Energy & Fuels 2009, 23, 553–557
553
CO2 Thermosiphon for Competitive Geothermal Power Generation Aleks D. Atrens,* Hal Gurgenci,* and Victor Rudolph The UniVersity of Queensland, Queensland Geothermal Energy Centre of Excellence, School of Engineering, St Lucia, Queensland 4072, Australia ReceiVed July 28, 2008. ReVised Manuscript ReceiVed October 7, 2008
Engineered geothermal systems represent a significant unutilized energy source, with the potential to assist in meeting growing energy demands with clean, renewable energy. Traditional geothermal systems use water as the working fluid. An alternative working fluid is carbon dioxide which offers potential benefits including favorable thermodynamic and transport properties and the potential for sequestration. An important feature is that CO2 does not dissolve mineral salts, and this will serve to reduce fouling and corrosion problems which afflict piping and surface equipment in conventional water cycles. Our modeling shows that a CO2-based power plant has net electricity production comparable to the traditional approach, but with a much simpler design, and demonstrates the comparative efficacy of CO2 as a heat extraction and working fluid. While the economic viability of a CO2-based system remains to be proven, this analysis provides a starting point for more detailed thermodynamic and economic models of engineered geothermal systems power conversion utilizing CO2.
1. Introduction Population growth coupled with increasing economic development and prosperity are resulting in unprecedented demands for energy. The environmental stresses, most prominently climate change, associated with expanding energy supply using current (fossil fuel) strategies have become unsupportable. Alternative baseload power which is free of CO2 emissions is the key to meeting this challenge. Engineered Geothermal Systems (EGS) have the potential to provide significant amounts of clean, baseload electricity. In Australia, there is an estimated recoverable heat resource of 22 000 EJ.3 A conservative estimate for the US is 280 000 EJ.1 This compares with an annual worldwide energy consumption of 477 EJ in 2005.8 EGS seeks to utilize hot rock reservoirs deeper than traditional near-surface volcanic geothermal energy. In Australia, depths of 4000-5000 m are required to reach temperatures of approximately 250 °C in the most prospective areas.3 These resources typically require engineering intervention to exploit the thermal energy stored in an EGS reservoir. One EGS approach is shown in Figure 1a. The geothermal heat is extracted from the reservoir using water flowing through a system of injection and production wells, spaced to ensure that the fluid reaches thermal equilibrium and adequate temperatures over the field lifetime. The hot water is the heat source for the electrical power generation system. To provide the necessary connection between injection and production wells and allow water to recirculate, it is generally necessary to * To whom correspondence should be addressed. E-mail: aleks.atrens@ uq.edu.au or
[email protected]. (1) Tester, J. W. The Future of Geothermal Energy; Massachusetts Institute of Technology: Boston, 2006. (2) Tester, J. W.; Anderson, B. J.; Batchelor, A. S.; Blackwell, D. D.; DiPippo, R.; Drake, E. M.; Garnish, J.; Livesay, B.; Moore, M. C.; Nichols, K.; Petty, S.; Veatch, R. W.; Baria, R.; Augustine, C.; Murphy, E.; Negraru, P.; Richards, M. Philos. Trans. R. Soc. London, A 2007, 365, 1057–1094. (3) Burns, K. L.; Weber, C.; Perry, J.; Harrington, H. J. Proc. World Geotherm. Congr. 2000, 99–108.
