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A novel design approach for small scale low enthalpy binary geothermal power plants
Energy Conversion and Management 64 (2012) 263–272
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
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
a r t i c l e
i n f o
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
a b s t r a c t In this paper a novel design approach for small scale low enthalpy binary geothermal power plants is proposed. 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 geothermal resource during the years. Hence, the binary geothermal power plants have to operate with conditions 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 geothermal 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 watersteam 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 temperature 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. ⇑ Tel.: +39 050 2217138; fax: +39 050 2217150. E-mail address: [email protected] 0196-8904/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.enconman.2012.04.017
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 literature. 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 optimized with design simulations in order to evaluate the best pressure that maximizes the thermal efficiency and the specific power output. Hence each plant parameter, such as turbine efficiency, 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 design conditions concerning the evaporation and condensation temperatures 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
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Nomenclature B EOS ORC _ m P T Yd
static exit pressure of expander (bar) equation of state Organic Rankine Cycle mass flow rate (kg/s) pressure (bar) temperature (K) Stodola’s constant of the expander (m2 s2 K1)
Greek symbols g efficiency q mass density (kg/m3) pffiffiffiffi / mass flow coefficient, temperature form (m s K)
by waste heat was presented. The characteristics of the exhaust heat has been changed using a design approach during the simulations in order to maximize the system efficiency. Gu and Sato [5,6] studied the supercritical cycles with internal regeneration for geothermal binary power plants to reach the maximum thermal efficiency optimizing the cycle state parameters such as condensing temperature and pressure. They investigated also different working fluids for a given liquid dominated geothermal resource and determined the most suitable for their application. In [7], artificial neural networks were used in order to optimize the design condition of supercritical ORC-binary with a life cycle cost approach. In [8], exergy analysis of a binary geothermal power plant was performed using actual plant data to assess the plant performance and identify sites of primary exergy destruction. With a design approach, the effects of turbine inlet pressure and temperature and the condenser pressure on the exergy and energy efficiencies, the net power output and the brine injection temperature were investigated and the trends were explained. In [9], the effects of the thermodynamic parameters on the internally regenerative ORC performances were examined, and the thermodynamic parameters of the ORC were optimized using the exergy efficiency as objective function by means of genetic algorithms. In [10], a parametric optimization and performance analysis of a waste heat recovery system at low temperature based on ORC, using several working fluids for power generation have been studied. The aim of the study was to highlight the best working fluid for the specific application. The same authors optimized an ORC with superheating under different heat source temperatures using several performance indicators in order to evaluate the best design conditions and the best working fluid [11]. In [12], an investigation on the parameter optimization and performance comparison of fluids in subcritical ORC and transcritical power cycle in low-temperature binary geothermal power system has been presented. The optimization procedure was conducted with a simulation program using five performance indicators. With the given heat source and heat sink conditions, performances of the working fluids have been evaluated and compared under their optimized internal operation parameters. In [13], both the thermodynamic and the economic optimization of a very small scale ORC in waste heat recovery application has been presented in order to obtain the optimal sizing of the ORC with respect to different parameters. Finally in [14], a complete optimization model of an ORC was proposed. To this aim the authors presented detailed performance models of each component in function of the main operative variables. The best values of the controlled variables, such as relative working fluid mass flow rate, were obtained in order to maximize either the power generation or the thermal efficiency. Also in this case, the uncontrolled variables, such as heat source temperature and flow rate, were fixed at their design values.
Subscripts air ambient air b brine d design point geo geothermal fluid in inlet n net off off-design R134a relative to the fluid R134a
All these kinds of design approach do not take into account the effects of the resource degradation on the plant performance and, consequently, the optimal designed geothermal power plant could not actually result the best solution using a larger perspective over their whole life. In literature, the problem of the performance assessment for ORC power plants in geothermal and waste-heat recovery applications under part load and off-design conditions has been investigated by some authors. All of them analyses the behavior of this kind of power plants when the thermodynamic features of the heat source and cooling sink are different from their starting values used in the design phase. Hence, they do not discuss the problem of the optimal design of ORC geothermal power plants when the most part of their operative conditions is different from the design point. In particular, in [15] once fixed the design conditions, results of performance studies for a binary pilot dual pressure cycle process with isobutane as working fluid were presented. The simulations, based on a mathematical model, whose detailed formulation is not reported by the author, were performed under varying geofluid inlet temperature and flow rate, varying ambient conditions, varying heat exchanger fouling and varying turbine configuration. The most meaningful result was that the decreases in geofluid temperature can be compensated for by the increase in geofluid flow. In [16], an accurate and well-described procedure was reported to predict the ORC power plant performance under off-design conditions when the hot brine and the cooling water temperatures vary through the year. When the design values of heat source and cooling water are 85 °C and 25 °C, respectively, the power plant was able to maintain acceptable performances also with temperature modifications in heat source and cooling water of about 15 °C and 5 °C. In [17], the impact of off-design operation on air-cooled binary geothermal power plant, when changes in the ambient air temperature, as well as the decline in resource productivity over time, occur, has been examined using Aspen Plus simulation software. The simulation results indicated that as plant operation deviates from the design resource and ambient scenario, its ability to convert the available energy in the inlet brine degrades. In [18] an Aspen Plus based simulation model of part load and off-design operation of an ORC unit for combined heat and power in the furniture manufacturing industry has been developed. The performances have been evaluated varying the condensation pressure and the input thermal power. Walnum et al. [19] focused on the off-design operation of ORCs for power generation from low temperature sources and compared the behavior of transcritical CO2 cycles and an ORC cycle with R123 as working fluid when the temperature and mass flow rate of the heat source vary. The main result was that the ORC is very sensitive to reduction in available heat. This required to operate the ORC with some degrees superheat. Finally in [20] the off-design
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behavior of solar-geothermal hybrid plant based on ORC has been evaluated when the solar derived thermal input varies through the year and the thermal features of the geothermal source and cold sink are fixed and equal to their design values. Taking into account the scientific contributions described above, in this paper a novel approach for the optimal design of binary ORC low enthalpy geothermal power plants is proposed. Indeed, the optimal design procedure is executed taking into account their whole operative life, that is simulated with a detailed off-design model. On the basis of the optimization process here proposed, the best design point is searched through the whole life of the power plant and not only at the starting of the well exploitation as commonly executed in literature. In particular, the design brine temperature is optimally selected in the range between its highest and lowest values. Then, the best configuration is highlighted using a procedure based on the maximization of the total actualized cash flows derived from green incentives for renewable electricity. These cash flows are calculated using off-design simulations of the whole operative life of the plants, when the brine and ambient air temperatures vary through the years and the days, respectively. Hence, the paper is structured in the following way: after the description of the binary ORC and the geothermal site, that have been taken into account as reference, the off-design simulation model is detailed described. The results of the simulation activity are successively presented and discussed. Then, the economic optimization 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 taken into account as reference in the novel design procedure described below, is composed by two circuits (Figs. 1 and 2), where the geothermal fluid (brine) and the organic fluid are present, respectively. In the primary circuit, the brine is sucked at 20 bar and 160 °C, that is its original temperature before the starting of the well exploitation. Then, it is cooled in a shell and tube heat exchanger to a temperature equal to 70 °C (5–6 in Figs. 1 and 2), that is higher than the crystallization temperature in order to have a safe margin with respect to the salt precipitation. Finally, it is injected back underground by the circulation pump. In the secondary circuit, the organic fluid, that is R134a, is pumped to a supercritical pressure (1–2 in Figs. 1 and 2). Then, it
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Fig. 2. Temperature-entropy diagram of the ORC (temperature of the geothermal fluid = 130 °C).
is superheated in the shell and tube heat exchanger by the cooling of the brine (2–3 in Figs. 1 and 2). In the expander the organic fluid expands to the condenser pressure producing electric power (3–4 in Figs. 1 and 2). The condensation is assured by dry air coolers without water consumption (4–1 in Figs. 1 and 2). Matching cycle to a given geothermal resource such that power output can be maximized is a very important aspect of every optimization process of ORC. Two major and largely interrelated components of the cycle are the working fluid and the turbine. Both components need careful consideration in order to optimize the amount of power that can be extracted from a specific resource [21]. For the particular features of the geothermal source considered in this paper, the supercritical configuration of the cycle and R134a as organic fluid, whose critical thermodynamic conditions are 40.59 bar and 101.1 °C, resulted the best options in order to maximize the design performance of the geothermal resource exploitation [22,23]. The internal regeneration in the ORC between the outlets of the expander and pump has not been considered because it can cause severe operative problems when the geothermal source temperature is low.
