Optimized geotermal binary power cycles Kontoleontos E., Mendrinos D., Karytsas C. Centre for Renewable Energy Sources, 9t km Maratonos ave., 9009 Pikermi Attikis, Greece ABSTRACT Tis study as been carried out for te LOW-BIN (Efficient Low Temperature Geotermal Binary Power) project, wic is supported by te European Commission FP6 program. Its aim is to study and recommend optimal Rankine cycles using Isobutane (R600a) and R34a as working fluids for two geotermal binary power macines. Te first one (ORC macine A) sould be able to generate electricity from low temperature geotermal resources, wit profitable operation down to 65 C. Te second one (ORC macine B) sould be able to cogenerate bot eat and power by eat recovery from te cooling water circuit, corresponding to geotermal fluids of 20-50ºC and cooling water supplying a district eating system at 60/80ºC. Te main Rankine Cycle parameters and components are modelled, suc as te sell and tube condenser and te geotermal plate eat excanger. Te objectives of te optimization are maximizing overall conversion efficiency and minimizing te cost of te plant, wic is represented as minimizing of te excangers surface. Troug tis study, a set of optimal solutions for ORC macines A and B are obtained, tat combine maximum plant s efficiency (6.7-7.4 %) and minimum cost. Eac optimal solution corresponds to an optimal Rankine Cycle and every parameter of te cycle is defined.. INTRODUCTION Te main objectives of te LOW-BIN project are to:. widen market perspectives of geotermal Rankine Cycle power generation by developing and demonstrating a unit tat can generate electricity from low temperature geotermal resources, wit temperature tresold for profitable operation at 65 C, compared wit 90-00 C of existing units. In tis study tis will be called ORC macine A. 2. develop and demonstrate a Rankine Cycle macine for cogeneration of eat and power by eat recovery from te cooling water circuit. Tis will lead in cogeneration of eat and power from Rankine Cycle units in present and future geotermal district eating scemes. In tis study tis will be called ORC macine B. Te ORC plants manufacturer TURBODEN is te industrial partner to te LOW-BIN project. Overall researc and demonstration is supported by te European Commission DG-TREN, troug its 6 t framework for support programme.
Tis paper presents te researc carried out in CRES until now towards te above objectives. Tis corresponds to studying and recommending optimal Rankine cycles for te two geotermal binary power macines mentioned above, e.g. ORC macines A and B. Based on our researc presented during te ENGINE worksop eld in Strasbourg in mid September 2006, we selected for optimization purposes water cooled macines due to te corresponding iger conversion efficiency and lower costs [4]. Isobutane (R600a) and R34a ave been selected as working fluids due to te following reasons: Tey are widely used wit excellent results in te eat pumps and cooling/refrigeration industry, wic involves inverse Rankine cycle macines. Bot isobutane (R600a) and R34a are available in te market. Te necessary parts for te corresponding Rankine cycle macine are also available in te market. CARRIER, te multinational air-conditioning manufacturer as lately developed a low cost 200 kwe geotermal binary power unit using R34a as working fluid. Te plant was installed in te Cena geotermal field in Alaska, USA, utilizing 74 C water. Two units ave been installed, wic commenced operation in August 2006 and December 2006 respectively. Ten te main Rankine Cycle parameters and components ave been defined. Te Rankine cycle plant is scematically presented in Figure. Figure : Binary plant layout. 2
