A novel design approach for small scale low enthalpy binary geothermal power plants Roberto Gabbrielli ⇑ Dipartimento di Ingegneria dell’Energia e dei Sistemi, Facoltà di Ingegneria, Università di Pisa, Largo L. Lazzarino, 56126 Pisa, Italy article info Article history: Received 1 February 2012 Received in revised form 25 April 2012 Accepted 27 April 2012 Available online 26 September 2012 Keywords: Off-design modelling Binary geothermal power plants Organic Rankine Cycle Design optimization abstract In this paper a novel design approach for small scale low enthalpy binary geothermal power plants is pro- posed. After the suction, the hot water (brine) superheats an organic fluid (R134a) in a Rankine cycle and, then, is injected back underground. This fact causes the well-known thermal degradation of the geother- mal resource during the years. Hence, the binary geothermal power plants have to operate with condi- tions that largely vary during their life and, consequently, the most part of their functioning is executed in off-design conditions. So, as the novel approach here proposed, the design temperature of the geothermal resource is selected between its highest and lowest values, that correspond to the beginning and the end of the operative life of the geothermal power plant, respectively. Hence, using a detailed off-design performance model, the optimal design point of the geothermal power plant is evaluated maximizing the total actualized cash flow from the incentives for renewable power generation. Under different renewable energy incentive scenarios, the power plant that is designed using the lowest temperature of the geothermal resource always results the best option. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction The exploitation of geothermal energy that is considered a renewable power source is limited in very narrow zones, where it is possible to find geothermal sources with high temperature at low depth that can be used economically. During last years, in order to enlarge the use of renewable power sources, some geo- thermal wells characterized by low temperature liquid-dominated sources that in the past were not considered suitable for power generation, have been planned to be valorised from the energy point of view. For this kind of geothermal sources, where water- steam cycle cannot be practically adopted, the application of closed binary Organic Rankine Cycle (ORC) is considered technically and economically feasible. The hot brine is sucked from the well, it is cooled during the heating of a suitable organic fluid and, finally, it is injected back underground. As well known, the injection of the cold brine causes the tem- perature reduction of the geothermal resource through the years. This phenomenon can become particularly critical during long operative life of low enthalpy binary ORCs. Indeed, in this kind of power plants also temperature decreases of few degrees can imply both severe operative problems to the most important equipment and a strong degradation of their thermodynamic performances, because they have to operate largely in off-design conditions. Hence, the operative problems described above require a careful design of the geothermal power plants, in order to select the best design conditions (such as the working fluid and the functioning pressures) in function of the well characteristics (temperature and mass flow rate of the brine) [1]. The problem of sizing and optimizing low temperature binary ORC geothermal power plants has been largely discussed in litera- ture. The most part of the contributions adopts a design approach, where the uncontrolled variables of the plant, as geothermal source temperature, are simply assumed constant and equal to their initial values and the design variables, as the highest pressure of the power generation cycle, are investigated in order to optimize a particular performance index. A brief overview of the most meaningful recent papers about this kind of approach is outlined in the following. In [2], a closed Rankine cycle with internal regeneration using either ammonia or an ammonia–water mixture as working fluid has been opti- mized with design simulations in order to evaluate the best pres- sure that maximizes the thermal efficiency and the specific power output. Hence each plant parameter, such as turbine effi- ciency, has been assumed constant. Optimal design criteria for ORCs using low-temperature geothermal heat sources have been proposed in [3]. Different working fluids were analyzed and the de- sign conditions concerning the evaporation and condensation tem- peratures of the ORC have been obtained minimizing the ratio of total heat transfer area to total net power. In [4] the performance analysis of an ORC system using HFC-245fa as working fluid driven 0196-8904/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.enconman.2012.04.017 ⇑ Tel.: +39 050 2217138; fax: +39 050 2217150. E-mail address: [email protected]Energy Conversion and Management 64 (2012) 263–272 Contents lists available at SciVerse ScienceDirect Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Transcript
Energy Conversion and Management 64 (2012) 263–272
Contents lists available at SciVerse ScienceDirect
A novel design approach for small scale low enthalpy binary geothermalpower plants
Roberto Gabbrielli ⇑Dipartimento di Ingegneria dell’Energia e dei Sistemi, Facoltà di Ingegneria, Università di Pisa, Largo L. Lazzarino, 56126 Pisa, Italy
a r t i c l e i n f o
Article history:Received 1 February 2012Received in revised form 25 April 2012Accepted 27 April 2012Available online 26 September 2012
Keywords:Off-design modellingBinary geothermal power plantsOrganic Rankine CycleDesign optimization
0196-8904/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.enconman.2012.04.017
In this paper a novel design approach for small scale low enthalpy binary geothermal power plants is pro-posed. After the suction, the hot water (brine) superheats an organic fluid (R134a) in a Rankine cycle and,then, is injected back underground. This fact causes the well-known thermal degradation of the geother-mal resource during the years. Hence, the binary geothermal power plants have to operate with condi-tions that largely vary during their life and, consequently, the most part of their functioning isexecuted in off-design conditions.
