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Modeling and simulation of the production process of electrical energy in a geothermal power plant
Mathematical and Computer Modelling (
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Mathematical and Computer Modelling journal homepage: www.elsevier.com/locate/mcm
Modeling and simulation of the production process of electrical energy in a geothermal power plant Eduardo Sanchez a , Carlos F. Torres b , Pablo Guillen c , German Larrazabal a,∗ a
Multidisciplinary Center for Scientific Visualization and Computing (CEMVICC), Faculty of Sciences and Technology (FACYT), University of Carabobo, Venezuela
b
Thermal Science Department, University of Los Andes, Merida, 5101, Venezuela
c
Program in Computational Science, University of Texas at El Paso, TX, USA
article
info
Article history: Received 26 November 2010 Received in revised form 15 March 2011 Accepted 16 March 2011 Keywords: Directed graphs Mathematical modeling Simulation Steam power cycles Geothermal electricity production Water thermodynamical properties
abstract In this work, the study, modeling and simulation of custom designed geothermal power plant production processes are presented. A model based on the thermodynamical steam power cycles theory is developed using directed graphs, in order to consider different types of geothermal power plant structural models to be studied. The model includes steady state forms of the thermodynamical mass and energy conservation laws for each one of the considered equipments, in order to study the mass and energy interactions among them. A computational implementation of the IAPWS-IF97 formulation for the calculation, also by steady state forms, of the physical properties of the water is also presented, thus providing a reliable and accurate method to calculate them in execution time. The analysis of both topological and thermodynamical feasibility of the proposed input models is also presented, as well as the analysis of the efficiency in terms of both generated and invested heat and power. The results are compared against reference results in the literature; these are presented in relation to the proposed models, by reporting the variations of the mentioned water properties and by stating the results of the production processes in terms of both mechanical power generation, and efficiency of the proposed structural models. © 2011 Elsevier Ltd. All rights reserved.
1. Introduction Nowadays, a considerable effort is being focused on the study of efficient methods for the appropriate exploitation of alternative sources of renewable energy. The current economic environment and impending climate change from the combustion of hydrocarbons make the use of alternative energy sources imperative for the near future. A clear example of this scenario has been given around the world with the design and operation of plants for the production of electrical energy through the use of geothermal resources, also known as geothermal power plants. These geothermal resources exist due to several factors within earth’s geology, such as the existence of molten rock (magma) from the earth’s core, which contributes to great quantities of heat, and the ascent of heated groundwater that has circulated from depths of several kilometers [1]. One of the earliest documented examples takes place in Italy, between 1904 and 1905 when Prince Piero Ginori Conti managed to establish a 3/4-horsepower reciprocating engine, fueled by steam separated from water, to drive a small generator [2] and by 1924, when the first commercial 250 kW geothermal power plant operated continuously [3]. Developments in geothermal energy production have been taken place ever since; for example in New Zealand at Wairakei in 1958; an experimental plant at Pathe, Mexico in 1959 and the first commercial plant at The Geysers in the United States in
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Corresponding author. E-mail addresses: [email protected] (E. Sanchez), [email protected] (C.F. Torres), [email protected] (P. Guillen), [email protected], [email protected] (G. Larrazabal). 0895-7177/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.mcm.2011.03.021
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1960 [1]. In modern days, efforts are necessary to find alternative energy resources; therefore, geothermal energy production systems come in handy since they are more competitive when compared to conventional fossil-fuel-based production systems and in the last five years, their direct use has increased approximately twofold [4]. In the United States specifically, several projects are being carried out successfully. One sample project consists of 10 generating plants in southern California’s Imperial Valley area. The plants follow the classic scheme for geothermal power plants to produce electricity solely from naturally occurring geothermal steam. Eight of the facilities in this area: Vulcan, Hoch, Elmore, Leathers and Salton Sea 1, 2, 3 and 4, are under contract to sell power to southern California companies under long term power purchase agreements [5]. Nevertheless, in order to improve current exploration and production techniques, additional efforts in research and development (R&D) should be considered. An important example is the drawback on behalf of one of the most important companies in the field within the current US administration, regarding the need to study abnormal seismic activity related to exploration efforts [6]. Similar efforts should also be devoted to both heat-transfer performance for lower-temperature fluids and development schemes for plant designs based on higher resource temperatures of the supercritical water. These efforts would lead to an order of magnitude (or more) gain in both reservoir performance and heat-to-power conversion efficiency [7]. Along with the mentioned efforts, a comprehensive assessment of enhanced, or engineered, geothermal systems should be carried out by the governments to evaluate the potential of geothermal energy becoming a major energy source. Three main components should be considered in the analysis [7]:
• Resource: estimating the magnitude and distribution of the geothermal resource. • Technology: establishing requirements for the production from geothermal reservoirs including drilling, reservoir design and stimulation, and thermal energy conversion to electricity.
• Economics: estimating costs for geothermal supplied electricity on a national scale using newly developed methods for mining heat from the earth. Examples of similar analyses have been carried out in different countries. In Morocco, hydrostratigraphical studies focused on the geochemistry of exploration models have been executed [8] stating the most important aspects of the geothermal potential efficient exploitation and taking special consideration into the characteristics of the reservoirs. Geothermal power plant designs have been shown to imply innovative ideas, given the need to adapt themselves to the features of geothermal resources reservoirs [2]. The complexity of these designs, given the need of integrating several mechanical components and the different difficulties concerning mathematical modeling, consequences of the present physical phenomena, make the availability of simulation tools an invaluable assistance for both plant design and building as for the planning of the operative activities [9]. Previous work regarding the computational simulation of thermodynamical systems has been considered [10] and similarly, so has been previous work relating the computational simulation and control of existing geothermal power plant production processes [11]. Once the plant has been built, the schematic description of its structure allows the creation of simulation and control tools, which at the same time present the computational core of interactive personnel training applications and similar, but these works assume the existence of a completely functional geothermal power plant. Likewise, in early stages of development and design, the study of the reservoir conditions could be used in order to simulate the production process that can arise from the future power plant to be built. In this work, the study, modeling and simulation of geothermal power plant production processes are presented, in order to gain both knowledge in the implications regarding energetic potential, and comprehension of the related physical phenomena and their characteristics related to the overall efficiency of the production processes. This model is intended as the main numerical core of an application for the computer aided design of geothermal power plants, in order to provide the user with the ability to study and simulate the functioning of any custom made design model for a geothermal power plants overall design before its construction. 2. Steam power cycles and involved equipments The numerical modeling of geothermal power plant production processes rests on the theory of thermodynamical steam power cycles [12,13]. These cycles study the variations of the state of a given substance in order to produce results in terms of mechanical power. Steam power cycles can be defined as a collection of equipments or control volumes, that cause changes in the state of a working fluid. The first theoretical aspect considers how functional relations among the different properties of the water can be defined. Specifically, how many properties have to be taken into consideration in order to be able to relate them to other intrinsic non-measurable properties of the water. There is a general rule to determine this required number of measurable properties and it is known as the state postulate. This is a very well-known result from thermodynamics [12]. Water has proven to work as a simple thermodynamical system due to experimental results [12,13], that is, a system in which in order to modify its intrinsic state, only one way of quasi-static work is needed. Thus, if we take this into consideration, then the state postulate for simple systems [12] is also of important consideration. Since one can choose any pair of independent properties, it is desirable that these two properties could be measurable [12,13], therefore pressure and temperature are considered.