2. MODELLING RANKINE CYCLE PARAMETERS 2.. Cooling eat excanger (condenser) For tis study we ave used sell and tube condenser, wic is standard practice in geotermal binary power plants. Te overall eat-transfer coefficient for te condenser is given by equation (): U o A A o i i + Ao ln o 2πkL ( r / r ) i + o () were A o and A i represents te out and in surface areas respectively of te inner tubes, L is te lengt of te tubes, i is te eat transfer coefficient inside te tubes were te cooling fluid flows, o is te eat transfer coefficient outside te tubes were te working fluid flows and k represents te termal conductivity of te tube s material. Te eat transfer coefficient outside te tubes is based on te following formula for laminar film condensation on orizontal tubes: o ( ρ ρ ) ρ 0.725 μ f d v ( T T ) g g fg w k 3 f 0.25 (2) were ρ and ρ v represent te density of working fluid in liquid and vapour forms respectively, fg is te latent eat, μ f is te dynamic viscosity of te working fluid, k f is te termal conductivity of te working fluid, d te outside diameter of te tube, T g is te saturation temperature of te fluid condensate and T w te temperature of te tube s wall. Te eat transfer coefficient inside te tubes for turbulent flow is based on te following formulas : Nuk i D Nu 0.023Re u D ρ Re μ 0.8 Pr 0.4 (3) were D stands for te outside diameter of te tube, k for te cooling water s termal conductivity, Nu is te Nusselt number, Pr te Prantl number, and Re te Reynolds number calculated for te ρ, μ cooling water s properties inside te tube. 3
2.2. Geotermal Heat Excanger (Evaporator) Te eat excanger used in tis study is of te plate eat excanger (PHE) type wit corrugated parallel plates attaced to one anoter and fitted into a casing. Te plates could ave a corrugation angle of β to te main flow direction but in tis analysis we maintained te flow to be parallel to te plates (β 90). Plate type excangers are preferred to sell and tube excangers, as far as it concerns te geotermal eat transfer, because te geotermal water usually contains dissolved particles or ions (silica SiO 2 or salts suc as calcium carbonate CaCO 3 ), wic tend to be deposited on te surfaces and cause fouling of te eat excanger. It is obvious tat it is easier to clean tem from te plates rater tan te tubes, as a plate eat excanger can be easily dismantled and cleaned eiter mecanically or cemically. Te overall eat-transfer coefficient: U o Δx (4) + + ktit wf gw were Δx represents te tickness of te plate, wf is te eat transfer coefficient of te working fluid, gw is te eat transfer coefficient of te ground water and k represents te termal conductivity of te plate s material, (titanium in tis study). Te eat transfer coefficient of te ground water for turbulent flow is based on te following formulas: u L p ρ Re μ 0.074 050 c f 0.2 Re Re c f St 2 2 3 Pr Nu St Re Pr Nu k gw L p (5) were L p is te lengt of te plate, Re te Reynolds number calculated for te ρ, μ geotermal water properties, c f te friction coefficient for te flat plate for Reynolds numbers as Re crit <Re L < 0 7, Nu is te Nusselt number, Pr te Prantl number, k te geotermal water termal conductivity. In order to compute te eat transfer coefficient of te working fluid different eat transfer coefficients are used for eac fluid pase regime. Tis is necessary as its corresponding flow in te geotermal eat excanger (evaporator) begins as single liquid pase flow, ten as evaporation starts it becomes two-pase flow, and finally wen all liquid as been turned into vapour it becomes single vapour pase flow. 4
