TOWARDS THE INCREASED UTILIZATION OF GEOTHERMAL ENERGY IN A DISTRICT HEATING NETWORK THROUGH THE USE OF A HEAT STORAGE

Transcription

1 TOWARDS THE INCREASED UTILIZATION OF GEOTHERMAL ENERGY IN A DISTRICT HEATING NETWORK THROUGH THE USE OF A HEAT STORAGE Sotros A. Kyraks (*), Paul L. Younger Unversty of Glasgow, School of Engneerng, James Watt Buldng, Glasgow, G1 QQ, Unted Kngdom *Correspondng Author, E-mal Address: s.kyraks.1@research.gla.ac.uk ABSTRACT Geothermal energy s a renewable energy source whch can provde base-load power supply both for electrcty and drect uses, such as space heatng. In ths paper, dstrct heatng systems that are fed by geothermal energy, the so-called geothermal dstrct heatng systems, are studed. It s proposed to apply a hot water storage tank n these systems to store hot water n tmes of low-load and release t to the system durng peak load perods n order to mnmse the use of peak-up bolers. For ths purpose, two dfferent models are presented and the results are shown for three dfferent cases of heat demand coverage by geothermal energy. Frst, a model for the szng of these systems s developed. The man fndngs hghlght the mportance of the nsulaton both for the storage tank and the ppelnes of the network. Secondly, a model that studes the daly and the annual operaton of the nstallaton s developed followed by an ntegrated economc and envronmental analyss of the proposed soluton The results ndcate that the proposed soluton s fnancally benefcal compared to the tradtonal case wthout use of the storage tank as all the fnancal ndces and cash flows are mproved. More specfcally, the levelsed cost of heatng decreases by.-1.% leadng to an ncreased potental ncome of per year, whle the NPV, the IRR and the BCR all ncrease. Furthermore, the emssons decrease by up to.% and the load factor ncreases by up to.%. Therefore, the proposed soluton s proved to be benefcal from an economc, envronmental and energetc pont of vew as more geothermal energy s utlsed n a more economcal way wth subsequent envronmental benefts. Keywords: Geothermal energy, Dstrct heatng, Heat storage, Heat network, Energy utlsaton

2 1. INTRODUCTION Geothermal energy s the energy contaned wthn Earth s crust and t orgnates from the processes that occur wthn Earth and heat conducton takng place to the upper layers [1]. Dependng on the temperature of the source, geothermal energy can have many uses, such as electrcty producton, space heatng, aquaculture, agrculture, snow meltng, dryng, dstllaton etc. [, ]. Theoretcally, temperatures hgher than 1 o C can be utlsed through the use of heat pumps []. Geothermal energy s a farly mature technology and s n use n many countres worldwde, wth Iceland, Turkey, USA, New Zealand, Indonesa and Phlppnes beng the poneers of geothermal development []. It can be stated that geothermal energy s a proven, cheap [] and renewable energy source [] that ts man advantage compared to the other renewable energy sources s that t can produce base-load energy and does not depend on the weather condtons []. On the other hand, geothermal energy depends a lot on the geologcal condtons onste and has a hgh rsk of uncertanty n the frst levels of exploraton. These factors together wth the poor fnancal support have lagged the overall development of geothermal energy []. In general, dstrct heatng refers to the producton of heat n a central plant and ts dstrbuton to the end-users va a ppelne network. A dstrct heatng network can have many heat sources, such as combned heat and power plants, whch s the most common source; conventonal bolers; waste ncnerators; ndustral waste heat source; solar collectors; heat pumps and geothermal energy []. The man advantages of dstrct heatng compared to local provson of heatng n each buldng are well summarsed n [,1] and nclude the hgher effcency of the whole procedure, the reducton of emssons, the faclty of waste heat recovery and the hgh level of relablty amongst others. The development of dstrct heatng s connected wth the avalable waste heat from power plants [1, 1]. In the majorty of the cases, a dstrct heatng network s fed by the waste heat of a power plant and the heat producton s a by-product of the process. Heat producton only statons whch feed a dstrct heatng system have been rarely used and are not studed extensvely. Concernng geothermal energy, the locatons where electrcty can be produced are lmted by the hgh temperature needed, whle n the case of heat producton the possble locatons are more wdespread snce a lower temperature s needed. In the case of heat producton unts, geothermal energy usually has a temperature whch s qute close to the requrement of the heat users [1]. For all the aforementoned, a purely heat-producton geothermal system whch feeds a dstrct heatng network seems a very valuable soluton. These systems, the so-called geothermal dstrct heatng systems (GDHS) are studed n ths paper. The studed systems combne all the aforementoned advantages offerng an effcent, cheap and envronmentally frendly soluton to the envronmental and energetc problem of nowadays [1, 1]. It should be noted that n the cases of hgher temperatures of geothermal water, a CHP plant can be used n whch the cooled water used for electrcty producton s then fed n the dstrct heatng network, but these systems wll not be studed n ths paper as they are lmted by the hgher temperatures needed. The most typcal users on a dstrct heatng system are dwellngs and the current research s based, but not lmted, on these users. Ther heat demand wthn a day s not constant and a typcal profle can be seen n Fg. 1. The publshed research on the operaton of a GDHS s very lmted. In [1], the authors develop a model for the operatonal optmzaton of an exstng