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Table 1 Equipment models and their related specific energy balances. Equipment
Governing energy balance
Separator Turbine Condenser Pump Flash valve
˙ (hi − ho ) = 0 m ˙ Turbine = m ˙ Turbine < 0 given ho < hi ˙ (ho − hi ), W W ˙ (ho − hi ), Q˙ Condenser < 0 given ho < hi Q˙ Condenser = m ˙ Pump = m ˙ Pump > 0 given ho > hi ˙ (ho − hi ), W W ˙ (hi − ho ) = 0 m
2.1. Conservation principles and model assumptions Three well-known results from thermodynamics are: the general mass conservation principle, which states: d
∫
dt
ρ dV = V
− ∫ i
ρ Vn dS
S
− i
− ∫ o
ρ Vn dS S
(1) o
where ρ is the density inside the control volume with surface S and volume V , i and o denote input and output states, respectively. Vn is the fluid velocity normal to the surface S in both i and o states. The general energy conservation principle is defined as: d dt
∫
˙ + eρ dV = Q˙ + W V
− [∫ i
eρ Vn dS S
] − i
− [∫ o
S
eρ Vn dS
] (2) o
˙ denote both general heat flow in time and general power of the control volume, h denotes the specific where Q˙ and W enthalpy and e represents the energy interactions. This total energy is defined as: e=h+
V2
+ gz (3) 2 where g is the standard earth’s gravity and z stands for the height. The following assumptions are considered for this stage of development, since they have shown to apply to geothermal processes due to experimental data [4,12–14]: 1. There is no variation in time for any of the involved properties. Let X (t ) be some property, we have that X ′ (t ) = 0. Therefore, the geothermal power plants operate in a steady-state condition. 2. The conditions of the fresh water are known at the production well. No simulations of the underground reservoir nor for the vertical flow of water through the production well were developed. 3. The pressure drops throughout the heat exchangers and pipelines are neglected. 4. The flow is uniform in the control volume inlets and outlets. 5. The turbines and pumps have isentropic efficiencies. 6. The kinetic and potential energy changes are negligible. 7. Fresh water properties have been used in the analysis instead of the thermodynamic properties of the geofluid. 8. The flashing process is accomplished at constant enthalpy. 9. Temperature and pressure losses of the geofluid are neglected in the separation and condensation processes. 10. Turbines can only interact with a condenser or directly with a generator; therefore, there cannot be successive turbine configurations. 2.2. Equipment model particularities In this section, the particular hypotheses and their effects over the previous results are introduced per each considered equipment model. The considered equipment models are shown in Table 1 along with their own specific energy balance; ˙ stands for the mass flow. where m The mass conservation principle states, equally for all of them, that mi = mo .
(4)
3. IAPWS-IF97 computer implementation Having explained how do the equipments will handle the state of the water, it is time to explain how can the thermodynamical properties of the water be calculated in execution time. In 1997, the The International Association for the Properties of Water and Steam (IAPWS) approved a new formulation of the thermodynamic properties of water and steam for industrial use (referred to as IAPWS-IF97), replacing the IFC-67 formulation that is familiar to many from its use in the 1967 ASME Steam Tables. An archival paper describing this formulation has been published [15], and it was considered in order to be implemented to make the application able to calculate the required properties in execution time.
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4. Efficiency and thermodynamical feasibility study of the proposed model The efficiency of a thermodynamical cycle is studied from the heat engines approach [12,13]. In this approach, if any cycle is considered from a black box perspective, one can see that they require an input heat flow and an input power in order to produce an outgoing heat flow and an outgoing power. Considering this, the efficiency τ (in terms of power) is measured ˙ net ) and the required energy required to produce it, expressed in terms of heat by the quotient of the produced net work (W (Q˙ in ); that is:
τ=
˙ net W Q˙ in
∑ = ∑ o
˙o − W
o
˙o − ho m
∑
˙i W
i
∑
˙i hi m
.
(5)
i
Regarding the thermodynamical and mechanical feasibility of a given model, the most important configurations for a power plant described in [2] were studied in order to provide the validation on any proposed power plant model. These validation focuses on the compatibility of the parameter’s values among provided equipments. 5. Thermodynamical cycles as directed graphs and topological feasibility The computational modeling for a generic input data structure for the description of a steam power cycle, considers graph theory tools. In general, any thermodynamical steam power cycle can be described as a directed graph G = (V , A, ϕ, φ) where:
• V denote set of nodes which represent the equipments composing the given cycle. • A denotes the set of edges which represent the direct interaction among two given nodes (equipments). Notice that there are no edges of the form (x, x) since no loops are considered. One should also notice that the multiplicity of the edges is less or equal to 1 since no multiple edges are considered among any given pair of equipments.
• Both ϕ and φ weight, any node (equipment) to its related mass, energy balance and functioning parameters, and any edge to its related set of thermodynamical properties. In this work, the computational representation for a graph is made trough its related weighted adjacency matrix, since the amount of equipment in a generic geothermal power plant, according to the experience, is small. Once the input model is provided, a Boolean adjacency matrix, which is defined as M = (mij )|V |2 where mij equals 1 if a direct interaction is possible among nodes i and j; and equals 0 if it is not, clearly describes whether the given input model is topologically feasible; that is, according to the functioning of the related equipment, this matrix states if a direct interaction among any couple of nodes is possible. If a given input model makes sense, topologically speaking, then the application verifies its thermodynamical feasibility. According to the functional definitions of the equipments, some cases of interactions require special attention. The first example of these cases of interaction is the interaction among the injection well and the condenser. Both values of input and output pressure, respectively, should match. The model verifies every occurrence of this case and advises the designer regarding the course of action in the case of a failed interaction proposal. The second case of interaction which requires validation is the interaction among the injection well and the pump, since both input and output pressures should match. The third case is the most complex to deal with, since it involves different branches of proposed solutions in case of an interaction failure. In this case, the interaction among the flash valve and the injection well is studied. As it has been mentioned, the injection well requires a minimum injection pressure in order to work, therefore, the flash valve output pressure has to match. So, first we come up to three possibles scenarios: 1. Direct injection is possible. 2. Flash valve design pressure is lower that the minimum injection pressure. In this case, a pump has to be considered in order to increase the pressure up to the desired value. 3. Flash valve design pressure is lower that the minimum injection pressure. In this case, a second flash valve has to be considered in order to decrease the pressure down the required value. Hence, every time an advise is given regarding interaction, the user may try to fix it, and recurrent interaction problems might arise, Fig. 1; therefore, those have to be studied. 5.1. Breadth first search algorithm and its application as simulation engine As it was previously mentioned, the models of custom designed geothermal power plants can be built according to specific interaction needs, thus yielding a variable topology of the underlying directed graph modeling the plant. Clearly, this interaction is important since it determines the behavior of the production process. That is why, an algorithm to correctly traverse the resulting considered graph has to be considered, in order to consider the variability of the implied interaction scheme and its effects in the simulation results. Logically, graph theory provides a traverse algorithm such as the one needed. Once a topologically feasible cycle model has been read, the Breadth First Search algorithm [16] traverses the graph thus executing the simulation process. Section 6.1.1 describes the specific role of this algorithm in terms of the execution of the simulation process.
