,r,,new and T tr,r,o = T tr,r,o,new Call One Iteraton Temperatures Functon T sth, new, T, and T, trc new trco new It should be noted that the above teraton concerns the temperatures of the network, so the object of the teraton concerns the ponts rather than the tme ntervals. When the above multple teraton converges, all the temperatures of the network wll be calculated for each pont, apart from the temperatures between the hot storage tank and the substaton and T tr,s,o ). The hot storage tank losses functon s called n order to calculate these (T HST,o values. So, fnally, all the temperatures across the network have been calculated. The outputs of ths functon, whch are the man outputs of the whole model, are the temperatures of the crtcal ponts of the whole network throughout the whole day, all the 148

151 mass exchanges of the network and the correspondng mass flow rates; the geothermal mass flow rate; as well as the number of wells that should be operated durng that day Optmum T G functon As already referred, the functon descrbed n secton calculates all the varables of the network havng as nput a temperature drop of the geothermal flud as well as an effcency of the nstallaton. As a frst step, these are the ntal estmates used as nputs n the whole model. But, then, these values have to be renewed n order to fnd them precsely for the studed day, because these values wll not be the same every day. Furthermore, as wll be seen n Eq. (4.19), the temperature drop of the geothermal flud s dfferent at each pont durng the day, whle these results depend on the ntal value used n secton In order to overcome the dependency of the results on the ntal estmaton of the temperature drop, an optmum value of the temperature drop that mnmzes ths dfference has to be found. In practce, ths wll be the fnal average temperature drop throughout the day. The functon descrbed n ths secton wll be the objectve functon that wll be called n a later functon and wll fnd the optmum value of the temperature drop of the geothermal flud. In ths functon, the only nput s a temperature drop of geothermal flud. Frstly, the network calculaton functon s called for the calculaton of the varables of the network. The rest of the nputs of ths functon wll be provded by the later functon that s callng the objectve functon descrbed here. Then, the temperature drop of the geothermal flud s calculated as follows: For each pont: T G = R m T tr,s, T tr,r,o } (4.19) η GHE Where all the terms have been explaned n prevous sectons The dfference of the above calculated values compared to the nput value of temperature drop can be easly calculated as: For each pont: ΔT = abs(δt G ΔT G ) } (4.20) 149

152 Fnally, the objectve functon,.e. the output of ths functon, wll be the summary of the above resduals: T tot T (4.21) Later on, n the functon that wll call ths objectve functon, the mnmzaton of ΔT tot wll be the objectve. Fndng the value of the geothermal temperature drop that provdes the mnmum value of ΔT tot means that ths s the optmum estmate, whch s the target of ths secton Effcences functon In ths functon, the thermal effcency of the geothermal part of the nstallaton as well as the total thermal effcency of the nstallaton wll be calculated. In the begnnng of the model, an effcency s used as an nput. Ths effcency s ntally consdered equal to both of the prevously referred effcences. If the peak-up bolers are used wthn the day, these effcences wll be dfferent and wll be calculated n ths functon, otherwse a more precse value of the unque thermal effcency wll be calculated. The nputs of ths functon are a temperature drop of the geothermal flud (ΔT G ), a value of total thermal effcency (η tot ) and the thermal effcency of the peak-up bolers (η b ). Intally, the network calculaton functon s called for the calculaton of all the varables of the network. As happens n the functon descrbed n secton , the rest of the nputs wll be calculated n the next, and fnal functon, that wll call the functon descrbed here. The heat energy of the stored water at the frst pont (Q 0 st ) can be calculated by Eq. (4.12) wthout dvdng by the tme frame ( ), whle for the last pont can be calculated n a smlar way as: Q N st = M N st Cp w (T N st mn(t tr,r,o )) (4.22) Then, t s assumed, that the feedng water of the peak-up boler s pumped from the cold storage tank, whose temperature s assumed to be 1 degree lower than the average temperature of the nlet of the return transmsson ppelne. The cold storage tank wll be 150

153 very close to the substaton, so the temperature of the water pumped n the tank wll be equal to that of the nlet of the return transmsson ppelne. On the other hand, the 1 degree s assumed to be the heat losses of the tank, takng nto account the heat losses of the hot storage tank as found n Chapter 3; t s lkely an overestmaton of ts real value. Of course, from an engneerng pont of vew, ths s acceptable as the error wll not be that bg and a possble overestmaton wll lead (as wll be seen below) to values of fuel used beng hgher than the real ones. T b,n = average(t tr,r, ) 1 (4.23) Where: T b,n = Input water temperature n the peak-up bolers (K) as: The total mass of water provded to the network by the boler can be easly calculated M b, tot M (4.24) b So, the heat provded by the boler to the network and the heat nput of the fuel to the boler are calculated as: Q b,tot = M b,tot Cp w (T b,out T b,n ) (4.25) Q f,tot = Q b,tot η b (4.26) The heat provded by geothermal energy throughout the day wll be calculated usng the new value of geothermal flow rate, whch s provded by the network calculaton functon whch s called n the begnnng of ths functon, and the temperature drop of the geothermal flud whch s used as nput n ths functon. Q G = m G Cp w T G (4.27) Afterwards, the total thermal effcency of the nstallaton can be calculated wth the followng equaton: 151

154 η tot = Q st DHD+Q st N 0 +Q G +Q f,tot (4.28) In order to defne the thermal effcency of the geothermal part of the nstallaton, the part of the daly heat demand that s covered by geothermal energy has to be calculated. For ths purpose, the followng equatons are used: M M (4.29) tr, S, tot tr,s DHD G = DHD (1 M b,tot M tr,s,tot ) (4.30) Where: M tr,s,tot = Total amount of water durng the studed day n the rght of the storage tank (kg) DHD G = Part of the daly heat demand covered by geothermal energy (kwh) So, the thermal effcency of the geothermal part of the nstallaton can be easly calculated n a smlar way as for the total thermal effcency as: η G = DHD N G+Q st Q 0 st +Q G (4.31) Obvously, f the peak-up boler s not used, all the heat demand wll be covered by geothermal energy and the two effcences wll be dentcal. Fnally, n order to calculate the necessary amount of fuel for each tme nterval, the followng set of equatons s used: For each tme nterval : Q b = M b Cp w (T b,out T b,n ) Q f = Q b M f = η b Q f LHV f } (4.32) Where: Q b = Heat provded by the peak-up bolers to the water n each tme nterval (J) Q f = Heat provded by the fuel n the peak-up bolers n each tme nterval (J) 152

155 M f = Amount of fuel used by the peak-up bolers n each tme nterval (kg) LHV f = Lower heatng value of the fuel used n the peak-up bolers ( J kg ) The fnal outputs of ths functon wll be a renewed value of the total thermal effcency of the nstallaton and of the geothermal part of the nstallaton (η tot and η G, respectvely) as well as the quantty of fuel used n the boler at each tme nterval (M f ) Fnal results functon Ths s the fnal functon of the model, whch provdes the fnal results for the studed day. Actually, n ths functon there are very few calculatons carred out and manly the prevous functons are called for that purpose. It should be noted that ths s the only functon whch s called n the man body of the code. All the other functons are called ether wthn ths functon or wthn other functons. The nputs of ths functon are the followng: Total heat demand data (HD ). 0 Mass and temperature of stored water at the last pont of the prevous day (M st and T st 0 ). Intal estmatons of the temperatures of the transmsson network ( T trho, nt, T and T trco, nt ). trc, nt Intal estmaton of the temperature drop of the geothermal flud ( T G, nt ). Intal estmaton of the total thermal effcency of the nstallaton ( Tot, nt ). In order to mnmze the nputs n ths functon, t s noted that t s necessary to use as nputs n any functon n Python, those varables that can change durng the calculatons. Although n prevous functons, some constant varables have been used as nputs, ths does not happen n ths case as the number of nputs n ths case would be very bg. Frstly, the optmum temperature drop of the geothermal flud has to be found. For that purpose, the objectve functon descrbed n secton wll be used. Python programmng language has a lot of bult-n optmzaton algorthms. The optmzaton method that s used n ths case s the bounded Brent s method (see, for example, Gonnet, 153

156 2002). The bounds of the optmzaton wll be ±5K around the ntal estmaton. It was shown n practce that ths range of boundares ncludes the optmum soluton n most of the cases and provdes a very acceptable computatonal tme. So, by applyng ths optmzaton method, the optmum value of the temperature drop of the geothermal flud s calculated. Then, the functon descrbed n secton s called n order to fnd the values of the total thermal effcency of the nstallaton as well as of the geothermal part of the nstallaton. It s recalled that that the optmum value of the temperature drop of the geothermal flud wll be used as an nput n ths functon. Then, the followng loop s used n order to fnd the fnal values of effcences: Whle abs(η G η tot,nt ) > 10 6 : Then: η tot,nt = η G Call Effcences Functon New values of the effcences } (4.33) It should be noted that n the above loop, the thermal effcency of the geothermal part of the nstallaton s compared wth the ntal estmaton of the total thermal effcency. As already mentoned, n the ntal estmaton t s assumed that the peak-up bolers are not used. So, when the above loop converges, the fnal effcences of the nstallaton wll be known as well as the mass of fuel used per tme nterval. Then, n order to calculate the fnal results, the network calculaton functon (see secton ) s called. The optmum value for the temperature drop of the geothermal flud s used as well as the fnal thermal effcency of the geothermal part of the nstallaton, whch have been both calculated before. Fnally, snce all the mass flow rates across the network are known, Eqs. (3.44)-(3.49) are appled to each tme nterval for the calculaton of the electrcal power provded by the pumps. The fnal outputs of ths functon, whch are the fnal outputs of the whole model, wll be summarsed n secton Herarchy of functons In the followng fgure, the herarchy of the functons used n ths model s shown n order to make the whole process more comprehensble. For the sake of smplcty, the functons descrbed n sectons wll be assgned wth the followng abbrevatons: 154

157 WMB (secton ) Water mass balances DHST (secton ) Dmensonng of the hot water storage tank HSTHB (secton ) Hot water storage tank heat balance PT (secton ) Ppelne temperatures SIT (secton 4.2.5) Sngle teraton temperatures NC (secton 4.2.6) Network calculaton ODT (secton 4.2.7) Optmum T G EFF (secton 4.2.8) Effcences FR (secton 4.2.9) Fnal results The begnnng of each arrow shows the callable functon and the correspondent end shows the functon wthn whch s called. For example, functon 5 calls functons 3 and 4, whle functons 5 s called by functon 6. Fgure 4.1 Herarchy of functons used n the developed model 155

158 4.2.3 Output data As mentoned before, the outputs of the model wll be the outputs of the fnal results functon descrbed n sectons The outputs of ths model are a number of dfferent txt fles, snce most of the varables have a number of dfferent values throughout the day. Those varables are recognsed below by the superscrpt and ther result s an array or a matrx of values. So, storng the results n dfferent fles makes the dstncton of the varables of dfferent category much easer. A txt fle s the smplest way of storng data, but, at the same tme, s the easer way to handle them and pass them n any other knd of post-processng that the user mght want. The results are dvded to four man categores whch are the general results, the results of the mass balances across the network, the results of the temperatures of the network and the data of the last pont or tme nterval of the day that are necessary to run the algorthm the next day. Of course, each category can contan numerous txt fles accordng to the nature of the varable stored. Furthermore, the exact way of storng the data depends also on the user. In our case, the way that the outputs wll be wrtten below do not necessarly represent the exact way they are stored, but they are wrtten n the most understandable way. The general results of ths model are the followng: The necessary geothermal flow rate (m G). The mass flow rate on the transmsson network on the left of the storage tank (m tr,g). The number of wells n operaton (N wells ). The average temperature drop of the geothermal flud, whch s the optmum value found by the functon descrbed n secton ( T G,opt ). The thermal effcency of the geothermal part of the nstallaton (η G ). The total thermal effcency of the nstallaton (η tot ). The total electrcal energy used by the pumps over the day (C el,day ). The results of the mass balances across the network that are provded by ths model are as follows: Man results: mass flow rate and the correspondng mass over a tme nterval of charged water n the storage tank (m ch and M ch, respectvely); mass flow rate 156

159 and the correspondng mass over a tme nterval of dscharged water from the storage tank (m ds and M ds, respectvely); mass flow rate and the correspondng mass over a tme nterval of the water provded to the network by the peak-up bolers (m b and M b, respectvely); mass flow rate and the correspondng mass over a tme nterval of fuel used n the peak-up bolers (m f and M f, respectvely); mass flow rate and the correspondng mass over a tme nterval of the water on the transmsson network n the rght of the storage tank and M tr,s, respectvely). (m tr,s Mass of stored water throughout the day (M st ). Ths varable s not wrtten on the man results as t contans one value more. Mass flow rates on each branch of the dstrbuton network throughout the day (m d,j). Then, the results of the temperatures of the network are dvded nto the followng two groups: Transmsson network: temperature at the nlet of the hot water storage tank (T HST, ); temperature of the stored water (T st ); temperature at the outlet of the hot water storage tank (T HST,o ); temperature at the outlet of the supply transmsson ppelne (T tr,s,o ); temperature at the nlet of the return transmsson ppelne (T tr,r, ); temperature at the outlet of the return transmsson ppelne (T tr,r,o ). Dstrbuton network: temperature at the nlet of the supply dstrbuton branches (T d,s, ); temperature at the outlet of the supply dstrbuton branches (T d,s,o ); temperature at the nlet of the return dstrbuton branches (T d,r, ); temperature at the outlet of the return dstrbuton branches (T d,r,o ). Fnally, the results of the last pont or tme nterval of the studed day that are necessary for the calculatons of the subsequent day are the followng (see also secton 4.2.1): Masses per tme nterval: mass on the transmsson network on the left of the storage tank (M tr,g ); mass on the transmsson network on the rght of the storage tank (M N tr,s ); mass of charged water n the storage tank (M N ch ); mass of 157

160 water dscharged from the storage tank (M N ds ); mass of water provded by the boler (M b N ). Storage data: temperature of stored water (T st N ); mass of stored water (M st N ). Mass flow rates on each branch of the dstrbuton network (m d,j N ). As the last category of output refers to the last pont or tme nterval of the studed day, they are assgned the temporal superscrpt N. The only excepton s the mass on the transmsson network on the left of the storage tank whch s constant throughout the day. 4.3 Operaton over a year The second model of ths Chapter studes the operaton of the nstallaton over a whole year. The model of secton 4.2 that studes the operaton over a random day s used as a bass for that purpose. More specfcally, ths model s appled n seres for each day across the year and the data of the last tme nterval or pont of one day are used on the followng day as the data of ther frst tme nterval or pont and then a few more calculatons are carred out. Although the model of ths secton uses many tmes the prevous model, ther natures are qute dfferent. The model of a random day wll actually be used as a tool by the techncans of the nstallaton n order to know n advance how they should operate the nstallaton a random day gven the heat demand. On the other hand, the model developed here wll theoretcally be used before the constructon of the nstallaton n order to calculate several energetc, economc and envronmental ndces of the nstallaton and compare these wth the correspondng ndces of a tradtonal geothermal dstrct heatng system that does not use a heat storage. Ths wll ndcate f eventually the ncluson of a heat storage s worthwhle or not and wll be done wth the methodology explaned n Chapter 5. In other words, ths model provdes manly the necessary nputs for Chapter 5. Furthermore, n ths secton the cold water storage tank and the peak-up bolers wll be szed, snce ths requres nstallaton data over the whole year rather than for a specfc day, as occurred n the man szng of the nstallaton n Chapter 3. The nputs of ths model are the same as of those of the prevous model apart from the heat demand data (total and dscretzed), where obvously the data of the whole year are used. Then, wthn the model these data are separated on the correspondng data for each dfferent day and a counter s assgned on each day so that the proper heat demand data are used each tme. Addtonally, the model developed n secton 4.2 requres some data from 158