Fig. 1. Plant layout of the binary ORC.
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At the design point, the main input data of the ORC used in the simulation analyses are: Gross power of the expander: 500 kW. This value is limited by the 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.
4.1. Expander The ORC expander has been supposed to operate as sliding pressure mode with fixed nozzle area [20]. Therefore, the inlet pressure depends on the flow characteristics of the machine and can be calculated using the Stodola’s ellipse approach [26–28]:
_ R134ainoff /off ¼ m
ð2Þ
From Eq. (2) it is possible to obtain the equation which has been implemented into the simulation model:
PR134ainoff ¼
The geothermal source, located in the center of Italy, can be considered at low enthalpy. As reported above, the starting temperature of the geofluid is 160 °C and the maximum allowable mass flow rate that can be sucked from the geothermal well is about 60 t/h. The injection of the cold brine is executed at 70 °C in order to avoid operative problems of salting scaling. This implies that the geothermal source temperature decreases during its exploitation. It has been assumed that the temperature decrease is constant and equal to 1 °C per year. Hence after 30 years of plant operative life, the brine temperature can be estimated equal to 130 °C. The daily variability of Tair has been characterized by its stochastic distribution using measured data for three different sites from Meteonorm Software [24]. These sites can be considered representative of three kinds of climate, where the temperatures are on average low (cold site), medium (warm site), and high (hot site). In this way it is possible to assess the effect of the particular climate on the results of the novel design approach here proposed. Supposing that the availability of the power plant is 80%, the operative hours with a particular Tair have been calculated (see Table 1). We supposed that the plant downtimes occur as an uniform distribution during a generic year.
where:
The off-design simulation model of the binary geothermal ORC power plant has been built with Aspen Plus simulation software. This tool does not provide the user with specific built-in routines for the off-design simulation of thermodynamic systems. Hence, a number of specific Fortran routines has been included in the model in order to obtain reliable results [25].
ð1Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ðBR134aoff =PR134ainoff Þ2 /off ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi /d 1 ðBR134ad =PR134aind Þ2
3. Site characteristics
4. The off-design simulation model
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T R134ainoff =PR134ainoff
Yd ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi _ 2R134ainoff T R134ainoff Y d þ B2R134aoff m
ð3Þ
P2R134aind B2R134ad P2R134aind /2d
The Stodola’s constants for the calculation of Yd have been evaluated using the values relative to the design conditions of the expander. The isentropic expansion efficiency has been evaluated using the simple formula reported below [29]:
"
goff
# _ R134ainoff qR134aind 0:1 m ¼ gd sin 0:5p _ R134aind qR134ainoff m
ð4Þ
4.2. Shell and tube supercritical heat exchanger First, for each design point the heat exchanger has been detailed designed from the thermo-mechanical point of view defining the main 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 simulation model using the option ‘‘simulation mode’’, so that the actual overall heat transfer coefficient, the pressure losses and the thermodynamic characteristics of the outlet streams have been calculated in function of the inlet streams for every operative condition. 4.3. Air cooler condenser Similarly to the previous heat exchanger, the off-design performances of the air cooled condenser have been evaluated using the option ‘‘simulation mode’’. After the detailed thermo-mechanical sizing of the air cooler for each design point, defining the main
Table 1 Frequency of the ambient air temperature and plant availability during a generic year for three different sites. Temperature (°C)
Cold climate
Warm climate
Hot climate
Number of calendar hours
% Hours
Hours of availability
Number of calendar hours
% Hours
Hours of availability
Number of calendar hours
% Hours
Hours of availability
5 0 5 10 15 20 25 30 35
350.4 1051.2 1927.2 1839.6 1489.2 1314 613.2 175.2 0
4 12 22 21 17 15 7 2 0
280.32 840.96 1541.76 1471.68 1191.36 1051.2 490.56 140.16 0
13 294 1271 2063 2067 1679 1064 306 3
0.15 3.36 14.51 23.55 23.60 19.17 12.15 3.49 0.03
10.4 235.2 1016.8 1650.4 1653.6 1343.2 851.2 244.8 2.4
0 87.6 876 1401.6 1752 2190 1752 438 262.8
0 1 10 16 20 25 20 5 3
0 70.08 700.8 1121.28 1401.6 1752 1401.6 350.4 210.24
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geometry characteristics, such as tubes and tubesheet layout and kind and number of fans, the outlet streams for each operative condition have been calculated evaluating the actual overall heat transfer coefficient and the pressure losses. 4.4. Property methods The thermodynamic and thermophysical characteristics of the geothermal brine have been assumed equal to those of pure water. Hence, the steam NBS/NRC tables [30] has been used for the simulation of the brine. To calculate the thermodynamic properties of ambient air, the cubic order Peng–Robinson equation of state (EOS) with Boston-Mathias alfa functions [31,32] has been adopted. The thermodynamic properties of R134a have been calculated using simply the cubic order Peng–Robinson EOS [31]. The validity of this EOS for the simulation of supercritical streams of R134a has been confirmed comparing the data obtained from the software with those available from the website of NIST [33]. For every case that has been simulated, the errors concerning the most important thermodynamic and thermophysical data between the simulated and the actual data always resulted lower than 2%. This fact 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 offdesign conditions it has been necessary to adopt some control rules. In particular the delivery of the R134a feed pump assures that the cold brine temperature at the outlet of the supercritical heat exchanger is equal to 70 °C, as required for scaling problems. Hence, it has been supposed that the pump motor is combined with an inverter in order to assure the necessary variation of the shaft speed. Moreover, the delivery pressure of the pump respects the pressure throttling characteristics of the expander in accordance with the Stodola’s ellipse. The condenser fan speed and, consequently, the cooling air mass flow rate have been assumed fixed without any control possibilities [20]. Hence, the floating condenser pressure [15] has been calculated in order to assure the complete condensation of the low
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pressure R134a stream. So, it increases/decreases when Tair increases/decreases. When the brine temperature decreases due to the exploitation of the geothermal well, its mass flow rate is increased in order to maintain practically unchanged the thermal input of the ORC as the following expression:
_ bd _ boff ¼ m m
T bind ð70 þ 273Þ T binoff ð70 þ 273Þ
ð5Þ
where Tb-in-d and Tb-in-off are the values of the brine temperature relative 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 plant have been compared (Fig. 3) in the successive optimization procedure. In particular, Tb-in-d assumes the following values: 160 °C, 150 °C, 140 °C and 130 °C. The first value regards the case when the design condition corresponds to the starting life of the plant, the second design temperature is that after 10 years of running, the third design temperature is that after 20 years, and, finally, the latter design condition corresponds to the end of the plant operative life that has been fixed equal to 30 years. For this case, it is necessary to observe that the design pressure has been selected equal to 45 bar in order to avoid the wet outlet of the expander (Fig. 3). The main results for the four design solutions are reported in Table 2. Evidently the design net efficiency decreases with Tb-in-d. It is important to stress that the comparison among the four power plants is executed using practically a fixed thermal input. Hence, _ bd for the lowest Tb-in-d does not mean that the higher value of m it is possible to use this design value also for the plant with the highest Tb-in-d. This would imply that the thermal power extracted from the geothermal well is much larger than the design value required for the production of the gross 500 kW and, consequently, the thermal annual degradation through the life would be largely higher than 1 °C per year only for this designed power plant.