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Fig. 1. Implicitly defined tree of interaction issues among the injection well and the flash valve and their related advised courses of action.
Turbine 1
Generator
Production Well 1
Injection Well
Pump
Condenser
Fig. 2. Proposed case of study: a dry steam geothermal power plant.
6. Test case results In this section, two cases are presented in order to appreciate the functioning of the simulation processes and the required validation schemes. 6.1. A rankine cycle underlying a dry steam geothermal power plant One of the most important test cases since it is one of the most frequent cases in the study of geothermal power plants [2] is the dry steam geothermal power plant. In this type of plant, steam comes out of the reservoir at such a high temperature, that it does not require any extra heating processes (see Fig. 2). However, for purposes of validation, we consider the case of a thermodynamical cycle which underlies the design of a dry steam power plant for which we consider the expected given heat of the condenser as a design parameter. This case and its related results can be compared against [13]. Table 2 shows that the functioning parameters are clearly given. Once the equipments are considered, the model determines the type of plant. In this case, the saturation pressure and temperature on the production well, 0.7 bar and 823 K, respectively, are compared against the water saturation temperature (778.57 bar). According to this result, the plant is a dry steam plant. Once the equipments have been entirely considered, the proposed energy interactions are studied. This is shown in Table 3. These proposed energy interactions are validated according to its adjacency, in terms of the maximum amount of allowed input and output connections for each equipment. If the validation is successful, the model is considered to be topologically feasible.
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Table 2 Topological description. Production well OUTPUT Mass flow = 37.8 kg/s ADVISE: Mass flow value under 100 kg/s: (37.8 kg/s) Potential and Kinetic Energies will be depreciated OUTPUT Pressure = 0.7 bar OUTPUT Temperature = 823 K OUTPUT Saturation Pressure = 778.572085444 bar Turbine HYPOTHESIS: Adiabatic turbine OUTPUT Pressure = 0.2 bar OUTPUT Temperature = 335 K Efficiency = 0.91 Condenser INPUT Given heat = 3270 kJ/kg Pump HYPOTHESIS: Adiabatic pump OUTPUT Pressure = 0.8 bar Injection well MINIMUM Value of pressure for INJECTION: 0.8 bar
Table 3 Proposed energy interactions. Connection from 0 to 1 called PW01-TUR01-201-W Connection from 1 to 2 called TUR01-COND01-202-W Connection from 2 to 3 called COND01-PMP01-203-W Connection from 3 to 4 called PMP01-IW01-204-W
Table 4 Production well data. Production well data: Plant input pressure: 0.7 bar Plant input temperature: 823 K Plant input mass flow: 37.8 kg/s No calculations are required for this equipment’s output
Table 5 Partial results of the water state. Calculated state: Density (rho) = 0.184366264695 kg/m3 Specificvolume(v ) = 5.42398579076 m3 /kg Viscosity (mu) = 3.06011233192e−05 kg/m s Specific internal energy (u) = 3216.55056667 kJ/kg Specific enthalpy (h) = 3596.22957202 kJ/kg Specific entropy (s) = 9.13534448599 kJ/(kg K) Isobaricspecificthermiccapacity(cp) = 2.16754550081 kJ/(kg K) Isochoricspecificthermiccapacity(c v ) = 1.70485438511 kJ/(kg K)
After the topological validation, the thermodynamical validation takes place. This validation considers, the direct interaction of the equipments from the perspective of their functioning parameters. In this case, interaction problems might arise from both the condenser and pump proposed models. Since a dry steam plant is being validated, it is required to match 0.8 bar at the injection well (considering the given data). The model studies the given condenser and pump adjacency and, since both pressures are equal (to 0.8 bar), the model states that interaction is possible among the present pump and the injection well. At this point, since both validation processes are successful, the simulation begins in the production well for which related results are shown in Table 4. Once the state of the water has been calculated, it is reported and then, it is transfered to the adjacent equipment; this set of results is shown in Table 5. The whole simulation process for each considered equipment and its results is described as follows: Turbine: For this equipment, the provided functioning parameters are: OUTPUT Heat: 0 kJ/s, OUTPUT Pressure: 0.2 bar, OUTPUT Temperature: 335 K and Operation efficiency: 0.9. The turbine output-related calculations are: INPUT Enthalpy: 3596.22 kJ/kg, INPUT Entropy: 9.13 kJ/(kg K), OUTPUT Enthalpy: 2612.46 kJ/kg, OUTPUT Entropy: 9.13 kJ/(kg K), OUTPUT Real steam enthalpy: 2710.84 kJ/kg, OUTPUT Quality: 0.91, OUTPUT Work: 885.38 kJ/kg, INPUT Mass flow from PRODUCTION WELL: 37.8 kg/s.
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Table 6 Production process overall results. Calculating final results Total work = 892.933362956 kJ/kg Input mass flow from production well = 37.8 kg/s Total produced power = 33752.8811197 kW Total given heat = 3270 kJ/kg Process efficiency = 0.273068306714
Turbine-Generator
Production Well Flash Valve Condenser
Injection Well Fig. 3. Proposed case of study: a dry steam power plant with interaction failures.