fracture the reservoir rock. Fracturing is commonly also applied in oil and gas reservoirs to increase productivity. The energy in the hot water from the production well is typically converted to electrical power in a Rankine cycle using an organic working fluid such as isopentane.4 A binary system is necessary because the salts dissolved in the water, most commonly carbonates and silicates,9 lead to unacceptable scaling10 and corrosion in the power conversion equipment11 in a direct steam system. 2. Theoretical Basis This paper considers an alternative approach for EGS: an integrated CO2-based power plant, or “CO2 thermosiphon”. As shown in Figure 1b, CO2 is used as the working fluid, which extracts heat from the reservoir and drives the turbine. The CO2 thermosiphon consists of an injection/production well system, the geothermal reservoir, a turbine, and a cooling system. Building on the concept as proposed in prior work,5-7 this paper evaluates the design as an alternative to a water-based system. For the modeling, the power plant processes have been considered to be ideal: losses from irreversible processes such as wellbore friction, turbulence, and pressure drops in process (4) DiPippo, R. Geothermal power plants: principles, applications and case studies; Elsevier: Oxford, 2005. (5) Brown, D. W. Proceedings of the Twenty-Fifth Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, CA, 2000, pp 233-238. (6) Gurgenci, H.; Rudolph, V.; Saha, T.; Lu, a. M. Proceedings of the Thirty-Third Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, CA, 2008, pp 283-289. (7) Pruess, K. Geothermics 2006, 35, 351–367. (8) Agency, I. E. World Energy Outlook 2007; International Energy Agency: Paris, 2007. (9) Andre, L.; Rabemanana, V.; Vuataz, F.-D. Geothermics 2006, 35, 507–531. (10) Moya, P.; DiPippo, R. Geothermics 2007, 36, 63–96. (11) Pa´tzay, G.; Sta´hl, G.; Ka´rma´n, F. H.; Ka´lma´n, E. Electrochim. Acta 1998, 43 (1-2), 137–147. (12) Span, R.; Wagner, W. J. Phys. Chem. Ref. Data 1996, 25 (6), 1509– 1596.
10.1021/ef800601z CCC: $40.75 2009 American Chemical Society Published on Web 12/15/2008
554 Energy & Fuels, Vol. 23, 2009
Atrens et al.
Figure 1. Concept for geothermal plant designs. (a) Traditional water-based binary plant design with associated organic Rankine cycle. (b) CO2 thermosiphon design. States 1-2 indicate injection well, 2-3 the reservoir, 3-4 the production well, 4-5 the turbine, and 5-1 the cooling system. There is uncertainty concerning κ (permeability) and A (contact area).18,19 The combined value used in this work corresponds to a reasonable value achievable with mature fracture stimulation technology.
equipment have been neglected. These assumptions simplify the modeling by neglecting second-order effects which do not affect the comparative insights or validity of the outcomes. This analysis has also assumed that the system contains only CO2, with no water present. The presence of water will have significant effects on the thermodynamic properties, and chemistry in both the reservoir and the surface equipment; because of the complex effects on the system, it has been neglected for this preliminary study. The evaluation was conducted on a basis of 80MWth of heat extracted per well couplet from the reservoir. This extraction rate is defined by the lifetime of the plant; heat extraction must be high enough to ensure cost-effective power generation but low enough to ensure that the reservoir does not cool too quickly. Calculations were based on equation of state formulations for CO2 utilizing Helmholtz free energy correlations,12 with thermodynamic states depicted on the T-s diagram in Figure 2. Injection and production wells (Figure 1b) have been modeled as reversible adiabatic processes (effectively isentropic), because in steady state they are expected to be in equilibrium with their surroundings. The equation relevant for wellbore flow is: ∆P ) Fg∆z
(1)
where F is density, g is gravitational acceleration, ∆z is change in height (from z ) 0 at the surface), and P is pressure. Note that friction losses and acceleration effects in the wellbore are (13) Vesovic, V.; Fenghour, A.; Wakeham, W. A. J. Phys. Chem. Ref. Data 1998, 27 (1), 31–44.
Figure 2. Temperature-entropy diagram for the CO2 thermosiphon power cycle. Numbered states correspond to Figure 1b.