161 the prevous day n order to carry out the calculatons. In ths case, the same data are also requred for the frst day of the whole year, but cannot be known snce theoretcally the nstallaton has not been bult yet. Addtonally, these data wll have a small mpact on the fnal results as the model wll run for a whole year and, therefore, any error wll dmnsh over tme. So, an ntal estmaton of these values has to be made n the begnnng of the algorthm. A logcal ntal estmaton can be based on the results from the desgn-day. Afterwards, the algorthm of secton 4.2 s appled for every day of the year and the outputs explaned n secton are avalable for each day of the year. As the nature of ths algorthm s dfferent, only some of these data are of nterest for ths model. Those data are ether the necessary data for the rest of the calculatons of ths model or are the necessary nput data for Chapter 5 and are drect outputs. Snce these data are avalable for each day, they can be easly stored together n bgger arrays, so that the results of the whole year, and not of each day separately, are avalable for post-processng. In the rest of ths secton, the varables over the whole year wll be ndexed wth the subscrpt an (annual). For example, f M st s the mass of stored water for each pont over a day, M st,an wll be the mass of stored water for each pont over the whole year. The only dfference s that, n ths case, the counter wll refer to the tme nterval over the whole year. The data of nterest n ths case are the followng: The electrcal power used by the pumps to overcome frcton losses (P el,an ) The geothermal mass flow rate (m G,an). The mass on the transmsson network n the rght of the storage tank (M tr,s,an ). The mass of water provded by the boler (M b,an ). The mass of fuel provded to the boler (M f,an ). The temperature at the nlet of the return transmsson ppelne (T tr,r,,an ). The temperature at the outlet of the supply transmsson ppelne (T tr,s,o,an ). The last varable s used only n order to have an overvew f at any tme of the year the temperature at the outlet of the supply transmsson ppelne falls below the mnmum value set by the requrements of the end-users (see secton 3.2.8). 159

162 The total electrcal energy used by the pumps throughout the year s calculated as: E el,tot = (P el,an TmeMesh/60) (4.34) In the above equaton, the fnal result wll be n Wh or kwh dependng on whether the power used s expressed n W or kw, respectvely. It s a user choce to get the results n these unts as t s more helpful for ther post-processng. In a smlar way, the total mass of fuel provded to the bolers throughout the year can be easly calculated by summng all ther ndvdual values. M M (4.35) f, tot f, an Then, the heat nput to the boler for each tme nterval can be calculated by Eqs. (4.25) and (4.25). The maxmum of these values equals the capacty of the peak-up bolers as ths value represents the maxmum heat that has to be provded by the bolers. Therefore, theoretcally no more heatng power more than ths wll have to be provded. Of course, n realty, the bolers wll probably be bgger n case of a geothermal system breakdown. So, the sze of the peak-up bolers wll be calculated by the followng equaton: Q pb = max ( M b,tot Cp w (T b,out T b,n ) ) (4.36) η b TmeMesh 60 In the above equaton, the terms TmeMesh and 60 n the denomnator are used n order to get the result drectly n unts of power (Watts). The szng of the cold water storage tank wll be done on the hypothess that ths storage tank wll operate as a more general storage devce compared to the hot water storage tank whch wll operate based on the fluctuaton of the heat demand. In other words, t should be taken nto account that the cold water storage tank should be able to store a bgger amount of water than the hot water storage tank n tmes of low load where the flow rates around the network wll be qute small. At these tmes, there wll be an ncreased need for storng a large amount of water that would otherwse crculate around the nstallaton. On the other hand, n a case of very bg fluctuatons of the heat demand wthn a day there s the case that the hot water storage tank wll be completely dscharged 160

163 to cover the heat demand and rght after that for the heat demand to be qute small, so that all ths amount of water wll need to be stored n the cold water storage tank. A logcal ntutve assumpton s that the volume of the storage tank wll be equal to the volume of the hot water storage tank ncreased by the equvalent volume whch s necessary to store the maxmum amount of water n the left of the storage tank over three consecutve tme ntervals. Takng nto account the maxmum amount of water on the left of the storage tank over three consecutve tme ntervals seems to be an acceptable and adequate soluton from an engneerng pont of vew. So, the volume of the storage tank s calculated by the followng equatons: M + V CST = V HST + max (M + ) ρ w (T) +1 = M tr,s + M tr,s + M tr,s (4.37) T = average(t tr,r,o,an ) } Where: V CST = Volume of the cold water storage tank (m 3 ) The second part of the above expresson s appled for every tme nterval apart from the frst and the last one, as the calculatons cannot be carred out n these cases. Furthermore, the reference densty of water s calculated for the average temperature around the year of the nlet supply transmsson ppelne, as ths s the nlet temperature on the cold storage tank also. A more precse soluton would be to take nto account the densty based on the temperature at each dfferent tme nterval on whch the mass surplus s calculated. But, n general, the fluctuaton of the temperature at the nlet of the supply transmsson ppelne s very small, so the fluctuaton of the densty s even smaller as the nfluence of the temperature on the densty of water s qute small. Therefore, ths selecton s defntely acceptable for the studed case. So, by usng expresson (4.36) the volume of the cold water storage tank s found. Then, by applyng the dmensonng of the hot water storage tank functon, the dmensons of the tank are also calculated. It s recalled that ths functon can be used for any storage tank as t ncludes calculaton on the geometry of the tank and calculatons based on the nternal pressure of the tank whch are both ndependent of the temperature wthn the tank. So, wth ths process the cold storage tank s szed and wth Eq. (4.36) the peak-up bolers are also szed. These were the two parts of the nstallaton whch were not szed wth the methodology of Chapter 3 as data of the whole year were necessary for that purpose. So, the szng of the nstallaton s also 161

164 complete now. Fnally, the average geothermal flow rate around the year s calculated by the followng equaton: m G = average(m G,an) (4.38) So, the fnal outputs of the whole model are the followng: Total electrcal energy used by the pumps (E el,tot ). Total mass of fuel used by the bolers (M f,tot ). Sze of the peak-up bolers (Q pb). Volume of the cold water storage tank (V CST ). The average geothermal mass flow rate (m G). 4.4 Results Operaton over random days As mentoned before, the model that studes the operaton of the nstallaton over a random day wll be manly used as a tool by the techncans of the nstallaton n order to know n advance how to operate the nstallaton over any day wth a known heat demand. So, only ndcatve results of random days can be shown here. Therefore, several ndcatve days have been chosen to show the effect of the szng of the nstallaton over ts operaton. The daly heat demands of the three days that were chosen as desgn-days n Chapter 3 are shown on Table 4.1. The days chosen n ths secton have daly heat demands that le between the heat demands of the desgn-days for each case of szng. For the case of smplcty, these days are named Day 1, Day 2, Day 3 and Day 4, respectvely, and ther daly heat demands are shown on Table 4.2. As can be seen on ths table, the four selected days cover a bg range of daly heat demands, from very low to very hgh heat demands. The mass of stored water for the four selected days for each case of szng are shown n Fgs , respectvely. 162

165 Table 4.1 Daly heat demands of the desgn-day for each case of szng as calculated n Chapter 3 Case Daly heat demand (kwh) 25%le %le %le Table 4.2 Daly heat demands of the random days chosen for study n ths secton Case Daly heat demand (kwh) Day Day Day Day Fgure 4.2 Mass of stored water for Day 1 (25%le szng) 163

166 Fgure 4.3 Mass of stored water for Day 1 (50%le szng) Fgure 4.4 Mass of stored water for Day 1 (75%le szng) 164

167 Fgure 4.5 Mass of stored water for Day 2 (25%le szng) Fgure 4.6 Mass of stored water for Day 2 (50%le szng) 165

168 Fgure 4.7 Mass of stored water for Day 2 (75%le szng) Fgure 4.8 Mass of stored water for Day 3 (25%le szng) 166

169 Fgure 4.9 Mass of stored water for Day 3 (50%le szng) Fgure 4.10 Mass of stored water for Day 3 (75%le szng) 167

170 Fgure 4.11 Mass of stored water for Day 4 (25%le szng) Fgure 4.12 Mass of stored water for Day 4 (50%le szng) 168

171 Fgure 4.13 Mass of stored water for Day 4 (75%le szng) Furthermore, n Table 4.3 the total mass of fuel used durng the day for each case s shown, whle n Table 4.4 the necessary geothermal flow rate for each case s shown. Table 4.3 Total mass of fuel (kg) used over the day for each case Case 25%le 50%le 75%le Day Day Day Day

172 Table 4.4 Necessary geothermal flow rate (kg/s) for each case Case 25%le 50%le 75%le Day Day Day Day Annual operaton In ths secton, the man results of the model of the annual operaton of the nstallaton wll be presented, whle the man results wll also be presented for the tradtonal case of operaton of a geothermal dstrct heatng system,.e. wthout a heat storage. The tradtonal case s defned as the followng case: No heat storage s used. The mass flow rate s not constant throughout the day, but follows the heat demand all the tme. When the geothermal energy cannot cover all the heat demand, peak-up bolers are used. Apart from the heat storage, the rest of the nstallaton has exactly the same dmensons as found n Chapter 3. In other words, n the tradtonal case, the operaton of an dentcal nstallaton wthout the heat storage whch s operated n the tradtonal way s studed. The man results of the studed case are shown on Table 4.5 for each case of szng, whle the results of the tradtonal operaton are shown on Table 4.6. By comparng these two tables, the advantages of the proposed case wll be dentfed. Fnally, n Fgs the volume of water stored n the hot water storage tank throughout the whole year s shown for each case of szng, respectvely. 170

173 Table 4.5 Man results of the studed case Case 25%le 50%le 75%le Total energy used by the pumps (kwh) Total fuel used by the bolers (kg) Average geothermal flow rate (kg/s) Sze of peak-up bolers (kw) Sze of cold storage tank (m 3 ) Table 4.6 Man results of the tradtonal operaton of the nstallaton Case 25%le 50%le 75%le Total energy used by the pumps (kwh) Total fuel used by the bolers (kg) Average geothermal flow rate (kg/s) Sze of peak-up bolers (kw) Fgure 4.14 Volume of stored water over the year (25%le szng) 171

174 Fgure 4.15 Volume of stored water over the year (50%le szng) Fgure 4.16 Volume of stored water over the year (75%le szng) 172

175 4.5 Dscusson Concernng the model of the operaton over a random day, several nterestng observatons can be made through the correspondng results. Frstly, t s shown that for the same day of study as the szng of the nstallaton ncreases less fuel s used. Ths s totally expected because as the szng ncreases, more geothermal energy s avalable to cover the heat demand. So, n the majorty of the cases more geothermal energy s used for that purpose. An nterestng excepton n the observaton of the hgher geothermal flow rate s n Day 1, n the medum szng of the nstallaton, where the geothermal flow rate s lower than that of the low szng of the nstallaton. Ths occurs ether because of the lmtatons of the geothermal flow rate (see Eq. (4.1)) or because the geothermal energy s much better harvested n ths case due to the hgher storage capacty. Furthermore, the heat storage also ncreases, whch means that more geothermal energy can be stored n tmes of low load. So, all these lead to the concluson that a larger szng of the geothermal nstallaton leads to a hgher fracton of the load beng covered by geothermal energy wth subsequent decrease of the use of fuel. The second observaton concerns the nfluence of the ncrease of the daly heat demand for the same szng of the nstallaton. It can be seen that as the heat demand ncreases more fuel s used to cover the heat demand whch s expected as the geothermal nstallaton has a specfc capacty and can never produce more heat than ths capacty. Ths happens although the geothermal flow rate also ncreases as the heat demand ncreases (see Table 4.4). The only excepton s the case of the medum szng of the nstallaton between Days 2 and 3 where the geothermal flow rate s lower n the second case, whch s not expected as the heat demand s hgher. Ths mght occur for the same reasons as n the prevous paragraph. So, n general, t can be sad that, for a specfc nstallaton, as the heat demand ncreases both the geothermal flow rate and the fuel used wll ncrease. If the heat demand s relatvely low compared to the capacty of the nstallaton (see 75%le case n Table 4.3), the mass of fuel used wll be zero and all the heat demand wll be covered by geothermal energy. A thrd observaton that arses from Table 4.3 n conjuncton wth Tables 4.1 and 4.2 s that when the heat demand of a specfc day s lower than the heat demand of the desgnday of the specfc nstallaton, then all the heat demand wll not be necessarly covered by geothermal energy. Ths s made clear on the case of Day 1: both n the low and the 173

176 medum szng there s some fuel used to cover the heat demand, although the heat demand of the desgn day of both cases s hgher than for Day 1. Ths happens because, as mentoned many tmes before, not only the total heat demand s mportant but also ts fluctuaton wthn the day. So, a specfc day can have such a fluctuaton of ts heat demand from one tme nterval to the other that the heat demand at a specfc tme cannot be covered wthout the help of the peak-up bolers. Ths observaton makes clear the mportance of the fluctuaton of the heat demand wthn the day. Concernng the results of the annual operaton of the nstallaton, some very nterestng ponts can be made both for the dfferent szng of the nstallaton when the heat storage s used as well as between the cases where the heat storage s used and not. Frstly, when the heat storage s used, t s seen by Table 4.5 that the energy used by the pumps decreases when the szng of the nstallaton ncreases. Ths s justfed by the fact that bgger ppelnes are used when the szng ncreases, so the frcton losses, and subsequently the power requred by the pumps, wll decrease (see also secton ). Therefore, the total energy used by the pumps throughout the year wll decrease. Then, t s observed that as the szng of the nstallaton ncreases the average geothermal flow rate throughout the year wll ncrease. Ths s totally expectable as the annual heat demand s obvously the same n each case and snce more geothermal energy s avalable as the szng ncreases, more geothermal energy wll be harvested. Another nterestng observaton on the geothermal flow rate s that the ncrease between the large and medum szng s not so bg as between the medum and the low szng. Intutvely, the medum szng s expected to be closer to the average demand throughout the year. So, n the case of the larger szng, the geothermal nstallaton wll be under-utlzed leadng to an average geothermal flow rate whch s hgher than that of the medum szng, but much smaller than ts maxmum flow rate (see Table 3.2). On the other hand, more geothermal energy harvested means that a hgher fracton of the annual heat demand s covered by geothermal energy, whch n turn means that a smaller fracton of ths demand has to be covered by the peak-up bolers. So, the fact that the fuel used throughout the year decreases as the szng of the nstallaton ncreases s totally justfed. For the same reason, the sze of the peak-up bolers also decreases as the szng ncreases, snce the peak demands that wll have to be covered by the bolers wll be lower. Fnally, as the system szng ncreases the sze of the cold storage tank ncreases. Ths s expected as the sze of the hot storage tank also ncreases as the system sze ncreases, as seen n Chapter 3, whle the second component whch defnes the sze of the 174

177 cold storage tank wll be almost the same for each case. Ths happens because ts numerator wll be exactly the same for each case and ts denomnator, whch s the densty of water, wll be roughly the same as the densty of water s almost constant for the range of the temperature used. In other words, the sze of the cold storage tank wll be almost drectly proportonal to the sze of the hot storage tank for a specfc heat demand throughout the year. So, as the szng ncreases, the sze of the hot storage tank ncreases and, subsequently, the sze of the cold storage tank wll ncrease. By comparng Tables 4.5 and 4.6, an ntal comparson between the studed case and the tradtonal operaton of a geothermal dstrct heatng system can be made. Frst, t can be seen that the energy used by the pumps throughout the year s almost the same whatever the heat storage s used or not, for each case of szng. Ths ndcates that the total flow rate throughout the nstallaton over a whole year wll be almost the same wthout beng affected by the presence of the heat storage. Then, t s observed that when the heat storage s used, the amount of fuel used throughout the year decreases. Ths ndcates that wth the ncluson of the heat storage, geothermal energy s utlsed n a more optmal way decreasng the relance on the peak-up bolers. Ths observaton s among the most mportant of ths thess. It can also be observed that the average geothermal flow rate ncreases when the heat storage s used, but only slghtly. Ths ncrease of the geothermal flow rate does not justfy the decrease of the fossl fuel consumpton, enhancng n ths way the role of the heat storage n better matchng demand and supply of heat. Another nterestng observaton concernng the mass of fuel used, s that the absolute decrease when the heat storage s used n the low and large szng cases s smaller than n the medum szng. Ths happen because n the low szng, the geothermal capacty s low compared to the heat demand on the majorty of the tmes around the year, so all the geothermal energy wll be sent tme drectly to the heat demand most of the tme durng the year. Ths can also be observed by Fg where t s seen that for a large amount of tme around the year the amount of stored water s relatvely low for the low szng of the nstallaton. So, the heat storage wll not have a bg mpact n ths case and the amount of fuel used wll be roughly the same ether whether the storage s used or not. On the other hand, n the large szng of the nstallaton the geothermal capacty s bg enough to cover alone the heat demand the majorty of tme. So, the amount of fuel used wll be small anyway and the decrease n the fuel consumpton wll be relatvely small. All these ndcate that the heat storage s better utlsed n the case of the medum szng of the nstallaton, although a decrease n fuel consumpton s observed n any case. Ths comes 175