Condenser: For this equipment, the provided functioning parameters are: INPUT Given heat: 3270 kJ/kg, INPUT/OUTPUT Mass flow: 37.8 kg/s, OUTPUT Pressure: 0.2 bar and OUTPUT Temperature: 335 K. Pump: For this equipment, the provided functioning parameters are: INPUT/OUTPUT Mass flow: 37.8 kg/s, OUTPUT Pressure: 0.8 bar and OUTPUT Temperature: 335 K. The output-related calculations are: INPUT Enthalpy: 251.39 kJ/kg, INPUT Entropy: 7.91 kJ/(kg K), OUTPUT Enthalpy: 258.94 kJ/kg, OUTPUT Entropy: 7.91 kJ/(kg K) and OUTPUT Work: 7.54 kJ/kg. Injection well: For this equipment, the provided functioning parameters are: Plant output pressure: 0.8 bar, Plant output temperature: 335 K and Plant output mass flow: 37.8 kg/s. The output-related calculation is: Plant output mass flow per day: 3265920 liters per day. Finally, the simulation ends, and the results are reported to the user/designer. These focus on the total produced work and, considering the given mass flow of water at the production well, the total mechanical power is calculated as well as the overall efficiency of the proposed process. The final results for this case are summarized in Table 6. 6.1.1. Description of the role of the breadth first search algorithm in the simulation process The standard behavior of this algorithm depends upon two functions defined within itself: process vertex and process edge [16]. Depending on how these functions behave, the algorithm will traverse the graph and provide the required information. In this case, the vertex processing consists on identifying it and according to its type (of equipment), to apply the balances from the previous state of the water to its next state. For edge processing, the calculations of every property are made in order to set the ground for the next vertex-related calculation. Specifically, considering the first presented example in Section 6.1, the algorithm begins its execution at the first vertex of the graph, which is always the production well. Actually, since the properties in the production well determine the type of plant to be validated and studied, this production well has to be defined, otherwise the model will not be considered as a valid model. After the required computations to determine the type of geothermal power plant are performed in the production well, the algorithm states that every adjacent edge and their related adjacent vertex have to be queued and processed [16]. In this example, this statement leads to the study of the state of the water at the outlet of the production well, which provides the require data to perform the computation in the turbine. Similarly, the algorithm continues with the analysis of the adjacent equipments, reporting the state of the water and then, the related computations in the condenser and then in the pump, until it reaches the final vertex. This vertex has to be an injection well, in order to provide a thermodynamically valid geothermal power plant model. Once the traversing ends, the results in terms of efficiency are computed and provided. 6.2. A failing proposed design The final case of study focuses on a design with interaction failures among the flash valve and the injection well (see Fig. 3). Once again, its working temperature range was considered based on [4]. In this case, the simulation stops at the interaction error and the user has to improve the proposed design as it is advised by the model. The topological description can be summarized in Table 7.
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Table 7 Topological description. Production well OUTPUT Mass flow = 37.8 kg/s ADVISE: Mass flow value under 100 kg/s: (37.8 kg/s) Potential and Kinetic Energies will be depreciated OUTPUT Pressure = 0.7 bar OUTPUT Temperature = 309.16 K OUTPUT Saturation Pressure = 778.572085444 bar Flash valve OUTPUT Pressure of saturated liquid = 0.9 bar OUTPUT Pressure of saturated steam = 15 bar Turbine HYPOTHESIS: Adiabatic turbine OUTPUT Pressure = 0.2 bar OUTPUT Temperature = 335 K Efficiency = 0.9 Condenser INPUT Given heat = 3270 kJ/kg Injection well MINIMUM Value of pressure for INJECTION: 0.8 bar
For this case, the proposed production well presents temperature and pressure values of 0.7 bar and 309.16 K, respectively and, it also presents a saturation pressure value of 0.0006 bar, which, according to the model, belong to a flashed steam geothermal power plant. Similarly, the topological validation of the proposed energy interactions are studied and, when finished, thermodynamical validation takes place. In this case, considering the provided data, it is required to match 0.8 bar at the injection well which is adjacent to a provided flash valve with a parameter design of 0.7 bar of output pressure. Considering this, the model requests an extra pump, in order to increase the provided flash valve output pressure so it can match the required value at the injection well. 7. Conclusions and future work In this work, we presented a model for the simulation of generic geothermal power plant production processes. The most important theoretical aspects were discussed. As it was mentioned, the model is intended to be the numerical core of an computer aided design application for the study of possible production processes considering the characteristics of the studied reservoirs. We presented two cases: one of them represents the most common occurrence in geothermal production processes schemes, i.e. dry steam geothermal production. The second considered test case, showed the assistance capability of the proposed model when it comes to mechanical interaction among the considered equipments. Considering the state of the art in development and simulation of thermodynamical systems for energy production, the model presents an innovative approach since it is specially intended for the study and simulation of custom designed geothermal power plants. Our current investigation heads towards both the development of the model and the improvement of the mentioned application. On a further basis, the model shall be improved by eliminating some of the considered hypotheses, as for example, the steady state functioning of the simulated production process thus, allowing time-based projections of the results in energy production. The application comprehends a user friendly drag-and-drop interface which allows the study of any proposed production process. Acknowledgement We would like to extend our sincere gratitude to Professor Guillermo Miranda, since his suggestions were critical and gladly given at all times. References [1] J. Lund, 100 years of geothermal production. Oregon, USA: Oregon Institute of Technology, Geo-Heat Center, GHC Bulletin, 2007, pp. 11–19. [2] R. Dipippo, An introduction to electric energy conversion systems for geothermal energy resources, Brown University and USA Department of Energy, June, 1978. [3] Z. Guzović, D. Lonˆcar, N. Ferdelji, Possibilities of electricity generation in the Republic of Croatia by means of geothermal energy, Energy 35 (2010) 3429–3440. [4] M. Yari, Exergetic analysis of various types of geothermal power plants, Renewable Energy 35 (2010) 112–121. [5] CalEnergy Generation Section, Worldwide project’s fact sheet: Imperial Valley (United States), 2009 (On line) (Cited on: September 16th 2010.) http://calenergy.com/projects2d.aspx. [6] J. Glanz, Geothermal project in California is shut down, The New York Times, 2009 (On line) (Cited on: September 16th 2010) http://www.nytimes.com/2009/12/12/science/earth/12quake.html.
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[7] The future of geothermal energy—impact of enhanced geothermal systems (EGS) on the United States in the 21st century. An assessment by an MIT-led interdisciplinary panel, Boston, USA, Massachusetts Institute of Technology, (On line) 2006 (Cited on: September 16th 2010.) [8] Y. Zarhloule, S. Bouri, A. Lahrach, M. Boughriba, A. El Mandour, H. Ben Dhia, Hydrostratigraphical study, geochemistry of thermal springs, shallow and deep geothermal exploration in Morocco: hydrogeothermal potentialities, in: Proceedings World Geothermal Congress, Antalya, Turkey, 24–29 April 2005. [9] H. Sigurdsson, A. Haraldsdotir, T. Gudmarsson, S. Jonsson, Real-time simulators for geothermal power plants and district heating systems, Reykjavik, Iceland, Rafhnnun Consulting Engineers, University of Iceland, Reykjavik Municipal District Heating Service, Orkustofnun, National Energy Authority, 1995. [10] S. Bhattacharjee, TEST-the expert system for thermodynamics, in: Proceedings American Society for Engineering Education Annual Conference and Exposition, Tennessee, USA, 22–25 June 2003. [11] F. Casella, Modeling, simulation and control of a geothermal power plant, Ph.D. Thesis, Milan Polytechnic, Milan, Italy, 1998. [12] K. Wark, Termodinámica, McGraw-Hill, Interamericana de España, SAU, Madrid, 2001 (in Spanish). [13] D. Burghardt, Ingeniería Termodinámica, Editores Industriales, México, DF, 1984 (in Spanish). [14] Y. Cengel, M. Boles, Thermodynamics: An Engineering Approach, second ed., McGraw-Hill, New York, USA, 2007. [15] International Association for the Properties of Water and Steam, Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam, 2007 [16] S. Skiena, The Algorithm Design Manual, Springer-Verlag New York, Inc., New York, USA, 1997.