Te eat transfer coefficient for two pase flow is based on te following formula wic was presented by Ayub [] in an extensive literature review for Plate Heat Excangers (PHEs): 0.424 2 0.2 0.35 k Re l l fg p 65 tp C (6) De LP pcr β were D e is te diameter (taken as twice te mean plate spacing in PHEs), k l te working fluid s termal conductivity for te liquid pase, fg is te latent eat, p is te working fluid s pressure in te inlet of te eat excanger, and β is te plate corrugation inclination angle. Tis correlation is not dimensionless and te values are based on Englis units, so in order to use it we converted it into SI units. Te eat transfer coefficients for single pase flow (liquid, gas) is based on te following formulas: u L ρ Re μ 0.074 050 c f 0.2 Re Re c f St 2 2 3 Pr Nu St Re Pr sp / l, g Nu k L (7) So we calculate tree overall eat-transfer coefficients, one for every pase and we come up wit te total coefficient : U sp / l sp / l Δx + + ktit gw, U tp tp Δx + + ktit gw, U sp / g sp / g Δx + + ktit gw U total U sp / l + U tp + U sp / g 3. RANKINE CYCLE OPTIMIZATION FOR DIFFERENT WORKING FLUIDS Te optimization tool used is code EASY (Evolutionary Algoritm System by National Tecnical University of Atens), ttp://velos0.ltt.mec.ntua.gr/easy. EASY is a generic optimization tool developed by te Parallel CFD and Optimization Unit of te Laboratory of Termal Turbomacines. EASY is based on Evolutionary Algoritms 5
and Artificial Intelligence and is capable to solve eiter single or multi-objective optimization problems, wit or witout constraints. It exploits Multi-level and/or Distributed exploration on te field of variables and can be efficiently combined wit oter deterministic optimization metods. It operates in parallel on Unix or Windows clusters and employs user friendly grapical interface. A detailed overview of te algoritmic features of EASY and its additional capabilities can be found in publications, suc as [2] and [3]. In order to optimize te Rankine cycle of a typical geotermal binary plant, te optimization s objectives, te variables, te variables limits and te constraints of te optimization ave to be defined. Objectives of te optimization Maximization of te overall net conversion efficiency of te plant: η cycle W turbine Q N eatexc pump ( 4 5 ) mwf ( 3 2 ) mwf Minimization of te cost of te plant. Since te cost of te eat excanger and te condenser constitute a major part of te plant cost, for our optimizing purposes te cost plant can be substituted by teir cost. So te new goal is to minimize te cost of te eat excanger and te condenser wic is proportional to teir surface Minimization of te excangers surface. Variables of te optimization N pump. te pressure of te liquid working fluid at te pump outlet, p 2 2. te ot ground water mass flow rate, m gr 3. te mass flow rate of te working fluid in te cycle, m wf 4. te temperature difference of te ground water in te eat excanger, ΔΤ Η 5. te temperature difference of te cooling water in te condenser, ΔΤ C Constraints of te optimization In te framework of te LOW-BIN project, te electrical power of te plant is at 200kW e and it is defined as a constraint in tis optimization. Tis indicates tat eac solution (eac optimal Rankine cycle) as to respect tis constraint (95kW is te minimum accepted value and 205kW te maximum accepted value). As mentioned above, in order to optimize te cycle, te working fluids tat were selected, are R34a and Isobutane (R600a). 4. TEMPERATURE THRESHOLD AT 65 C (ORC MACHINE A) 4.. R34a For te ORC macine A, te limits of te optimization variables are sown in table, wile te results of te optimization are plotted in figure 2 in te case of R34a used 6