178 n agreement wth Fgs where t s observed that n the medum szng of the nstallaton, more water s stored compared to the maxmum capacty of the storage n each case. In the low szng of the nstallaton, as mentoned before, a large amount of tme the storage s not used as all the geothermal producton s sent drectly to the load, whle n the large szng of the nstallaton, the storage s not used that much manly n perods of low load (summer months) as the heat demand can be covered solely by the adjustment of the geothermal flow rate n the approprate value. Fnally, the sze of the bolers ncreases when the heat storage s not used, whch s expected as more and probably hgher peak demands wll occur n ths case. But, the ncrease n the sze of the peak-up bolers when the heat storage s not used s small compared to the ncrease n the mass of fuel used. Ths denotes that the peak demands throughout the year wll be roughly the same numercally no matter whether the heat storage s used or not, but these wll be much more frequent when the heat storage s not used. Ths reconcles the apparent dsagreement between the ncrease of the sze of the peak-up bolers and the ncrease n fuel consumpton. A more detaled comparson between the studed and the tradtonal case wll be carred out n Chapter 5, where economc, envronmental and further energetc detals wll be calculated. 4.6 Summary Ths Chapter studes n detal the operaton of the nstallaton szed n Chapter 3 ether for a random day or for a whole year. So, two models were developed for the study of these two cases. The model that studes the operaton of the nstallaton over a random day was explaned n secton 4.2, whle the model that studes the annual operaton was explaned n secton 4.3. Then, the results for both models were shown n secton 4.4 followed by an extensve dscusson n secton 4.5. In the frst model, the nputs are the szng of the nstallaton from Chapter 3. The topology of the nstallaton that was also used as an nput n Chapter 3 together wth the heat demand of the random studed day are the other nputs of ths model. Furthermore, some ntal estmatons whch are derved from the desgn-day of the specfc case are also used as nputs. By applyng the model descrbed n secton 4.2, the operatonal strategy of the nstallaton for the studed day wll be known. It s recalled that the operatonal strategy s defned as the complete knowledge of the operaton of the nstallaton durng the studed 176

179 day,.e. the necessary geothermal flow rate, when and by how much should the storage tank be charged or dscharged, when and by how much should the peak-up bolers be used etc. Furthermore, an analytcal mappng of the temperatures n the crtcal ponts of the nstallaton wll also be known over the day. Fnally, the electrcty used by the pumps as well as the fuel used by the peak-up bolers throughout the day wll also be known wth the applcaton of ths model. In other words, ths model shows how the nstallaton that s already bult should be operated n a day wth a known or predcted heat demand. Practcally, t s much easer to predct the weather condtons rather than the heat demand of a specfc (usually the next) day. For that purpose, an attempt to connect the gven heat demand wth the weather condtons of the area was attempted n Appendx B. The results of ths Appendx are dscouragng as t s shown that the correlaton between the heat demand and the weather condtons s not always straghtforward as other factors, such socal factors or the heat capacty of the buldng, greatly nfluence the heat demand. These factors are, n general, dffcult to predct, so ths correlaton s dffcult to be produced. Of course, general conclusons cannot be made as ths correlaton and ts nfluencng factors are very casespecfc and n our case are not known. Theoretcally, f ths correlaton s acheved, then by ntegratng ths correlaton wth the model developed n secton 4.2, the operaton of the nstallaton can be known the next day gven the weather condtons. Intutvely, ths s more useful than predctng the heat demand for any day as the weather forecasts are typcally provded by professonals on the feld and the accuracy s much hgher than predctng the heat demand. So, f a robust correlaton s bult between the heat demand and the weather condtons, then one of the basc nputs of the model wll be much more accurate and, subsequently, the operatonal strategy provded wll be more precse and close to the realty. The other two man nputs of the model,.e. the szng and the topology of the nstallaton, are constant and cannot cause any errors to the results. So, f the thrd nput s more accurate, then, the accuracy of the results wll ncrease a lot. In the second model, the frst model s used as a bass and s appled serally for each day of the year. In the frst model, some varables from the prevous day of study are needed as nputs, whle some of the results from the last tme nterval wll be used as nputs n the next day. In ths case, the outputs of the prevous day are used automatcally as nputs of the next day. In general, the nputs of ths model are the same as n the prevous model apart from the heat demand, where the heat demand of the whole year s used. The outputs of ths model are the same as for the prevous one, but they concern the whole year 177

180 obvously. The outputs of nterest n ths case are manly the total electrcty used by the pumps and the mass of fuel used by the peak-up bolers throughout the year and the average geothermal flow rate. The frst two comprse the man operatonal costs of the nstallaton and wll be among the man nputs n the economc analyss of the nstallaton that wll be presented n the next Chapter, whle the average geothermal flow rate wll be used for the calculaton of the man energetc ndces of the nstallaton. Fnally, ths model provdes also the sze of the cold water storage tank as well as of the peak-up bolers, fllng the gap n the model of Chapter 3. As the frst model studes the operaton of the nstallaton over a random day, t was appled to four random days around the year wth daly heat demands between the lmts set by the three desgn-days for each case of szng. The man fndngs of ths model are the followng: For the same day of study, as the szng of the nstallaton ncreases, more geothermal energy s used leadng to the reducton of the fuel used. So, a bgger fracton of the daly heat demand s covered by geothermal energy. For the same szng of the nstallaton, as the daly heat demand of the studed day ncreases, then both the geothermal flow rate and the mass of fuel ncrease. If the daly heat demand s lower than the daly heat demand of the desgn-day of the specfc nstallaton, then t s not necessary for all the heat demand to be covered by geothermal energy only. The fluctuaton of the heat demand across the day s equally mportant for the operaton of the nstallaton wth the daly heat demand. The second model s then appled for the three cases of szng usng the heat demand around the year and an ntal comparson s carred out wth the tradtonal operaton of these systems where no heat storage s used. The man fndngs n ths case are as follows: In the case of usng the heat storage, as the szng of the nstallaton ncreases, then the electrcty used by the pumps decreases, the mass of fuel used by the peak-up bolers decreases, and the sze of the peak-up bolers decreases, whle on the other hand, the average geothermal flow rate and the volume of the cold water storage tank ncrease. 178

181 For the same szng of the nstallaton, when comparng the case of usng the heat storage and the tradtonal case, t s observed that the electrcty used by the pumps s roughly the same, the mass of fuel used by the bolers decreases when the heat storage s used wth a subsequent decrease n the sze of the bolers, whle on the other hand the average geothermal flow rate ncreases. The heat storage seems to be better utlsed n the medum szng of the nstallaton (50%le). A more comprehensve and detaled comparson between the studed case of ncludng a heat storage n the system and the tradtonal case wll be carred out n the next Chapter, where the man fndngs of the second model of ths Chapter wll be used as nput. So, concludng, the frst model n ths Chapter s a very useful tool for the techncans of the nstallaton that can know n advance how to operate the nstallaton over a day wth a gven (or predcted) heat demand, whle the second model szes the rest of the nstallaton that could not be szed n Chapter 3, and provdes the man runnng costs of the nstallaton together wth the average geothermal flow rate. All these wll be among the man nputs n the next Chapter. 179

182 5 ECONOMIC, ENVIRONMENTAL AND ENERGETIC ANALYSIS OF A GEOTHERMAL DISTRICT HEATING SYSTEM 5.1 Introducton In ths Chapter, the economc, envronmental and energetc feasblty of the proposed operaton of a geothermal dstrct heatng system (GDHS) wth a storage tank wll be studed and a comparson wth the tradtonal case wll be carred out. The man goal of ths Chapter s to compare the studed case of ths thess wth the tradtonal operaton of these systems n order to conclude eventually f t s worthwhle ntegratng a storage tank or not. In other words, ths Chapter does not compare the studed case wth alternatve technologes, but only wth the tradtonal case (.e. wth no storage). For that purpose, as wll be made clear later on ths Chapter, some parameters that wll be consdered common between the two cases wll be neglected. So, some of the results mght not depct ther actual values n terms of real nstallatons and, therefore, a straght comparson wth typcal values of other technologes should not be made. But, these values are consdered adequate to make a comparson between the studed and the tradtonal case. Ths comparson wll be made for each case of szng of the nstallaton n order to dentfy the nfluence of the szng on the economcs of the nstallaton. The man nputs of ths Chapter are the outputs of the model of the annual operaton of the nstallaton that was studed n secton 4.3, and the captal costs of several parts of the unt. In ths Chapter, the nputs are much less than n the prevous two Chapters, so these wll not be explaned n a separate secton. Then, through the methodology presented the basc economc, envronmental and energetc ndces of the studed case wll be calculated and a comparson wth the tradtonal case (for whch the same ndces wll also be calculated), wll be made. The fnal answer that wll be attempted to be provded n ths Chapter s the followng: Is t worthwhle ncludng a heat store wthn the proposed operaton of a geothermal dstrct heatng system or not? In ths secton, a bref ntroducton n ths Chapter was gven. In secton 5.2, the methodology for all the necessary calculatons wll be explaned n detal, whle n secton 5.3 the results of the studed and the tradtonal case wll be shown. Fnally, a dscusson on 180

183 the results wll be provded n secton 5.4, followed by some concludng remarks n secton Methodology Economc analyss In ths secton, the calculaton of the basc economc ndces both of the studed nstallaton as well as of the tradtonal case wll be explaned. The calculatons are the same for both cases (apart from the captal cost of the storage tanks that wll be zero n the tradtonal case as there s no storage n ths case). The cash flows for these two cases wll be also explaned for that purpose. Intally, the fnancal outflows and ncomes of the nvestment have to be calculated. These wll be explaned n detal n the followng two sectons Calculaton of the nvestment expendture The nvestment expendture conssts of the followng parts: Intal captal cost. Captal cost of some unts that wll be replaced after some years of operaton. Runnng costs n the frst year of operaton. Runnng costs n subsequent years. The calculaton of these parts, whch are necessary for all the subsequent calculaton wll be explaned n ths secton. Frst, t s assumed that the nstallaton s bult n year n=0 and t starts operatng n year n=1. Both the ntal captal and runnng costs wll be calculated for the year n=0, but for the cash flows, the runnng costs from year n=1 and onwards wll be taken nto account, as the nstallaton wll operate n these years. The ntal captal cost of the nstallaton s calculated by the followng equaton: 0 CC tot = CC dr + CC HST + CC CST + CC 0 pb + CC 0 0 np + CC ot (5.1) 181

184 Where: 0 CC tot = Total ntal (year n=0) captal cost ( ) CC 0 0 dr, CC HST, CC 0 CST, CC 0 pb, CC 0 0 np, CC ot = Intal captal cost of several equpment used durng the constructon of the nstallaton (Drllng, hot and cold water storage tanks, peakup bolers, network ppelnes and other costs, respectvely) ( ) In applyng the above equaton, typcal costs for specfc components of the captal expendture were assembled on the bass of dscusson wth UK practtoners n the geothermal drect use sector. For the drllng costs, t was assumed that the frst deep borehole would cost 1.5M, decreasng to 1M for later boreholes. The latter are cheaper as ground condtons would be better known n advance and the rsk of drllng would decrease. Furthermore, t s assumed that one re-njecton well wll also be drlled n each case of study n order to mantan the flow of geothermal flud n the underground and avod the degradaton of the geothermal resource. It should be ponted out that the number of wells calculated n Chapter 3 are the producton wells, as based on these the avalable geothermal flow rate was calculated. So, f the number of producton wells calculated n Chapter 3 are N wells, then the total number of wells wll be N wells + 1 and the cost of drllng wll be gven n mllon as follows: CC 0 dr = N wells 1 (5.2) The captal cost of the network ppelnes ncludes the cost of materals, whch are carbon steel and mneral wool (nsulaton), the cost of weldng and the cvls costs for buryng the ppes underground. The cost of the materal s calculated by Eqs. (3.41)-(3.42) snce the dmensons of the ppelnes are known. The unt cost of carbon steel s estmated at 400/tonne and the cost of mneral wool at 60/m 3. The cost of weldng s assumed to be 1000 per weld and meter of dameter and there wll be one weldng every 6 meters of ppelne. Fnally, the cvls costs are assumed to be 300 per meter of ppelne. So, for each par of ppelnes, ther captal cost wll be calculated by the followng equatons: CC 0 np = 2 (CC mat CC weld 0 ) + CC cvl (5.3) 0 CC weld = 1000 D p,o L p 6 (5.4) 0 CC cvl = 300 L p (5.5) 182

185 Where: 0 CC mat = Captal cost of the materals of the ppelnes n year n=0 ( ) 0 CC weld = Captal cost of the weldng of the ppelnes n year n=0 ( ) 0 CC cvl = Cvls costs for the buryng of the ppelnes n year n=0 ( ) D p,o = External dameter of the ppelnes (not ncludng the nsulaton) (m) L p = Length of each ppelne (m) In Eq. (5.3), the factor 2 s used n the frst two terms n order to account for both the supply and the return ppelne. On the other hand, t s not used n the calculaton of the cvl costs as one excavaton wll be done for each par of ppelnes. The costs n Eqs. (5.3)-(5.5) are all gven n. Concernng the costs of the tanks, these nclude the materals, cvls costs, the erecton on slab and other mnor costs. The materals of the storage tanks nclude carbon steel as the man materal of the tank, mneral wool for nsulaton, mld steel as the materal of the cover of the tank and concrete whch s used as the base of the tank. The thckness of carbon steel has been calculated n Chapter 3, whle the thckness of the mneral wool s assumed to be 20cm, the thckness of the cover s assumed to be 3mm and the thckness of the concrete base to be 50cm. So, snce the dameter of each storage tank s known from Chapters 3 and 4, respectvely, the volume of each materal can be easly calculated. Then, the volume of each materal s calculated by the unt costs n order to dentfy the cost of each materal. Fnally, all the costs are summed together for the calculaton of the cost of each tank. So, ndcatvely, the cost of materals of the hot water storage tank wll be gven as: 0 CC mat,hst = V c,steel C u,c,steel + V ns C u,ns + V cov C u,cov + V con C u,con (5.6) Where: 0 CC mat,hst = Intal captal cost of the materals of the hot water storage tank ( ) V c,steel, V ns, V cov, V con = Volumes of the carbon steel, nsulaton, cover and concrete used n the hot water storage tank, respectvely (m 3 ) C u,c,steel, C u,ns, C u,cov, C u,con = Unt cost of carbon steel, nsulaton, cover and concrete, respectvely ( m 3) 183

186 In the above equaton, the unt costs of carbon steel and of the nsulaton are the same as those for the ppelnes, whle the unt cost for the cover s assumed to be the same as that of carbon steel. Furthermore, the unt cost of concrete s assumed to be equal to 50/m 3. The other costs of the tank are assumed on the bass of recent projects n the UK. More detals on these assumptons can be found n Appendx C. Eventually, the captal cost of the hot water storage tank, for example, wll be calculated as: 0 0 CC HST = CC mat,hst + CC (5.7) In the above equaton, the second part refers to the other costs ncluded n the calculaton of the captal cost of the tanks. Moreover, for the cost of the peak-up bolers, an average captal cost of 200/kW 2 s assumed for ndustral gas bolers. So, the captal cost of the peak-up bolers s calculated as: CC 0 pb = 200 Q pb (5.8) In the above equaton, the thermal power of the peak-up bolers (Q pb ) has been calculated n Chapter 4, and has to be used n unts of kw. Fnally, other mnor costs nclude pumps, heat exchangers, n-house nstallatons, salares of workers etc., all of whch have been estmated from recent analogous projects n the UK. So, by applyng Eqs. (5.1)-(5.8) the calculaton of the ntal or up-front captal cost of the nstallaton s possble. As mentoned before, n the tradtonal case of operaton, the costs of the hot and cold storage tank wll not be calculated by Eq. (5.7), but wll be equal to zero as no storage tank s bult n ths case. As mentoned before, several parts of the nstallaton wll need to be replaced after several years of operaton, snce they have a lmted lfetme. More specfcally, t s assumed that the peak-up bolers wll be replaced after 20 years of operaton, whle the heat exchangers and the pumps wll be replaced after 15 years of operaton. Ther cost at the tme of the replacement wll be calculated based on ther ntal captal cost and an average annual ncrease of the equpment whch can be ether set equal to the dscount rate