Fig. 3. Pressure-enthalpy diagram of the four ORC power plants at their design point.
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Table 2 Performance of the four ORC at their design point. Tb-in-d (°C)
Mass flow rate of R134a (kg/s) Mass flow rate of geofluid (kg/s) Inlet turbine pressure (bar) Inlet turbine temperature (°C) Surface of the heater (m2) Gross power (kW) Net efficiency (%)
160
150
140
130
14.71 9.65 50 150 390 500 9.1
15.81 10.98 50 140 350 500 8.7
17.35 12.79 50 130 330 500 8.1
19.07 15.81 45 120 315 500 7.2
Moreover, the values of the extracted and reinjected geofluid mass flow are so low that the degradation of the mass flow does not occur. Hence, it can be assumed that the features of the geothermal resource assure the brine mass flow exploitation required in the following analyses. 6. Results and discussion of the off-design simulations For each design point, the operating conditions of the ORC geothermal power plants have been investigated through their whole life using off-design simulations when the brine temperature (Tb-in-off) and Tair varied from 160 °C to 130 °C with a step of 10 °C and from 5 °C to 35 °C with a step of 5 °C, respectively. Once fixed the design point, during a generic operating year when Tb-in-off is supposed constant, the mass flow rate of R134a and the turbine inlet pressure increase with Tair (Figs. 4 and 5). This is due to the fact that the condensation pressure grows when Tair is higher and, consequently, since the specific enthalpy of R134a at the outlet of condenser becomes lower, it is necessary more R134a for the right cooling of the brine. The growth of the mass flow rate of R134a and the exhaust pressure causes the corresponding growth of the inlet pressure on the basis of the Stodola’s ellipse, too. When Tb-in-off degrades through the operative life of the plant, the mass flow rate of R134a grows largely. Its specific enthalpy at the outlet of the shell and tube heat exchanger is lower and at fixed thermal input of the ORC it is necessary evidently to increase the mass flow rate of R134a. This implies the pressure growth due to the mechanism of the Stodola’s ellipse. The variation of mass flow rate and pressure is larger for plants with higher Tb-in-d, because when Tb-in-off decreases it becomes more distant from the design value. It is interesting to note that for each value of Tb-in-off the expander outlet becomes wet when Tair is higher than a specific threshold value. Indeed, the increase of the pressure moves the expansion line towards lower entropy values. This phenomenon is larger for higher Tb-in-d. Due to the particular features of the centrifugal expander suitable for organic fluids, the moist condition inside the expander has been considered non feasible because it can cause severe mechanical damages to the rotor and stator, that have been designed for dry stream [19]. For a specific design point, the net efficiency (Fig. 6) always improves when the ambient temperature (i.e. the cold sink of the cycle) is lower. The degradation of Tb-in-off induces obviously a reduction of the efficiency. This reduction is larger for higher values of Tb-in-d, because the operative conditions go away from the design values. Hence in the last operative years, when Tb-in-off is low, the plant with the lowest design temperature is characterized by the highest net efficiency. When Tair assumes high values, the net efficiency (Fig. 6) becomes lower than zero. In this condition the auxiliary consumption due to pumps and fan becomes higher than the gross power produced by the expander. This does not happen when Tb-in-d assumes the lowest value. This fact demonstrates the most suitability of this design configuration to geothermal source degradation.
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.
7. Optimal geothermal plant selection The selection of the best geothermal power plant has been executed comparing the net present value of the total income from the electricity selling through the whole life of the plants. During the
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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.
first 15 years, the income derives from the feed-in tariff for renewable power generation. After the incentive period, the electricity is sold to the national grid with a lower price. In this context, the plant cost of each designed alternative has not been taken into account, because it is practically equal and, consequently, does not influence the optimal selection. Indeed, from the mechanical point of view, each equipment has been designed obviously considering
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.
the most severe operating condition during the whole life. For example, the most critical couple of values of pressure and temperature, that are located just at the inlet of the shell and tube heat exchanger, has been taken into account for the definition of the tube thickness. The pressure, that can assume high values, is practically
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Fig. 7. Annual plant capacity factor during the plant life for three sites (cold, warm and hot).
the most important mechanical design parameter. On the contrary, variations of the temperature imply slight modification of the allowable stress of the materials. Taking into account that when the expander outlet is wet the ORC binary plant has to be stopped in order to avoid mechanical damages of the expander, the maximum design pressure value is practically limited to about 80 bar for each power plant. Moreover, the size of the heater, and that of the air cooled condenser and turbine are characterized by a contrary trend with respect the Tb-in-d. If the heater of the plant with the lowest Tb-in-d has the lowest size, its condenser and its turbine are the largest, because the thermal power released to the environment and the R134a design mass flow are the largest, respectively. The civil construction cost, due to the building and to the site refurbishment, 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 affect the overall capital cost and, consequently, the construction and installation cost of each design configuration does not vary. Even the maintenance cost of each plant can be considered practically the same between the four options analyzed. The net present value has been evaluated using a discount rate equal to 6%, and considering three different feed-in tariffs for geo-
Fig. 8. Annual production of electricity during the plant life for three sites (cold, warm and hot).