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Mathematical and Computer Modelling journal homepage: www.elsevier.com/locate/mcm
Modeling and simulation of the production process of electrical energy in a geothermal power plant Eduardo Sanchez a , Carlos F. Torres b , Pablo Guillen c , German Larrazabal a,∗ a
Multidisciplinary Center for Scientific Visualization and Computing (CEMVICC), Faculty of Sciences and Technology (FACYT), University of Carabobo, Venezuela
b
Thermal Science Department, University of Los Andes, Merida, 5101, Venezuela
c
Program in Computational Science, University of Texas at El Paso, TX, USA
article
info
Article history: Received 26 November 2010 Received in revised form 15 March 2011 Accepted 16 March 2011 Keywords: Directed graphs Mathematical modeling Simulation Steam power cycles Geothermal electricity production Water thermodynamical properties
abstract In this work, the study, modeling and simulation of custom designed geothermal power plant production processes are presented. A model based on the thermodynamical steam power cycles theory is developed using directed graphs, in order to consider different types of geothermal power plant structural models to be studied. The model includes steady state forms of the thermodynamical mass and energy conservation laws for each one of the considered equipments, in order to study the mass and energy interactions among them. A computational implementation of the IAPWS-IF97 formulation for the calculation, also by steady state forms, of the physical properties of the water is also presented, thus providing a reliable and accurate method to calculate them in execution time. The analysis of both topological and thermodynamical feasibility of the proposed input models is also presented, as well as the analysis of the efficiency in terms of both generated and invested heat and power. The results are compared against reference results in the literature; these are presented in relation to the proposed models, by reporting the variations of the mentioned water properties and by stating the results of the production processes in terms of both mechanical power generation, and efficiency of the proposed structural models. © 2011 Elsevier Ltd. All rights reserved.
1. Introduction Nowadays, a considerable effort is being focused on the study of efficient methods for the appropriate exploitation of alternative sources of renewable energy. The current economic environment and impending climate change from the combustion of hydrocarbons make the use of alternative energy sources imperative for the near future. A clear example of this scenario has been given around the world with the design and operation of plants for the production of electrical energy through the use of geothermal resources, also known as geothermal power plants. These geothermal resources exist due to several factors within earth’s geology, such as the existence of molten rock (magma) from the earth’s core, which contributes to great quantities of heat, and the ascent of heated groundwater that has circulated from depths of several kilometers [1]. One of the earliest documented examples takes place in Italy, between 1904 and 1905 when Prince Piero Ginori Conti managed to establish a 3/4-horsepower reciprocating engine, fueled by steam separated from water, to drive a small generator [2] and by 1924, when the first commercial 250 kW geothermal power plant operated continuously [3]. Developments in geothermal energy production have been taken place ever since; for example in New Zealand at Wairakei in 1958; an experimental plant at Pathe, Mexico in 1959 and the first commercial plant at The Geysers in the United States in
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Corresponding author. E-mail addresses: [email protected] (E. Sanchez), [email protected] (C.F. Torres), [email protected] (P. Guillen), [email protected], [email protected] (G. Larrazabal). 0895-7177/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.mcm.2011.03.021
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1960 [1]. In modern days, efforts are necessary to find alternative energy resources; therefore, geothermal energy production systems come in handy since they are more competitive when compared to conventional fossil-fuel-based production systems and in the last five years, their direct use has increased approximately twofold [4]. In the United States specifically, several projects are being carried out successfully. One sample project consists of 10 generating plants in southern California’s Imperial Valley area. The plants follow the classic scheme for geothermal power plants to produce electricity solely from naturally occurring geothermal steam. Eight of the facilities in this area: Vulcan, Hoch, Elmore, Leathers and Salton Sea 1, 2, 3 and 4, are under contract to sell power to southern California companies under long term power purchase agreements [5]. Nevertheless, in order to improve current exploration and production techniques, additional efforts in research and development (R&D) should be considered. An important example is the drawback on behalf of one of the most important companies in the field within the current US administration, regarding the need to study abnormal seismic activity related to exploration efforts [6]. Similar efforts should also be devoted to both heat-transfer performance for lower-temperature fluids and development schemes for plant designs based on higher resource temperatures of the supercritical water. These efforts would lead to an order of magnitude (or more) gain in both reservoir performance and heat-to-power conversion efficiency [7]. Along with the mentioned efforts, a comprehensive assessment of enhanced, or engineered, geothermal systems should be carried out by the governments to evaluate the potential of geothermal energy becoming a major energy source. Three main components should be considered in the analysis [7]:
• Resource: estimating the magnitude and distribution of the geothermal resource. • Technology: establishing requirements for the production from geothermal reservoirs including drilling, reservoir design and stimulation, and thermal energy conversion to electricity.
• Economics: estimating costs for geothermal supplied electricity on a national scale using newly developed methods for mining heat from the earth. Examples of similar analyses have been carried out in different countries. In Morocco, hydrostratigraphical studies focused on the geochemistry of exploration models have been executed [8] stating the most important aspects of the geothermal potential efficient exploitation and taking special consideration into the characteristics of the reservoirs. Geothermal power plant designs have been shown to imply innovative ideas, given the need to adapt themselves to the features of geothermal resources reservoirs [2]. The complexity of these designs, given the need of integrating several mechanical components and the different difficulties concerning mathematical modeling, consequences of the present physical phenomena, make the availability of simulation tools an invaluable assistance for both plant design and building as for the planning of the operative activities [9]. Previous work regarding the computational simulation of thermodynamical systems has been considered [10] and similarly, so has been previous work relating the computational simulation and control of existing geothermal power plant production processes [11]. Once the plant has been built, the schematic description of its structure allows the creation of simulation and control tools, which at the same time present the computational core of interactive personnel training applications and similar, but these works assume the existence of a completely functional geothermal power plant. Likewise, in early stages of development and design, the study of the reservoir conditions could be used in order to simulate the production process that can arise from the future power plant to be built. In this work, the study, modeling and simulation of geothermal power plant production processes are presented, in order to gain both knowledge in the implications regarding energetic potential, and comprehension of the related physical phenomena and their characteristics related to the overall efficiency of the production processes. This model is intended as the main numerical core of an application for the computer aided design of geothermal power plants, in order to provide the user with the ability to study and simulate the functioning of any custom made design model for a geothermal power plants overall design before its construction. 2. Steam power cycles and involved equipments The numerical modeling of geothermal power plant production processes rests on the theory of thermodynamical steam power cycles [12,13]. These cycles study the variations of the state of a given substance in order to produce results in terms of mechanical power. Steam power cycles can be defined as a collection of equipments or control volumes, that cause changes in the state of a working fluid. The first theoretical aspect considers how functional relations among the different properties of the water can be defined. Specifically, how many properties have to be taken into consideration in order to be able to relate them to other intrinsic non-measurable properties of the water. There is a general rule to determine this required number of measurable properties and it is known as the state postulate. This is a very well-known result from thermodynamics [12]. Water has proven to work as a simple thermodynamical system due to experimental results [12,13], that is, a system in which in order to modify its intrinsic state, only one way of quasi-static work is needed. Thus, if we take this into consideration, then the state postulate for simple systems [12] is also of important consideration. Since one can choose any pair of independent properties, it is desirable that these two properties could be measurable [12,13], therefore pressure and temperature are considered.