187 or another value dependng on the specfc market and ts trends. So, these costs are calculated by an equaton lke the followng: CC x n = CC x 0 (1 + AAI CC,x ) n (5.9) Where: n CC x = Captal cost of x equpment of the nstallaton n year n ( ) 0 CC x = Captal cost of x equpment of the nstallaton n year n=0 ( ) AAI CC,x = Average annual ncrease of the captal cost of x equpment (%) The above equaton refers to any of the aforementoned equpment. In our case, the average annual ncrease of any part of the captal cost s assumed to be 3%. These costs of replacement wll have to be taken nto account n the calculaton of the cash flows of the nstallaton. The runnng costs of the nstallaton nclude the cost of fuel used by the bolers, the cost of electrcty used by the pumps, the salares of workers, the carbon taxes and other mnor costs. The calculaton of these costs for the frst year of operaton wll be shown, and then the calculaton of ther values n the next years whch are necessary for the cash flows wll be explaned. The total fuel used over the year as well as the total electrcty used by the pumps has been calculated n Chapter 4. Then, for the calculaton of the unt cost for gas, whch s the fuel used and electrcty, ther hstorc prces for non-domestc users are used. These hstorc prces were found on the webste of the Department of Energy and Clmate Change of the UK 3. A chart of these prces s ncluded n Appendx D. Then, the values for 2013 have been used as unt costs for gas and electrcty. So, the ntal runnng costs of the fuel and electrcty are calculated, respectvely, as: RC f 0 = M f,tot C u,f (5.10) RC 0 el = E el,tot C u,el (5.11)

188 Where: RC 0 f, RC 0 el = Annual runnng cost of fuel and electrcty n year n=0 ( ) M f,tot = Total mass of fuel used by the peak-up bolers per year (kg) E el,tot = Total electrcty used by the pumps per year (kwh) C u,f = Unt cost of fuel ( kg ) C u,el = Unt cost of electrcty ( kwh ) The salares of workers are qute case-specfc, so n our case these are assumed based on an average salary of 2500 per month. Then, the cost of carbon taxes s assumed to be 15 per tonne of CO2 emtted n the envronment. The latter wll be calculated n a followng secton. So, the ntal runnng cost of carbon taxes s calculated as: RC 0 ct = 15 M CO2,tot (5.12) Where: 0 RC ct = Annual runnng cost for carbon taxes n year n=0 ( ) M CO2,tot = Annual CO2 emssons of the nstallaton (tn) In the above equaton, the total mass of CO2 emtted has to be used (n tonnes). Ths value wll be calculated n secton Fnally, the other runnng costs nclude any other costs that mght occur durng the operaton of the nstallaton and are assumed to be equal to for every case. Therefore, the total ntal runnng cost of the nstallaton s calculated by the followng equaton: 0 RC tot = RC 0 f + RC 0 el + RC 0 w + RC 0 0 ct + RC ot (5.13) Where: 0 RC tot = Total annual runnng cost of the nstallaton n year n=0 ( ) RC 0 0 w, RC ot = Annual runnng costs of workers and others n year n=0 ( ) As mentoned earler, the nstallaton s assumed to be operatng from year n=1 onwards. So, the runnng costs used n the calculaton of the cash flows wll be calculated from that year and after, although the ntal runnng costs wll be used n the calculaton of some economc ndces as wll be seen later. Therefore, an average annual ncrease for 186

189 each part of the runnng cost wll be consdered and ts value after n years wll be calculated by an equaton smlar to Eq. (5.9). RC x n = RC x 0 (1 + AAI RC,x ) n (5.14) Where: n RC x = Annual runnng cost of x knd n year n ( ) 0 RC x = Annual runnng cost of x knd n year n=0 ( ) AAI RC,x = Average annual ncrease of the runnng cost of x knd (%) So, an average annual ncrease for each part of the runnng cost has to be consdered. For the case of the fuel, the charts of ts hstorc prces s used as happened for the calculaton of ts unt prces that was used n Eq. (5.10). In ths case, the unt prce of fuel over the last ten years s consdered and ts annual ncrease from year to year s calculated. Then, the average of these annual ncreases s calculated and s assumed that the annual ncrease from now onwards wll be equal to ths average annual ncrease of the prevous ten years. Exactly the same process s followed for the calculaton of the average annual ncrease of the electrcty cost. The average annual ncrease of the salares of workers s assumed to be 2.5%, whle the average annual ncrease of other runnng costs s assumed to be equal to the dscount rate, whch n our case s assumed to be 5%. Fnally, the cost of the carbon taxes s assumed to be constant over the years, as there s no certanty over ts evoluton n the future. So, ts average annual ncrease wll be 0% Calculaton of ncome The ncome n ths study conssts of the followng three parts: A fxed cost per day whch guarantees a certan ncome and s used for the repayment of the ntal captal cost. For each case, t s fxed n such a value so that the ntal captal cost s repad wthn 10 years. A varable cost whch depcts the real consumpton of energy. As a base case for ths research, the varable cost s fxed at 0.02/kWh of heatng provded. 187

190 A fnancal ncentve recently establshed n the UK, the so-called RHI (Renewable Heat Incentve), whch provdes 0.05/kWh of renewable heat provded. Ths value ncreases by 2.5% each year and the ncentve s provded for the frst 20 years of operaton of the nstallaton. So, the ncomes of the nvestment n year n=0 are calculated by the followng equatons: 0 IC tot = IC fx + IC var + IC RHI (5.15) IC 0 fx 10 1 CC 0 tot (1 AAI ) hp (5.16) 0 0 IC var = AHD C hp,u (5.17) 0 IC RHI = AHD G 0.05 (5.18) Where: 0 IC tot = Total ncome of the nvestment n year n=0 ( ) IC 0 fx, IC 0 0 var, IC RHI = Fxed, varable and ncome from the RHI n year n=0 ( ) AAI hp = Average annual ncrease of the prce of heatng (%) 0 C hp,u = Unt prce of heatng n year n=0 ( kwh ) AHD = Annual heat demand (kwh) AHD G = Annual heat demand covered by geothermal energy, whch s calculated n secton (kwh) It s recalled that the nstallaton wll start operatng at year n=1, so the ncomes wll also start from ths year onwards. The calculaton of the above values s takng place only for computatonal purposes and n order to make the followng calculatons easer. As mentoned before, the fxed cost s calculated on the bass of repayng the ntal captal cost n 10 years. By observng Eq. (5.16), t s seen that the counter n the denomnator starts from =1. Ths happens because the nstallaton starts operatng n year n=1, so the revenue wll start from that year, as stated prevously. Furthermore, t s seen 188

191 that n order to get the value of the fxed cost, a smple dvson by the number of years s not made, but an average annual ncrease n the heatng prce s taken nto account. Ths happens, because the prce of heatng should ncrease every year n order to compensate for the ncrease n the expendture and general year-on-year nflaton. So, the fxed cost wll ncrease over the followng years wth an average annual ncrease of the heatng prce whch, n our case, s assumed to be 3% lower than the average annual ncrease of the fuel. The same average annual ncrease wll also apply to the varable cost of heatng. Fnally, as mentoned before, the ncome from the RHI subsdy wll ncrease by 2.5% each year. So, the ncome of the nvestment the followng years wll be gven by the followng equatons: IC n tot = IC n fx n + IC var n + IC RHI (5.19) IC n fx = IC 0 fx (1 + AAI hp ) n (5.20) n IC var 0 = IC var (1 + AAI hp ) n (5.21) If n 20: n 0 Then: IC RHI = IC RHI ( ) n } (5.22) n Else: IC RHI = 0 AAI hp = AAI RC,f 0.03 (5.23) Where: n IC tot = Total ncome of the nvestment n year n ( ) IC 0 fx, IC 0 0 var, IC RHI = Fxed, varable and ncome from the RHI n year n ( ) AAI RC,f = Average annual ncrease of the runnng cost of fuel (%) Calculaton of the fnancal ndces Intally, the comparson between the studed and the tradtonal case of a geothermal dstrct heatng system wll be based on the comparson of several fnancal ndces of each case. The calculaton of the necessary captal and runnng costs has been done n the 189

192 prevous secton. The defntons and explanatons of the followng economc ndces were well summarsed n Chapter 2. The frst fnancal ndex used s the levelsed cost of heatng (LCH),.e. the mnmum prce that heat should be sold to the consumers n order to have a feasble nvestment and s equvalent to the unt cost of energy (UCE) descrbed n Chapter 2. Ths s calculated by Eqs. (2.35) and (2.36) properly formulated for our problem as follows: LCH = CC 0 tot CRF+RC tot AHD (5.24) CRF = IR 1 (1+IR) N (5.25) Where: LCH = Levelsed cost of heatng ( kwh ) CRF = Cost recovery factor (Dmensonless) In Eq. (5.24), the whole captal cost should be ncluded, takng nto account both the ntal captal cost as well as the cost of replacement of any unts n the future, as explaned earler. For that purpose, no temporal superscrpt has been assgned to ths varable. The captal cost of the next years should be reduced n current values through the dscount rate. So, the total captal cost that wll be used n Eq. (5.24) s calculated through the followng equaton: CC tot nn n CCtot n (5.26) n0 (1 DR) Where: DR = Dscount rate (Dmensonless) Then, the runnng cost of year n=0 s also used n the numerator of Eq. (5.24). So, t s seen that the values of the total captal cost and of the runnng cost both n year n=0 are used for the calculaton of the levelsed cost of heatng. Furthermore, the cost recovery factor s used n Eq. (5.24) n order to break down the captal cost over the whole nvestment perod. As can be observed n ths equaton, the runnng cost of one year, and 190

193 more specfcally of year n=0, s used. Ths s the only case where the runnng cost of year n=0, whch does not exst n realty, wll be used. Furthermore, the captal cost that refers to one year has to be used also. Although the total captal cost s all spent n specfc years of the nvestment, and manly n year n=0, t actually refers to all the years of operaton and, theoretcally, has to be re-pad n these years. Therefore, the cost recovery factor s mplemented so that both the captal and the runnng costs refer to one year of operaton of the nstallaton. The levelsed cost of heatng cannot provde useful nformaton for one nvestment, but for the comparson between two or more nvestments. When comparng two or more nvestments, the nvestment wth the lower levelsed cost s the more feasble one, as a lower levelsed cost ndcates that ths nvestment can be equally feasble wth the other one even f the heat s sold cheaper. In other words, for the same sellng prce of heat, the ncome and the benefts of the nstallaton wth lower levelsed cost wll be hgher. The second fnancal ndex that s used s the net present value (NPV) of the nvestment, whch s defned as the summary of the dscounted cash flows over the whole nvestment perod. In other words, the net cash flow s calculated for each year of operaton and the dscount rate s used n order to transform ths n today s value. Then, all these dscounted values are summed together and provde the net present value of the nvestment. So, the net present value s calculated by the followng equatons: For each year of operaton n: NCF n = IC n tot CC n n tot RC tot } (5.27) DNCF n = NCFn (1+DR) n NPV nn n DNCF (5.28) n0 Where: NCF n = Net cash flow n year n ( ) DNCF n = Dscounted net cash flow of year n ( ) In Eq. (5.27) the net cash flow n year n=0 has to be taken nto account also. Theoretcally, f the net present value s postve, ths ndcates that the nvestment s feasble. From another pont of vew, when comparng two nvestments the nvestment 191

194 wth the hgher net present value s the more feasble one. The dscount rate that s used n ths study s assumed to be constant and equal to 5%. The thrd fnancal ndex that s used s the nternal rate of return of the nvestment (IRR). Ths s defned as the dscount rate that nullfes the net present value. So, n ths case, the net present value s set equal to zero n Eq. (5.28) and then ths equaton together wth expresson (5.27) are solved for the dscount rate. So, the nternal rate of return s calculated by the followng expresson. IRR = DR (for NPV = 0) (5.29) In theory, the value of the nternal rate of return when compared wth the current nterest rate can ndcate how feasble an nvestment s. If the IRR s hgher than the nterest rate, then the nvestment s feasble, whle f t s lower the nvestment s unfeasble. When comparng two or more nvestments, the one wth the hgher IRR s the more feasble and fnancally safe nvestment as t s further from the current nterest rate. The fourth, and fnal, fnancal ndex s the benefts-to-costs rato of the nvestment (BCR). Ths ndex s defned as the sum of the dscounted benefts of each year dvded by the sum of the dscounted captal costs of each year. In the numerator, the benefts are defned as the dfference of the ncome mnus the runnng costs, so the captal costs are not taken nto account there, but only n the denomnator. In other words, the benefts-to-costs rato s the rato of the earnngs to the captal expendtures. Therefore, the BCR s calculated by the followng expressons: For each year of operaton n: ABF n = IC n n tot RC tot } (5.30) DABF n = ABFn (1+DR) n For each year of operaton n: DCC n = CC n tot } (5.31) (1+DR) n 192

195 BCR nn n0 nn n0 DABF DCC n n (5.32) Where: ABF n = Annual benefts n year n ( ) DABF n = Dscounted annual benefts n year n ( ) DCC n = Dscounted captal cost n year n ( ) The benefts-to-costs rato can ndcate ether f one nvestment s feasble or not, but t can also ndcate whch nvestment f more feasble among two or more nvestments. For an nvestment to be feasble, the benefts-to-cost ratos has to be hgher than 1,.e. the net benefts to be hgher than the captal expendtures. When comparng two or more nvestments, the nvestment wth the hgher value of the benefts-to-costs rato s more feasble as t ndcates hgher values of benefts. In ths secton, the calculaton of four dfferent fnancal ndces that can ndcate f the proposed soluton s more feasble than the tradtonal case from an economc pont of vew was explaned. As mentoned before, all the ndces have the capablty to show whch of the two cases s more feasble, whle the NPV, the IRR and the BCR can also show f an nvestment s feasble, n general, or not wthout comparng both of them. For example, f the values of the IRR for the two cases are 1% and 2%, respectvely, ths ndcates that the second case s more feasble than the frst one, but n realty, both these values are lower than the current nterest rates (around 6% or more). So, none of these nvestments are feasble. Therefore, not only a comparson between the two cases should be made, but the values of these ndces should also ndcate that the nvestments are feasble. Furthermore, t should be mentoned that the IRR, the BCR and, partally, the LCH provde qualtatve nformaton about the nvestment, and not quanttatve. In other words, ther values are ndependent of the sze of the nvestment. Two nvestments wth completely dfferent captal costs and ncomes can have the same values of the above ndces. Only, the NPV provdes quanttatve nformaton about the nvestment and s a very good ndcator of the economc sze of the nvestment. Fnally, these ndces are used snce they can ndcate the more feasble of two possble nvestments; however, f the results are close one another, then one of the ndces mght not depct the truth. So, all of them are used together n order to obtan more robust results. 193

196 Cash flows of the nvestment The cash flow of an nvestment s a graph whch depcts the monetary value of the nvestment at each specfc perod over tme. It ncludes all the expendture that occurs from the constructon and durng the operaton of the nstallaton,.e. all the captal and runnng costs, as well as the ncome. In order to calculate the cash flow of an nvestment the followng steps have to be mplemented: The captal and the runnng costs of the nstallaton are calculated for each year of operaton. In our case, ths has been carred out wth Eqs. (5.1)-(5.9) and (5.10)-(5.14), respectvely. The total ncome s calculated for each year of operaton through Eqs. (5.15)- (5.23). Both the ncome and the aforementoned costs are calculated on ther real value at the specfc year and are not dscounted. The net cash flow for each year of operaton s calculated by reducng the captal and runnng costs of each year from the total ncome. Fnally, the cumulatve net cash flow s calculated for each year and ths result s plotted aganst tme. So, snce the captal and runnng costs as well as the total ncome are calculated for each year, the followng equatons are appled for the calculaton of the cash flow of the nvestment: NCF n = IC n tot CC n tot n RC tot (5.33) For each year of operaton from 1 to n: CNCF n = CNCF n 1 + NCF n } (5.34) Where: CNCF n = Cumulatve net cash flow n year n ( ) As seen above, Eq. (5.34) s vald from year n=1. Ths happens because, obvously, f t was appled n year n=0, the calculaton of the cumulatve net cash flow n year n=-1 would be necessary. Ths value does not exst, so the cumulatve net cash flow n year n=0 s calculated as: 194