3 GDHS wth the objectve of mnmzng the runnng costs, whle n [1] the authors develop a novel control strategy of the system wth the objectve of maxmum exergetc effcency. In realty, the general approach to cover the heat demand s to fluctuate the geothermal producton accordng to the heat demand tll ts maxmum capacty and when the heat demand s hgher than the maxmum geothermal producton, fossl-fuel peak-up bolers wll cover the excess heat demand. In ths paper, a dfferent approach for the coverage of the heat demand n proposed. More specfcally, t s proposed to keep the geothermal producton constant each day and add a hot water storage tank, where hot water wll be stored n tmes of low-load, and ths stored hot water wll be released n the network to cover the peak demands. Wth ths approach, more geothermal energy wll be utlsed, whle less fossl fuel wll be used wth subsequent envronmental benefts. The fnancal vablty of ths proposal s crucal and wll be studed n detal. Furthermore, t should be made clear that t s not attempted to totally phase out the peak-up bolers, but to mnmse ther use, as there would be some bolers anyway n the nstallaton for back-up purposes, but also ths would lead to an over dmensonng of the whole nstallaton whch would turn the nvestment to unfeasble. In general, the concept of storng energy n a sensble heat storage has been extensvely studed [0, 1, ]. In the majorty of the cases, stratfed water tanks are used [, ]. Ths happens because the nlet temperature of the storage tank s usually varable comng from a CHP plant [, ] or from solar collectors []. On the other hand, the end-users need a specfc temperature for ther requrements. So, a stratfed tank wth a hgh degree of stratfcaton has a maxmum possble temperature on ts top, whch s sent to the users, and a mnmum temperature on ts bottom whch s sent n the producton unt [, ]. A novelty of ths paper, s that t s proposed not to use a stratfed water tank, but a fully mxed storage tank nstead. More specfcally, two storage tanks wll be used, one on the supply and one on the return lnes of the system that wll store hot and cold water, respectvely. The hot water storage tank wll be studed n detal as the cold water storage tank wll be used as a regulator of the flow to the geothermal heat exchanger. For sake of smplcty, n the rest of the text the word tank wll refer to the hot water storage tank unless otherwse stated. In a GDHS, the producton temperature s almost constant compared to the aforementoned cases, so t s expected to operate more smoothly n ths way. Furthermore, n a GDHS the flow rates are qute hgh as wll be seen n the results, so t s qute hard to mantan the stratfcaton wthn the tank.

4 Fgure 1. The average heat demand for a set of houses [0] The noveltes of ths paper are the followng: The frst and most basc novelty s the new way of operaton of the GDHS whch s proposed and studed. Based on ths drecton, two ntegrated models for the szng and desgn of the system as well as for the n-advance knowledge of the operaton of the system are bult and presented. Fnally, as referred prevously, the use of a fully mxed tank nstead of a stratfed tank s another novelty of ths paper. The structure of the paper s as follows: In ths secton a general ntroducton n the concept of a GDHS was gven; the second secton analyses the methodology of the whole approach; the thrd secton provdes the results of the analyss together wth the dscusson and the last secton concludes the paper.. METHODOLOGY A smplfed scheme of the studed nstallaton s shown n Fg.. The geothermal flud s pumped n the surface through the producton well (P.W.) and ts heat s transferred to water through a geothermal heat exchanger (G.H.E.) n order to avod scalng and corroson to the man network. The heated water s then dstrbuted to the end users through a transmsson and dstrbuton network and returns to the GHE to be reheated and contnue ts cycle. Fnally, the cooled geothermal water s pumped n the underground through a re-njecton well (R.W.). The study s dvded nto two man parts. In the frst part, an ntegrated algorthm for the szng of the nstallaton s bult. It should be noted that the nstallaton wll operate on daly cycles. In the second part, an algorthm whch provdes detals for the daly operaton of the nstallaton s bult and then ths algorthm s extended n order to study the annual operaton of the nstallaton. By studyng the annual operaton of the nstallaton, the basc operatonal costs wll be known and these wll be used to carry out an economc and envronmental analyss of ths proposal and a comparson between the proposed and the tradtonal operaton of a GDHS.

5 Fgure. A smplfed scheme of the studed nstallaton (G.H.E. = Geothermal Heat Exchanger, H.S.T. = Hot Storage Tank, C.S.T. = Cold Storage Tank, SS=Substaton) It was attempted to make the whole model as generc as possble as the desgn of a GDHS s very case-specfc by ts own nature. Therefore, many varables of the problem, such as the length of the dstrbuton network, were arbtrary nputs by the author, whle n realty, these wll be the real nputs by the user..1 Szng of the nstallaton In the frst part of the study, an ntegrated model for the szng of the nstallaton was bult. The geothermal data, the heat demand data throughout a whole year and the topology of the nstallaton were used as nputs, whle the szng of the nstallaton s the output. The heat demand data should have a fne tme dscretzaton for more accurate results. Snce the nstallaton operates on daly cycles, a specfc day has to be chosen as the desgn-day on whch all the desgn wll be based. In ths study, three dfferent cases were studed for whch more detals wll be gven on the results secton. Some ntal values of the basc parameters of the nstallaton, such as the temperatures across the network, have to be used n the begnnng of the calculatons. Then, the desgn-day s selected by the user. In our approach, the geothermal flow rate whch wll be constant throughout the day, has such a value that the heat demand of ths day can be covered by geothermal energy only. Snce the geothermal flow rate wll be constant, then the mass flow rate on the left of the storage tank (or the mass n each tme nterval, M tr,g ) wll be constant as t wll be equal to a specfc proporton of the geothermal flow rate whch s also an output of ths algorthm. In ths paper, t s preferred to use the mass throughout a tme nterval n the calculatons, as the heat demand data are known per tme nterval. The mass on the rght of the storage tank (M tr,s ) wll, n contrast, be varable throughout the day accordng to the heat demand. Based on the values of these masses, the masses of charged, dscharged and stored water throughout the desgn day as well as the volume of the storage tank can be calculated, respectvely, as:

6 M ch = M tr,g M tr,s (1) M ds = M tr,s M tr,g () M st = M ch M ds 1 + M st () M 0 st = 0 () ) V st = max (M st ρ SF () Equaton () s an assumpton whch denotes that there s no stored water n the frst tme nterval. It should be noted that the tank wll not be always full as n the case of the stratfed tank, but t wll be charged or dscharged wth water, changng the volume of stored water contnuously, accordng to the excess or shortage of heat demand. For the calculaton of the temperature evoluton of the stored water the followng energy conservaton equaton s appled [1]: ρ Cp V st T st +1 T st = Q + Q () Q loss dt 1 1 In the above equaton, the left hand sde s the accumulaton term, balanced by the heat surplus due to chargng, the heat shortage due to dschargng and the heat losses of the tank. Snce the storage tank s fully mxed, the temperature n each tme nterval wll be the same everywhere wthn the tank and equal to the storage temperature. The terms of Eq. () are multpled by the tme-step (dt) n order to convert them n energy terms and the rght hand sde energy terms are then gven by the followng set of equatons: 1 Q + = M ch Cp (T st,n T a ) () Q = M ds Cp (T st T a ) () Q loss = Q loss,top + Q loss,sde + Q loss,bot () 1

7 In Eq. (), the terms on the rght hand sde are the heat losses from the top, sde and bottom part of the storage tank, respectvely. In the top and sde parts, the heat losses consst of heat losses due to convecton and radaton to the ambent ar and conducton through the dfferent layers of the tank, whle n the bottom part the heat losses are due to conducton to the underground. For the calculaton of the convectve heat transfer coeffcent n the top part of the tank, the equatons for flow parallel to horzontal body are used, whle for the sde part the equatons for flow vertcal to a cylndrcal body are used. Therefore, the heat losses for each part of the tank are calculated by equatons summarsed n Table 1 [1]. In the cases of the top and sde part of the tank, the calculatons depend on the temperature of the stored water each tme and the outer surface temperature of the tank, therefore the heat transfer coeffcents are assgned wth a temporal superscrpt. In the case of the bottom part, the heat transfer coeffcent depends only on the materals, therefore, t s constant all the tme. The system of equatons ()-(1) s solved wth an teratve method n order to provde the evoluton of the temperature of the stored water Table 1. Sets of equatons used for the calculaton of the heat losses of the storage tank Top Part () Sde Part () Bottom Part (1) Q loss,top = K top A (T st T a ) dt Q loss,sde = K sde A (T st T a ) dt Q loss,bot = K bot A (T st T s ) dt 1 K top = t j k j j h c,top h r,top 1 K sde = t j k j j h c,sde h r,sde 1 = t j K j bot k j h c.top = Nu k ar D st h c,sde = Nu k ar D st If Re < : Nu = 0. Pr 1/ Re 1/ Else-f < Re < : Nu = 0.0 Pr 0. Re 0. Else: Nu = 0.0 Pr 1/ Re 0. h r,top = ε cv σ (T sur + Ta ) (T sur If < Re < : Nu = Re1/ Pr 1/ [1 + Else: [1+ 0. Pr ] 1/ Nu = Re1/ Pr 1/ [ Pr ] 1/ Re 1 ] 000 / Re [ ] / + T a ) h r,sde = ε cv σ (T sur + Ta ) (T sur + T a ) 1

8 For the szng of the ppelnes of the network, an optmzaton algorthm s bult. The objectve functon s the mnmzaton of the total cost of the ppelnes, whch ncludes 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. Other possble costs are not taken nto account snce these are consdered equal for each case. The optmzaton parameters are the external dameter of the ppelne and the thckness of the nsulaton. Standardsed values of external dameters accordng to EN0 [] were used. The cost of the heat losses s calculated by multplyng the heat losses by a unt prce of heatng. For the calculaton of the heat losses, a system of double underground pre-nsulated ppes was used (Fg.). The ppelnes are dscretzed n space and for each par of dscretzed ppes the average values for the supply and return temperatures are consdered. The equatons summarsed n [] are then used for the calculaton of the heat losses. It s found that an optmum space dscretzaton of the ppelnes s m Fgure. Studed system of double underground pre-nsulated ppelnes [] 1 1 The power of the pumps and, fnally, the cost of electrcty are calculated by the followng equatons, respectvely: 1 P p = ρ g (δh l + δh elev ) V η p (1) C el,tot = P p (AOH) C el,u (1) The frcton losses n Eq. (1) are calculated by the Darcy-Wesbach equaton. Snce the ppelnes are szed and ther heat losses are known, then the temperatures across the network can be calculated. So, all the necessary data for the szng of the nstallaton are known. Fnally, the effcency of the nstallaton for the desgn day can be calculated as: η G,D = DHD D m G,D Cp dt G,D 00 (1)