thermal electricity production until the 15th year. After the 15th year the electricity selling revenue has been considered equal to 101 €/MWh [34]. In this way it is possible to evaluate the effect of the renewable power incentive scenario on the selection of best geothermal power plant design configuration. Due to the plant stoppages cited above, the plant capacity factor, whose trend is reported in Fig. 7, is lower than the expected value due to the failures. The geothermal power plant designed with the lowest Tb-ind is characterized by the highest capacity factor, because it is more suitable to face the decline of the brine temperature. The capacity factor of the other options becomes lower than 10–20% at the end of the operative life. Hence, their operation does not result practically useful after the 20–25th year. Using the net power produced, it is possible to evaluate the annual production of electricity, as reported in Fig. 8. The capacity factor and the net efficiency decrease through the years and, consequently, the electricity production is characterized by a similar trend. During the first years of operation, the plant designed with Tb-in-d equal to 130 °C has a lower productivity due to its lower effi-
R. Gabbrielli / Energy Conversion and Management 64 (2012) 263–272 Table 3 Total production of electricity and net present value during the whole plant life for each incentive scenario and for each site. Sizing Tb-in-d (°C)
Total production of electricity (GWh)
Net present value (M€) Incentive: 120 €/MWh
Incentive: 200 €/MWh
Incentive: 250 €/MWh
Cold climate 130 69.70 140 58.34 150 53.69 160 54.54
3.61 3.48 3.37 3.40
5.39 5.35 5.26 5.28
6.57 6.53 6.44 6.45
Warm climate 130 64.18 140 49.74 150 45.17 160 47.45
3.35 3.14 3.02 3.11
5.01 4.90 4.80 4.88
6.04 6.00 5.90 5.99
Hot climate 130 140 150 160
3.12 2.79 2.70 2.84
4.68 4.41 4.33 4.48
5.65 5.43 5.34 5.50
58.82 42.33 38.73 42.45
ciency, but the degradation of its production is weaker than that of the other plants. Finally, in Table 3 the total production of electricity and the net present value for each designed plant are summarized. For each kind of site considered, the plant with the lowest Tb-in-d always results the best option as each renewable energy incentive scenario. The total production of electricity is largely higher than those of the others, even if the NPV is only slightly larger, because most of its production is executed after several years (please note that it 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 brine and ambient air temperature modifications than the others. 8. Conclusions and future work In this paper a novel approach for the design point selection of small scale ORC binary geothermal power plants has been proposed. Four design points relative to different values of the brine temperature during geothermal well exploitation have been compared from the economic point of view using off-design simulations of the whole operating life. Maintaining constant the thermal input from the geothermal source implies that the operative condition becomes very far from the design point. In particular, the large increase of the R134a mass flow rate and, consequently, of the highest pressure implies severe modifications of the expander outlet. Indeed, this can result wet so that the plant cannot operate in order to safe the mechanical components of the expander. So, the availability of the geothermal plants results quite low during the last 10 years of running. When the liquid-dominated geothermal resource is affected by thermal degradation, the novel design approach here proposed results very effective to highlight the power plant configuration that is characterized by best economic performance. It has been demonstrated that it is always better to size ORC power plants using the brine temperature corresponding to the end of the well exploitation as design value rather than the initial value as commonly executed in the sector. Hence, it is more important to have higher performances through the plant life than at the design point. When high temperatures of brine are used for the sizing, large repowering (re-sizing) of the power plants is required in order to assure high plant capacity factor also after resource thermal degradation. Hence, taking into account some uncertainties about design problem proposed in this paper, such as the actual geothermal res-
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ervoir lifetime and the geofluid behavior, the investor can actually select or not the most profitable power plant that is sized with the end-of-life brine temperature in accordance with his risk approach. Future analyses could concern the possibility to integrate other renewable power sources, such as biomass and solar thermal power, in order to improve the thermodynamic performance of the plants, for example increasing the brine temperature to more acceptable values. In this way, the capacity factor of the power plants could largely improve. This integration, in particular with solar thermal power, could be particularly useful when the ambient air temperature assumes the highest values (i.e. the highest irradiation periods), causing the most severe operating conditions. Further, the effect of different control rules on the plant performances could be assessed. For example, it would be interesting to evaluate the operating behavior of the geothermal power plants when the brine mass flow rate is kept constant through the life of the plants. In this way the thermal input of ORC is decreasing and, consequently, the geothermal source degradation is lower. Finally, it will be interesting to analyze the effect of the wet air during the rainy days on the off-design behavior of the condenser. This aspect, that has not been taken into account in this paper, might be advantageous to raise the cooling effect. Acknowledgements The author wishes to thank Irene Fastelli (Enel – Engineering and Innovation, Technical Research Area, Pisa, Italy) for her support provided during the research, a part of which has been described in this paper. Moreover the author wants to thank the reviewers for their useful contributions to improving this paper. References [1] DiPippo R. Ideal thermal efficiency for geothermal binary plants. Geothermics 2007;36:276–85. [2] Desideri U, Bidini G. Study of possible optimization criteria for geothermal power plants. Energy Convers Manage 1997;38:1681–91. [3] Hettiarachchi HDM, Golubovic M, Worek WM, Ikegami Y. Optimum design criteria for an organic Rankine cycle using low-temperature geothermal heat source. Energy 2007;32:1698–706. [4] Wei D, Lu X, Lu Z, Gu J. Performance analysis and optimization of organic Rankine cycle (ORC) for waste heat recovery. Energy Convers Manage 2007;48:1113–9. [5] Gu Z, Sato H. Optimization of cyclic parameters of a supercritical cycle for geothermal 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-binary geothermal power plant: simav case study. Appl Therm Eng 2011;31:3922–8. [8] Kanoglu M, Bolatturk A. Performance and parametric investigation of a binary geothermal power plant by exergy. Renew Energy 2008;33:2366–74. [9] Dai Y, Wang J, Gao L. Parametric optimization and comparative study of organic Rankine cycle (ORC) for low grade waste heat recovery. Energy Convers Manage 2009;50:576–82. [10] Roy JP, Mishra MK, Misra A. Parametric optimization and performance analysis of a waste heat recovery system using organic Rankine cycle. Energy 2010;35:5049–62. [11] Roy JP, Mishra MK, Misra A. Performance analysis of an organic Rankine cycle with superheating under different heat source temperature conditions. Appl Energy 2011;88:2995–3004. [12] Shengjun Z, Huaixin W, Tao G. Performance comparison and parametric optimization of subcritical organic Rankine cycle (ORC) and transcritical power cycle system for low-temperature geothermal power generation. Appl Energy 2011;88:2740–54. [13] Quoilin S, Declaye S, Tchanche BF, Lemort V. Thermo-economic optimization of waste heat recovery organic Rankine cycles. Appl Therm Eng 2011;31:2885–93. [14] Sun J, Li W. Operation optimization of an organic rankine cycle (ORC) heat recovery power plant. Appl Therm Eng 2011;31:2032–41. [15] Bliem Jr. Design and off-design operation of a dual-boiling binary geothermal power plant. AIChE Symp Ser 1980;76:163–72. [16] Gurgenci H. Performance of power plants with organic Rankine cycles under part-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-cooled binary power plant. Trans – Geotherm Res Coun 2002:701–5.
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R. Gabbrielli / Energy Conversion and Management 64 (2012) 263–272
[18] Moro R, Pinamonti P, Reini M. ORC technology for waste-wood to energy conversion in the furniture manufacturing industry. Therm Sci 2008;12:61–73. [19] Walnum HT, Ladam Y, Neksa P, Andresen T. Off-design operation of ORC and CO2 power production cycles for low temperature surplus heat recovery. Int J Low-Carbon Technol 2011;6:134–40. [20] Astolfi M, Xodo L, Romano M, Macchi E. Technical and economical analysis of a solar-geothermal hybrid plant based on an organic Rankine cycle. Geothermics 2011;40:58–68. [21] Sauret E, Rowlands AS. Candidate radial-inflow turbines and high-density working fluids for geothermal power systems. Energy 2011;36:4460–7. [22] Augustine C, Field R, DiPippo R, Gigliucci G, Fastelli I, Tester J. Modeling and analysis of sub- and supercritical binary Rankine cycles for low- to midtemperature geothermal resources. In: Geothermal resources council annual meeting 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. Solargeothermal hybrid cycle analysis for low enthalpy solar and geothermal resources. In: Proceedings world geothermal congress 2010 Bali, Indonesia; 25–29 April, 2010. [24] http://www.meteonorm.com/pages/en/meteonorm.php:website of the software Meteonorm. [25] Gabbrielli R, Singh R. Off-design performance analysis of existing combined cycle power plant integrated with parabolic trough solar field. In: Proceedings
[26]
[27] [28]
[29]
[30] [31] [32]
[33] [34]
of 4th international conference on the future of gas turbine technology, Brussels, Belgium; 15–16 October, 2008. Cooke DH. Modeling of off-design multistage turbine pressures by Stodola’s ellipse. Energy incorporated PEPSEÒ user’s group meeting, Richmond, USA; 2– 3 November, 1983. Cooke DH. On prediction of off-design multistage turbine pressures by Stodola’s ellipse. Trans ASME-J Eng Gas Turb Power 1985;107:596–606. Zhang N, Cai R. Analytical solutions and typical characteristics of part-load performances of single shaft gas turbine and its cogeneration. Energy Convers Manage 2002;43:1323–37. Keeley KR. A theoretical investigation of the part-load characteristics of LP steam turbine stages. CEGB memorandum RD/L/ES0817/M88. Central Electrical Generating Board, UK; 1988. Haar, Gallagher, Kell. NBS/NRC steam tables. Washington: Hemisphere Publishing Corporation; 1984. Peng DY, Robinson DB. A new two-constant equation-of-state. Ind Eng Chem Fundam 1976;15:59–64. Boston JF, Mathias PM. Phase equilibria in a third-generation process simulator. In: Proceedings of 2nd international conference on phase equilibria and fluid properties in the chemical process industries, West Berlin, West Germany; 1980. p. 823–49. NIST chemistry webbook. [visited 07.11]. http://www.gse.it/attivita/Incentivazioni%20Fonti%20Rinnovabili/Pagine/ QuadroNormativo.aspx [visited 07.11].