neglected; this study assumed a system where these are optimized to be negligible. The important implication of this equation is that pressure changes within the wellbore in proportion to fluid density. For CO2 there is a large pressure increase in the injection well but only a small pressure drop in the production well (due to the much lower density). This results in a net increase in pressure over the subsurface system, a buoyancy drive, that allows the CO2 design to operate as a thermosiphon, without a pump. The reservoir was modeled as Darcy flow in a single channel. The precise behavior of the reservoirs utilized by EGS is
CO2 Thermosiphon
Energy & Fuels, Vol. 23, 2009 555
dependent on location and even then largely unknown, so for comparative analysis we use a simple porous flow model. The reservoir system was evaluated iteratively using the equations: m ˙ µ∆L FκA
(2)
Tres - Tinj L
(3)
∆P ) ∆T ) ∆L
where P is pressure, L is length, m ˙ is mass flow, µ is temperature-dependent viscosity (calculated from Helmholtz free energy13), F is density, κ is permeability, A is area, T is temperature, with Tres being reservoir temperature and Tinj being injection temperature. The pressure drop through the reservoir is proportional to the ratio of viscosity to density. A major advantage of CO2 compared to water is its lower viscosity to density ratio (less than 30% of that of water, when averaged over the reservoir) allowing larger mass flows. This compensates for a lower heat capacity and results in extraction of thermal energy similar to water. Equation 3 assumes a linear temperature increase over the reservoir. Realistically, temperature profiles depend on fluid properties, lifetime of the resource, and the reservoir configuration, resulting in different effects on fluid pressure losses. However, for the preliminary comparative analysis, this simplified case is adequate; changes to the temperature profile make only minor differences in power output. Note that pressure at the exit of the reservoir in this analysis is below hydrostatic reservoir pressure; it is assumed that fractures are self-propped and not dependent on high fluid pressures to allow fluid flow. It is also assumed that this will not result in significant inflows to the production well from elsewhere in the reservoir system. For the modeling of surface equipment, the turbine (states 4-5, Figures 1 and 2) is considered isentropic. Work output is given by: W)m ˙
∫ PdV
(4)
where, m ˙ is mass flow, P is pressure, and dV is volume change. This equation shows that pressure and volume change over the turbine generates the power output. Although the CO2 turbine operates with high outlet backpressure and fluid density, which implies a small volume change, the work generated is considerable because of the larger mass flow with the CO2 design. The cooling system (states 5-1, Figures 1 & 2) cools CO2 to close to ambient temperature. This was specified as 25 °C, easily achievable in many regions of the world. Some geothermal resources exist in locations where an outlet temperature of 25 °C is not achievable, and then the CO2 system operates with decreased power production, particularly where the fluid cannot be cooled below the critical temperature. 3. Results Modeling of the process with MATLAB, using parameters given in Figure 1, shows that the CO2 thermosiphon has an electrical production of 17 MWe from heat extraction of 80 MWth. The equivalent ideal water-based system was also modeled and estimated to produce 18 MWe. The two power plant designs generate similar power output, and although the CO2 system’s production is slightly less, it has significantly (14) Bonk, D. L.; McDaniel, H. M.; DeLallo, M. R.; Zaharchuk, R. Presented at the 13th International Conference on Fluidized-Bed Combustion, Kissimmee, FL, 1995.
lower complexity. The cooling systems for the CO2 and waterbased processes have comparable duties and will be similar in cost. The remaining significant difference between the systems lies in the different turbines that will be required. Since no largescale CO2 turbines have been constructed, we develop a method to estimate the cost. The assumption is that a CO2 turbine and a steam turbine having the same outlet size would have comparable cost. We then correlate steam turbine cost to outlet diameter (Figure 3a), based on data for cost,14,15 rating (Figure 3b) and exhaust diameter16 (Figure 3c). Assuming a low nominal exit velocity of 10 m s-1 to minimize kinetic energy losses, the outlet diameter of CO2 turbines were calculated (Figure 3d), and costs derived from the diameter-cost correlation. The CO2 turbines are about half the cost of isopentane turbines, which is reasonable since the process design requires that CO2 turbines operate under high backpressure, leading to smaller size. We observe that the CO2-based system does not require the secondary fluid heat exchanger, working fluid, or water circulation pumps. The turbine is significantly smaller than for the alternative binary system. The reduction in equipment requirements and size translates directly to lower surface equipment capital cost, indicating that CO2-based EGS power plants offer substantial opportunity for lower cost per unit of net electricity production. 