So, as the novel approach here proposed, the design temperature of the geothermal resource is selectedbetween its highest and lowest values, that correspond to the beginning and the end of the operative lifeof the geothermal power plant, respectively. Hence, using a detailed off-design performance model, theoptimal design point of the geothermal power plant is evaluated maximizing the total actualized cashflow from the incentives for renewable power generation. Under different renewable energy incentivescenarios, the power plant that is designed using the lowest temperature of the geothermal resourcealways results the best option.
� 2012 Elsevier Ltd. All rights reserved.
1. Introduction
The exploitation of geothermal energy that is considered arenewable power source is limited in very narrow zones, whereit is possible to find geothermal sources with high temperatureat low depth that can be used economically. During last years, inorder to enlarge the use of renewable power sources, some geo-thermal wells characterized by low temperature liquid-dominatedsources that in the past were not considered suitable for powergeneration, have been planned to be valorised from the energypoint of view. For this kind of geothermal sources, where water-steam cycle cannot be practically adopted, the application of closedbinary Organic Rankine Cycle (ORC) is considered technically andeconomically feasible. The hot brine is sucked from the well, it iscooled during the heating of a suitable organic fluid and, finally,it is injected back underground.
As well known, the injection of the cold brine causes the tem-perature reduction of the geothermal resource through the years.This phenomenon can become particularly critical during longoperative life of low enthalpy binary ORCs. Indeed, in this kind ofpower plants also temperature decreases of few degrees can implyboth severe operative problems to the most important equipmentand a strong degradation of their thermodynamic performances,because they have to operate largely in off-design conditions.
ll rights reserved.
Hence, the operative problems described above require a carefuldesign of the geothermal power plants, in order to select the bestdesign conditions (such as the working fluid and the functioningpressures) in function of the well characteristics (temperatureand mass flow rate of the brine) [1].
The problem of sizing and optimizing low temperature binaryORC geothermal power plants has been largely discussed in litera-ture. The most part of the contributions adopts a design approach,where the uncontrolled variables of the plant, as geothermalsource temperature, are simply assumed constant and equal totheir initial values and the design variables, as the highest pressureof the power generation cycle, are investigated in order to optimizea particular performance index.
A brief overview of the most meaningful recent papers aboutthis kind of approach is outlined in the following. In [2], a closedRankine cycle with internal regeneration using either ammoniaor an ammonia–water mixture as working fluid has been opti-mized with design simulations in order to evaluate the best pres-sure that maximizes the thermal efficiency and the specificpower output. Hence each plant parameter, such as turbine effi-ciency, has been assumed constant. Optimal design criteria forORCs using low-temperature geothermal heat sources have beenproposed in [3]. Different working fluids were analyzed and the de-sign conditions concerning the evaporation and condensation tem-peratures of the ORC have been obtained minimizing the ratio oftotal heat transfer area to total net power. In [4] the performanceanalysis of an ORC system using HFC-245fa as working fluid driven
B static exit pressure of expander (bar)EOS equation of stateORC Organic Rankine Cycle_m mass flow rate (kg/s)
P pressure (bar)T temperature (K)Yd Stodola’s constant of the expander (m�2 s�2 K�1)
Greek symbolsg efficiencyq mass density (kg/m3)/ mass flow coefficient, temperature form (m s
ffiffiffiffiKp
)
Subscriptsair ambient airb brined design pointgeo geothermal fluidin inletn netoff off-designR134a relative to the fluid R134a
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by waste heat was presented. The characteristics of the exhaustheat has been changed using a design approach during the simula-tions in order to maximize the system efficiency. Gu and Sato [5,6]studied the supercritical cycles with internal regeneration for geo-thermal binary power plants to reach the maximum thermal effi-ciency optimizing the cycle state parameters such as condensingtemperature and pressure. They investigated also different work-ing fluids for a given liquid dominated geothermal resource anddetermined the most suitable for their application.
In [7], artificial neural networks were used in order to optimizethe design condition of supercritical ORC-binary with a life cyclecost approach. In [8], exergy analysis of a binary geothermal powerplant was performed using actual plant data to assess the plantperformance and identify sites of primary exergy destruction. Witha design approach, the effects of turbine inlet pressure andtemperature and the condenser pressure on the exergy and energyefficiencies, the net power output and the brine injection temper-ature were investigated and the trends were explained. In [9], theeffects of the thermodynamic parameters on the internally regen-erative ORC performances were examined, and the thermodynamicparameters of the ORC were optimized using the exergy efficiencyas objective function by means of genetic algorithms. In [10], aparametric optimization and performance analysis of a waste heatrecovery system at low temperature based on ORC, using severalworking fluids for power generation have been studied. The aimof the study was to highlight the best working fluid for the specificapplication. The same authors optimized an ORC with superheat-ing under different heat source temperatures using several perfor-mance indicators in order to evaluate the best design conditionsand the best working fluid [11]. In [12], an investigation on theparameter optimization and performance comparison of fluids insubcritical ORC and transcritical power cycle in low-temperaturebinary geothermal power system has been presented. The optimi-zation procedure was conducted with a simulation program usingfive performance indicators. With the given heat source and heatsink conditions, performances of the working fluids have beenevaluated and compared under their optimized internal operationparameters. In [13], both the thermodynamic and the economicoptimization of a very small scale ORC in waste heat recoveryapplication has been presented in order to obtain the optimal siz-ing of the ORC with respect to different parameters. Finally in [14],a complete optimization model of an ORC was proposed. To thisaim the authors presented detailed performance models of eachcomponent in function of the main operative variables. The bestvalues of the controlled variables, such as relative working fluidmass flow rate, were obtained in order to maximize either thepower generation or the thermal efficiency. Also in this case, theuncontrolled variables, such as heat source temperature and flowrate, were fixed at their design values.