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
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
a r t i c l e
i n f o
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
a b s t r a c t In this paper a novel design approach for small scale low enthalpy binary geothermal power plants is proposed. 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 geothermal resource during the years. Hence, the binary geothermal power plants have to operate with conditions 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 geothermal 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 watersteam 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 temperature 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. ⇑ Tel.: +39 050 2217138; fax: +39 050 2217150. E-mail address: [email protected] 0196-8904/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.enconman.2012.04.017
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 literature. 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 optimized with design simulations in order to evaluate the best pressure that maximizes the thermal efficiency and the specific power output. Hence each plant parameter, such as turbine efficiency, 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 design conditions concerning the evaporation and condensation temperatures 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
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Nomenclature B EOS ORC _ m P T Yd
static exit pressure of expander (bar) equation of state Organic Rankine Cycle mass flow rate (kg/s) pressure (bar) temperature (K) Stodola’s constant of the expander (m2 s2 K1)
Greek symbols g efficiency q mass density (kg/m3) pffiffiffiffi / mass flow coefficient, temperature form (m s K)
by waste heat was presented. The characteristics of the exhaust heat has been changed using a design approach during the simulations in order to maximize the system efficiency. Gu and Sato [5,6] studied the supercritical cycles with internal regeneration for geothermal binary power plants to reach the maximum thermal efficiency optimizing the cycle state parameters such as condensing temperature and pressure. They investigated also different working fluids for a given liquid dominated geothermal resource and determined the most suitable for their application. In [7], artificial neural networks were used in order to optimize the design condition of supercritical ORC-binary with a life cycle cost approach. In [8], exergy analysis of a binary geothermal power plant was performed using actual plant data to assess the plant performance and identify sites of primary exergy destruction. With a design approach, the effects of turbine inlet pressure and temperature and the condenser pressure on the exergy and energy efficiencies, the net power output and the brine injection temperature were investigated and the trends were explained. In [9], the effects of the thermodynamic parameters on the internally regenerative ORC performances were examined, and the thermodynamic parameters of the ORC were optimized using the exergy efficiency as objective function by means of genetic algorithms. In [10], a parametric optimization and performance analysis of a waste heat recovery system at low temperature based on ORC, using several working fluids for power generation have been studied. The aim of the study was to highlight the best working fluid for the specific application. The same authors optimized an ORC with superheating under different heat source temperatures using several performance indicators in order to evaluate the best design conditions and the best working fluid [11]. In [12], an investigation on the parameter optimization and performance comparison of fluids in subcritical ORC and transcritical power cycle in low-temperature binary geothermal power system has been presented. The optimization procedure was conducted with a simulation program using five performance indicators. With the given heat source and heat sink conditions, performances of the working fluids have been evaluated and compared under their optimized internal operation parameters. In [13], both the thermodynamic and the economic optimization of a very small scale ORC in waste heat recovery application has been presented in order to obtain the optimal sizing of the ORC with respect to different parameters. Finally in [14], a complete optimization model of an ORC was proposed. To this aim the authors presented detailed performance models of each component in function of the main operative variables. The best values of the controlled variables, such as relative working fluid mass flow rate, were obtained in order to maximize either the power generation or the thermal efficiency. Also in this case, the uncontrolled variables, such as heat source temperature and flow rate, were fixed at their design values.
Subscripts air ambient air b brine d design point geo geothermal fluid in inlet n net off off-design R134a relative to the fluid R134a
All these kinds of design approach do not take into account the effects of the resource degradation on the plant performance and, consequently, the optimal designed geothermal power plant could not actually result the best solution using a larger perspective over their whole life. In literature, the problem of the performance assessment for ORC power plants in geothermal and waste-heat recovery applications under part load and off-design conditions has been investigated by some authors. All of them analyses the behavior of this kind of power plants when the thermodynamic features of the heat source and cooling sink are different from their starting values used in the design phase. Hence, they do not discuss the problem of the optimal design of ORC geothermal power plants when the most part of their operative conditions is different from the design point. In particular, in [15] once fixed the design conditions, results of performance studies for a binary pilot dual pressure cycle process with isobutane as working fluid were presented. The simulations, based on a mathematical model, whose detailed formulation is not reported by the author, were performed under varying geofluid inlet temperature and flow rate, varying ambient conditions, varying heat exchanger fouling and varying turbine configuration. The most meaningful result was that the decreases in geofluid temperature can be compensated for by the increase in geofluid flow. In [16], an accurate and well-described procedure was reported to predict the ORC power plant performance under off-design conditions when the hot brine and the cooling water temperatures vary through the year. When the design values of heat source and cooling water are 85 °C and 25 °C, respectively, the power plant was able to maintain acceptable performances also with temperature modifications in heat source and cooling water of about 15 °C and 5 °C. In [17], the impact of off-design operation on air-cooled binary geothermal power plant, when changes in the ambient air temperature, as well as the decline in resource productivity over time, occur, has been examined using Aspen Plus simulation software. The simulation results indicated that as plant operation deviates from the design resource and ambient scenario, its ability to convert the available energy in the inlet brine degrades. In [18] an Aspen Plus based simulation model of part load and off-design operation of an ORC unit for combined heat and power in the furniture manufacturing industry has been developed. The performances have been evaluated varying the condensation pressure and the input thermal power. Walnum et al. [19] focused on the off-design operation of ORCs for power generation from low temperature sources and compared the behavior of transcritical CO2 cycles and an ORC cycle with R123 as working fluid when the temperature and mass flow rate of the heat source vary. The main result was that the ORC is very sensitive to reduction in available heat. This required to operate the ORC with some degrees superheat. Finally in [20] the off-design
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behavior of solar-geothermal hybrid plant based on ORC has been evaluated when the solar derived thermal input varies through the year and the thermal features of the geothermal source and cold sink are fixed and equal to their design values. Taking into account the scientific contributions described above, in this paper a novel approach for the optimal design of binary ORC low enthalpy geothermal power plants is proposed. Indeed, the optimal design procedure is executed taking into account their whole operative life, that is simulated with a detailed off-design model. On the basis of the optimization process here proposed, the best design point is searched through the whole life of the power plant and not only at the starting of the well exploitation as commonly executed in literature. In particular, the design brine temperature is optimally selected in the range between its highest and lowest values. Then, the best configuration is highlighted using a procedure based on the maximization of the total actualized cash flows derived from green incentives for renewable electricity. These cash flows are calculated using off-design simulations of the whole operative life of the plants, when the brine and ambient air temperatures vary through the years and the days, respectively. Hence, the paper is structured in the following way: after the description of the binary ORC and the geothermal site, that have been taken into account as reference, the off-design simulation model is detailed described. The results of the simulation activity are successively presented and discussed. Then, the economic optimization 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 taken into account as reference in the novel design procedure described below, is composed by two circuits (Figs. 1 and 2), where the geothermal fluid (brine) and the organic fluid are present, respectively. In the primary circuit, the brine is sucked at 20 bar and 160 °C, that is its original temperature before the starting of the well exploitation. Then, it is cooled in a shell and tube heat exchanger to a temperature equal to 70 °C (5–6 in Figs. 1 and 2), that is higher than the crystallization temperature in order to have a safe margin with respect to the salt precipitation. Finally, it is injected back underground by the circulation pump. In the secondary circuit, the organic fluid, that is R134a, is pumped to a supercritical pressure (1–2 in Figs. 1 and 2). Then, it
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Fig. 2. Temperature-entropy diagram of the ORC (temperature of the geothermal fluid = 130 °C).
is superheated in the shell and tube heat exchanger by the cooling of the brine (2–3 in Figs. 1 and 2). In the expander the organic fluid expands to the condenser pressure producing electric power (3–4 in Figs. 1 and 2). The condensation is assured by dry air coolers without water consumption (4–1 in Figs. 1 and 2). Matching cycle to a given geothermal resource such that power output can be maximized is a very important aspect of every optimization process of ORC. Two major and largely interrelated components of the cycle are the working fluid and the turbine. Both components need careful consideration in order to optimize the amount of power that can be extracted from a specific resource [21]. For the particular features of the geothermal source considered in this paper, the supercritical configuration of the cycle and R134a as organic fluid, whose critical thermodynamic conditions are 40.59 bar and 101.1 °C, resulted the best options in order to maximize the design performance of the geothermal resource exploitation [22,23]. The internal regeneration in the ORC between the outlets of the expander and pump has not been considered because it can cause severe operative problems when the geothermal source temperature is low.