as working fluid. A representative solution and eat excanger geometry are presented in tables 2 and 3 respectively. Table. Upper and lower limits of te optimization variables for R34a. Variable Lower limit Upper Limit p 2 (kpa) 750 200 m gr (kg/sec) 45 55 m R34a (kg/sec) 0 20 ΔΤ H ( C) 0 30 ΔΤ C ( C) 7.5 2.5 0 optimal solutions - R34a 9.8 excangers' surface 9.6 9.4 9.2 9 8.8 8.6 8.4 0.066 0.067 0.068 0.069 0.07 0.07 0.072 0.073 0.074 binary plant's overall efficiency Figure 2: Rankine cycle optimization- optimal solutions for R34a. Eac point of te above cart, wic is called te Pareto front, represents an optimal solution tat respects te constraints of te optimization. Eac solution is represented by two numbers wic constitute te objectives of te optimization, te eat transfer surface of te excangers (geotermal eat excanger and R34a condenser) and te overall conversion efficiency of te binary plant. Additionally, eac solution resulted from a different combination of te optimization variables and corresponds to an optimal Rankine cycle. Te Pareto front supplied us wit 50 7
optimal solutions and te selection of a solution depends on wic of te two objectives we want to give priority. A representative solution (pointed wit te arrow in te figure) as been selected in order to observe te values of several important parameters of te optimized Rankine cycle, wic are presented in table 2. Table 2. A representative solution for R34a. Parameter Value Range p 2 (kpa) 99 750-200 m gr (kg/sec) 5.2 45-55 m R34a (kg/sec) 7.5 0-20 ΔΤ H ( C) 8.6 0-30 ΔΤ C ( C) 7.5 7,5 2,5 R34a pump power (kw) 3.4 Cooling water flow (kg/sec) 6 Surface of te condenser (m 2 ) 5.5 Surface of te eat excanger (m 2 ) 4.0 Total H.E. surface (m 2 ) 9.5 Net conversion efficiency 7.6 Net Electrical Power (kw) 202 It is obvious tat te outlet pressure of te pump, p 2 (wic is indicated by te temperature of te ground water), acieves te value of te upper limit in order to take total advantage of te ground eat and maximize te electrical power and proportionally te overall efficiency of te plant. In order to get an idea about te dimensions of te excangers, according to te surface of te optimal solution, typical dimensions used in our study are presented in table 3. Table 3. Typical features and dimensions of eat excangers for R34a P.H.E. - plate eat excanger Sell and tube condenser Lengt of te plate (m) 0.8 Diameter of te tube (cm).3 Widt of te plate (m) 0.3 Total lengt of te tubes (m) 36 Number of plates 7 Number of tubes 29 Total tickness (m) 0.04 Lengt of te condenser (m) 5 8
4.2. Ιsobutane R600a For te ORC macine A, te limits of te optimization variables are sown in table 4, wile te results of te optimization are plotted in figure 3 in te case of R600a used as working fluid. A representative solution and eat excanger geometry are presented in tables 5 and 6 respectively. Table 4. Upper and lower limits of te optimization variables for R600a. Variable Lower limit Upper Limit p 2 (kpa) 390 620 m gr (kg/sec) 45 55 m isob (kg/sec) 0 20 ΔΤ H ( C) 0 30 ΔΤ C ( C) 7.5 2.5 6 optimal solutions - isobutan 5 excangers' surface 4 3 2 0 0.06 0.062 0.064 0.066 0.068 0.07 0.072 binary plant's overall efficiency Figure 3: Rankine cycle optimization- optimal solutions for R600a. 9
Table 5. A representative solution for R600a. Parameter Value Range P 2 (kpa) 69 390-620 m gr (kg/sec) 46 45-55 m isob (kg/sec) 0.2 0-20 ΔΤ H ( C) 2.8 0-30 ΔΤ C ( C) 7.5 7,5 2,5 pump power ( kw) 3.9 Cooling water flow (kg/sec) 9 Surface of te condenser (m 2 ) 7.0 Surface of te eat excanger (m 2 ) 5.7 Total H.E. surface (m 2 ) 2.7 Net conversion efficiency 7.04 Net electrical Power (kw) ~ 200 Table 6. Typical features and dimensions of eat excangers for R34a P.H.E. - plate eat excanger Sell and tube condenser Lengt of te plate (m) 0.8 Diameter of te tube (cm).3 Widt of te plate (m) 0.3 Total lengt of te tubes (m) 7 Number of plates 29 Number of tubes 35 Total tickness (m) 0.07 Lengt of te condenser (m) 5 4.3. Comparison between R34a and Isobutane Comparison of te optimal solutions for te ORC macine A for te working fluids R34a and isobutene (R600a) is sown in figure 4, wile a comparison of te