All these kinds of design approach do not take into account theeffects of the resource degradation on the plant performance and,consequently, the optimal designed geothermal power plant couldnot actually result the best solution using a larger perspective overtheir whole life.
In literature, the problem of the performance assessment forORC power plants in geothermal and waste-heat recovery applica-tions under part load and off-design conditions has been investi-gated by some authors. All of them analyses the behavior of thiskind of power plants when the thermodynamic features of the heatsource and cooling sink are different from their starting valuesused in the design phase. Hence, they do not discuss the problemof the optimal design of ORC geothermal power plants when themost part of their operative conditions is different from the designpoint. In particular, in [15] once fixed the design conditions, resultsof performance studies for a binary pilot dual pressure cycle pro-cess with isobutane as working fluid were presented. The simula-tions, based on a mathematical model, whose detailedformulation is not reported by the author, were performed undervarying geofluid inlet temperature and flow rate, varying ambientconditions, varying heat exchanger fouling and varying turbineconfiguration. The most meaningful result was that the decreasesin geofluid temperature can be compensated for by the increasein geofluid flow. In [16], an accurate and well-described procedurewas reported to predict the ORC power plant performance underoff-design conditions when the hot brine and the cooling watertemperatures vary through the year. When the design values ofheat source and cooling water are 85 �C and 25 �C, respectively,the power plant was able to maintain acceptable performancesalso with temperature modifications in heat source and coolingwater of about 15 �C and 5 �C. In [17], the impact of off-designoperation on air-cooled binary geothermal power plant, whenchanges in the ambient air temperature, as well as the decline inresource productivity over time, occur, has been examined usingAspen Plus simulation software. The simulation results indicatedthat as plant operation deviates from the design resource andambient scenario, its ability to convert the available energy inthe inlet brine degrades. In [18] an Aspen Plus based simulationmodel of part load and off-design operation of an ORC unit forcombined heat and power in the furniture manufacturing industryhas been developed. The performances have been evaluated vary-ing the condensation pressure and the input thermal power. Wal-num et al. [19] focused on the off-design operation of ORCs forpower generation from low temperature sources and comparedthe behavior of transcritical CO2 cycles and an ORC cycle withR123 as working fluid when the temperature and mass flow rateof the heat source vary. The main result was that the ORC is verysensitive to reduction in available heat. This required to operatethe ORC with some degrees superheat. Finally in [20] the off-design
Fig. 2. Temperature-entropy diagram of the ORC (temperature of the geothermalfluid = 130 �C).
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behavior of solar-geothermal hybrid plant based on ORC has beenevaluated when the solar derived thermal input varies through theyear and the thermal features of the geothermal source and coldsink are fixed and equal to their design values.
Taking into account the scientific contributions describedabove, in this paper a novel approach for the optimal design of bin-ary ORC low enthalpy geothermal power plants is proposed. In-deed, the optimal design procedure is executed taking intoaccount their whole operative life, that is simulated with a detailedoff-design model. On the basis of the optimization process hereproposed, the best design point is searched through the whole lifeof the power plant and not only at the starting of the well exploi-tation as commonly executed in literature.
In particular, the design brine temperature is optimally selectedin the range between its highest and lowest values. Then, the bestconfiguration is highlighted using a procedure based on the maxi-mization of the total actualized cash flows derived from greenincentives for renewable electricity. These cash flows are calcu-lated using off-design simulations of the whole operative life ofthe plants, when the brine and ambient air temperatures varythrough the years and the days, respectively.
Hence, the paper is structured in the following way: after thedescription of the binary ORC and the geothermal site, that havebeen taken into account as reference, the off-design simulationmodel is detailed described. The results of the simulation activityare successively presented and discussed. Then, the economic opti-mization and the best power plant selection are reported. Finally,conclusions and future works are outlined.
2. The binary ORC geothermal power plant
The binary ORC geothermal power plant, that has been takeninto account as reference in the novel design procedure describedbelow, is composed by two circuits (Figs. 1 and 2), where the geo-thermal fluid (brine) and the organic fluid are present, respectively.In the primary circuit, the brine is sucked at 20 bar and 160 �C, thatis its original temperature before the starting of the well exploita-tion. Then, it is cooled in a shell and tube heat exchanger to a tem-perature equal to 70 �C (5–6 in Figs. 1 and 2), that is higher thanthe crystallization temperature in order to have a safe margin withrespect to the salt precipitation. Finally, it is injected back under-ground by the circulation pump.