9 Snce the ntal assumptons are made, the equatons (1)-(1) are used for the szng of the nstallaton. Through these equatons, new values of the ntal assumptons are calculated. Therefore, an teratve process wll be followed tll the convergence of the problem.. Operatonal and economc analyss The second part of the study s dvded n three dfferent sub-parts. In the frst two parts, the operaton of the nstallaton s studed over a random day and over a year, respectvely, whle n the thrd part an ntegrated economc and envronmental analyss of the nvestment together wth a comparson wth the tradtonal case are carred out. Frstly, a robust model s bult for the study of the operaton of the nstallaton n a random day. More specfcally, n ths model the nputs are the outputs of the frst part of the study,.e. the szng of the nstallaton, and the heat demand of a random day. In other words, the szng of the nstallaton s now known and ths algorthm wll provde the operatonal strategy of the nstallaton for a day wth a known or predcted heat demand under the operaton proposed n ths paper. By operatonal strategy, the author defnes the complete knowledge of the operaton of the nstallaton, for example, 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. Theoretcally, 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 comng day that has a known, or predcted n realty, heat demand. Intally, the necessary geothermal flow rate can be calculated by the followng properly re-arranged energy conservaton equaton: 0 m G = DHD + M st 0 Cp (T 0 st T a ) 00 η G 00 Cp dt G (1) 1 In the above equaton, DHD s the daly heat demand, whle the factors wth the superscrpt 0 denote values of the frst tme nterval of the studed day, whch n realty would be the values from the last tme nterval of the prevous day. Therefore, these specfc values wll be known. Actually, these factors take nto account any remanng energy from the stored water of the prevous day. Obvously, n ths case the ntal mass of stored water s not necessarly zero as n secton.1, but s a known value from the prevous day. Furthermore, any possble mass of stored water n the end of the day s not taken nto account now, snce the masses are not known yet. At the moment, t s also consdered that the peak-up bolers wll not be used throughout the day, whle the total effcency of the nstallaton (η tot ) and the temperature drop of the geothermal flud (dt G ) are ntal estmatons. Later on, all these assumptons wll be checked and renewed through an teratve process.

10 Snce the geothermal flow rate s known, then the same process as n secton.1 can be followed for each tme nterval to calculate all the masses and the temperatures across the network. The only dfference, as already sad, s that the ntal mass of stored water mght not be zero as n Eq. (). Furthermore, n some cases the mass of stored water wthn the day wll be zero, so the mass of dscharged water wll not be calculated by Eq. (), but wll also be equal to zero. In order to dentfy f the peak-up bolers should be used, the followng loop s appled: For each tme nterval : If M = M st + M ch Then M b = abs(m) M ds < 0 (1) Else M b = In the above loop M b s the mass of water that should be provded to the network by the boler. Therefore, for a specfc boler and a known temperature ncrease n the boler s water, the mass of fuel provded to the boler wll be known. Snce all the masses and temperatures of the network are known across the day, a renewed value of the temperature drop of the geothermal flud can be calculated. If the peak-up boler has been used, the part of the daly heat demand that s covered by geothermal energy (DHD G ) can be easly calculated. It s remnded that Eq. (1) refers n the geothermal part of the nstallaton, but snce t s not known n advance f the peakup bolers wll be used, t s wrtten n more general terms. Fnally, any possble mass of stored water n the end of the day has to be taken nto account now. Therefore, a renewed value of the effcency of the geothermal part of the nstallaton can be calculated as: 1 DHD G + M N st Cp (T N st T a ) η G = 00 [m G Cp ΔT new G + M 0 st Cp (T 0 st T a )] (1) Then, a renewed value of the geothermal flow rate can be calculated by Eq. (1) and the whole process s repeated tll convergence of the problem. The output of ths model s the operatonal strategy of the nstallaton as well as the total amount of fuel used by the peak-up bolers and the total amount of electrcty used by the pumps throughout the day. In the second sub-part, the above model s extended for the study of the operaton of the nstallaton over a whole year. The extended model wll actually repeat the prevous process for each day of the year serally just by usng the data of the last tme nterval of the prevous day as the data of the frst tme nterval of the next day. The outputs of ths model wll be the same as those of the prevous model, but n ths case, the outputs of nterest are the total amount of fuel and the total electrcty used throughout the year. These comprse the man operatonal costs of the nstallaton and together wth some

11 assumptons about the other operatonal and mantenance costs, the total annual runnng costs of the nstallaton wll be known. The total annual runnng costs are used together wth the captal costs n the thrd and last sub-part for an ntegrated economc analyss of the nvestment. A comparson wll be made wth the tradtonal approach n order to examne f the proposed soluton s feasble. Furthermore, the total amount of fuel per year wll be used to carry out an envronmental analyss of the nstallaton. The captal cost of the nstallaton s calculated by the followng equaton: (1) CC tot = CC dr + CC H.S.T. + CC C.S.T. + CC np + CC b + CC ot In applyng ths equaton, we assembled typcal costs for specfc components of the captal expendture on the bass of dscusson wth UK practtoners n the geothermal drect use sector. On ths bass, we assume: Drllng costs: 1.M mllon for the frst deep borehole, decreasng to 1M for alter borehole. The latter are cheaper as ground condtons are better known n advance and the rsk of drllng decreases. Network ppelnes costs: captal costs nclude materals (carbon steel and mneral wool for nsulaton), the cost of weldng and the cvl costs for buryng the ppes underground. The cost of carbon steel s 00/tonne and the cost of mneral wool s consdered to be 0/m. The cost of weldng s assumed to be 00 per weld and metre of dameter), and the cvl costs are 00/m of ppelne. Tank costs: captal costs nclude materals whch have the same prce as for the ppelnes, cvl costs, the erecton on slab and other mnor costs whch are assumed on the bass of recent projects n the UK. Peak-up and back-up bolers: 00/kW as an average prce of ndustral gas bolers n [cf Other mnor costs nclude pumps, n-house nstallaton, salares of workers etc., all of whch we have estmated from recent analogous projects n the UK. The economc analyss s done by comparng several fnancal ndces of both nvestments as well as ther cash-flows. The man fnancal ndex s the levelsed cost of heatng whch s calculated by the annuty method as []: LCH = CC CRF + OC AHD (0) 0 1 In the above equaton, CRF s the cost recovery factor whch s calculated as:

12 CRF = r 1 (1 + r) IP (1) The other fnancal ndces used for the comparson of the two cases are the net present value (NPV), the nternal rate of return (IRR) and the benefts-to-cost rato (BCR) []. In the followng, few detals wll be gven on the calculaton of the nflows and outflows of the nvestment, as these are necessary for the calculaton of the fnancal ndces and for the cash flow graphs. The nflow of the nvestment conssts of the followng three parts: A fxed cost per day whch guarantees a certan ncome and s used for the repayment of the captal cost. It s fxed n such a value so that the ntal captal cost s repad wthn years. A varable cost whch depcts the real consumpton of energy and s fxed n 0.0/kWh of heat provded. A fnancal ncentve recently establshed n UK, the so-called RHI (Renewable Heat Incentve), whch provdes 0.0/kWh of renewable heat provded. Ths value ncreases by.% each year and the ncentve s provded for the frst 0 years of operaton. The latter mght not always be the case, but n ths study the calculatons of the economc analyss wll be made for the cases that the RHI s taken and not taken nto account n order to dentfy the nfluence of a fnancal subsdy n a renewable project. The outflows of the nvestment consst of the captal and operatonal costs. The man captal cost shown n the results are upfront costs, whle t s assumed that the bolers wll be replaced after 0 years of operaton and the heat exchangers and the pumps wll be replaced after 1 years. Concernng the operatonal costs, ther average annual ncrease was calculated for the last years, and t s assumed that ther annual ncrease n the future wll be equal to ths value. Fnally, the dscount rate, the nterest rate and the nvestment perod were assumed to be %, % and 0 years, respectvely. Furthermore, snce the total amount of fuel used per year s known, the emssons can be easly calculated through the stochometry of the fuel and charts of combuston. In ths study, only the local emssons wll be calculated, as t s very dffcult to quantfy the emssons durng the constructon of a GDHS. The only publshed value of the levelsed lfe-cycle emssons of a geothermal heat only project s n [] and equals to g CO /kwh. Furthermore, n ths study the comparson between the two cases s carred out and not wth other alternatve energy sources, and therefore, the comparson of the local emssons s consdered to be suffcent for that purpose. Fnally, the load factor s calculated as the rato of the average geothermal flow rate throughout the year dvded by the maxmum avalable geothermal flow rate. Any possble out of operaton hours are not taken nto account.. RESULTS AND DISCUSSION 0

13 .1 Szng of the nstallaton The heat demand data used as a test case were provded by the Estates and Buldngs Offce of the Unversty of Glasgow and refer to several buldngs managed by the specfc offce. The annual heat demand s around 00MWh wth an average and peak demand of. and 1MW, respectvely, whle the tme dscretzaton of the data s 0 mnutes. A plot of the data can be seen n Fg. In ths fgure, n can be seen that the heat demand s very peaky and t s made obvous that t would not be vable to sze the geothermal nstallaton to cover all the heat demand. The other necessary data are case-specfc for each problem. In realty, these wll be the nputs by the user of the model. In our case, these are chosen arbtrarly by the authors. A lst of the basc nputs of the problem can be seen n Table. As already mentoned, a specfc day has to be chosen by the user as the desgn-day. In our case, three dfferent days are chosen and studed n order to study the effect of the heat demand coverage by geothermal energy on the vablty of the project. More specfcally, the chosen days are those that ther daly heat demand s equal to the th -, 0 th - and th -centle of the daly heat demands of the whole year. For sake of smplcty, these cases wll be called -C, 0-C and -C n the rest of the paper, respectvely. So, three dfferent and very dscrete cases whch affect prmarly the szng of the nstallaton wll be studed. Ther effect on the economcs of the nstallaton wll be studed n the next secton Fgure. Heat demand data for the year of study 0 1 Table Man nput data Data Value