197 CNCF 0 = NCF 0 0 = CC tot (5.35) So, by applyng Eqs. (5.33)-(5.35), the cumulatve net cash flow has been calculated and the cash flow graph can be drawn. At ths pont, t s very mportant to note, that n year n=0 that the nstallaton s theoretcally constructed, there are nether runnng costs nor any ncome. Therefore, the net cash flow n year zero s calculated by the proper form of Eq. (5.33) as shown n the second part of Eq. (5.35), where only the ntal captal cost s taken nto account Envronmental analyss In ths secton, the methodology that has to be carred out for the envronmental analyss of the nstallaton wll be shown. Because the man scope of ths Chapter s to compare the proposed soluton wth the tradtonal case only, the local envronmental mpact,.e. the local emssons, wll be taken nto account. It s assumed that the emssons durng the constructon of the nstallaton as well as of ts spare parts wll be roughly the same between the two cases. So, only the emssons durng the operaton of the nstallaton wll be taken nto account. These emsson are assumed to arse from the followng three sources: Combuston of fossl-fuel n the peak-up bolers. Electrcty used by the pumps. Emssons by the geothermal producton tself. The emssons by the geothermal producton are assumed to be neglgble (Rybach, 2003, amongst others), whle the emssons from the electrcty used by the pumps are not taken nto account. The latter s because, as shown n Chapter 4, the amount of electrcty used both n the proposed and n the tradtonal case s almost the same. So, the emssons that wll arse by the use of electrcty wll be roughly the same between the two cases. Snce the scope of ths Chapter s to do, manly, a comparson between the two cases and not wth other technologes, these emssons wll not be taken nto account. Therefore, the emssons of the nstallaton wll nclude only the emssons from the combuston of the fuel n the peak-up bolers. 195

198 In general, the emssons that arse from the combuston of a fuel (fossl or not) depend manly on the composton of the fuel and, secondly, on the excess ar and the condtons of the combuston. In our case, the followng assumptons are made: The fuel used s natural gas, whch conssts 100% from methane. The ar-to-fuel rato s above the stochometrc value requred for ths combuston. Therefore, all the methane s combusted and there s no methane n the exhaust gases. The combuston s perfect and snce the fuel s methane, the only drect emsson s carbon doxde (CO2), whle there are no other carbon or sulphur oxdes n the exhaust gases. The other substances contaned n the exhaust gases wll be water, ntrogen and possbly some oxygen whch are not pollutants. The peak-up bolers operate wth NOx elmnaton technologes and, therefore, the NOx wll be neglected. So, the only emssons of the nstallaton that wll be taken nto account are the carbon doxde emssons that occur durng the combuston of methane. The combuston of methane n excess ar obeys the followng smplfed formula: CH O 2 CO H 2 0 (5.36) By applyng, the analogy of moles between the methane combusted and the produced carbon doxde n the above formula, then for 1 mole of methane combusted there s 1 mole of produced carbon doxde. Then, n order to convert ths analogy nto analogy of masses, the molecular weght for methane and carbon doxde have to be used. The molecular weghts of these two substances have the followng values 4 : M r,ch4 = (5.37) M r,co2 = (5.38) The unts n the molecular masses are grammars per mole of the substance. In other words, 1 mole of methane s equal to grammars. Therefore, by applyng the

199 molecular masses shown above to the mole analogy, we can get the mass analogy through the followng reasonng path: 1 mol of CH 4 = 1 mol of CO gr of CH 4 = gr of CO 2 1 gr of CH 4 = = gr of CO 2 1 kg of CH 4 = kg of CO 2 } (5.39) So, wth the above expresson t s shown that for each klogram of methane combusted, there wll be klograms of carbon doxde emtted n the atmosphere. The total amount of fuel used n each case has been calculated n Chapter 4. So, the total annual emssons of carbon doxde can be easly calculated by the followng equaton: M CO2,tot = M f,tot (5.40) Ths wll be the only pollutant from the whole process that wll be taken nto account for the comparson of the two cases Energetc ndces of the nstallaton In ths secton, the way of calculatng two energetc ndces of the nstallaton wll be explaned. These two ndces are the load factor (LF) of the nstallaton and the fracton of the annual heat demand that s covered by geothermal energy (ε G ). The load factor s defned as the proporton of the average geothermal mass flow rate throughout the year to the maxmum avalable geothermal flow rate. So, ths ndex s calculated by the followng equaton: LF = m G m G,max (5.41) Where: m G = Average geothermal flow rate ( kg ) s m G,max = Maxmum avalable geothermal flow rate ( kg s ) The numerator of the above equaton has been calculated n Chapter 4, through the applcaton of the algorthm of the annual operaton. The denomnator s calculated n 197

200 Chapter 3, Table 3.2, and s the geothermal flow rate of the desgn-day for each case of szng of the nstallaton. The maxmum avalable geothermal flow rate can also be calculated as the product of the number of producton wells by the mass flow rate of one well. m G,max = N wells m well (5.42) So, wth these equatons the load factor of the nstallaton can be easly calculated. As observed by Eq. (5.41), the load factor ndcates how close the operaton of the nstallaton s to the full load operaton. A hgh value of load factor shows that the nstallaton s workng on average close to the full load. In geothermal energy, as well as n the other renewables, t s desrable for the operaton to be as close as possble to the full load, as n ths way the maxmum utlsaton of the source s acheved. For renewable energes, whch n general have a very low runnng cost, t s of the utmost mportance to obtan the maxmum potental of the source, snce t s usually rather expensve to buld the nstallaton. So, snce the expensve nstallaton s bult, the maxmum use of the source s desred. The second energetc ndex of the nstallaton s the fracton of the annual heat demand that s covered by geothermal energy to the total annual heat demand. E G = AHD G AHD (5.43) It should be noted that n the above equaton, the values of the heat demand over the whole year are used, n contrast to Eq. (4.29) where the equvalent values for the studed day are used. The denomnator of the above equaton can be easly calculated as the summary of the heat demand over the whole year whch s a basc nput of the whole study. Ths value s ndependent of the case of szng, as t obvously depends on the heat users only, and s always constant. In our case, the total annual heat demand s equal to: AHD = kwh (5.44) For the calculaton of the annual heat demand that s covered by geothermal energy, the calculaton of the annual heat demand that s covered by the peak-up bolers s necessary. The total amount of fuel that s used n the peak-up bolers throughout the year has been 198

201 calculated for each case n Chapter 4. Then, the heat provded by the combuston of the fuel to the network s calculated by the followng equaton: Q f,tot = M f,tot LHV f η b (5.45) Where all the varables have been explaned n Chapter 4. The thermal effcency of the boler s assumed to be constant and equal to 88%, whle the lower heatng value of the fuel wll always be known by the composton of the fuel. A part of ths heat wll reach the end users and wll be the part of the annual heat demand that s covered by the peak-up bolers. Ths s defned by takng nto account all the possble heat losses from the bolers to the end users. As mentoned earler n ths thess, t s assumed that the peak-up bolers are very close to the substaton. So, any possble heat losses n the transmsson network are neglected. Furthermore, t s assumed that the heat losses n the substaton are also neglgble. So, the only heat losses that have to be taken nto account are those n the dstrbuton network. For that purpose, the followng effcences for each branch of the supply and return dstrbuton ppelnes, respectvely, are defned: η d,s,j = T d,s,o,j T a T d,s,,j T a (5.46) η d,r,j = T d,r,o,j T a T d,r,,j T a (5.47) Where: T d,s,o,j, T d,s,,j, T d,r,o,j, T d,r,,j = Supply/return outlet and nlet temperatures of ppelne j, respectvely (K) By the two above equatons, the effcences of the supply and return ppelnes of each branch of the dstrbuton network are calculated. In our case, for the sake of smplcty an average thermal effcency of the supply and return ppelnes wll be used. These are calculated as follows: η d,s = average(η d,s,j ) (5.48) 199

202 η d,r = average(η d,r,j ) (5.49) The above two average effcences account for all the heat losses that occur from the bolers to the end-users. The thermal effcency of the bolers has already been taken nto account n Eq. (5.45). A fnal factor that has to be taken nto account for the calculaton of the heat demand that s provded by the peak-up bolers s the thermal effcency of the nhouse nstallaton. Ths thermal effcency s consdered to be constant for each case and equal to 92%. Eventually, the annual heat demand that s covered by the peak-up bolers wll be calculated as: AHD pb = Q f,tot η d,s η d,r η dw (5.50) Fnally, the annual heat demand that s covered by geothermal energy can be easly calculated by reducng the annual heat demand that s covered by the peak-up bolers from the total annual heat demand. AHD G = AHD AHD pb (5.51) So, by applyng Eqs. (5.43)-(5.51) the fracton of the total heat demand that s covered by geothermal energy can be calculated. It s easly understood that the hgher possble value of ths fracton s desred, because ths would mean the maxmum contrbuton of geothermal energy to the heat demand coverage and the mnmum contrbuton (or usage) of the peak-up bolers. In ths secton, the calculatons for two basc ndces that wll be used for the energetc evaluaton of the nstallaton have been shown. These ndces are the load factor and the fracton of the heat demand that s covered by geothermal energy. It s desrable for both of these factors to attan the maxmum possble value. For the load factor, ths would ndcate that the nstallaton s operatng as close as possble to ts full load, whch s always somethng desrable for renewable energy sources, whle for the fracton ths would ndcate that the contrbuton of geothermal energy to the heat demand coverage would be maxmsed, wth subsequent mnmsaton of the use of peak-up bolers. 200

203 5.3 Results In ths secton, the results of the economc, envronmental and energetc analyss of the studed case as well as of the tradtonal operaton of the nstallaton wll be shown for each case of szng. The economc results wll be shown both for the case that the RHI (Renewable Heat Incentve), whch s a fnancal subsdy as explaned before, s ncluded and not. In ths way, t s attempted to hghlght any potental advantages that a fnancal subsdy can have n a renewable project. Intally, n Table 5.1 the unt prces of fuel and electrcty are shown for each case. As mentoned n secton 5.2.1, these prces depend on the amount of fuel and electrcty use, respectvely, so for dfferent cases of szng these can be dfferent. Then, n Table 5.2 the equvalent average annual ncrease of the prces of fuel and electrcty are also shown. All these values are necessary for the next results and are shown here n order to have a complete overvew of the results. In both tables, the results are shown both for the studed and the tradtonal case. Table 5.1 Unt prces of fuel and electrcty for each case of szng Case 25%le 50%le 75%le Operaton wth the storage tank Unt prce of fuel (./kwh) Unt prce of electrcty ( /kwh) Operaton wthout the storage tank Unt prce of fuel ( /kwh) Unt prce of electrcty ( /kwh)

204 Table 5.2 Average annual ncrease of the prce of fuel and electrcty for each case of szng Case 25%le 50%le 75%le Operaton wth the storage tank Average annual ncrease of fuel prce (%) Average annual ncrease of electrcty prce (%) Operaton wthout the storage tank Average annual ncrease of fuel prce (%) Average annual ncrease of electrcty prce (%) The man ntal captal costs for each case of szng are shown n Table 5.3 both for the studed and the tradtonal case. The correspondng runnng costs n year n=0 for the same cases are shown n Table 5.4. In these and the rest of ths secton, the studed case of usng the heat storage wll be assgned wth the abbrevaton W, whle the tradtonal case wthout the heat storage wll be assgned wth the abbrevaton Wo. Table 5.3 Man ntal captal costs of the studed and the tradtonal case for each case of szng 0 CC dr 0 CC HST 0 CC pb 0 CC 0 np CC tot 25%le W %le Wo %le W %le Wo %le W %le Wo

205 Table 5.4 Man ntal runnng costs of the studed and the tradtonal case for each case of szng RC f 0 0 RC el 0 RC tot 25%le W %le Wo %le W %le Wo %le W %le Wo Then, the results of the fnancal ndces of the nvestment are shown n Tables 5.5 and 5.6 for the cases that the RHI s taken nto account and not. In both tables, the results are shown for each case of szng and both for the studed and the tradtonal case. It should be noted that the levelsed cost of heatng does not depend on the RHI, snce the ncome of the nvestment s not taken nto account for ts calculaton, so t has the same value ether f the RHI s taken nto account or not. As can be seen n these tables and wll be explaned further n the next secton, the NPV, the IRR and the BCR are negatve for the low szng of the nstallaton whch means that the nvestment s not feasble. For that purpose, the cash flows wll be shown for ths case, but only for the other two cases of szng. These cash flows are shown on Fgs. (5.1)-(5.4). Table 5.5 Fnancal ndces of the studed and the tradtonal case (RHI ncluded) LCH ( /kwh) NPV ( 10 6 ) IRR (%) BCR (-) 25%le W <0 <0 <0 25%le Wo <0 <0 <0 50%le W %le Wo %le W %le Wo

206 Table 5.6 Fnancal ndces of the studed and the tradtonal case (RHI not ncluded) LCH ( /kwh) NPV ( 10 6 ) IRR (%) BCR (-) 25%le W <0 <0 <0 25%le Wo <0 <0 <0 50%le W %le Wo %le W %le Wo Fgure 5.1 Cash flow of the nvestment wth the RHI subsdy (25%le szng) 204

207 Fgure 5.2 Cash flow of the nvestment wthout the RHI subsdy (25%le szng) Fgure 5.3 Cash flow of the nvestment wth the RHI subsdy (50%le szng) 205

208 Fgure 5.4 Cash flow of the nvestment wthout the RHI subsdy (50%le szng) Fgure 5.5 Cash flow of the nvestment wth the RHI subsdy (75%le szng) 206

209 Fgure 5.6 Cash flow of the nvestment wthout the RHI subsdy (75%le szng) Fnally, the results of the envronmental and energetc analyss both for the studed and the tradtonal case and for each case of szng are shown n Table 5.7. Table 5.7 Results of the envronmental and energetc analyss of the nstallaton Annual CO2 emssons (kg) Load factor (%) Proporton of heat demand covered by geothermal energy (%) 25%le W %le Wo %le W %le Wo %le W %le Wo

210 5.4 Dscusson The frst mportant observatons of ths Chapter arse from Tables 5.1 and 5.2 n whch the unt prce of fuel and electrcty as well as ther average annual ncreases are shown for each case of szng both for the studed and the tradtonal case. Frstly, t s observed that these values can be dfferent between some cases because, as mentoned before these values depend on the annual use of fuel and electrcty, respectvely. Furthermore, t s seen that dscrete values are obtaned only and do not le n a contnuous range of values. If the annual use of ether fuel or electrcty les wthn a specfc range, then ts unt prce and ts average annual ncrease wll get a specfc value defned by the hstorcal data. Secondly, t s observed that as the szng of the nstallaton ncreases both the unt prce of fuel and electrcty ncrease too. As t was shown n Chapter 4, both the use of fuel and electrcty decrease as the szng of the nstallaton ncreases. These denote, n smple words, that when more fuel or electrcty s used, then ts prce decreases, whch s ntutvely sensble from a market pont of vew. Thrdly, t s observed that as the szng of the nstallaton ncreases, the average annual ncrease of fuel and electrcty prces both have a decreasng trend. So, under the same reasonng as prevously, ths shows that when more fuel or electrcty s used, ts average annual ncrease rses, whch has an opposng trend to ts unt prce. In other words, when more fuel or electrcty s bought, ts prce s lower but ts average annual ncrease wll be hgher. Obvously, these observatons apply both for the studed and the tradtonal case. The man captal costs of the nstallaton can be seen n Table 5.3 from whch mportant conclusons can be drawn both for cases of dfferent szng as well as between the studed and the tradtonal case for the same szng of the nstallaton. Frstly, t can be observed that both the captal cost of drllng and the captal cost of the ppelnes s exactly the same between the studed and the tradtonal case for the same case of szng. Ths s totally expected, as between the studed and the tradtonal case the only dfferences are the use of the heat storage under a dfferent operatonal strategy, whle the rest of the nstallaton s the same. So, the number of wells and the ppelnes, and subsequently ther captal cost, wll be exactly the same between these cases. Secondly, t s seen that as the szng of the nstallaton ncreases, both the captal cost of drllng and the captal cost of the ppelnes ncrease. These are also expected because, as seen n Chapter 3, a larger szng of the nstallaton requres more wells to be drlled, whch of course ncreases the total cost of drllng, whle on the other hand, a larger szng of the nstallaton denotes hgher mass 208