In the secondary circuit, the organic fluid, that is R134a, ispumped to a supercritical pressure (1–2 in Figs. 1 and 2). Then, it
Fig. 1. Plant layout of
is superheated in the shell and tube heat exchanger by the coolingof the brine (2–3 in Figs. 1 and 2). In the expander the organic fluidexpands to the condenser pressure producing electric power (3–4in Figs. 1 and 2). The condensation is assured by dry air coolerswithout water consumption (4–1 in Figs. 1 and 2). Matching cycleto a given geothermal resource such that power output can bemaximized is a very important aspect of every optimization pro-cess of ORC. Two major and largely interrelated components ofthe cycle are the working fluid and the turbine. Both componentsneed careful consideration in order to optimize the amount ofpower that can be extracted from a specific resource [21]. For theparticular features of the geothermal source considered in this pa-per, the supercritical configuration of the cycle and R134a as or-ganic fluid, whose critical thermodynamic conditions are40.59 bar and 101.1 �C, resulted the best options in order to maxi-mize the design performance of the geothermal resource exploita-tion [22,23]. The internal regeneration in the ORC between theoutlets of the expander and pump has not been considered becauseit can cause severe operative problems when the geothermalsource temperature is low.
the binary ORC.
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At the design point, the main input data of the ORC used in thesimulation analyses are:
� Gross power of the expander: 500 kW. This value is limited bythe characteristics of the geothermal heat source.� The inlet expander pressure is 50 bar [22,23].� The isoentropic efficiency of the expander is 85% [20,22,23].� The isoentropic efficiency of the pump is 80%.� The generator efficiency is 98%.� The approach point in the shell and tube heat exchanger
between the brine inlet and the R134a outlet is 10 �C.� The condenser pressure and temperature are 8 bar and 31 �C,
respectively.� The ambient air temperature (Tair) is equal to 15 �C.
3. Site characteristics
The geothermal source, located in the center of Italy, can beconsidered at low enthalpy. As reported above, the starting tem-perature of the geofluid is 160 �C and the maximum allowablemass flow rate that can be sucked from the geothermal well isabout 60 t/h. The injection of the cold brine is executed at 70 �Cin order to avoid operative problems of salting scaling. This impliesthat the geothermal source temperature decreases during itsexploitation. It has been assumed that the temperature decreaseis constant and equal to 1 �C per year. Hence after 30 years of plantoperative life, the brine temperature can be estimated equal to130 �C.
The daily variability of Tair has been characterized by its sto-chastic distribution using measured data for three different sitesfrom Meteonorm Software [24]. These sites can be considered rep-resentative of three kinds of climate, where the temperatures areon average low (cold site), medium (warm site), and high (hot site).In this way it is possible to assess the effect of the particular cli-mate on the results of the novel design approach here proposed.
Supposing that the availability of the power plant is 80%, theoperative hours with a particular Tair have been calculated (seeTable 1). We supposed that the plant downtimes occur as an uni-form distribution during a generic year.
4. The off-design simulation model
The off-design simulation model of the binary geothermal ORCpower plant has been built with Aspen Plus simulation software.This tool does not provide the user with specific built-in routinesfor the off-design simulation of thermodynamic systems. Hence,a number of specific Fortran routines has been included in themodel in order to obtain reliable results [25].
Table 1Frequency of the ambient air temperature and plant availability during a generic year for
The ORC expander has been supposed to operate as sliding pres-sure mode with fixed nozzle area [20]. Therefore, the inlet pressuredepends on the flow characteristics of the machine and can be cal-culated using the Stodola’s ellipse approach [26–28]:
The Stodola’s constants for the calculation of Yd have been evalu-ated using the values relative to the design conditions of theexpander.
The isentropic expansion efficiency has been evaluated usingthe simple formula reported below [29]:
goff ¼ gd sin 0:5p_mR134a�in�off
_mR134a�in�d
qR134a�in�d
qR134a�in�off
� �0:1" #
ð4Þ
4.2. Shell and tube supercritical heat exchanger
First, for each design point the heat exchanger has been detaileddesigned from the thermo-mechanical point of view defining themain geometry characteristics, such as tubes and tubesheet layout,tube length, number of baffles and diameter of shell and nozzles.Then, the heat exchanger has been inserted within the simulationmodel using the option ‘‘simulation mode’’, so that the actual over-all heat transfer coefficient, the pressure losses and the thermody-namic characteristics of the outlet streams have been calculated infunction of the inlet streams for every operative condition.