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Table 1 Equipment models and their related specific energy balances. Equipment
Governing energy balance
Separator Turbine Condenser Pump Flash valve
˙ (hi − ho ) = 0 m ˙ Turbine = m ˙ Turbine < 0 given ho < hi ˙ (ho − hi ), W W ˙ (ho − hi ), Q˙ Condenser < 0 given ho < hi Q˙ Condenser = m ˙ Pump = m ˙ Pump > 0 given ho > hi ˙ (ho − hi ), W W ˙ (hi − ho ) = 0 m
2.1. Conservation principles and model assumptions Three well-known results from thermodynamics are: the general mass conservation principle, which states: d
∫
dt
ρ dV = V
− ∫ i
ρ Vn dS
S
− i
− ∫ o
ρ Vn dS S
(1) o
where ρ is the density inside the control volume with surface S and volume V , i and o denote input and output states, respectively. Vn is the fluid velocity normal to the surface S in both i and o states. The general energy conservation principle is defined as: d dt
∫
˙ + eρ dV = Q˙ + W V
− [∫ i
eρ Vn dS S
] − i
− [∫ o
S
eρ Vn dS
] (2) o
˙ denote both general heat flow in time and general power of the control volume, h denotes the specific where Q˙ and W enthalpy and e represents the energy interactions. This total energy is defined as: e=h+
V2
+ gz (3) 2 where g is the standard earth’s gravity and z stands for the height. The following assumptions are considered for this stage of development, since they have shown to apply to geothermal processes due to experimental data [4,12–14]: 1. There is no variation in time for any of the involved properties. Let X (t ) be some property, we have that X ′ (t ) = 0. Therefore, the geothermal power plants operate in a steady-state condition. 2. The conditions of the fresh water are known at the production well. No simulations of the underground reservoir nor for the vertical flow of water through the production well were developed. 3. The pressure drops throughout the heat exchangers and pipelines are neglected. 4. The flow is uniform in the control volume inlets and outlets. 5. The turbines and pumps have isentropic efficiencies. 6. The kinetic and potential energy changes are negligible. 7. Fresh water properties have been used in the analysis instead of the thermodynamic properties of the geofluid. 8. The flashing process is accomplished at constant enthalpy. 9. Temperature and pressure losses of the geofluid are neglected in the separation and condensation processes. 10. Turbines can only interact with a condenser or directly with a generator; therefore, there cannot be successive turbine configurations. 2.2. Equipment model particularities In this section, the particular hypotheses and their effects over the previous results are introduced per each considered equipment model. The considered equipment models are shown in Table 1 along with their own specific energy balance; ˙ stands for the mass flow. where m The mass conservation principle states, equally for all of them, that mi = mo .
(4)
3. IAPWS-IF97 computer implementation Having explained how do the equipments will handle the state of the water, it is time to explain how can the thermodynamical properties of the water be calculated in execution time. In 1997, the The International Association for the Properties of Water and Steam (IAPWS) approved a new formulation of the thermodynamic properties of water and steam for industrial use (referred to as IAPWS-IF97), replacing the IFC-67 formulation that is familiar to many from its use in the 1967 ASME Steam Tables. An archival paper describing this formulation has been published [15], and it was considered in order to be implemented to make the application able to calculate the required properties in execution time.
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4. Efficiency and thermodynamical feasibility study of the proposed model The efficiency of a thermodynamical cycle is studied from the heat engines approach [12,13]. In this approach, if any cycle is considered from a black box perspective, one can see that they require an input heat flow and an input power in order to produce an outgoing heat flow and an outgoing power. Considering this, the efficiency τ (in terms of power) is measured ˙ net ) and the required energy required to produce it, expressed in terms of heat by the quotient of the produced net work (W (Q˙ in ); that is:
τ=
˙ net W Q˙ in
∑ = ∑ o
˙o − W
o
˙o − ho m
∑
˙i W
i
∑
˙i hi m
.
(5)
i
Regarding the thermodynamical and mechanical feasibility of a given model, the most important configurations for a power plant described in [2] were studied in order to provide the validation on any proposed power plant model. These validation focuses on the compatibility of the parameter’s values among provided equipments. 5. Thermodynamical cycles as directed graphs and topological feasibility The computational modeling for a generic input data structure for the description of a steam power cycle, considers graph theory tools. In general, any thermodynamical steam power cycle can be described as a directed graph G = (V , A, ϕ, φ) where:
• V denote set of nodes which represent the equipments composing the given cycle. • A denotes the set of edges which represent the direct interaction among two given nodes (equipments). Notice that there are no edges of the form (x, x) since no loops are considered. One should also notice that the multiplicity of the edges is less or equal to 1 since no multiple edges are considered among any given pair of equipments.
• Both ϕ and φ weight, any node (equipment) to its related mass, energy balance and functioning parameters, and any edge to its related set of thermodynamical properties. In this work, the computational representation for a graph is made trough its related weighted adjacency matrix, since the amount of equipment in a generic geothermal power plant, according to the experience, is small. Once the input model is provided, a Boolean adjacency matrix, which is defined as M = (mij )|V |2 where mij equals 1 if a direct interaction is possible among nodes i and j; and equals 0 if it is not, clearly describes whether the given input model is topologically feasible; that is, according to the functioning of the related equipment, this matrix states if a direct interaction among any couple of nodes is possible. If a given input model makes sense, topologically speaking, then the application verifies its thermodynamical feasibility. According to the functional definitions of the equipments, some cases of interactions require special attention. The first example of these cases of interaction is the interaction among the injection well and the condenser. Both values of input and output pressure, respectively, should match. The model verifies every occurrence of this case and advises the designer regarding the course of action in the case of a failed interaction proposal. The second case of interaction which requires validation is the interaction among the injection well and the pump, since both input and output pressures should match. The third case is the most complex to deal with, since it involves different branches of proposed solutions in case of an interaction failure. In this case, the interaction among the flash valve and the injection well is studied. As it has been mentioned, the injection well requires a minimum injection pressure in order to work, therefore, the flash valve output pressure has to match. So, first we come up to three possibles scenarios: 1. Direct injection is possible. 2. Flash valve design pressure is lower that the minimum injection pressure. In this case, a pump has to be considered in order to increase the pressure up to the desired value. 3. Flash valve design pressure is lower that the minimum injection pressure. In this case, a second flash valve has to be considered in order to decrease the pressure down the required value. Hence, every time an advise is given regarding interaction, the user may try to fix it, and recurrent interaction problems might arise, Fig. 1; therefore, those have to be studied. 5.1. Breadth first search algorithm and its application as simulation engine As it was previously mentioned, the models of custom designed geothermal power plants can be built according to specific interaction needs, thus yielding a variable topology of the underlying directed graph modeling the plant. Clearly, this interaction is important since it determines the behavior of the production process. That is why, an algorithm to correctly traverse the resulting considered graph has to be considered, in order to consider the variability of the implied interaction scheme and its effects in the simulation results. Logically, graph theory provides a traverse algorithm such as the one needed. Once a topologically feasible cycle model has been read, the Breadth First Search algorithm [16] traverses the graph thus executing the simulation process. Section 6.1.1 describes the specific role of this algorithm in terms of the execution of the simulation process.