key variables corresponding to te optimal solutions selected above is sown in table 7. By comparing te optimal solutions between Isobutane and R34a, it becomes evident tat te surface of te eat excangers needed for R34a is less tan te one for Isobutane wen te plant s efficiency is around 7% in bot cases. On te oter and owever, te geotermal water flow rate, te working fluid mass flow rate and necessary auxiliary pumping power are iger in te case of R34a tan in R600a. As te vapor density of R600a is more tan 3 times less tan te one of R34a te necessary turbine volume for R600a sould be around 2 times iger tan te one of R34a, furter increasing te cost difference between te two macines. 0
8 6 Comparison R34a - isobutan isobutan R34a excangers' surface 4 2 0 8 0.06 0.062 0.064 0.066 0.068 0.07 0.072 0.074 binary plant's overall efficiency Figure 4: Rankine cycle optimization- optimal solutions for bot R34a and R600a. Table 7. Rankine cycle variables for selected optimal solutions for R34a and R600a. Variable Isobutane R34a P 2 (kpa) 69 99 m gr (kg/sec) 46 5.2 m working fluid (kg/sec) 0.2 7.5 ΔΤ H ( C) 2.8 8.6 ΔΤ C ( C) 7.5 7.5 pump power ( kw) 3.9 3.4 Cooling water flow (kg/sec) 9 6 Surface of te condenser (m 2 ) 7.0 5.5 Surface of te eat excanger (m 2 ) 5.7 4.0 Total H.E. surface (m 2 ) 2.7 9.5 Net conversion efficiency 7.04 7.6
5. TEMPERATURE THRESHOLD AT 20 C (ORC MACHINE B) As we ave described before, in ORC macine B te optimization concerns of a Rankine Cycle for cogeneration of eat and power by eat recovery from te cooling water circuit since te geotermal fluids is of 20ºC and te cooling water supplies a district eating system at 60/80 ºC. In tis analysis te variables are four since te temperature difference of te cooling fluid in te condenser, ΔΤ C, is stable at ΔΤ cond. 20 ºC. Te variables limits are sown in table 8, wile te te optimal solutions are presented in figure 5, wile te key cycle variables for one optimal solution are sown in table 9, togeter wit te ones corresponding to te ORC macine A. Table 8. Upper and lower limits of te optimization variables for ORC macine B. Variable Lower limit Upper Limit p 2 (kpa) 300 3500 m gr (kg/sec) 45 70 m R34a (kg/sec) 25 40 ΔΤ H ( C) 5 30 40 optimal solutions - R34a 35 excangers' surface 30 25 20 5 0.048 0.05 0.052 0.054 0.056 0.058 0.06 0.062 binary plant's overall efficiency Figure 5: Rankine cycle optimization- optimal solutions for ORC macine B. 2
Table 9. Rankine cycle variables for selected optimal solutions for ORC macine B and R34a as working fluid. Variable 20 ο C 65 o C P 2 (kpa) 3499 99 m gr (kg/sec) 52 5.2 m R34a (kg/sec) 35 7.5 ΔΤ H ( C) 26 8.6 ΔΤ C ( C) 20 7.5 Cooling Temperature ( C) 60 0 Condensing Temperature ( C) 80 30 R34a pump power (kw) 58 3.4 cooling water flow (kg/sec) 66 6 Surface of te condenser (m 2 ) 22.0 5.5 Surface of te eat excanger (m 2 ) 2.0 4.0 Total H.E. surface (m 2 ) 24.0 9.5 Net conversion efficiency 5.93 7.6 Net electrical Power (kw) 207 202 By comparing ORC macines A to B for R34a, it is observed tat tere is a significant difference in te mass flow rate of te working fluid and te pump power (4kW to 60kW). On te oter and, te cooling fluid flow needed for ORC macine B is muc less tan ORC macine A and tis is due to te temperature difference of te cooling fluid in te condenser wic is ΔΤ C. 20 ºC for ORC macine B wen ΔΤ C. 7.5 ºC for ORC macine A. It is also evident tat wen te ground water reaces 20 ºC, te surface of te geotermal eat excanger is less, due to te iger temperature difference between te geotermal water and te R34a. We can also observe tat a major difference exists in te value of te condenser s surface wic is attributed to te extremely small temperature difference between te condensing temperature and te cooling water outlet temperature. 6. COMPARISON WITH EXISTING BINARY MACHINES OPTIMIZED FOR 00 Ο C GEOTHERMAL WATER In order to examine te feasibility of te two ORC macines, one last optimization run was performed using a standard ORC plant for geotermal water supply of 00 C, but using R34a as refrigerant, in order to obtain comparable results. Te comparison of all tree macines is sown in figure 6 and table 0. 3