4.3. Air cooler condenser
Similarly to the previous heat exchanger, the off-design perfor-mances of the air cooled condenser have been evaluated using theoption ‘‘simulation mode’’. After the detailed thermo-mechanicalsizing of the air cooler for each design point, defining the main
R. Gabbrielli / Energy Conversion and Management 64 (2012) 263–272 267
geometry characteristics, such as tubes and tubesheet layout andkind and number of fans, the outlet streams for each operative con-dition have been calculated evaluating the actual overall heattransfer coefficient and the pressure losses.
4.4. Property methods
The thermodynamic and thermophysical characteristics of thegeothermal brine have been assumed equal to those of pure water.Hence, the steam NBS/NRC tables [30] has been used for the simu-lation of the brine. To calculate the thermodynamic properties ofambient air, the cubic order Peng–Robinson equation of state(EOS) with Boston-Mathias alfa functions [31,32] has beenadopted. The thermodynamic properties of R134a have been calcu-lated using simply the cubic order Peng–Robinson EOS [31]. Thevalidity of this EOS for the simulation of supercritical streams ofR134a has been confirmed comparing the data obtained from thesoftware with those available from the website of NIST [33]. Forevery case that has been simulated, the errors concerning the mostimportant thermodynamic and thermophysical data between thesimulated and the actual data always resulted lower than 2%. Thisfact assured the goodness of the simulated results.
4.5. Operative control in off-design conditions
In order to assure the right functioning of the plant also in off-design conditions it has been necessary to adopt some controlrules. In particular the delivery of the R134a feed pump assuresthat the cold brine temperature at the outlet of the supercriticalheat exchanger is equal to 70 �C, as required for scaling problems.Hence, it has been supposed that the pump motor is combinedwith an inverter in order to assure the necessary variation of theshaft speed. Moreover, the delivery pressure of the pump respectsthe pressure throttling characteristics of the expander in accor-dance with the Stodola’s ellipse.
The condenser fan speed and, consequently, the cooling airmass flow rate have been assumed fixed without any control pos-sibilities [20]. Hence, the floating condenser pressure [15] has beencalculated in order to assure the complete condensation of the low
Fig. 3. Pressure-enthalpy diagram of the four
pressure R134a stream. So, it increases/decreases when Tair in-creases/decreases.
When the brine temperature decreases due to the exploitationof the geothermal well, its mass flow rate is increased in order tomaintain practically unchanged the thermal input of the ORC asthe following expression:
where Tb-in-d and Tb-in-off are the values of the brine temperature rel-ative to the design point and to a generic year through the plant life,respectively.
5. Design conditions
Four design conditions for the ORC geothermal power planthave been compared (Fig. 3) in the successive optimizationprocedure. In particular, Tb-in-d assumes the following values:160 �C, 150 �C, 140 �C and 130 �C. The first value regards the casewhen the design condition corresponds to the starting life of theplant, the second design temperature is that after 10 years ofrunning, the third design temperature is that after 20 years, and,finally, the latter design condition corresponds to the end of theplant operative life that has been fixed equal to 30 years. For thiscase, it is necessary to observe that the design pressure has beenselected equal to 45 bar in order to avoid the wet outlet of theexpander (Fig. 3).
The main results for the four design solutions are reported inTable 2. Evidently the design net efficiency decreases with Tb-in-d.It is important to stress that the comparison among the four powerplants is executed using practically a fixed thermal input. Hence,the higher value of _mb�d for the lowest Tb-in-d does not mean thatit is possible to use this design value also for the plant with thehighest Tb-in-d. This would imply that the thermal power extractedfrom the geothermal well is much larger than the design valuerequired for the production of the gross 500 kW and, consequently,the thermal annual degradation through the life would be largelyhigher than 1 �C per year only for this designed power plant.
ORC power plants at their design point.
Table 2Performance of the four ORC at their design point.
Tb-in-d (�C)
160 150 140 130
Mass flow rate of R134a (kg/s) 14.71 15.81 17.35 19.07Mass flow rate of geofluid (kg/s) 9.65 10.98 12.79 15.81Inlet turbine pressure (bar) 50 50 50 45Inlet turbine temperature (�C) 150 140 130 120Surface of the heater (m2) 390 350 330 315Gross power (kW) 500 500 500 500Net efficiency (%) 9.1 8.7 8.1 7.2
Fig. 4. Variation of the R134 mass flow rate during the life and the day. (a) Tb-in-d =160 �C, (b) Tb-in-d = 150 �C, (c) Tb-in-d = 140 �C, (d) Tb-in-d = 130 �C.
268 R. Gabbrielli / Energy Conversion and Management 64 (2012) 263–272
Moreover, the values of the extracted and reinjected geofluid massflow are so low that the degradation of the mass flow does not oc-cur. Hence, it can be assumed that the features of the geothermalresource assure the brine mass flow exploitation required in thefollowing analyses.
6. Results and discussion of the off-design simulations
For each design point, the operating conditions of the ORCgeothermal power plants have been investigated through theirwhole life using off-design simulations when the brine tempera-ture (Tb-in-off) and Tair varied from 160 �C to 130 �C with a step of10 �C and from �5 �C to 35 �C with a step of 5 �C, respectively.