14 Mass flow rate of each well (kg/s) 0 Temperature of the geothermal flud (K).1 Length of transmsson ppelne (m) 0 Mnmum temperature dfference on the hot sde of the G.H.E. (K) Ambent desgn temperature (K) As already mentoned, a specfc day has to be chosen by the user as the desgn-day. In our case, three dfferent days are chosen and studed n order to study the effect of the heat demand coverage by geothermal energy on the vablty of the project. More specfcally, the chosen days are those that ther daly heat demand s equal to the th -, 0 th - and th -centle of the daly heat demands of the whole year. For sake of smplcty, these cases wll be called -C, 0-C and -C n the rest of the paper, respectvely. So, three dfferent and very dscrete cases whch affect prmarly the szng of the nstallaton wll be studed. Ther effect on the economcs of the nstallaton wll be studed n the next secton. The man results are shown n Table and refer to the desgn-day for each case. As can be seen n ths Table, the temperature drop of the geothermal flud s almost the same n each case and s very close to 0K degrees. Therefore, the geothermal power ncreases almost proportonally wth the number of wells. The effcency of the nstallaton ncreases as the coverage by geothermal energy ncreases and ts value ranges roughly between.-.1%. Table Man results of the szng of the nstallaton Case -C 0-C -C No of wells 1 m G (kg/s) m tr,s (kg/s). 0.. Q G (kw) dt G (K) η tot (%)..1. V st (m ) D st, H st (m) The volume of the storage tank ncreases wth the ncrease of the coverage by geothermal energy, but not proportonally. Ths happens because the mass of stored water, and volume of storage tank subsequently, depends strongly of the fluctuaton

15 of the heat demand wthn the specfc chosen day. Two days mght have the same daly heat demand, but the fluctuaton wthn the day can be very dfferent. Furthermore, from a thermo-economc perspectve t s found that the optmum heghtto-dameter rato of the storage tank s equal to 1. Fnally, t can be seen that the rato m tr,s/m G s almost the same n the three cases, almost equal to 1., but not exactly the same as t s a value provded by the algorthm, as mentoned earler. Ths fndng also agrees wth the lterature [] that states that ths value has to be hgher than 1. In Fgs. a-c, the mass of stored water and n Fgs. a-c ts temperature evoluton throughout the day are shown, respectvely. The dfferent values of the stored water n each case reflect the dfference n the mass flow rates and n the volume of the storage tank as shown n Table. It can be seen that the graphs follow the same trend n each case. The hgher temperature decreases occur durng the frst and, manly, the last hours of the day where the storage tank s almost empty. The rest of the day the heat losses of the tank are almost neglgble. The only excepton s the graph that depcts the temperature evoluton of stored water n the smaller szng (Fg. a), where especally n the frst hours there s a much steeper decrease n the temperature. Ths happens because there s no stored water for many hours and the mathematcal model shows some nstablty. The Fgs. a-c hghlght the effect of the nsulaton, whch n our case s 0cm, showng that the heat losses n a well-nsulated tank can be mnmzed. The thckness of the nsulaton comes also n agreement wth publshes values []. Fgure a. Mass of stored water over tme (-C) Fgure a. Temperature evoluton of stored water over tme (-C)

16 Fgure b. Mass of stored water over tme (0-C) Fgure b. Temperature evoluton of stored water over tme (0-C) Fgure c. Mass of stored water over tme (-C) Fgure c. Temperature evoluton of stored water over tme (-C) 1 In Table, the desgn temperatures of the transmsson network are shown. Snce the length of the transmsson network s 0m, the temperature drop n the ppelnes s n the range of K/km. Ths value s somewhat lower than those presented n the lterature, e.g. n [1]. Ths happens because n the developed algorthm, the heat losses of the ppelnes are taken nto account and a qute thck nsulaton s used. Ths can also be seen n Table where the dmensons of the ppelnes of the transmsson network are shown. Probably, n realty the heat losses were not taken nto account as much as they should. Furthermore, the fact that these are smulaton results and not real data mght be partly a reason for ths dsagreement.

17 Although the results are qute lower than other publshed ones, t can be seen that there are some mportant dfferences between them. Ths happens because the optmzaton algorthm does not take nto account, on the other hand, only the heat losses, but also the captal and runnng costs, so t seems that for dfferent flow rates the optmum cases are relatvely dfferent. But, n any case, the heat losses are qute small hghlghtng ths way the effect of the nsulaton and the advantages of ths algorthm. Fnally, t was shown that the heat losses of the ppelnes are mnmsed f the supply and the return ppelnes are lad as close to each other as possble Table Desgn temperatures of the transmsson network (S = Supply, R = Return, Temperatures n K) Case -C 0-C -C S-Inlet... S-Outlet..0.0 R-Inlet R-Outlet Table Optmum dmensons of the transmsson network (cm) Case -C 0-C -C D 1... D o t ns