Fig. 1. Plant layout of the binary ORC.
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At the design point, the main input data of the ORC used in the simulation analyses are: Gross power of the expander: 500 kW. This value is limited by the 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.
4.1. Expander The ORC expander has been supposed to operate as sliding pressure mode with fixed nozzle area [20]. Therefore, the inlet pressure depends on the flow characteristics of the machine and can be calculated using the Stodola’s ellipse approach [26–28]:
_ R134ainoff /off ¼ m
ð2Þ
From Eq. (2) it is possible to obtain the equation which has been implemented into the simulation model:
PR134ainoff ¼
The geothermal source, located in the center of Italy, can be considered at low enthalpy. As reported above, the starting temperature of the geofluid is 160 °C and the maximum allowable mass flow rate that can be sucked from the geothermal well is about 60 t/h. The injection of the cold brine is executed at 70 °C in order to avoid operative problems of salting scaling. This implies that the geothermal source temperature decreases during its exploitation. It has been assumed that the temperature decrease is constant and equal to 1 °C per year. Hence after 30 years of plant operative life, the brine temperature can be estimated equal to 130 °C. The daily variability of Tair has been characterized by its stochastic distribution using measured data for three different sites from Meteonorm Software [24]. These sites can be considered representative of three kinds of climate, where the temperatures are on average low (cold site), medium (warm site), and high (hot site). In this way it is possible to assess the effect of the particular climate on the results of the novel design approach here proposed. Supposing that the availability of the power plant is 80%, the operative hours with a particular Tair have been calculated (see Table 1). We supposed that the plant downtimes occur as an uniform distribution during a generic year.
where:
The off-design simulation model of the binary geothermal ORC power plant has been built with Aspen Plus simulation software. This tool does not provide the user with specific built-in routines for the off-design simulation of thermodynamic systems. Hence, a number of specific Fortran routines has been included in the model in order to obtain reliable results [25].
ð1Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ðBR134aoff =PR134ainoff Þ2 /off ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi /d 1 ðBR134ad =PR134aind Þ2
3. Site characteristics
4. The off-design simulation model
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T R134ainoff =PR134ainoff
Yd ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi _ 2R134ainoff T R134ainoff Y d þ B2R134aoff m
ð3Þ
P2R134aind B2R134ad P2R134aind /2d
The Stodola’s constants for the calculation of Yd have been evaluated using the values relative to the design conditions of the expander. The isentropic expansion efficiency has been evaluated using the simple formula reported below [29]:
"
goff
# _ R134ainoff qR134aind 0:1 m ¼ gd sin 0:5p _ R134aind qR134ainoff m
ð4Þ
4.2. Shell and tube supercritical heat exchanger First, for each design point the heat exchanger has been detailed designed from the thermo-mechanical point of view defining the main 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 simulation model using the option ‘‘simulation mode’’, so that the actual overall heat transfer coefficient, the pressure losses and the thermodynamic characteristics of the outlet streams have been calculated in function of the inlet streams for every operative condition. 4.3. Air cooler condenser Similarly to the previous heat exchanger, the off-design performances of the air cooled condenser have been evaluated using the option ‘‘simulation mode’’. After the detailed thermo-mechanical sizing of the air cooler for each design point, defining the main
Table 1 Frequency of the ambient air temperature and plant availability during a generic year for three different sites. Temperature (°C)
Cold climate
Warm climate
Hot climate
Number of calendar hours
% Hours
Hours of availability
Number of calendar hours
% Hours
Hours of availability
Number of calendar hours
% Hours
Hours of availability
5 0 5 10 15 20 25 30 35
350.4 1051.2 1927.2 1839.6 1489.2 1314 613.2 175.2 0
4 12 22 21 17 15 7 2 0
280.32 840.96 1541.76 1471.68 1191.36 1051.2 490.56 140.16 0
13 294 1271 2063 2067 1679 1064 306 3
0.15 3.36 14.51 23.55 23.60 19.17 12.15 3.49 0.03
10.4 235.2 1016.8 1650.4 1653.6 1343.2 851.2 244.8 2.4
0 87.6 876 1401.6 1752 2190 1752 438 262.8
0 1 10 16 20 25 20 5 3
0 70.08 700.8 1121.28 1401.6 1752 1401.6 350.4 210.24
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geometry characteristics, such as tubes and tubesheet layout and kind and number of fans, the outlet streams for each operative condition have been calculated evaluating the actual overall heat transfer coefficient and the pressure losses. 4.4. Property methods The thermodynamic and thermophysical characteristics of the geothermal brine have been assumed equal to those of pure water. Hence, the steam NBS/NRC tables [30] has been used for the simulation of the brine. To calculate the thermodynamic properties of ambient air, the cubic order Peng–Robinson equation of state (EOS) with Boston-Mathias alfa functions [31,32] has been adopted. The thermodynamic properties of R134a have been calculated using simply the cubic order Peng–Robinson EOS [31]. The validity of this EOS for the simulation of supercritical streams of R134a has been confirmed comparing the data obtained from the software with those available from the website of NIST [33]. For every case that has been simulated, the errors concerning the most important thermodynamic and thermophysical data between the simulated and the actual data always resulted lower than 2%. This fact 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 offdesign conditions it has been necessary to adopt some control rules. In particular the delivery of the R134a feed pump assures that the cold brine temperature at the outlet of the supercritical heat exchanger is equal to 70 °C, as required for scaling problems. Hence, it has been supposed that the pump motor is combined with an inverter in order to assure the necessary variation of the shaft speed. Moreover, the delivery pressure of the pump respects the pressure throttling characteristics of the expander in accordance with the Stodola’s ellipse. The condenser fan speed and, consequently, the cooling air mass flow rate have been assumed fixed without any control possibilities [20]. Hence, the floating condenser pressure [15] has been calculated in order to assure the complete condensation of the low
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pressure R134a stream. So, it increases/decreases when Tair increases/decreases. When the brine temperature decreases due to the exploitation of the geothermal well, its mass flow rate is increased in order to maintain practically unchanged the thermal input of the ORC as the following expression:
_ bd _ boff ¼ m m
T bind ð70 þ 273Þ T binoff ð70 þ 273Þ
ð5Þ
where Tb-in-d and Tb-in-off are the values of the brine temperature relative 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 plant have been compared (Fig. 3) in the successive optimization procedure. In particular, Tb-in-d assumes the following values: 160 °C, 150 °C, 140 °C and 130 °C. The first value regards the case when the design condition corresponds to the starting life of the plant, the second design temperature is that after 10 years of running, the third design temperature is that after 20 years, and, finally, the latter design condition corresponds to the end of the plant operative life that has been fixed equal to 30 years. For this case, it is necessary to observe that the design pressure has been selected equal to 45 bar in order to avoid the wet outlet of the expander (Fig. 3). The main results for the four design solutions are reported in Table 2. Evidently the design net efficiency decreases with Tb-in-d. It is important to stress that the comparison among the four power plants is executed using practically a fixed thermal input. Hence, _ bd for the lowest Tb-in-d does not mean that the higher value of m it is possible to use this design value also for the plant with the highest Tb-in-d. This would imply that the thermal power extracted from the geothermal well is much larger than the design value required for the production of the gross 500 kW and, consequently, the thermal annual degradation through the life would be largely higher than 1 °C per year only for this designed power plant.