Once fixed the design point, during a generic operating yearwhen Tb-in-off is supposed constant, the mass flow rate of R134aand the turbine inlet pressure increase with Tair (Figs. 4 and 5). Thisis due to the fact that the condensation pressure grows when Tair ishigher and, consequently, since the specific enthalpy of R134a atthe outlet of condenser becomes lower, it is necessary moreR134a for the right cooling of the brine. The growth of the massflow rate of R134a and the exhaust pressure causes the corre-sponding growth of the inlet pressure on the basis of the Stodola’sellipse, too. When Tb-in-off degrades through the operative life of theplant, the mass flow rate of R134a grows largely. Its specific enthal-py at the outlet of the shell and tube heat exchanger is lower and atfixed thermal input of the ORC it is necessary evidently to increasethe mass flow rate of R134a. This implies the pressure growth dueto the mechanism of the Stodola’s ellipse. The variation of massflow rate and pressure is larger for plants with higher Tb-in-d, be-cause when Tb-in-off decreases it becomes more distant from the de-sign value. It is interesting to note that for each value of Tb-in-off theexpander outlet becomes wet when Tair is higher than a specificthreshold value. Indeed, the increase of the pressure moves theexpansion line towards lower entropy values. This phenomenonis larger for higher Tb-in-d. Due to the particular features of the cen-trifugal expander suitable for organic fluids, the moist condition in-side the expander has been considered non feasible because it cancause severe mechanical damages to the rotor and stator, that havebeen designed for dry stream [19].
For a specific design point, the net efficiency (Fig. 6) always im-proves when the ambient temperature (i.e. the cold sink of the cy-cle) is lower. The degradation of Tb-in-off induces obviously areduction of the efficiency. This reduction is larger for higher val-ues of Tb-in-d, because the operative conditions go away from thedesign values. Hence in the last operative years, when Tb-in-off islow, the plant with the lowest design temperature is characterizedby the highest net efficiency. When Tair assumes high values, thenet efficiency (Fig. 6) becomes lower than zero. In this conditionthe auxiliary consumption due to pumps and fan becomes higherthan the gross power produced by the expander. This does not hap-pen when Tb-in-d assumes the lowest value. This fact demonstratesthe most suitability of this design configuration to geothermalsource degradation.
7. Optimal geothermal plant selection
The selection of the best geothermal power plant has been exe-cuted comparing the net present value of the total income from theelectricity selling through the whole life of the plants. During the
Fig. 5. Variation of the turbine inlet pressure during the life and the day. (a) Tb-in-d =160 �C, (b) Tb-in-d = 150 �C, (c) Tb-in-d = 140 �C, (d) Tb-in-d = 130 �C.
Fig. 6. Variation of the net efficiency during the life and the day. (a) Tb-in-d = 160 �C,(b) Tb-in-d = 150 �C, (c) Tb-in-d = 140 �C, (d) Tb-in-d = 130 �C.
R. Gabbrielli / Energy Conversion and Management 64 (2012) 263–272 269
first 15 years, the income derives from the feed-in tariff for renew-able power generation. After the incentive period, the electricity issold to the national grid with a lower price. In this context, theplant cost of each designed alternative has not been taken into ac-count, because it is practically equal and, consequently, does notinfluence the optimal selection. Indeed, from the mechanical pointof view, each equipment has been designed obviously considering
the most severe operating condition during the whole life. Forexample, the most critical couple of values of pressure and temper-ature, that are located just at the inlet of the shell and tube heat ex-changer, has been taken into account for the definition of the tubethickness. The pressure, that can assume high values, is practically
Fig. 7. Annual plant capacity factor during the plant life for three sites (cold, warmand hot).
Fig. 8. Annual production of electricity during the plant life for three sites (cold,warm and hot).
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the most important mechanical design parameter. On the contrary,variations of the temperature imply slight modification of theallowable stress of the materials. Taking into account that whenthe expander outlet is wet the ORC binary plant has to be stoppedin order to avoid mechanical damages of the expander, the maxi-mum design pressure value is practically limited to about 80 barfor each power plant. Moreover, the size of the heater, and thatof the air cooled condenser and turbine are characterized by a con-trary trend with respect the Tb-in-d. If the heater of the plant withthe lowest Tb-in-d has the lowest size, its condenser and its turbineare the largest, because the thermal power released to the environ-ment and the R134a design mass flow are the largest, respectively.The civil construction cost, due to the building and to the site refur-bishment, evidently does not change between the power plants,because the overall size of the plant can be considered the same.Hence on the complex these different costs do not practically affectthe overall capital cost and, consequently, the construction andinstallation cost of each design configuration does not vary. Eventhe maintenance cost of each plant can be considered practicallythe same between the four options analyzed.