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Fig. 1. Implicitly defined tree of interaction issues among the injection well and the flash valve and their related advised courses of action.
Turbine 1
Generator
Production Well 1
Injection Well
Pump
Condenser
Fig. 2. Proposed case of study: a dry steam geothermal power plant.
6. Test case results In this section, two cases are presented in order to appreciate the functioning of the simulation processes and the required validation schemes. 6.1. A rankine cycle underlying a dry steam geothermal power plant One of the most important test cases since it is one of the most frequent cases in the study of geothermal power plants [2] is the dry steam geothermal power plant. In this type of plant, steam comes out of the reservoir at such a high temperature, that it does not require any extra heating processes (see Fig. 2). However, for purposes of validation, we consider the case of a thermodynamical cycle which underlies the design of a dry steam power plant for which we consider the expected given heat of the condenser as a design parameter. This case and its related results can be compared against [13]. Table 2 shows that the functioning parameters are clearly given. Once the equipments are considered, the model determines the type of plant. In this case, the saturation pressure and temperature on the production well, 0.7 bar and 823 K, respectively, are compared against the water saturation temperature (778.57 bar). According to this result, the plant is a dry steam plant. Once the equipments have been entirely considered, the proposed energy interactions are studied. This is shown in Table 3. These proposed energy interactions are validated according to its adjacency, in terms of the maximum amount of allowed input and output connections for each equipment. If the validation is successful, the model is considered to be topologically feasible.
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Table 2 Topological description. Production well OUTPUT Mass flow = 37.8 kg/s ADVISE: Mass flow value under 100 kg/s: (37.8 kg/s) Potential and Kinetic Energies will be depreciated OUTPUT Pressure = 0.7 bar OUTPUT Temperature = 823 K OUTPUT Saturation Pressure = 778.572085444 bar Turbine HYPOTHESIS: Adiabatic turbine OUTPUT Pressure = 0.2 bar OUTPUT Temperature = 335 K Efficiency = 0.91 Condenser INPUT Given heat = 3270 kJ/kg Pump HYPOTHESIS: Adiabatic pump OUTPUT Pressure = 0.8 bar Injection well MINIMUM Value of pressure for INJECTION: 0.8 bar
Table 3 Proposed energy interactions. Connection from 0 to 1 called PW01-TUR01-201-W Connection from 1 to 2 called TUR01-COND01-202-W Connection from 2 to 3 called COND01-PMP01-203-W Connection from 3 to 4 called PMP01-IW01-204-W
Table 4 Production well data. Production well data: Plant input pressure: 0.7 bar Plant input temperature: 823 K Plant input mass flow: 37.8 kg/s No calculations are required for this equipment’s output
Table 5 Partial results of the water state. Calculated state: Density (rho) = 0.184366264695 kg/m3 Specificvolume(v ) = 5.42398579076 m3 /kg Viscosity (mu) = 3.06011233192e−05 kg/m s Specific internal energy (u) = 3216.55056667 kJ/kg Specific enthalpy (h) = 3596.22957202 kJ/kg Specific entropy (s) = 9.13534448599 kJ/(kg K) Isobaricspecificthermiccapacity(cp) = 2.16754550081 kJ/(kg K) Isochoricspecificthermiccapacity(c v ) = 1.70485438511 kJ/(kg K)
After the topological validation, the thermodynamical validation takes place. This validation considers, the direct interaction of the equipments from the perspective of their functioning parameters. In this case, interaction problems might arise from both the condenser and pump proposed models. Since a dry steam plant is being validated, it is required to match 0.8 bar at the injection well (considering the given data). The model studies the given condenser and pump adjacency and, since both pressures are equal (to 0.8 bar), the model states that interaction is possible among the present pump and the injection well. At this point, since both validation processes are successful, the simulation begins in the production well for which related results are shown in Table 4. Once the state of the water has been calculated, it is reported and then, it is transfered to the adjacent equipment; this set of results is shown in Table 5. The whole simulation process for each considered equipment and its results is described as follows: Turbine: For this equipment, the provided functioning parameters are: OUTPUT Heat: 0 kJ/s, OUTPUT Pressure: 0.2 bar, OUTPUT Temperature: 335 K and Operation efficiency: 0.9. The turbine output-related calculations are: INPUT Enthalpy: 3596.22 kJ/kg, INPUT Entropy: 9.13 kJ/(kg K), OUTPUT Enthalpy: 2612.46 kJ/kg, OUTPUT Entropy: 9.13 kJ/(kg K), OUTPUT Real steam enthalpy: 2710.84 kJ/kg, OUTPUT Quality: 0.91, OUTPUT Work: 885.38 kJ/kg, INPUT Mass flow from PRODUCTION WELL: 37.8 kg/s.
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Table 6 Production process overall results. Calculating final results Total work = 892.933362956 kJ/kg Input mass flow from production well = 37.8 kg/s Total produced power = 33752.8811197 kW Total given heat = 3270 kJ/kg Process efficiency = 0.273068306714
Turbine-Generator
Production Well Flash Valve Condenser
Injection Well Fig. 3. Proposed case of study: a dry steam power plant with interaction failures.