18 . Economc and envronmental analyss The basc results of the economc and envronmental analyss of the nvestment together wth a comparson wth the tradtonal case of not usng a storage tank wll be shown n ths secton. Furthermore, the basc results from the annual operaton of the nstallaton that are used n the economc analyss wll also be shown. The szng of the nstallaton shown n secton.1 for each case, together wth the annual heat demand, were used n the algorthm of the annual operaton of the nstallaton to calculate the basc operatonal costs. In Table, the captal and operatonal costs for each case wth and wthout the storage tank are shown and refer to the frst year of operaton. Frst, t can be seen that the captal cost of the proposed case s lower than the tradtonal case for each szng of the nstallaton, although the proposed case has the extra cost of the storage tank. Ths happens because n the case wthout the storage tank, bgger peak-up bolers are needed to cover the peak demands and ths dfference n the sze of the bolers s bg enough to cover the cost of the storage tank. It can also be seen that the captal cost ncreases as the szng of the nstallaton ncreases, whch s totally expected as more wells are needed. Concernng the operatonal cost of fuel, t s seen that for each case of szng the cost of fuel s smaller n the case wth the storage tank than wthout the storage tank. Ths shows that by applyng the storage tank fuel s saved, whch means that a hgher fracton of the heat demand s covered by geothermal energy. Addtonally, t s seen that when the szng of the nstallaton ncreases, the cost of fuel decreases. Ths s also expected because by ncreasng the szng of the nstallaton, and more specfcally of the geothermal part, more geothermal energy wll be produced and wll cover heat demand, whch subsequently wll decrease the use of fuel. By observng ths data, t s observed that the bggest decrease of fuel cost when usng the tank s n the mddle case of szng (0-C), whch means that n ths case the storage tank s utlsed n the optmum way. In the smaller case of szng (-C), most of the geothermal energy wll be sent drectly to the consumpton, so the rest of the heat demand that would be covered by the bolers wll not be that dfferent between the proposed and the studed case. Therefore, the dfference n the cost of fuel s relatvely small. On the other hand, n the bggest szng of the nstallaton (- C), a very bg part of the load s covered by geothermal energy n any case and the fuel that needs to be used s qute small. Although the cost of fuel f the storage tank s used s the half compared to the tradtonal case, t can be seen that ths cost s qute small anyway. The operatonal cost of the pumps s almost the same between the case wth and wthout the storage tank. Ths means that the pumps consume almost the same amount of electrcty no matter f the storage tank s used or not. On the other hand, as the szng of the nstallaton ncreases, the operatonal cost of the pumps decreases. Ths s justfed by the fact that as the szng ncreases, the sze of the ppelnes also ncreases (see Table ) and the pumpng costs, have a decreasng trend. Fnally, the total operatonal cost s always smaller when the storage tank s used, and decreases when the szng of the nstallaton ncreases. Ths s justfed by the prevous observatons. So, both the captal and the operatonal costs are smaller when the

19 storage tank s used, whle the frst one ncreases and the second one decreases wth the ncrease of the szng of the nstallaton. Table Captal and operatonal costs of all the cases (W = Wth the storage tank, Wo = Wthout the storage tank, Costs n ) CC dr CC H.S.T. CC mp CC b CC tot OC f OC p OC tot -C W C Wo C W C Wo C W C Wo Table Man results of the fnancal and envronmental analyss RHI ncluded LCH ( /kwh) NPV( ) IRR (%) BCR ( ) Annual CO emssons Load factor (%) (kg) -C-W 0.0 <0 <0 <0 0. -C-Wo 0.01 <0 <0 <0. 0-C-W C-Wo C-W C-Wo RHI not ncluded

20 -C-W 0.0 <0 <0 <0 0. -C-Wo 0.01 <0 <0 <0. 0-C-W C-Wo C-W C-Wo In Table, the man results of the economc and envronmental analyss are shown for all the three cases of szng wth and wthout the storage tank as well as when the RHI subsdy s taken nto account or not. The levelsed cost of heatng, the annual CO emssons and the load factor do not depend on the RHI, so ther values are the same ether f t s taken nto account or not. Furthermore, t can be seen that n every case the fnancal factors ndcate that the proposed case s fnancally favourable compared to the tradtonal case. More specfcally, the levelsed cost of heatng decreases, whle the NPV, IRR and BCR all ncrease. It can also be seen that the bggest change n the fnancal favourablty of the nvestment occurs n the mddle szng case where, as already referred, the storage mpacts most. Ths dfference n the levelsed cost of heatng denotes an ncreased potental ncome between 000 and 00 dependng on the case f the heat storage s used. A very mportant fndng from Table s that the vablty of the nvestment ncreases when the szng of the nstallaton ncreases. So, f there s no restrctng factor such as non-favourable geologcal condtons, the geothermal nstallaton should be szed on the maxmum szng, even f the storage mpacts most the medum szng of the nstallaton. Furthermore, t can be seen that the nvestment of the mnmum szng of the nstallaton s not vable n any case although the use of the heat store s benefcal. Ths happens because the operatonal costs are very hgh compared to the nflows of the nvestment. In order to overcome ths problem a soluton would be to ncrease the varable cost of heatng ( nd part of the ncome), so that the nflow of the nvestment wll ncrease. But, n general, szng the nstallaton to cover a small part of the load by geothermal energy should be avoded. Another crucal fndng from Table, s the tremendous assstance of a fnancal subsdy on a renewable project. As can be seen n the results, all the fnancal ndces ncrease by 0% or more when the RHI s taken nto account. Ths can also be made clear n Fgs. a, b, a and b where the cash flow charts of the mddle and hgh szng of the nstallaton are shown for the cases that the RHI s taken and s not taken nto account, respectvely. As can be seen n these graphs, the effect of the RHI s very mportant and decreases the payback perod of the nvestment. It should be noted that the change n the slope n