The net present value has been evaluated using a discount rateequal to 6%, and considering three different feed-in tariffs for geo-
thermal electricity production until the 15th year. After the 15thyear the electricity selling revenue has been considered equal to101 €/MWh [34]. In this way it is possible to evaluate the effectof the renewable power incentive scenario on the selection of bestgeothermal power plant design configuration. Due to the plantstoppages cited above, the plant capacity factor, whose trend is re-ported in Fig. 7, is lower than the expected value due to the fail-ures. The geothermal power plant designed with the lowest Tb-in-
d is characterized by the highest capacity factor, because it is moresuitable to face the decline of the brine temperature. The capacityfactor of the other options becomes lower than 10–20% at the endof the operative life. Hence, their operation does not result practi-cally useful after the 20–25th year.
Using the net power produced, it is possible to evaluate the an-nual production of electricity, as reported in Fig. 8. The capacityfactor and the net efficiency decrease through the years and, con-sequently, the electricity production is characterized by a similartrend. During the first years of operation, the plant designed withTb-in-d equal to 130 �C has a lower productivity due to its lower effi-
Table 3Total production of electricity and net present value during the whole plant life foreach incentive scenario and for each site.
R. Gabbrielli / Energy Conversion and Management 64 (2012) 263–272 271
ciency, but the degradation of its production is weaker than that ofthe other plants.
Finally, in Table 3 the total production of electricity and the netpresent value for each designed plant are summarized. For eachkind of site considered, the plant with the lowest Tb-in-d always re-sults the best option as each renewable energy incentive scenario.The total production of electricity is largely higher than those ofthe others, even if the NPV is only slightly larger, because mostof its production is executed after several years (please note thatit is more effective to produce electricity during the first 15 years,when the incentive is higher and the discount rate factor is lower).This fact confirms that this plant results more suitable for brineand ambient air temperature modifications than the others.
8. Conclusions and future work
In this paper a novel approach for the design point selection ofsmall scale ORC binary geothermal power plants has been pro-posed. Four design points relative to different values of the brinetemperature during geothermal well exploitation have been com-pared from the economic point of view using off-design simula-tions of the whole operating life.
Maintaining constant the thermal input from the geothermalsource implies that the operative condition becomes very far fromthe design point. In particular, the large increase of the R134a massflow rate and, consequently, of the highest pressure implies severemodifications of the expander outlet. Indeed, this can result wet sothat the plant cannot operate in order to safe the mechanical com-ponents of the expander. So, the availability of the geothermalplants results quite low during the last 10 years of running.
When the liquid-dominated geothermal resource is affected bythermal degradation, the novel design approach here proposed re-sults very effective to highlight the power plant configuration thatis characterized by best economic performance. It has been dem-onstrated that it is always better to size ORC power plants usingthe brine temperature corresponding to the end of the well exploi-tation as design value rather than the initial value as commonlyexecuted in the sector. Hence, it is more important to have higherperformances through the plant life than at the design point.
When high temperatures of brine are used for the sizing, largerepowering (re-sizing) of the power plants is required in order toassure high plant capacity factor also after resource thermal degra-dation. Hence, taking into account some uncertainties about designproblem proposed in this paper, such as the actual geothermal res-
ervoir lifetime and the geofluid behavior, the investor can actuallyselect or not the most profitable power plant that is sized with theend-of-life brine temperature in accordance with his risk approach.
Future analyses could concern the possibility to integrate otherrenewable power sources, such as biomass and solar thermalpower, in order to improve the thermodynamic performance ofthe plants, for example increasing the brine temperature to moreacceptable values. In this way, the capacity factor of the powerplants could largely improve. This integration, in particular withsolar thermal power, could be particularly useful when theambient air temperature assumes the highest values (i.e. the high-est irradiation periods), causing the most severe operating condi-tions. Further, the effect of different control rules on the plantperformances could be assessed. For example, it would be interest-ing to evaluate the operating behavior of the geothermal powerplants when the brine mass flow rate is kept constant throughthe life of the plants. In this way the thermal input of ORC isdecreasing and, consequently, the geothermal source degradationis lower. Finally, it will be interesting to analyze the effect of thewet air during the rainy days on the off-design behavior of thecondenser. This aspect, that has not been taken into account in thispaper, might be advantageous to raise the cooling effect.
Acknowledgements
The author wishes to thank Irene Fastelli (Enel – Engineeringand Innovation, Technical Research Area, Pisa, Italy) for her supportprovided during the research, a part of which has been described inthis paper. Moreover the author wants to thank the reviewers fortheir useful contributions to improving this paper.
References
[1] DiPippo R. Ideal thermal efficiency for geothermal binary plants. Geothermics2007;36:276–85.
[2] Desideri U, Bidini G. Study of possible optimization criteria for geothermalpower plants. Energy Convers Manage 1997;38:1681–91.
[3] Hettiarachchi HDM, Golubovic M, Worek WM, Ikegami Y. Optimum designcriteria for an organic Rankine cycle using low-temperature geothermal heatsource. Energy 2007;32:1698–706.
[4] Wei D, Lu X, Lu Z, Gu J. Performance analysis and optimization of organicRankine cycle (ORC) for waste heat recovery. Energy Convers Manage2007;48:1113–9.