211 flow rates and, subsequently, bgger ppelnes whch are requred to compensate wth these hgher flow rates. The latter obvously leads to an ncreased captal cost for the ppelnes and s n agreement wth the results of Chapter 3 concernng the sze of the ppelnes. Thrdly, t s noted that for the same case of szng, the cost of the heat storage tank s obvously hgher n the studed case, snce n the tradtonal case there s no heat storage and ts cost s zero. Furthermore, t can be seen that as the szng of the nstallaton ncreases, the cost of the heat storage tank ncreases. The latter s also expected because the larger szng of the nstallaton requres bgger heat storage, as can be dentfed from Chapter 3, whch ncreases ts captal cost. Fourthly, the cost of the peak-up bolers has a decreasng trend as the szng of the nstallaton ncreases and s also smaller for the studed case. Both of these results are n agreement wth the results of the sze of the peakup bolers shown n Chapter 4. Takng nto account these results and the fact that the cost of the bolers s assumed to be drectly proportonal to ther sze, then the mpacts on ther cost shown n Table 5.3 are justfed. Furthermore, t can be observed that as the szng of the nstallaton ncreases, the total captal cost ncreases whch s sensble takng nto account the prevous observatons and the fact that larger szng denotes bgger nstallaton and, subsequently, hgher captal cost. Fnally, the most mportant observaton of Table 5.3 s the fact that for the same case of szng, the total captal cost wll be hgher n the tradtonal case than n the studed case. So, the studed case has a lower captal cost compared to the tradtonal case, although the extra cost of the heat storage tank s taken nto account. Ths happens, manly, because of the hgher captal cost of the peak-up bolers n the tradtonal case, whch offsets the dfference due to the heat storage. Then, n Table 5.4 the annual runnng costs of the nstallaton for each case are shown. It s observed that the cost of fuel for the same case of szng s hgher for the tradtonal case n whch the heat storage s not used, whle ths cost decreases as the szng of the nstallaton ncreases. Both these observatons are expected takng nto account the mass of fuel used for each case as shown n Tables 4.5 and 4.6, respectvely, and the fact that the cost of fuel s proportonal to ts total amount used. Furthermore, t s shown that for the same case of szng the cost of electrcty s almost the same between the studed and the tradtonal case, whle the cost of electrcty decreases as the szng of the nstallaton ncreases. Ths s also expected for the same reasons as for the cost of fuel. Takng ths nto account, the fact that the total runnng cost decreases as the szng of the nstallaton ncreases s totally sensble. Fnally, t s shown that for the same case of szng the total runnng cost wll be lower n the studed case. So, a frst major concluson of ths Chapter 209

212 s that both the captal and the runnng costs wll be lower for the studed case than for the tradtonal case of operaton of a geothermal dstrct heatng system. The man fnancal ndces of the nvestment for each case of szng are shown n Tables 5.5 and 5.6 for the cases that the RHI subsdy n taken nto account and not, respectvely. These two tables hghlght some very mportant drawbacks. Frstly, t s shown that for the same case of szng all the fnancal ndces mprove when the heat storage s used. More specfcally, the levelsed cost of heatng decreases, whle the NPV, the IRR and the BCR all ncrease. For example, the dfference n the RHI denotes an ncreased potental annual ncome of dependng on the case of szng. The maxmum ncrease n annual ncome s for the medum case of szng, whch denotes that the best mprovement n the fnancal performance occurs n ths case. The second nterestng drawback hghlghted by these tables s the nfluence of the szng of the nstallaton on the fnancal vablty of the nvestment. It can be seen, that all the fnancal factors mprove when the szng of the nstallaton ncreases. Ths happens manly because, as wll also be seen later, a larger szng of the nstallaton ndcates that more geothermal energy s used to cover the heat demand, whch subsequently leads to ncreased ncome from the RHI ncentve. Another factor that causes the hgher vablty of the larger szng are the lower runnng costs n ths case, whch ncrease the net annual ncome of the nvestment. So, t can be sad that f there s no restrctng factor such as non-favourable geologcal condtons, the geothermal nstallaton should be szed on the maxmum possble szng, even f the heat storage mpacts most affect the medum szng, as shown prevously. A thrd really mportant observaton whch arses from the comparson of Tables 5.5 and 5.6 s the nfluence of the RHI subsdy n the vablty of the nvestment. As t can be clearly seen, all the fnancal ndces mprove a lot when the RHI s taken nto account. For example, the NPV can ncrease up to 84%, the IRR can ncrease up to 87%, whle the BCR can ncrease up to 56% when the RHI s taken nto account. The only fnancal ndex whch remans the same s the levelsed cost of heatng whch does not depend on the RHI. Therefore, these results defntely prove the tremendous mpact of a fnancal subsdy n a renewable project. Up to ths pont, the dscusson was focused on whether the studed case s more vable than the tradtonal case. By observng these two tables, t can also be seen f each nvestment alone s feasble or not. It can be seen that the nvestment s not vable for the 210

213 lower szng of the nstallaton ether f the RHI s taken nto account or not, because the NPV, the IRR and the BCR are all negatve. Ths defntely ndcates that ths nvestment s not vable. A further nvestgaton on the vablty of ths nvestment wll be carred out on the next secton n whch two solutons whch can mprove ts vablty wll be examned. For the cases of larger szng, t can be seen that the nvestments are defntely vable for the case that the RHI s taken nto account, whle for the case that the RHI s not taken nto account the vablty or, more properly sad, the economc attractveness of the medum szng s somehow questonable. Ths happens because of the values of the IRR shown. As mentoned before, the value of the IRR has to be hgher than the current nterest rate of the market. In our case, ths s defntely the case. But n practce, the values of the IRR have to be typcally hgher than 15% n order to have greater securty and n order to take nto account any non-predcted factors that can nfluence the nvestment. So, although ths case s defntely vable as the results show, t mght not be very attractve for nvestors. For the case of the larger szng of the nstallaton, the nvestment s vable and very attractve even when the RHI s not ncluded. In general, t can be stated that the nvestment s feasble for the medum and the large szng of the nstallaton and the feasblty s greatly enhanced wth the ncluson of the RHI subsdy. All these observatons concernng the fnancal feasblty of the nvestments, are also depcted n Fgs n whch the cash flows of each nvestment are shown. As expected, the cash flow for the lower szng of the nstallaton wll have negatve values as shown n Fgs. 5.1 and 5.2 snce the nvestment s not vable. Then, t s observed that for each case of szng, the studed case s more vable as the monetary flow s hgher at each tme. The fact that the storage mpacts most the medum szng s also observed as the dfference between the two lnes s bgger n ths case compared to the larger szng case. The change n the nclnaton n the 20 th year of the nvestment occurs, frstly because the RHI stops beng provded after that year, as explaned n the methodology secton, and secondly n ths year the peak-up bolers are replaced. The latter are a relatvely expensve tem as seen n Table 5.3, so ths change n nclnaton s justfed even n the cash flows where the RHI s not taken nto account. Furthermore, the nfluence of the RHI s also made clear through these cash flows as t can be seen that the monetary values are much hgher when the RHI s taken nto account. Fnally, t can be seen that the pay-back perod of the nvestment s qute low when the RHI s taken nto account, whle t ncreases a lot when t s not taken nto account, although these pay-back perods can stll be regarded as very acceptable. More specfcally, the pay-back perod s around 4 and 3 years for the medum and larger szng of the nstallaton, respectvely, when the RHI s taken nto 211

214 account, whle the same values are around 7-8 and 6 years, respectvely, when the RHI s not taken nto account. The latter shows agan the nfluence of the RHI and the fact that the nvestment wth the larger szng has the hgher vablty as mentoned before also. Concernng the annual CO2 emssons of the nstallaton, t can be seen n Table 5.7 that these decrease when the heat storage s used for every case of szng. Ths s totally expected, snce the emssons are drectly proportonal to the mass of fuel used and, as t was shown n Chapter 4, ths decreases when the heat storage s used. The relatve decrease of the emssons n the lower case of szng s small snce, as mentoned before, almost all the geothermal producton s sent drectly to the heat load and, therefore, the change n the operaton of the peak-up bolers, and subsequently ther emssons, wll not be very hgh. On the other hand, the hghest absolute decrease of the emssons s for the medum case of szng, whch ndcates agan that the storage mpacts are greatest n ths case. An nterestng observaton s also that the hghest relatve decrease of the emssons s for the larger case of szng, where the absolute decrease s around 50%. But, n ths case, the emssons are relatvely low anyway, so t can be ndeed stated that the medum case of szng s mpacted more. It can also be observed that as the szng of the nstallaton ncreases, the emssons wll decrease as the amount of fuel used wll also decrease. Snce the szng of the nstallaton ncreases, more geothermal energy and less fuel are used, so the emssons wll decrease. As for the load factor of the geothermal part of the nstallaton, t can be seen n Table 5.7 that t ncreases when the heat storage s used. Ths ndcates that when the heat storage s used, the geothermal part of the nstallaton operates at a hgher average flow rate, thus ncreasng the utlzaton of geothermal energy compared to the tradtonal case of operaton. On the other hand, t s also shown that the load factor decreases as the szng of the nstallaton ncreases. Ths happens because, as the szng of the nstallaton ncreases, the potental geothermal producton also ncreases, so there can be many tmes over the year that the heat demand can be covered just by a part of the geothermal producton. In other words, more geothermal energy that s avalable for the same overall heat demand as the szng ncreases, so the smaller the fracton of t that wll be used to cover the same heat demand. In the lower case of szng, the potental geothermal producton s low, so almost all the geothermal producton s sent drectly to the heat demand. For example, n our case, the load factor s % when the heat storage s used, whch means that the geothermal nstallaton s workng very close to ts full capacty all over the year. 212

215 Fnally, n Table 5.7 the proporton of the total heat demand that can be covered by geothermal energy s shown. It s observed that when the heat storage s used, a hgher proporton of the heat demand s covered by geothermal energy. Ths s expected from the prevous results, where t was shown that when the heat storage s appled, more geothermal energy s utlsed and less fuel s used. Ths ndcates that a hgher proporton of the heat demand wll be covered by geothermal energy. Furthermore, as the szng of the nstallaton ncreases, more geothermal energy s avalable, so obvously, a hgher proporton of the heat demand wll be covered by geothermal energy. 5.5 Further nvestgaton on the fnancal vablty of the nvestment As shown n the prevous secton, the case of the lower szng of the nstallaton (25%le case) s not fnancally vable. In ths secton, two potental solutons n order to overcome ths problem wll be examned. The frst of the followng potental solutons and, under certan crcumstances that wll be explaned later n ths secton, the second too, can also be appled n the other cases of szng ether n order to ncrease ther vablty or f these are not vable too. The frst possble soluton that could ncrease the vablty of the nvestment s to ncrease the ncome of the nvestment. The most obvous way to do ths s by ncreasng the varable cost of heatng, whch up to now was prced at 0.02/kWh of heat delvered to the end-users. Practcally, ths value was qute low as n realty the varable cost of heatng s 0.05/kWh or hgher. So, the same analyss whch was explaned n secton wll be appled for hgher values of the varable cost of heatng. In ths case, only the curves for the studed case wth the use of the heat storage wll be shown as t s not attempted to check f t s worthwhle ncludng a heat storage or not, but to check the general vablty of the nvestment. Nevertheless, t was clearly shown n the prevous two sectons that t s fnancally worthwhle ncludng a heat storage n a geothermal dstrct heatng system. The results of ths analyss for the 25%le szng case and for the cases that the RHI s taken and not taken nto account are shown n Fgs. 5.7 and 5.8, respectvely. As expected, the ncrease of the varable cost of heatng can defntely ncrease the vablty of the nvestment. As shown on Fgs. 5.7 and 5.8, the ncrease of the varable cost of heatng ncreases the monetary value of the nvestment n any perod of tme. Furthermore, by comparng these two fgures wth Fgs , t s observed that for the 213

216 lower case of szng a smlar cash flow s acheved at a varable cost of 0.05/kWh when compared to the medum szng and at a varable cost of /kWh when compared to the larger szng of the nstallaton. Ths shows that more than a two-fold ncrease s requred n the lower case of szng to acheve the same cash flow as wth the other cases. Even f not the same cash flow s desrable, t s shown n the two above fgures that the case wth a varable cost of 0.03/kWh s barely vable and not so attractve. Fgure 5.7 Influence of the varable cost of heatng on the cash flow of the nvestment (RHI ncluded- 25%le szng) 214

217 Fgure 5.8 Influence of the varable cost of heatng on the cash flow of the nvestment (RHI not ncluded- 25%le szng) So, the frst vable case s for the varable cost of heatng to be 0.04/kWh whch s double the ntally used value. Although ths value s double compared to the other cases of szng, t remans relatvely low when compared to varable costs that are appled n the tradtonal heatng systems. So, wth ths analyss t was shown that by ncreasng the varable cost of heatng wthn logcal lmts, and usually below the values of tradtonal heatng systems, t can make nvestment feasble. The second soluton that could ncrease the vablty of the nvestment s the decrease of the nvestment expendture. By observng n detal Table 5.3, t can be seen that the total captal cost between the three cases of szng s not very dfferent, especally when takng nto account that ths refers to the whole perod of the nvestment. On the other hand, t s observed n Table 5.4 that the runnng cost s consderably more dfferent between the three cases compared to the captal cost and t s maxmum for the lower case of szng. The runnng cost conssts manly of the cost of fuel and the cost of electrcty used by the pumps, as mentoned before. The cost of fuel cannot be controlled easly as t depends on the heat demand. On the other hand, the cost of electrcty depends manly on the mass flow rate and the dmensons of the ppelnes. Wth the approach followed throughout ths thess, the mass flow rates over the transmsson network depend roughly on the szng of 215

218 the nstallaton, whle those over the dstrbuton network depend on the heat demand. The heat demand s constant for each case of szng, so the mass flow rates on the dstrbuton network wll be roughly the same over the year for each case of szng. It should be noted that ths statement refers to the whole year and not the desgn-day, where (as shown n Chapter 3) the mass flow rates on the dstrbuton network wll obvously be dfferent. So, snce the mass flow rates wll be the same, t seems a sensble choce to ncrease the sze of the ppelnes of the dstrbuton network n order to decrease the frcton losses, and subsequently the cost. Ths change wll ncrease the captal cost of these ppelnes whch s contradctory to the decrease of the runnng cost. Whether ths change mproves the vablty of the nvestment wll be examned below. So, the same analyss wll be carred out for two dfferent cases for the szng of the dstrbuton network. For the sake of smplcty, these two cases wll refer to the szng of the dstrbuton network for the medum and large cases of szng. In other words, the only dfference n the next two studed cases wll only be the sze of the dstrbuton network, whle everythng else (ncludng the number of wells, the sze of the storage tank and the sze of the peak-up bolers) wll be the same as n the lower case of szng. These two cases wll be symbolsed as 25T-50D and 25T-75D, respectvely, n the followng. The graphs of the cash flows for these two cases are shown n Fgs both for the cases that the RHI s ncluded and not ncluded. By comparng these cash flows wth the ones showed n Fgs. 5.1 and 5.2 whch refer to the 25%le szng, both for the transmsson and dstrbuton network, t can be clearly seen that the feasblty of the nvestment ncreases very slghtly n the two new cases. Szng the dstrbuton network for a larger case of szng seems to mprove the feasblty of the nvestment. But ths mprovement s so slght as to be barely vsble n the graphs, and t defntely does not make the nvestment feasble. So, t can be concluded that ths soluton does not mprove the feasblty of the nvestment mportantly and t s thus not recommended. 216

219 Fgure 5.9 Cash flow of the nvestment wth the RHI subsdy (25T-50D szng) Fgure 5.10 Cash flow of the nvestment wthout the RHI subsdy (25T-50D szng) 217

220 Fgure 5.11 Cash flow of the nvestment wth the RHI subsdy (25T-75D szng) Fgure 5.12 Cash flow of the nvestment wthout the RHI subsdy (25T-75D szng) 218