21 these graphs n the 0 years of the nvestment s because the RHI s not provded after ths perod of tme, so the ncome conssts only of the frst two parts after the 0 th year of operaton. It can also be made clear that the effect of the heat storage s much more mportant n the case of the mddle szng of the nstallaton compared to the case of the hgh szng. Concernng the emssons of the nstallaton, t can be seen that the emssons of CO decrease f the heat storage s used for any case of szng of the nstallaton. Ths s totally expected, snce the emssons are drectly proportonal to the amount of fuel used. The relatve decrease of the emssons n the -C s small snce, as already mentoned, almost all the geothermal producton s sent drectly to the heat load and, therefore, the change n the operaton of the peak-up bolers s not tremendous. On the other hand, the hghest absolute decrease of emssons s for the 0-C case where the mpact of the heat storage s the maxmum. It can also be seen that the emssons decrease as the szng of the nstallaton ncreases. Snce the szng of the nstallaton ncreases, more geothermal energy and less fuel are used, so the emssons wll decrease. Ths fndngs and trends are n agreement wth the results shown on Table about the operatonal cost of fuel. Fnally, n Table t can be seen that the load factor of the geothermal part of the nstallaton ncreases when the heat store s used. Ths means that the geothermal part of the nstallaton operates n a hgher average flow rate ncreasng ths way the utlsaton of geothermal energy. On the other hand, 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 ncreases, so there can be many tmes of the year that the heat demand can be covered just by a part of the geothermal producton. When the szng of the nstallaton s the smallest one, the potental geothermal producton s low, so almost all the geothermal producton s sent drectly to the heat demand. For example, n our case, n the smallest szng of the nstallaton the load factor s.% when the heat store s used, whch means that the geothermal nstallaton s workng very close to ts full capacty all the year. 0 Fgure a. Cash flow wth the RHI subsdy (0-C) Fgure a. Cash flow wth the RHI subsdy (-C)

22 Fgure b. Cash flow wthout the RHI subsdy (0-C) Fgure b. Cash flow wthout the RHI subsdy (-C) 1. CONCLUSION The effect of applyng a hot water storage tank to cover a part of the peak-load n a GDHS under a dfferent control strategy has been studed n ths paper. Typcally, n these systems the geothermal flow rate s varable wthn the day accordng to the heat demand and the peak demands are covered by bolers. It s proposed to keep the geothermal flow rate constant throughout the day and store hot water n tmes of low-load and release t n peak demand tmes. Frst, an algorthm for the szng of the nstallaton was developed and the outcome of ths algorthm was used as nput n the second algorthm whch studes the operaton of the nstallaton over a random day and over a whole year. Fnally, an ntegrated economc and envronmental analyss of the proposed soluton together wth a comparson wth the tradtonal operaton of a GDHS was carred out. All the calculatons have been done for three test cases of szng of the geothermal part of the nstallaton. More specfcally, they were done for the days that ther daly heat demand was the th -, 0 th - and th -centle (called -C, 0-C and -C n bref) of the daly heat demands of the whole year, respectvely. The conclusons that are drawn from ths study are the followng: The heat losses of the storage tank can be mnmsed f the tank s well nsulated. In our case, an nsulaton of 0cm was used and the heat losses were neglgble n most of the cases. The mportance of the heat losses n the ppelnes at the ntal desgn stage was hghlghted. An optmzaton algorthm for ther szng that takes nto account ther heat losses was bult. The results ndcate that by usng the specfc algorthm, the heat losses are much smaller than other publshed values. Ths ndcates that the heat losses were probably underestmated n the past and that they should be defntely taken nto account on the desgn stage of the network.

23 Both the captal and the operatonal costs are proved to be lower for the studed case compared to the tradtonal approach for any case of szng. As the szng of the nstallaton ncreases, t was shown that the captal cost ncreases whle the operatonal costs decrease. All the fnancal ndces are more attractve n the proposed case compared to the tradtonal approach for any case of szng. The levelsed cost of heatng decreases, whle the NPV, the IRR and the BCR decrease. The hghest mpact of the storage occurs n the 0-C case where the heat store s utlsed n an optmum way. On the other hand, the fnancal vablty of the nvestment ncreases as the szng of the nstallaton ncreases. Therefore, the maxmum vablty occurs n the -C case. The emssons of the nstallaton decrease when the heat store s used snce less fuel s used to cover the peak demands. The bggest absolute and relatve decreases n the emssons occur n the 0-C and n the -C case, respectvely. Fnally, the load factor of the geothermal part of the nstallaton ncreases when the heat store s appled for any case, meanng that more geothermal energy s utlsed. Therefore, t can be concluded that by applyng a heat storage under the proposed control strategy n a GDHS the overall producton of heat s cheaper and the peak-up bolers are used less. Increased utlsaton of geothermal energy as well as substantal reducton of emssons s also succeeded wth the proposed approach. All these hghlght the fnancal and envronmental benefts of ths approach whch are necessary for sustanable growth. 1 0 ACKNOWLEDGEMENTS 1 The authors would lke to thank Cluff Geothermal Ltd., the Energy Technology Partnershp (ETP) and the Unversty of Glasgow for fundng ths research project. NOMENCLATURE Symbol Quantty SI Unt A Area m AHD Annual heat demand J AOH Annual operatng hours Dmensonless BCR Benefts-to-cost rato Dmensonless

24 C Cost CC Captal Cost Cp Specfc heat capacty J kg K CRF Cost recovery factor Dmensonless D Dameter m δh Frcton losses m DHD Daly heat demand kwh dt Temperature dfference K dt Tme dfference s g Gravtatonal acceleraton m s H Heght m h Convectve heat transfer coeffcent W m K IP Investment perod Years r Interest rate Dmensonless IRR Internal rate of return Dmensonless K Overall heat transfer coeffcent W m K k Conductve heat transfer coeffcent W m K LCH Levelsed cost of heatng kwh M Mass kg m Mass flow rate kg s NPV Net present value Nu Nusselt number Dmensonless OC Operatonal cost P Electrcal power W Pr Prandtl number Dmensonless Q Heat J or kwh Q Heat power W Re Reynolds number Dmensonless

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