Fig. 3. Pressure-enthalpy diagram of the four ORC power plants at their design point.
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Table 2 Performance of the four ORC at their design point. Tb-in-d (°C)
Mass flow rate of R134a (kg/s) Mass flow rate of geofluid (kg/s) Inlet turbine pressure (bar) Inlet turbine temperature (°C) Surface of the heater (m2) Gross power (kW) Net efficiency (%)
160
150
140
130
14.71 9.65 50 150 390 500 9.1
15.81 10.98 50 140 350 500 8.7
17.35 12.79 50 130 330 500 8.1
19.07 15.81 45 120 315 500 7.2
Moreover, the values of the extracted and reinjected geofluid mass flow are so low that the degradation of the mass flow does not occur. Hence, it can be assumed that the features of the geothermal resource assure the brine mass flow exploitation required in the following analyses. 6. Results and discussion of the off-design simulations For each design point, the operating conditions of the ORC geothermal power plants have been investigated through their whole life using off-design simulations when the brine temperature (Tb-in-off) and Tair varied from 160 °C to 130 °C with a step of 10 °C and from 5 °C to 35 °C with a step of 5 °C, respectively. Once fixed the design point, during a generic operating year when Tb-in-off is supposed constant, the mass flow rate of R134a and the turbine inlet pressure increase with Tair (Figs. 4 and 5). This is due to the fact that the condensation pressure grows when Tair is higher and, consequently, since the specific enthalpy of R134a at the outlet of condenser becomes lower, it is necessary more R134a for the right cooling of the brine. The growth of the mass flow rate of R134a and the exhaust pressure causes the corresponding growth of the inlet pressure on the basis of the Stodola’s ellipse, too. When Tb-in-off degrades through the operative life of the plant, the mass flow rate of R134a grows largely. Its specific enthalpy at the outlet of the shell and tube heat exchanger is lower and at fixed thermal input of the ORC it is necessary evidently to increase the mass flow rate of R134a. This implies the pressure growth due to the mechanism of the Stodola’s ellipse. The variation of mass flow rate and pressure is larger for plants with higher Tb-in-d, because when Tb-in-off decreases it becomes more distant from the design value. It is interesting to note that for each value of Tb-in-off the expander outlet becomes wet when Tair is higher than a specific threshold value. Indeed, the increase of the pressure moves the expansion line towards lower entropy values. This phenomenon is larger for higher Tb-in-d. Due to the particular features of the centrifugal expander suitable for organic fluids, the moist condition inside the expander has been considered non feasible because it can cause severe mechanical damages to the rotor and stator, that have been designed for dry stream [19]. For a specific design point, the net efficiency (Fig. 6) always improves when the ambient temperature (i.e. the cold sink of the cycle) is lower. The degradation of Tb-in-off induces obviously a reduction of the efficiency. This reduction is larger for higher values of Tb-in-d, because the operative conditions go away from the design values. Hence in the last operative years, when Tb-in-off is low, the plant with the lowest design temperature is characterized by the highest net efficiency. When Tair assumes high values, the net efficiency (Fig. 6) becomes lower than zero. In this condition the auxiliary consumption due to pumps and fan becomes higher than the gross power produced by the expander. This does not happen when Tb-in-d assumes the lowest value. This fact demonstrates the most suitability of this design configuration to geothermal source degradation.
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.
7. Optimal geothermal plant selection The selection of the best geothermal power plant has been executed comparing the net present value of the total income from the electricity selling through the whole life of the plants. During the
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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.
first 15 years, the income derives from the feed-in tariff for renewable power generation. After the incentive period, the electricity is sold to the national grid with a lower price. In this context, the plant cost of each designed alternative has not been taken into account, because it is practically equal and, consequently, does not influence the optimal selection. Indeed, from the mechanical point of view, each equipment has been designed obviously considering
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.
the most severe operating condition during the whole life. For example, the most critical couple of values of pressure and temperature, that are located just at the inlet of the shell and tube heat exchanger, has been taken into account for the definition of the tube thickness. The pressure, that can assume high values, is practically
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Fig. 7. Annual plant capacity factor during the plant life for three sites (cold, warm and hot).
the most important mechanical design parameter. On the contrary, variations of the temperature imply slight modification of the allowable stress of the materials. Taking into account that when the expander outlet is wet the ORC binary plant has to be stopped in order to avoid mechanical damages of the expander, the maximum design pressure value is practically limited to about 80 bar for each power plant. Moreover, the size of the heater, and that of the air cooled condenser and turbine are characterized by a contrary trend with respect the Tb-in-d. If the heater of the plant with the lowest Tb-in-d has the lowest size, its condenser and its turbine are the largest, because the thermal power released to the environment and the R134a design mass flow are the largest, respectively. The civil construction cost, due to the building and to the site refurbishment, 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 affect the overall capital cost and, consequently, the construction and installation cost of each design configuration does not vary. Even the maintenance cost of each plant can be considered practically the same between the four options analyzed. The net present value has been evaluated using a discount rate equal to 6%, and considering three different feed-in tariffs for geo-
Fig. 8. Annual production of electricity during the plant life for three sites (cold, warm and hot).