221 By the analyss shown n ths secton, t can be concluded that f a geothermal dstrct heatng system wth or wthout the heat storage s not fnancally vable, the only effectve soluton to that problem s to ncrease the ncome of the nvestment by ncreasng the varable cost of heatng. It was further proved that ths ncrease of the varable cost usually les wthn the margns of the varable cost of alternatve heatng technologes. So, t can be stated that, even f the ntally selected varable cost has to be ncreased, ths technology wll reman compettve to other heatng technologes. Fnally, the effect of a fnancal subsdy n a renewable heat project was once agan hghlghted as t was shown that the nvestment reaches the fnancal attractveness of the cases of larger szng wth a lower varable cost of kWh n the case that the RHI s taken nto account. In other words, f a fnancal subsdy s provded, then the necessary ncrease of the varable cost of heatng that wll turn the nvestment to vable wll be lower compared to the case that a subsdy s not provded. 5.6 Summary In ths Chapter, an economc, envronmental and energetc analyss of a geothermal dstrct heatng wth a heat storage, whch s the studed case n ths thess, was carred out and a comparson wth the tradtonal case of not usng a heat storage was done. Concernng the economc analyss of the nvestment, the man captal and runnng costs were ntally calculated for both cases as well as the captal costs of replacement of some parts of the nstallaton and the evoluton of the runnng costs over the nvestment perod. Afterwards, usng these captal and runnng costs, several fnancal ndces of the nvestments were calculated n order to make the comparson between the two cases. Then, the annual emssons of carbon doxde were calculated for the envronmental analyss of the nstallaton, whle for the energetc analyss two separate energetc ndces were used. The frst energetc ndex that was used was the load factor of the nstallaton whch depcts how close to the nomnal load the nstallaton s operatng over the year, whle the second energetc ndex was the proporton of the annual heat demand that s covered by geothermal energy. The results have hghlghted some very mportant nsghts on the economc, envronmental and energetc aspects ether when the studed case s compared wth the tradtonal case, whch s the man pont of nterest of ths Chapter, as well as when cases 219

222 of dfferent szng of the geothermal part of the nstallaton are compared wth each other. The man concludng remarks of ths Chapter are the followng: Both the captal and runnng costs of the nstallaton are lower n the studed case compared to the tradtonal case for any case of szng. The captal cost of the nstallaton ncreases as the szng of the nstallaton ncreases, whle on the other hand, the runnng costs of the nstallaton s decreased as less fuel and electrcty are used when the szng ncreases. All the fnancal ndces show that the studed case of usng a heat storage n a geothermal dstrct heatng system s more attractve than the tradtonal case of not usng a heat storage. More specfcally, the levelsed cost of heatng decreases, whle the NPV, the IRR and the BCR all ncrease. Ths s the case for any case of szng of the nstallaton. The effect of a fnancal subsdy, such as the Renewable Heat Incentve (RHI) n our case, was hghlghted. All the fnancal ndces of the nstallaton ncrease a lot when the RHI s taken nto account. The most attractve case of szng from an economc pont of vew s the larger case of szng. Ths happens manly because more geothermal energy s used to cover the heat demand and, therefore, the ncome from the RHI ncreases. Furthermore, the runnng costs wll be lower n the cases of larger szng. Therefore, t can be sad that, as long as other crcumstances allow ths, the szng of the geothermal component of the nstallaton should be as large as possble. On the other hand, the heat storage seems to mpact more the medum case of szng as n ths case, the hgher relatve ncreases of the fnancal ndces occur. The emssons of the nstallaton decrease when the heat storage s used for each case of szng as less fuel s used to cover the peak demands. The emssons decrease as the szng of the nstallaton ncreases as less fuel s used as well. As happens wth the economc analyss, the medum szng of the nstallaton s mpacted most from an envronmental pont of vew when the heat storage s used. The load factor of the nstallaton ncreases when the heat storage s used, also for each case of szng. Ths means that for the studed case more geothermal 220

223 energy s utlsed from the same geothermal nstallaton, whch s somethng desrable as for any renewable energy source. Furthermore, the load factor of the nstallaton decreases as the szng of the nstallaton ncreases, whch means that the nstallaton s workng further from ts full or nomnal capacty. Ths s expected as the maxmum avalable geothermal energy s ncreased, so for the same annual heat demand the load factor wll decrease. Fnally, the proporton of the heat demand that s covered by geothermal energy ncreases when the heat storage s used. Ths proporton also ncreases as the szng of the nstallaton ncreases, whch s somethng expected as more geothermal energy s avalable to cover the same heat demand. In general, t can be concluded that by applyng a heat storage under the proposed operatonal strategy n a geothermal dstrct heatng system, both the captal and the runnng costs decrease, whle the overall producton of heat s cheaper. The latter s probably the most mportant concluson of ths thess. Furthermore, the peak-up bolers are used less and more geothermal energy s utlsed compared to the tradtonal case. Ths leads to less emssons to the envronment and a hgher fracton of the heat demand to be covered by geothermal energy. So, all these results support a defnte answer to the queston gven n the begnnng of ths Chapter, whch defned the scope of t. It can be defntely sad that the proposed case s better than the tradtonal case, from the economc, envronmental and energetc ponts of vew. 221

224 6 CONCLUSION 6.1 Achevement of am and objectves A comprehensve study of geothermal dstrct heatng systems (GDHSs) was carred out n ths thess. Intally, a detaled lterature revew was presented, n whch t was dentfed that there was a gap n the way of operaton of these systems. More specfcally, there was no publshed research whch examned the operaton of a GDHS, but only practcal experence s known about that. For that purpose, the study of the operaton of a GDHS was a major part of ths thess. Furthermore, as for any renewable system t s desrable to maxmse the utlsaton of the lowest-carbon source, whch n our case s geothermal energy. Ths s partcularly mportant for renewable systems as these are captal ntensve nvestments and t s of the utmost mportance to maxmse ther utlsaton n order to ncrease the cost-effectveness of the nvestment. These two factors are the man drvers for the focus of ths study. Tradtonally, a GDHS vares ts heat output accordng to the heat demand up to ts maxmum capacty and n the cases that geothermal energy cannot cover all the heat demand, fossl-fuel peak-up bolers are mplemented. In ths study, t s proposed to keep the geothermal producton constant throughout the day and ntegrate a fully-mxed hot water storage tank where hot water can be stored n tmes of low load, whch can subsequently be released nto the network to releve peak demands. The operaton of the nstallaton wll be scheduled on a daly bass, whle t s re-terated that the studed unts are assumed to be heat producton only unts (whch s common for geothermal energy) and offer hgher flexblty compared to CHP unts. It s also recalled that through ths approach t s not ntended to totally phase out the peak-up bolers (as ths would probably render the nvestment unfeasble), but to reduce ther use. The am of ths thess was to study the energetc, economc and envronmental effect of ncludng a heat storage n a geothermal dstrct heatng system under the proposed novel operatonal strategy. The am of the thess was acheved by fulfllng the three objectves defned n secton 1.1. The frst objectve was to develop a model for the szng of a GDHS whch would operate under ths mode of operaton. Through the developed algorthm, a specfc 222

225 representatve day s chosen as the desgn-day and the whole szng s based on ths day. In our case, three very dfferent and dscrete days were chosen as the desgn-days n order to show the nfluence of the szng of the nstallaton on the results. More specfcally, those days where the days that ther daly heat demand s equal to the 25 th -, 50 th - and 75 th centle of the daly heat demands of the whole year. The results show that the effcency of the nstallaton s very hgh and approxmately % dependng on the case of szng. It was also shown that the mass flow rates throughout the network were qute hgh whch makes the use of a fully-mxed tank (nstead of a stratfed tank) a sensble and logcal choce. Probably the most mportant concluson drawn from ths part of the study was the mportance of the nsulaton on the heat losses of the storage tank and the ppelnes. More specfcally, t was shown that the heat losses of the storage tank wll be neglgble f a thck nsulaton (n our case the thckness selected was 20cm) s used. For the ppelnes of the network, an optmzaton algorthm was bult whch took nto account ther captal cost, the cost of electrcty used to overcome the frcton losses and the cost of the heat losses. By applyng ths algorthm, the obtaned values of the heat losses were much smaller than other publshed values, whch ndcates that the heat losses were probably underestmated prevously and have to be taken nto account durng the ntal desgn of the ppelne system. Ths hghlghts the power of ths optmsaton algorthm The second objectve s the development of a model for the detaled study of the operaton of the nstallaton. In ths model, the outcomes of the frst model were used as nputs. Frstly, an algorthm that provdes the operatonal strategy of the nstallaton over a random day wth a gven heat demand was bult. By operatonal strategy s defned the complete knowledge of the operaton of the nstallaton ths day, such as the knowledge of the temperatures and the mass flow rates throughout the nstallaton and for each tme nterval. Ths algorthm can be potentally a powerful tool for the operators of the nstallaton who wll know n advance how to operate the nstallaton on any day f they know (or can predct) ts heat demand. Then, ths model was extended n order to buld an extended model for the study the operaton of the nstallaton over a whole year. The man outputs of ths model are the amount of electrcty used by the pumps of the nstallaton as well as the amount of fuel used by the peak-up bolers, both for the whole year, and comprse the man runnng costs of the nstallaton. A comparson of these values for the studed and the tradtonal case of operaton of GDHS was carred out and t was found that when the heat storage s mplemented less fuel s used and more geothermal energy s utlsed, whle the amount of electrcty used s roughly the same. Furthermore, the results ndcate that the heat storage mpacts most the medum szed nstallaton. On the other 223

226 hand, t was shown that as szng ncreases proportonately less fuel s used and more geothermal energy s utlsed. So, t can be concluded that although the mpact of the storage s hgher n a modest szng of the nstallaton, the nstallaton should be szed as bg as possble n order to maxmse the use of geothermal energy. The thrd and last objectve of ths study was the development of an ntegrated model for the calculaton of the economc, energetc and envronmental ndces of the nstallaton together wth a comparson wth the tradtonal case. It was shown that when heat storage s used, both the captal and runnng costs of the nstallaton are lower when compared to the tradtonal case. Therefore, all the fnancal ndces obtaned more favourable values for the studed case compared to the tradtonal operaton. More specfcally, the levelsed cost of heatng decreases, whle the NPV, the IRR and the BCR all ncrease. Addtonally, the effect of a fnancal subsdy, such as the Renewable Heat Incentve (R.H.I.) n our case, n a renewable heatng project was hghlghted, as all the fnancal ndces ncreased mportantly when the R.H.I. was taken nto account. Yet agan, a conflctng pont arose, as on the one hand the storage mpacts more the medum case of szng from an economc pont of vew, but on the other hand, the most fnancally attractve case s the larger case of szng. Of course, the second case s usually preferred and as proposed before, the geothermal part of the nstallaton should be szed as large as possble. Furthermore, t was shown that when the heat storage s used the load factor of the nstallaton ncreases, whch means that the nstallaton s workng for more hours n ts full load and more geothermal energy s used. Subsequently, a larger part of the total heat demand wll be covered by geothermal energy. Fnally, by mplementng the heat storage, the annual emssons of the nstallaton wll decrease. By the conclusons drawn from the last part of the study, a defnte answer can be gven to the man queston of ths thess, whch was whether t s worthwhle ncludng a heat storage under the proposed operatonal strategy n a GDHS or not. It was clearly shown that for any case of szng of the nstallaton, by applyng the heat storage the overall producton of heat s cheaper and the peak-up bolers are used less. The utlsaton of geothermal energy, whch has numerous advantages as explaned earler, s ncreasng wth subsequent reducton n the emssons of the nstallaton. So, t can be defntely stated that the ntegraton of a heat storage under the proposed mode of operaton s benefcal for a GDHS from economc, energetc and envronmental ponts of vew. Therefore, the am of ths thess has been fully acheved. 224

227 6.2 Summary of contrbutons of the thess The am of ths thess was fully acheved together wth ts man objectves. The man contrbutons of ths thess n the feld can be summarsed as: The proposton of the ntegraton of a heat storage n a geothermal dstrct heatng system under a novel operatonal strategy. It was shown that ths proposton s benefcal for the system under an economc, energetc and envronmental pont of vew. The provson of a robust algorthm for the szng of the nstallaton whch would operate under the new operatonal strategy. Useful nsghts were obtaned for the szng and operaton of several parts of the nstallaton. The most mportant nsght was the mportance of the heat losses of the ppelne whch was revealed by the optmsaton algorthm that was developed for ther szng. Ths algorthm can also be used for the szng of any par of underground pre-nsulated ppelnes, f the boundary condtons are known. Ths s a contrbuton out of the man lne of the thess. The provson of a model that can provde the operatonal strategy of the nstallaton n any day wth a known heat demand. Ths model can theoretcally be used by the operators of the nstallaton f they can calculate or predct the heat demand of the studed day one day n advance whch s reasonably achevable usng weather forecasts. If the heat demand s known, ths model wll provde them wth all the necessary nformaton about how they should operate the nstallaton throughout the day. The provson of a model that can provde useful nformaton about the operaton of the nstallaton over a whole year. The provson of a model that can calculate the economc and energetc ndces of the nstallaton as well as ts annual emssons. A second model was also bult that can provde the same values of a tradtonal GDHS. The provson of a model that s coupled wth the latter model and can make a robust comparson of the aforementoned ndces whch can show f the proposed soluton s benefcal aganst the tradtonal case or not. In our case, the results of ths model showed the frst mentoned, and most mportant, contrbuton of ths thess,.e. the economc, energetc and envronmental effectveness of ths proposton. 225

228 6.3 Recommendatons for future work In ths fnal secton of the thess, some recommendatons for future work wll be gven. These nclude recommendatons on the mprovement and enrchment of the algorthms and proposal of further steps that should be taken usng these algorthms. Fnally, a smlar approach for the modellng of a future energy system based on geothermal dstrct heatng wll be proposed. The frst part of ths study presented a robust algorthm for the szng of a GDHS under the proposed operatonal strategy. A frst mprovement on the model would be to add the sub-models of other parts of the nstallaton, manly of the geothermal heat exchanger and of the substaton, whch n ths study were consdered as black-boxes. The geothermal heat exchanger was not further studed n ths thess as t s consdered that t s a standardsed equpment and that t was not worthwhle studyng t further, whle a possble study for ts optmsaton would be qute long and beyond the scope of ths thess. On the other hand, the substaton of the nstallaton was not also studed further, as no detals could be found n the lterature about these and t s envsaged that ther confguraton wll be very casespecfc and, therefore, dffcult to model genercally. Furthermore, dependng on the case a substaton mght not even exst n an nstallaton. Moreover, the models for the szng and the operaton of the nstallaton dd not take nto account the behavour of the end-users, but took nto account only the temperature drop n the boundares of the branches of the dstrbuton network. In other words, the boundary of the study were the boundares of the man branches of the dstrbuton network. The models could be further extended n order to take nto account more detals of the dstrbuton network as well as the characterstcs and the nterface of each end-user (or at least of each dfferent knd of end-user). Obvously, these addtons would also affect the economc, energetc and envronmental analyss whch should be properly modfed. A basc dsadvantage of all the models, and especally of the szng model, s that they have not been valdated aganst real data. Ths happened partally due to the lack of real data as some parts of the nstallaton are not (or not known to be) deployed yet n realty, such as the proposed fully mxed tank, whle for other parts, such as the ppelnes, t was really hard to get real data from thrd partes. So, the valdaton of the developed models aganst real data s crucal for ther possble practcal and real-lfe applcaton. If the 226