45 40 R34a - temperature tresold at 65,00,20 65 00 20 surface of te excangers 35 30 25 20 5 0 5 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 overall efficiency of te binary plant Figure 6: Rankine cycle optimization- optimal solutions for R34a macines. Table 0. Rankine cycle variables for selected optimal solutions for tree ORC macines (A, B and Standard) wit R34a as working fluid. Variable Heat & power cogeneration 20 ο C Power generation 65 o C Standard binary power plant, 00 ο C P 2 (kpa) 3499 99 552 m gr (kg/sec) 52 5.2 45 m R34a (kg/sec) 35 7.5 7.8 ΔΤ H ( C) 26 8.6 20.0 ΔΤ C ( C) 20 7.5 7.5 Cooling Temp ( C) 60 0 0 Condensing Temp ( C) 80 30 27 R34a pump power (kw) 58 3.4 8.5 cooling water flow (kg/sec) 66 6 0 Condenser surface (m²) 22.0 5.5 4.6 Surface of te PHE (m²) 2.0 4.0 5.4 Total H.E. surface (m²) 24.0 9.5 0 Net conversion efficiency 5.93 7.6 7.7 Net electrical Power (kw) 207 202 204 4
By comparing te optimum Rankine cycles of 65 C to standard binary macines of 00 C we come up wit te following conclusions: As far as it concerns te net conversion efficiency, te efficiency of te 65 C binary cycle ( 6.7-7.3%) is a little less tan tis of te 00 C binary cycle ( 7.0-8.%), wic is predictable since te temperature of te geotermal water is lower. Tis observation sows tat even by using geotermal water of 65 C, te conversion efficiency remains at te same levels as in binary units of 00 C. As far as it concerns te cost of te plant, by comparing te total surface of te eat excangers, te supply of te working fluid and te ot ground water supply, it is obvious tat tere is no significant difference wic sows tat te Rankine cycles of 65 C don t contribute to te increase of te plant s cost. By comparing ORC macine B (cogeneration of eat and power of 20 C geotermal water) to standards binary macines optimized for 00 C geotermal fluid supply, we come up wit te following conclusions: As far as it concerns te net conversion efficiency, te efficiency of te 20 C binary cycle ( 5.0-6.%) is less tan te one of te 00 C binary cycle ( 7.0-8.%). As far as it concerns te cost of te plant, by comparing te total surface of te excangers, te supply of te working fluid and te ot ground water supply, it is obvious tat tere is a difference wic sows tat te Rankine cycles of 20 C contribute to a remarkable increase of te plant s cost (almost te twofold cost). REFERENCES [] Ayub Z.H., Plate eat excanger literature survey and new eat transfer and pressure drop correlations for te refrigerant evaporators, Heat Transfer Engineering 24 (5) (2003) 3-6. [2] Giannakoglou, K.C., Design of Optimal Aerodynamic Sapes using Stocastic Optimization Metods and Computational Intelligence, Progress in Aerospace Sciences, 38, pp. 43-76, 2002. [3] Karakasis, M., Giotis, A.P., Giannakoglou, K.C., Efficient Genetic Optimization Using Inexact Information and Sensitivity Analysis. Application in Sape Optimization Problems, ECCOMAS CFD Conference 200, Swansea, Wales, 200. [4] Mendrinos D., Kontoleontos E., Karytsas C., Geotermal Binary Plants: Water or Air Cooled?. Presented during te ENGINE worksop 5 on Electricity Generation from Enanced Geotermal Systems, Strasbourg, France, 4-6 September 2006. [5] Brasz J., Biedermann B., Holdmann G., Power Production from a Moderate Temperature Geotermal Resource, GRC annual meeting, Reno, NV, USA, September 25-28, 2005. 5