[5] Gu Z, Sato H. Optimization of cyclic parameters of a supercritical cycle forgeothermal power generation. Energy Convers Manage 2001;42:1409–16.
[6] Gu Z, Sato H. Performance of supercritical cycles for geothermal binary design.Energy Convers Manage 2002;43:961–71.
[7] Arslan O, Yetik O. ANN based optimization of supercritical ORC-binarygeothermal power plant: simav case study. Appl Therm Eng 2011;31:3922–8.
[8] Kanoglu M, Bolatturk A. Performance and parametric investigation of a binarygeothermal power plant by exergy. Renew Energy 2008;33:2366–74.
[9] Dai Y, Wang J, Gao L. Parametric optimization and comparative study oforganic Rankine cycle (ORC) for low grade waste heat recovery. EnergyConvers Manage 2009;50:576–82.
[10] Roy JP, Mishra MK, Misra A. Parametric optimization and performance analysisof a waste heat recovery system using organic Rankine cycle. Energy2010;35:5049–62.
[11] Roy JP, Mishra MK, Misra A. Performance analysis of an organic Rankine cyclewith superheating under different heat source temperature conditions. ApplEnergy 2011;88:2995–3004.
[12] Shengjun Z, Huaixin W, Tao G. Performance comparison and parametricoptimization of subcritical organic Rankine cycle (ORC) and transcriticalpower cycle system for low-temperature geothermal power generation. ApplEnergy 2011;88:2740–54.
[14] Sun J, Li W. Operation optimization of an organic rankine cycle (ORC) heatrecovery power plant. Appl Therm Eng 2011;31:2032–41.
[15] Bliem Jr. Design and off-design operation of a dual-boiling binary geothermalpower plant. AIChE Symp Ser 1980;76:163–72.
[16] Gurgenci H. Performance of power plants with organic Rankine cycles underpart-load and off-design conditions. Sol Energy 1986;36:45–51.
[17] Mines GL. Evaluation of the impact of off-design operation on an air-cooledbinary power plant. Trans – Geotherm Res Coun 2002:701–5.
272 R. Gabbrielli / Energy Conversion and Management 64 (2012) 263–272
[18] Moro R, Pinamonti P, Reini M. ORC technology for waste-wood to energyconversion in the furniture manufacturing industry. Therm Sci2008;12:61–73.
[19] Walnum HT, Ladam Y, Neksa P, Andresen T. Off-design operation of ORC andCO2 power production cycles for low temperature surplus heat recovery. Int JLow-Carbon Technol 2011;6:134–40.
[20] Astolfi M, Xodo L, Romano M, Macchi E. Technical and economical analysis of asolar-geothermal hybrid plant based on an organic Rankine cycle. Geothermics2011;40:58–68.
[21] Sauret E, Rowlands AS. Candidate radial-inflow turbines and high-densityworking fluids for geothermal power systems. Energy 2011;36:4460–7.
[22] Augustine C, Field R, DiPippo R, Gigliucci G, Fastelli I, Tester J. Modeling andanalysis of sub- and supercritical binary Rankine cycles for low- to mid-temperature geothermal resources. In: Geothermal resources council annualmeeting 2009, (Geothermal 2009) geothermal resources council. Transactions,vol. 33, Reno, Nevada, USA; 4–7 October 2009. p. 604–8.
[23] Greenhut AD, Tester JW, DiPippo R, Field R, Love C, Nichols K, et al. Solar-geothermal hybrid cycle analysis for low enthalpy solar and geothermalresources. In: Proceedings world geothermal congress 2010 Bali, Indonesia;25–29 April, 2010.
[24] http://www.meteonorm.com/pages/en/meteonorm.php:website of thesoftware Meteonorm.
[25] Gabbrielli R, Singh R. Off-design performance analysis of existing combinedcycle power plant integrated with parabolic trough solar field. In: Proceedings
of 4th international conference on the future of gas turbine technology,Brussels, Belgium; 15–16 October, 2008.
[26] Cooke DH. Modeling of off-design multistage turbine pressures by Stodola’sellipse. Energy incorporated PEPSE� user’s group meeting, Richmond, USA; 2–3 November, 1983.
[27] Cooke DH. On prediction of off-design multistage turbine pressures byStodola’s ellipse. Trans ASME-J Eng Gas Turb Power 1985;107:596–606.
[28] Zhang N, Cai R. Analytical solutions and typical characteristics of part-loadperformances of single shaft gas turbine and its cogeneration. Energy ConversManage 2002;43:1323–37.
[29] Keeley KR. A theoretical investigation of the part-load characteristics of LPsteam turbine stages. CEGB memorandum RD/L/ES0817/M88. CentralElectrical Generating Board, UK; 1988.
[31] Peng DY, Robinson DB. A new two-constant equation-of-state. Ind Eng ChemFundam 1976;15:59–64.
[32] Boston JF, Mathias PM. Phase equilibria in a third-generation processsimulator. In: Proceedings of 2nd international conference on phaseequilibria and fluid properties in the chemical process industries, WestBerlin, West Germany; 1980. p. 823–49.