Condenser: For this equipment, the provided functioning parameters are: INPUT Given heat: 3270 kJ/kg, INPUT/OUTPUT Mass flow: 37.8 kg/s, OUTPUT Pressure: 0.2 bar and OUTPUT Temperature: 335 K. Pump: For this equipment, the provided functioning parameters are: INPUT/OUTPUT Mass flow: 37.8 kg/s, OUTPUT Pressure: 0.8 bar and OUTPUT Temperature: 335 K. The output-related calculations are: INPUT Enthalpy: 251.39 kJ/kg, INPUT Entropy: 7.91 kJ/(kg K), OUTPUT Enthalpy: 258.94 kJ/kg, OUTPUT Entropy: 7.91 kJ/(kg K) and OUTPUT Work: 7.54 kJ/kg. Injection well: For this equipment, the provided functioning parameters are: Plant output pressure: 0.8 bar, Plant output temperature: 335 K and Plant output mass flow: 37.8 kg/s. The output-related calculation is: Plant output mass flow per day: 3265920 liters per day. Finally, the simulation ends, and the results are reported to the user/designer. These focus on the total produced work and, considering the given mass flow of water at the production well, the total mechanical power is calculated as well as the overall efficiency of the proposed process. The final results for this case are summarized in Table 6. 6.1.1. Description of the role of the breadth first search algorithm in the simulation process The standard behavior of this algorithm depends upon two functions defined within itself: process vertex and process edge [16]. Depending on how these functions behave, the algorithm will traverse the graph and provide the required information. In this case, the vertex processing consists on identifying it and according to its type (of equipment), to apply the balances from the previous state of the water to its next state. For edge processing, the calculations of every property are made in order to set the ground for the next vertex-related calculation. Specifically, considering the first presented example in Section 6.1, the algorithm begins its execution at the first vertex of the graph, which is always the production well. Actually, since the properties in the production well determine the type of plant to be validated and studied, this production well has to be defined, otherwise the model will not be considered as a valid model. After the required computations to determine the type of geothermal power plant are performed in the production well, the algorithm states that every adjacent edge and their related adjacent vertex have to be queued and processed [16]. In this example, this statement leads to the study of the state of the water at the outlet of the production well, which provides the require data to perform the computation in the turbine. Similarly, the algorithm continues with the analysis of the adjacent equipments, reporting the state of the water and then, the related computations in the condenser and then in the pump, until it reaches the final vertex. This vertex has to be an injection well, in order to provide a thermodynamically valid geothermal power plant model. Once the traversing ends, the results in terms of efficiency are computed and provided. 6.2. A failing proposed design The final case of study focuses on a design with interaction failures among the flash valve and the injection well (see Fig. 3). Once again, its working temperature range was considered based on [4]. In this case, the simulation stops at the interaction error and the user has to improve the proposed design as it is advised by the model. The topological description can be summarized in Table 7.
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Table 7 Topological description. Production well OUTPUT Mass flow = 37.8 kg/s ADVISE: Mass flow value under 100 kg/s: (37.8 kg/s) Potential and Kinetic Energies will be depreciated OUTPUT Pressure = 0.7 bar OUTPUT Temperature = 309.16 K OUTPUT Saturation Pressure = 778.572085444 bar Flash valve OUTPUT Pressure of saturated liquid = 0.9 bar OUTPUT Pressure of saturated steam = 15 bar Turbine HYPOTHESIS: Adiabatic turbine OUTPUT Pressure = 0.2 bar OUTPUT Temperature = 335 K Efficiency = 0.9 Condenser INPUT Given heat = 3270 kJ/kg Injection well MINIMUM Value of pressure for INJECTION: 0.8 bar
For this case, the proposed production well presents temperature and pressure values of 0.7 bar and 309.16 K, respectively and, it also presents a saturation pressure value of 0.0006 bar, which, according to the model, belong to a flashed steam geothermal power plant. Similarly, the topological validation of the proposed energy interactions are studied and, when finished, thermodynamical validation takes place. In this case, considering the provided data, it is required to match 0.8 bar at the injection well which is adjacent to a provided flash valve with a parameter design of 0.7 bar of output pressure. Considering this, the model requests an extra pump, in order to increase the provided flash valve output pressure so it can match the required value at the injection well. 7. Conclusions and future work In this work, we presented a model for the simulation of generic geothermal power plant production processes. The most important theoretical aspects were discussed. As it was mentioned, the model is intended to be the numerical core of an computer aided design application for the study of possible production processes considering the characteristics of the studied reservoirs. We presented two cases: one of them represents the most common occurrence in geothermal production processes schemes, i.e. dry steam geothermal production. The second considered test case, showed the assistance capability of the proposed model when it comes to mechanical interaction among the considered equipments. Considering the state of the art in development and simulation of thermodynamical systems for energy production, the model presents an innovative approach since it is specially intended for the study and simulation of custom designed geothermal power plants. Our current investigation heads towards both the development of the model and the improvement of the mentioned application. On a further basis, the model shall be improved by eliminating some of the considered hypotheses, as for example, the steady state functioning of the simulated production process thus, allowing time-based projections of the results in energy production. The application comprehends a user friendly drag-and-drop interface which allows the study of any proposed production process. Acknowledgement We would like to extend our sincere gratitude to Professor Guillermo Miranda, since his suggestions were critical and gladly given at all times. References [1] J. Lund, 100 years of geothermal production. Oregon, USA: Oregon Institute of Technology, Geo-Heat Center, GHC Bulletin, 2007, pp. 11–19. [2] R. Dipippo, An introduction to electric energy conversion systems for geothermal energy resources, Brown University and USA Department of Energy, June, 1978. [3] Z. Guzović, D. Lonˆcar, N. Ferdelji, Possibilities of electricity generation in the Republic of Croatia by means of geothermal energy, Energy 35 (2010) 3429–3440. [4] M. Yari, Exergetic analysis of various types of geothermal power plants, Renewable Energy 35 (2010) 112–121. [5] CalEnergy Generation Section, Worldwide project’s fact sheet: Imperial Valley (United States), 2009 (On line) (Cited on: September 16th 2010.) http://calenergy.com/projects2d.aspx. [6] J. Glanz, Geothermal project in California is shut down, The New York Times, 2009 (On line) (Cited on: September 16th 2010) http://www.nytimes.com/2009/12/12/science/earth/12quake.html.
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[7] The future of geothermal energy—impact of enhanced geothermal systems (EGS) on the United States in the 21st century. An assessment by an MIT-led interdisciplinary panel, Boston, USA, Massachusetts Institute of Technology, (On line) 2006 (Cited on: September 16th 2010.) [8] Y. Zarhloule, S. Bouri, A. Lahrach, M. Boughriba, A. El Mandour, H. Ben Dhia, Hydrostratigraphical study, geochemistry of thermal springs, shallow and deep geothermal exploration in Morocco: hydrogeothermal potentialities, in: Proceedings World Geothermal Congress, Antalya, Turkey, 24–29 April 2005. [9] H. Sigurdsson, A. Haraldsdotir, T. Gudmarsson, S. Jonsson, Real-time simulators for geothermal power plants and district heating systems, Reykjavik, Iceland, Rafhnnun Consulting Engineers, University of Iceland, Reykjavik Municipal District Heating Service, Orkustofnun, National Energy Authority, 1995. [10] S. Bhattacharjee, TEST-the expert system for thermodynamics, in: Proceedings American Society for Engineering Education Annual Conference and Exposition, Tennessee, USA, 22–25 June 2003. [11] F. Casella, Modeling, simulation and control of a geothermal power plant, Ph.D. Thesis, Milan Polytechnic, Milan, Italy, 1998. [12] K. Wark, Termodinámica, McGraw-Hill, Interamericana de España, SAU, Madrid, 2001 (in Spanish). [13] D. Burghardt, Ingeniería Termodinámica, Editores Industriales, México, DF, 1984 (in Spanish). [14] Y. Cengel, M. Boles, Thermodynamics: An Engineering Approach, second ed., McGraw-Hill, New York, USA, 2007. [15] International Association for the Properties of Water and Steam, Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam, 2007 [16] S. Skiena, The Algorithm Design Manual, Springer-Verlag New York, Inc., New York, USA, 1997.