thermal electricity production until the 15th year. After the 15th year the electricity selling revenue has been considered equal to 101 €/MWh [34]. In this way it is possible to evaluate the effect of the renewable power incentive scenario on the selection of best geothermal power plant design configuration. Due to the plant stoppages cited above, the plant capacity factor, whose trend is reported in Fig. 7, is lower than the expected value due to the failures. The geothermal power plant designed with the lowest Tb-ind is characterized by the highest capacity factor, because it is more suitable to face the decline of the brine temperature. The capacity factor of the other options becomes lower than 10–20% at the end of the operative life. Hence, their operation does not result practically useful after the 20–25th year. Using the net power produced, it is possible to evaluate the annual production of electricity, as reported in Fig. 8. The capacity factor and the net efficiency decrease through the years and, consequently, the electricity production is characterized by a similar trend. During the first years of operation, the plant designed with Tb-in-d equal to 130 °C has a lower productivity due to its lower effi-
R. Gabbrielli / Energy Conversion and Management 64 (2012) 263–272 Table 3 Total production of electricity and net present value during the whole plant life for each incentive scenario and for each site. Sizing Tb-in-d (°C)
Total production of electricity (GWh)
Net present value (M€) Incentive: 120 €/MWh
Incentive: 200 €/MWh
Incentive: 250 €/MWh
Cold climate 130 69.70 140 58.34 150 53.69 160 54.54
3.61 3.48 3.37 3.40
5.39 5.35 5.26 5.28
6.57 6.53 6.44 6.45
Warm climate 130 64.18 140 49.74 150 45.17 160 47.45
3.35 3.14 3.02 3.11
5.01 4.90 4.80 4.88
6.04 6.00 5.90 5.99
Hot climate 130 140 150 160
3.12 2.79 2.70 2.84
4.68 4.41 4.33 4.48
5.65 5.43 5.34 5.50
58.82 42.33 38.73 42.45
ciency, but the degradation of its production is weaker than that of the other plants. Finally, in Table 3 the total production of electricity and the net present value for each designed plant are summarized. For each kind of site considered, the plant with the lowest Tb-in-d always results the best option as each renewable energy incentive scenario. The total production of electricity is largely higher than those of the others, even if the NPV is only slightly larger, because most of its production is executed after several years (please note that it 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 brine and ambient air temperature modifications than the others. 8. Conclusions and future work In this paper a novel approach for the design point selection of small scale ORC binary geothermal power plants has been proposed. Four design points relative to different values of the brine temperature during geothermal well exploitation have been compared from the economic point of view using off-design simulations of the whole operating life. Maintaining constant the thermal input from the geothermal source implies that the operative condition becomes very far from the design point. In particular, the large increase of the R134a mass flow rate and, consequently, of the highest pressure implies severe modifications of the expander outlet. Indeed, this can result wet so that the plant cannot operate in order to safe the mechanical components of the expander. So, the availability of the geothermal plants results quite low during the last 10 years of running. When the liquid-dominated geothermal resource is affected by thermal degradation, the novel design approach here proposed results very effective to highlight the power plant configuration that is characterized by best economic performance. It has been demonstrated that it is always better to size ORC power plants using the brine temperature corresponding to the end of the well exploitation as design value rather than the initial value as commonly executed in the sector. Hence, it is more important to have higher performances through the plant life than at the design point. When high temperatures of brine are used for the sizing, large repowering (re-sizing) of the power plants is required in order to assure high plant capacity factor also after resource thermal degradation. Hence, taking into account some uncertainties about design problem proposed in this paper, such as the actual geothermal res-
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ervoir lifetime and the geofluid behavior, the investor can actually select or not the most profitable power plant that is sized with the end-of-life brine temperature in accordance with his risk approach. Future analyses could concern the possibility to integrate other renewable power sources, such as biomass and solar thermal power, in order to improve the thermodynamic performance of the plants, for example increasing the brine temperature to more acceptable values. In this way, the capacity factor of the power plants could largely improve. This integration, in particular with solar thermal power, could be particularly useful when the ambient air temperature assumes the highest values (i.e. the highest irradiation periods), causing the most severe operating conditions. Further, the effect of different control rules on the plant performances could be assessed. For example, it would be interesting to evaluate the operating behavior of the geothermal power plants when the brine mass flow rate is kept constant through the life of the plants. In this way the thermal input of ORC is decreasing and, consequently, the geothermal source degradation is lower. Finally, it will be interesting to analyze the effect of the wet air during the rainy days on the off-design behavior of the condenser. This aspect, that has not been taken into account in this paper, might be advantageous to raise the cooling effect. Acknowledgements The author wishes to thank Irene Fastelli (Enel – Engineering and Innovation, Technical Research Area, Pisa, Italy) for her support provided during the research, a part of which has been described in this paper. Moreover the author wants to thank the reviewers for their useful contributions to improving this paper. References [1] DiPippo R. Ideal thermal efficiency for geothermal binary plants. Geothermics 2007;36:276–85. [2] Desideri U, Bidini G. Study of possible optimization criteria for geothermal power plants. Energy Convers Manage 1997;38:1681–91. [3] Hettiarachchi HDM, Golubovic M, Worek WM, Ikegami Y. Optimum design criteria for an organic Rankine cycle using low-temperature geothermal heat source. Energy 2007;32:1698–706. [4] Wei D, Lu X, Lu Z, Gu J. Performance analysis and optimization of organic Rankine cycle (ORC) for waste heat recovery. Energy Convers Manage 2007;48:1113–9. [5] Gu Z, Sato H. Optimization of cyclic parameters of a supercritical cycle for geothermal 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-binary geothermal power plant: simav case study. Appl Therm Eng 2011;31:3922–8. [8] Kanoglu M, Bolatturk A. Performance and parametric investigation of a binary geothermal power plant by exergy. Renew Energy 2008;33:2366–74. [9] Dai Y, Wang J, Gao L. Parametric optimization and comparative study of organic Rankine cycle (ORC) for low grade waste heat recovery. Energy Convers Manage 2009;50:576–82. [10] Roy JP, Mishra MK, Misra A. Parametric optimization and performance analysis of a waste heat recovery system using organic Rankine cycle. Energy 2010;35:5049–62. [11] Roy JP, Mishra MK, Misra A. Performance analysis of an organic Rankine cycle with superheating under different heat source temperature conditions. Appl Energy 2011;88:2995–3004. [12] Shengjun Z, Huaixin W, Tao G. Performance comparison and parametric optimization of subcritical organic Rankine cycle (ORC) and transcritical power cycle system for low-temperature geothermal power generation. Appl Energy 2011;88:2740–54. [13] Quoilin S, Declaye S, Tchanche BF, Lemort V. Thermo-economic optimization of waste heat recovery organic Rankine cycles. Appl Therm Eng 2011;31:2885–93. [14] Sun J, Li W. Operation optimization of an organic rankine cycle (ORC) heat recovery power plant. Appl Therm Eng 2011;31:2032–41. [15] Bliem Jr. Design and off-design operation of a dual-boiling binary geothermal power plant. AIChE Symp Ser 1980;76:163–72. [16] Gurgenci H. Performance of power plants with organic Rankine cycles under part-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-cooled binary 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 energy conversion in the furniture manufacturing industry. Therm Sci 2008;12:61–73. [19] Walnum HT, Ladam Y, Neksa P, Andresen T. Off-design operation of ORC and CO2 power production cycles for low temperature surplus heat recovery. Int J Low-Carbon Technol 2011;6:134–40. [20] Astolfi M, Xodo L, Romano M, Macchi E. Technical and economical analysis of a solar-geothermal hybrid plant based on an organic Rankine cycle. Geothermics 2011;40:58–68. [21] Sauret E, Rowlands AS. Candidate radial-inflow turbines and high-density working fluids for geothermal power systems. Energy 2011;36:4460–7. [22] Augustine C, Field R, DiPippo R, Gigliucci G, Fastelli I, Tester J. Modeling and analysis of sub- and supercritical binary Rankine cycles for low- to midtemperature geothermal resources. In: Geothermal resources council annual meeting 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. Solargeothermal hybrid cycle analysis for low enthalpy solar and geothermal resources. In: Proceedings world geothermal congress 2010 Bali, Indonesia; 25–29 April, 2010. [24] http://www.meteonorm.com/pages/en/meteonorm.php:website of the software Meteonorm. [25] Gabbrielli R, Singh R. Off-design performance analysis of existing combined cycle power plant integrated with parabolic trough solar field. In: Proceedings
[26]
[27] [28]
[29]
[30] [31] [32]
[33] [34]
of 4th international conference on the future of gas turbine technology, Brussels, Belgium; 15–16 October, 2008. Cooke DH. Modeling of off-design multistage turbine pressures by Stodola’s ellipse. Energy incorporated PEPSEÒ user’s group meeting, Richmond, USA; 2– 3 November, 1983. Cooke DH. On prediction of off-design multistage turbine pressures by Stodola’s ellipse. Trans ASME-J Eng Gas Turb Power 1985;107:596–606. Zhang N, Cai R. Analytical solutions and typical characteristics of part-load performances of single shaft gas turbine and its cogeneration. Energy Convers Manage 2002;43:1323–37. Keeley KR. A theoretical investigation of the part-load characteristics of LP steam turbine stages. CEGB memorandum RD/L/ES0817/M88. Central Electrical Generating Board, UK; 1988. Haar, Gallagher, Kell. NBS/NRC steam tables. Washington: Hemisphere Publishing Corporation; 1984. Peng DY, Robinson DB. A new two-constant equation-of-state. Ind Eng Chem Fundam 1976;15:59–64. Boston JF, Mathias PM. Phase equilibria in a third-generation process simulator. In: Proceedings of 2nd international conference on phase equilibria and fluid properties in the chemical process industries, West Berlin, West Germany; 1980. p. 823–49. NIST chemistry webbook.