4. Discussion The ability of the CO2 thermosiphon to generate power with simpler design is due to thermodynamic and transport properties. The low viscosity to density ratio of CO2 ensures there is a small pressure drop in the reservoir compared to water. This is important if CO2 is used directly in the turbine. The buoyancy drive or thermosiphon allows pressure to be gained through the subsurface region, removing the need for a circulation pump. To achieve similar buoyancy effects with water, boiling would be necessary inside the production wellbore, leading to precipitation scaling. This is a common and challenging problem in geothermal plant operation, involving modified well equipment17 or frequent workovers.4 The nonpolar nature of CO2 makes mineral salts insoluble, permitting its direct use in the turbine and eliminating the risk of scaling. Further, as CO2 is only corrosive in the presence of water, using dry CO2 would facilitate choice of construction materials. EGS can lose significant amounts of the heat extraction fluid. The reservoirs are generally sealed from the surface by impermeable sedimentary layers but fluid can be lost sideways or down into the formation. Some operations have reported steady losses as large as 10%.18 Losses during reservoir development could be much higher, e.g. 70% in Hijori.1 Such losses present a challenge for the binary water system, particularly in arid regions (such as many of the best sites in central Australia), where there is no makeup water available. The permanent loss of CO2 into a secure site represents a geosequestration benefit and, depending on the carbon credit scheme and local conditions, could offset the makeup costs or even contribute an additional income stream to the power provider. (15) Turton, R.; Bailie, R. C.; Whiting, W. B.; Shaeiwitz, J. A. Analysis, synthesis, and design of chemical processes, 2nd ed.; Prentice Hall PTR: Upper Saddle River, NJ, 2003. (16) SiemensAG, Industrial Steam Turbines, 2005. (17) Gunnarsson, I.; Arno´rsson, S. Geothermics 2005, 34 (3), 320–329. (18) Murphy, H.; Brown, D.; Jung, R.; Matsunaga, I.; Parker, R. Geothermics 1999, 28, 491–506. (19) Sausse, J.; Fourar, M.; Genter, A. Geothermics 2006, 35 (5-6), 544–560.
556 Energy & Fuels, Vol. 23, 2009
Atrens et al.
Figure 3. Rating, cost, and exhaust diameter correlations for turbines. (a) Correlation of cost with turbine output, based on known correlations for small steam turbines,15 and data points for large turbines.14 (b) Correlation of cost and rating for turbines using different fluids. (c) Correlation of cost with exhaust diameter, with data for steam turbines produced by Siemens.16 (d) Correlation of turbine exhaust diameter with density for a flow of 100 kg s-1, for different fluid velocities. The dotted line represents the maximum exhaust diameter used for steam turbines before additional cylinders are added.
This modeling suggests that a CO2 thermosiphon offers advantages within an engineered geothermal power generation system. The challenges are to develop and prove CO2 turbines of high efficiency and to optimize the geothermal field configuration for the larger volumetric flow rates of CO2 compared to water. As noted in section 2, there are significant effects from the presence of water, and this is an important area for additional research. Plans are currently being prepared for a trial design (5 MWe) of a CO2 thermosiphon, to be implemented in Australia by 2013. If that pilot proves viable, a commercial design (50 MWe) could be constructed by 2018. 5. Methods All modeling was conducted using MATLAB and based on Helmholtz free energy equations of state. The general approach was to begin at a state with two specified intensive properties. The equation of state was then used to determine whichever properties (out of P, T, F, u, h, s) were unspecified. Each operation within the process was specified by equations of change in two intensive properties; after each property change, the equation of state was evaluated to determine the remaining properties. Turbine cost estimation was based on data for steam turbine exhaust diameter, cost, and power output. Established correlations between cost and rating (power output) were combined with exhaust outlet sizes to produce an estimate of cost based on outlet size. For the three different fluids (steam, isopentane,