229 valdaton takes place, t s strongly beleved that these models can be drectly (or wth few modfcatons) appled n real projects. The whole analyss n ths thess was appled for three dfferent dscrete cases of szng of the nstallaton whch were explaned n detal n Chapter 3. These cases were the days whose daly heat demands correspond to the 25 th -, 50 th - and 75 th -centle of the daly heat demands of the whole year. These three cases were chosen as logcal choces that could depct small, medum and large cases of szng. A next step could study cases of smaller or larger szng of the geothermal nstallaton. Concernng the smaller szng, t s ntutvely understood that very small szng of the geothermal nstallaton s not possble as ths would requre a very low geothermal flow rate, whch would defntely make the nvestment unfeasble. In other words, when borehole drllng s done for a geothermal well, a mnmum flow rate s requred otherwse the drllng s not successful or operatonal. Ths mnmum flow rate excludes the cases of very small szng of the nstallaton, let s say of less than the 5 th - or 10 th - centle of the daly heat demands of the year. On the other hand for the case of very large szng of the nstallaton, n ths thess t was chosen n advance not to study such a case as ths would lead to under-utlsaton of the geothermal feld and would possbly render the nvestment unfeasble. Whether ths case s true depends on how peaky are the extreme peak demands. If these are very peaky, ths would mean that a part of the geothermal nstallaton would work for only a few hours per year, whch s defntely unfeasble. If these peak demands were more frequent and not very peaky, then t mght be possble to sze the nstallaton for a hgher coverage by geothermal energy, albet t s farly certan that 100% coverage by geothermal energy would be very costly. After all, as was already mentoned, there wll be some bolers n the nstallaton anyway for back-up purposes. For that reason, t s never attempted to acheve 100% coverage by geothermal energy. But, the upper feasble lmt of the szng of the geothermal nstallaton would be a very nterestng pont. Therefore, a study that would address these ssues n detal would be qute useful. Another ssue that could be researched further, whch was also explaned n Chapter 4, s the development of a tool relatng the heat demand data to weather condtons. Ths relatonshp can be extremely useful because t can be ntegrated wth the model of the daly operatonal strategy of the nstallaton developed n Chapter 4, and ths model wll be able to provde the operatonal strategy of the nstallaton f the weather data are known (or predcted) nstead of the heat demand. Ths s desrable as t s much easer and more effectve to predct the weather condtons of the next day compared to ts heat demand. A 227

230 frst attempt at developng ths relatonshp was made n Appendx B, n whch the results were not so encouragng ether because the approach was too smplstc or because the data n the studed case are very stochastc. Furthermore, ths was not studed further n ths thess as t was out of ts scope. So, an obvous further work arsng from ths thess would be the development of a robust model that connects the heat demand wth the weather condtons. Fnally, a smlar study that could be based n the logc of ths thess concernng the management of the geothermal nstallaton would be the ntegraton wth a heat pump for the further harvestng of geothermal energy. More specfcally, an nstallaton lke ths can be seen n Fg In such an nstallaton, the cooled water that exts the geothermal heat exchanger nstead of beng re-njected n the underground (or sent to others uses) wll be fed nto heat pumps whch can upgrade the temperature of fresh water to the desred level. The heated fresh water can ether be stored n the hot storage tank or be fed drectly n the network. But, the exstence of the storage tank s agan necessary. The man advantage of ths system s that for the same geothermal potental more heat wll be harvested through the use of the heat pump. Therefore, for the coverage of the same heat demand the geothermal nstallaton can be smaller. Fgure 6.1 Layout of the proposed system (G.H.E. = Geothermal Heat Exchanger, SS = Substaton, P.W. = Producton Well, R.W. = Re-njecton Well, H.S.T. = Hot Water Storage Tank, C.S.T. = Cold Water Storage Tank, P el = Electrcal Power) 228

231 On the other hand, the extra captal cost of the heat pump and of the ppelnes connectng t to the network and the storage tanks as well as the extra operatonal cost of the electrcal power used by the heat pump wll be the man dsadvantages of ths proposal. The proposed nstallaton can be operated under three alternatve modes. The frst alternatve s the heat pump to operate n a 24/7 mode. The second alternatve s the heat pump to operate only durng the nght hours n whch the prce of electrcty s usually lower, thus decreasng ths addtonal operatonal cost. A thrd alternatve whch can be applcable n a future energy system s that the heat pump can operate only when there s an excess of electrcty n the electrcal network, whch can be the case n a future electrcal system wth a hgh penetraton of ntermttent renewable energy sources. Ths proposton on the one hand wll make the operaton of ths system more complex, but on the other hand, wll offer very cheap (or even free) electrcty to the heat pump as ths would be an amount of electrcty that would be rejected. The latter would also be an advantage for the renewable electrcal producers as ths can be a potental addtonal ncome for them (as ths electrcty would be rejected as mentoned before) and ths could also ncrease the stablty of the electrcal network. Of course, all these alternatves would requre a detaled analyss n order to conclude f they are vable or not, but t s strongly beleved that under the operaton of the system presented n ths thess, these systems would be qute promsng. 229

232 APPENDICES 230

233 Appendx A Senstvty analyss of two basc parameters of the system 231

234 In ths Appendx, a senstvty analyss of two basc parameters of a geothermal dstrct heatng system s carred out n order to examne ther effect on the whole system. These parameters are the temperature dfference on the hot sde of the geothermal heat exchanger ( T h,ghe ) and the rato of the mass flow rates of the transmsson network (R m ) and they have a crucal effect on the operaton of the system. In the begnnng of the algorthm explaned n Chapter 3, ntal values are assgned to these parameters and these are kept constant throughout the whole process. If the fnal results are physcally acceptable, then the algorthm s consdered converged, whle f ths s not the case, then the proper adjustment of these parameters has to be done. In order to adjust these parameters ther effects on several varables of the system have to be evaluated. These effects are studed n ths Appendx. More specfcally, the nfluence of the two aforementoned parameters on the temperature dfference on the cold sde of the geothermal heat exchanger ( T c,ghe ), the outlet temperature of the supply transmsson ppelne (T tr,s,o ), the captal cost of the ppelnes (CC ppes ) and the number of wells s analysed. The results of ths analyss are shown n the followng graphs, and based on these results an teratve loop was added to the basc code for the adjustment of the parameters. More detals on ths possble source of error, the fnal loop that s added n the man code and a short dscusson on these results are provded n secton

235 Fgure A-A1 Temperature dfference on the cold sde of the geothermal heat exchanger vs the temperature dfference on the hot sde of the geothermal heat exchanger Fgure A-A2 Outlet temperature of the supply transmsson ppelne vs the temperature dfference on the hot sde of the geothermal heat exchanger 233

236 Fgure A-A3 Captal cost of the ppelnes vs the temperature dfference on the hot sde of the geothermal heat exchanger Fgure A-A4 Number of producton wells vs the temperature dfference on the hot sde of the geothermal heat exchanger 234

237 Fgure A-A5 Temperature dfference on the cold sde of the geothermal heat exchanger vs the rato of the mass flow rates of the transmsson network Fgure A-A6 Outlet temperature of the supply transmsson ppelne vs the rato of the mass flow rates of the transmsson network 235

238 Fgure A-A7 Captal cost of the ppelnes vs the rato of the mass flow rates of the transmsson network Fgure A-A8 Number of producton wells vs the rato of the mass flow rates of the transmsson network 236

239 Appendx B Relatonshp between the heat demand and the weather condtons 237

240 B1) Introducton The energy consumpton n buldngs accounts for a large fracton of the total energy use worldwde. More specfcally, n Europe, the energy use n buldngs accounts for 40% of the total energy use and 36% of total CO2 emssons (European Parlament and Councl, 2010). Therefore, t s easly understood that n order to fulfl the energy goals set worldwde the buldng sector should be taken very serously nto account. Ths can happen by optmsng the whole process of energy producton, dstrbuton and consumpton wthn the buldngs. A crucal factor of the above process s an accurate a pror predcton of the energy consumpton. An accurate predcton mproves the effcency and performance of the energy producton, reducng the envronmental mpact. The man energy forms wthn a buldng are heatng/coolng, hot santary water and electrcty consumpton. In ths study, the focus wll be on the predcton of the heat demand of the buldng. A general revew of the predcton methods of the energy consumpton has been provded by Zhao and Magoules (2012). In general, ths problem s qute complex as many factors should be taken nto account, such as the weather condtons, the structure of the buldng, the habts of ts occupants (the so-called socal factor) and many others. Therefore, many dfferent predcton methods or models have been developed. These can be categorsed n the physcal or engneerng models, the black-box models and the statstcal models. The physcal or engneerng models are based on the physcal prncples whch govern the heat losses of the buldng and take nto account the dfferent layers throughout ts wall, the dfference between the ambent and the ndoor temperature, the heat gans wthn the buldng etc. Many commercal tools have been developed for that purpose, such as TRNSYS and EnergyPlus 5. Usually, the physcal models are qute complex and are not so easy to apply n realty as t s qute dffcult to obtan all the characterstcs of the buldng. Therefore, some more smplfed methods have been developed. The most well-known method s the degree-day method, whch s a very smple method for the calculaton of the heat demand knowng only the ambent temperature (Gelegens, 2009; Schoenau and Kehrg, 1990; Coskun, 2010). Ths method s very smple and therefore not so accurate. Catalna et al. (2013) developed a multple regresson model between the heat demand and the dfference between the ndoor and the outdoor temperature, the total heat transfer coeffcent

241 and the south equvalent surface. The results of ths approach were qute satsfactory. Another smplfed model was also appled by Afram and Janab-Sharf (2015) that predcted the daly energy consumpton profle for resdental buldngs. The nterested reader can fnd more detals on the aforementoned methods n the work of Zhao and Magoules (2012). A black-box model s used when the physcal model s not completely known or s very complex to mplement practcally. In these cases, the nputs and the outputs of the model are known and the black-box approach s used to buld the nter-connectng functon. The most common types of black-box models are the artfcal ntellgence methods and these are further dvded n the Artfcal Neural Networks (ANNs) and the Support Vector Machnes (SVMs). A revew of these methods n the buldng energy systems can be found n the works of Krart (2003) and Douns (2010). These systems have been used wdely the last years for the heat demand forecastng n buldngs (Kalogrou, 2006; Kreder et al., 1995; Shamshrband et al., 2015) and the accuracy of the results s usually the best among the methods used. On the other hand, these models need a lot of hstorcal data whch are not always avalable and t s very dffcult to pont out the optmum parameters of the problem. Fnally, the fact that the physcs of the problem are not dentfed through these methods makes a lot of academcs, manly, to avod these methods. Another method whch s not so common and combnes the physcal and the black-box models s the grey-box approach, n whch there s a theoretcal knowledge of the system whch s combned wth measurements n order to produce ts mathematcal descrpton. For example, Zhou et al. (2008) developed an ntegrated model for the predcton of the heat demand whch uses as nputs the temperature and the relatve humdty, that are calculated through a modfed grey model, as well as the solar radaton whch s calculated through a regressve model. The nterested reader can fnd other applcatons of the grey-box approach n the work of Guo et al. (2011). The statstcal models are producng sngle or multple correlatons between the heat demand data and, usually, the weather condtons. In general, the statstcal methods are dvded n the autoregressve models, the ntegrated models and the movng average models (Popescu et al. 2008). Hstorcal data are used for the producton of the correlaton and, then, ths correlaton s used to predct the future heat demand. The basc advantage of these models s that they are qute fast and smple to use, but ther accuracy s not that good as t s not easy to capture the socal factor and the buldng envelope. An attempt to take nto 239

242 account the socal factor was done by Dotzauer (2002) where t s stated that the socal factor s of utmost mportance and should be defntely taken nto account. So, Dotzauer (2002) separated the heat demand functon nto two parts, the temperature dependent part and the part that depcts the socal behavour. Popescu et al. (2008) are producng multple correlatons between the current weather condtons and data of prevous tme ntervals tryng to capture the socal factor. The correlaton factors are qute satsfyng, but when these correlatons are tested aganst new data then the results are qute varable. In ths part of the thess, smple correlatons wll be produced between the heat demand data and the weather condtons, n whch the socal factor and the buldng envelope wll be taken nto account. The correlatons wll be qute smple because, as stated by Dotzauer (2002), there wll always be falures n the predcton of the weather whch s used for the predcton of the heat demand. Therefore, complex models can provde errors and more smple models can provde the same satsfactory results. In order to take nto account the socal factor, dfferent correlatons wll be produced for each season/day/hour. For example, t s expected that for the same temperature the heat demand wll be dfferent between summer and wnter, or between a workng and a non-workng day. The optmum splttng of the data wll also be researched. Few research has been carred out on the bass of thnnng the data. Ma et al. (2014) categorsed the buldngs accordng to ther functon and found dfferent correlatons for each buldng, whle Yao and Steemers (2005) dd a break-down analyss of the load startng from the applances and buldng-up the total load. Concernng the buldng envelope, data of the prevous tme steps wll be used n the correlatons. Apart from the work of Popescu et al. (2008), there has been no other publshed work, up to the authors knowledge, usng data of the prevous tme steps. The structure of ths study s as follows: In ths secton, a bref ntroducton n the problem of the heat demand predcton was gven. In secton B2, the methodology wll be explaned focusng on the dfferent knds of data-splttng that wll be tested. In secton B3, the results wll be shown and dscussed, whle secton B4 wll conclude ths study. B2) Methodology In ths secton, a bref descrpton of the methodology followed wll be gven. The heat demand data used n the modellng were provded by the Estates and Buldng Offce of the Unversty of Glasgow and refer to a cluster of buldngs managed by the Unversty. On the 240

243 other hand, the weather data used were obtaned by the Brtsh Atmospherc Data Centre (BADC) 6 and refer to the Klpatrck area of Glasgow, whch s a vllage n the west of Glasgow on a straght lne dstance of almost 14km. The data from the meteorologcal staton of ths area were chosen as these were the most precse data, the other operatng statons were almost n the same dstance and, most mportantly, there were very few mssng data. There were avalable data for the whole 2012 and for the frst fve months of Therefore, the correlatons were done for the 2012 data and, then, these correlatons were tested for the 2013 data. As mentoned prevously, there were very few mssng data from the specfc staton. More specfcally, there were mssng data n two days of 2012 and n one day of These three, n total, days were not taken nto account n the calculatons. In order to determne all the correlatons, the MATLAB curve fttng tool was used. A novelty of ths study, s that for the calculaton of the fttng lnes/curves the method used was not the typcal least-squares method n whch the sum of the squares of the resduals s mnmsed, but a specal feature of the MATLAB curve fttng tool called Robust=LAR, n whch the sum of the absolute values of the resduals s mnmsed. The advantage of ths method s that t weakens the effects of possble outlers n the data whch would lead to not so realstc fttngs usng the typcal method. For the evaluaton of the goodness of the fttng the value of R 2 (Co-effcent of determnaton) was calculated for each case by the followng sets of equatons: R 2 = 1 SSE SST (A-B1) SSE = (HD HD ) 2 (A-B2) SST = (HD HD ) 2 (A-B3) Where: R 2 = Coeffcent of determnaton (Dmensonless) SSE = Sum of squared errors (kwh) SST = Total sum of squares (kwh)

244 (kwh) HD, HD = Predcted and observed heat demand for each tme nterval, respectvely HD = Average predcted heat demand (kwh) The frst part of the modellng s the dentfcaton of the optmum set of the dependent varables. In other words, the correlaton between the heat demand and dfferent dependent varables wll be tested n order to check whch one produces the best fttng. The dependent varables wll always be two and one of them wll always be the temperature at the current tme-step as t s assumed to be the man drvng force of the heat demand. The other varables that wll be checked are the temperature and the heat demand n several prevous tme-steps n order to capture the effect of the buldng envelope. At the same tme the optmum knd of correlaton wll be dentfed. After the above ssues are dentfed, then the possble correlatons wll be calculated and tested. In Fg.A-B1, the 2012 data are shown where t s made clear that t s mpossble to obtan a sngle correlaton that can ft satsfactorly these very sparse data. Therefore, t s necessary to splt the data nto dfferent tme perods n order to capture possble socal varances. The dfferent temporal data-splttng wll be the followng: Dfferent seasons. The data wll be spltted n four dfferent seasons wthn the year,.e. January-March, Aprl-June, July-September and October-December. Splttng n workng and non-workng days. Dfferent hours. Dfferent correlatons wll be carred out for each hour of the day. Therefore, there wll be 24 dfferent correlatons. 242

245 Fgure A-B data B3) Results B3-1) Optmum fttng functons Frstly, the optmum combnaton of dependent varables wll be examned. As mentoned earler, one of the dependent varables wll always be the temperature at the specfc tme step, whle the ndependent varable wll be the heat demand at the specfc tme step,.e. the predcted heat demand. The other dependent varable wll be ether the temperature or the heat demand on varous prevous tme steps. In our case, the tme step s one hour. The prevous tme steps studed are one, fve and twenty-four hours earler n order to capture possble dfferent nfluences of the buldng envelope. The second case was a random choce between the two extremes of one and twenty-four hours. The results can be seen n Table A-B1 for 3 dfferent possble correlatons, 1 st -2 nd and 3 rd polynomal. It should be mentoned that both dependent varables were rsen n the same force. The exponental and logarthmc correlatons were also tested, but the produced results were much worse, so for sake of smplcty they are not shown n ths paper. It should be noted that these results refer to the 2012 data. 243