and CO2), densities were used, coupled with assumed exhaust velocities (10 m s-1 for CO2, 50 m s-1 for isopentane), to estimate the turbine exhaust size. Note that CO2 is assumed to have a conservatively low exhaust velocity (this increases exhaust size). The estimated exhaust sizes were used to produce a plot showing the costs of turbines for different fluids at various ratings. For the CO2, process evaluation was initiated at the surface of the injection well, where the temperature and pressure were specified. The pressure and enthalpy change down the wellbore were calculated from: ∆P ) Fg∆z
(5)
2
V ∆z (6) P - 2∆z Fg These equations were evaluated at intervals of 50 m to account for variable density over the depth of the well. Velocities were calculated from the mass flow, density, and diameter of the well (taken as 0.5 m). ∆h ) g∆z -
4m ˙ (7) πFD2 Once the state at the base of the injection wellbore was calculated, the reservoir was evaluated through the equations: V)
∆P ) -
m ˙ µ∆L FκA
(8)
CO2 Thermosiphon
Energy & Fuels, Vol. 23, 2009 557
Tres - Tinj (9) L These equations were evaluated at 10 m intervals. Viscosity was determined from Helmholtz free energy correlations based on temperature and density at each iteration interval. κ and A are both uncertain and have an identical effect on the pressure drop through the reservoir. These two variables have been specified as a combined constant, determined from an impedance of 0.1 MPa(L s-1)-1 for an identical reservoir flowing 100 L s-1 of H2O. After the conditions at the exit of the reservoir had been calculated through this procedure, the heat influx to the process was obtained from: ∆T ) ∆L
˙ ∆h1 QIN ) m
The calculation proceeded from the mass flow and enthalpy change on the water side of the heat exchanger. A minimum approach temperature between the water and isopentane of 5 °C was specified, resulting in a minimum water temperature of 30 °C. The isopentane heat exchanger inlet conditions were specified as 25 °C, 3.2 MPa. The mass flow of isopentane was then varied until a ratio of isopentane to water was found that produced maximum power output from the process (approx 45% more mass of isopentane than water). This corresponded to a heat exchanger isopentane outlet temperature of 188 °C. The isopentane then passes through the turbine, with work calculated as:
(10)
where ∆h1 is the difference in enthalpies between the entry and exit of the reservoir. The calculations were repeated with varying mass flow rates until the specified heat extraction of 80 MWth was achieved. Since the mass flow affects pressure drop, an iterative procedure is required. The production wellbore followed the same equations and procedures as for the injection wellbore. The turbine was evaluated by specifying:
˙ ∆h Wturb ) m
(15)
∆s ) 0 Pout ) 0.077 MPa
(16) (17)
∆s ) 0
(11)
where the outlet pressure corresponds to the vapor pressure of isopentane at 25 °C. The cooling process for the isopentane is then calculated for an outlet state of saturated liquid at 25 °C. The net work for the binary system needs to account for both the turbine work produced and the work provided to the isopentane and water pumps. The water pump is specified to pressurize the water at 30 °C from 2.6 to 7.5 MPa. With work calculated from:
Pout ) Pinj
(12)
˙ ∆h WH2Opump ) m
where Pout indicates the turbine outlet pressure, and Pinj indicates the injection pressure (for CO2 this is 6.4 MPa). The work output from the turbine was then calculated from: ˙ ∆h2 Wturb ) m
(13)
where ∆h2 is the change in enthalpy between the turbine inlet and outlet. At this point, the states at both the inlet and the outlet of the condenser are known, and the system is completely defined. The H2O/isopentane binary plant was evaluated using the same general principles. The subsurface evaluation using water as the heat extraction fluid used the same procedures as described above. The water system includes the water/isopentane heat exchanger, requiring additional calculation steps. The heat exchanger heat transfer was calculated from: ˙ ∆h QHX ) m
(14)
(18)
Most EGS operations are designed with another pump submerged in the production well. This is not included in the present analysis. Such pumps introduce a further plant complication and significant additional cost to water-based systems, favoring a CO2 thermosiphon system even more. The isopentane pump is specified to pressurize the isopentane at 25 °C from 0.077 to 3.2 MPa, with work calculated from: ˙ ∆h Wisopump ) m
(19)
The net work for the binary plant was calculated from: Wnet ) Wturb - WH2Opump - Wisopump
(20)
Acknowledgment. We thank the Queensland State Government, whose funding of the Queensland Geothermal Energy Centre of Excellence made this work possible. We also thank Andrejs Atrens and Stephen D. C. Andrews for reading and editing the manuscript. EF800601Z
