ARTICLE pubs.acs.org/EF
Economic Optimization of a CO2-Based EGS Power Plant Aleks D. Atrens,* Hal Gurgenci, and Victor Rudolph The University of Queensland, Queensland Geothermal Energy Centre of Excellence, St. Lucia, Queensland 4072, Australia ABSTRACT: CO2-based enhanced geothermal systems (EGSs) have been examined from a reservoir-oriented perspective, and as a result thermodynamic performance is well explored. Economics of the system are still not well understood, however. In this study, the economics of the CO2-based EGS technology is explored for an optimized power plant design and best-available cost estimation data. We demonstrate that near-optimum turbine exhaust pressure can be estimated from surface temperature. We identify that achievable cooling temperature is an important economic site consideration alongside resource temperature. The impact of time required to sufficiently dry the reservoir prior to power generation is also addressed. The role of sequestration as part of CO2-based EGS is also examined, and we conclude that if fluid losses occur, the economic viability of the concept depends strongly on the price associated with CO2.
1. INTRODUCTION Examination of the CO2-based enhanced geothermal system (EGS) concept has focused to-date on technical aspects, predominantly reservoir considerations,18 and process modeling and design.9,10 Ultimately, the viability of the concept depends on economics, and the ultimately preferred design will be one that is economically optimized. A preliminary analysis of economics for the system has previously been conducted.11 That analysis found the following: • There were economic arguments to proceed with further analysis. • Economics were highly tentative due to uncertainties of well cost estimates. • Larger wellbore diameters were economically favored. • Inclusion of compressors was economically favored. • CO2-based EGSs should be focused on climates with lower ambient temperatures. This work extends that economic analysis using new data on the cost of increasing well diameter for well cost estimation and considering a number of additional issues. Analysis is accomplished by finding the expected cost per kilowatt of electrical generation capacity for a nominal plant size of 50 MWe net, operating within typical site constraints. A conceptual sketch of the system is shown in Figure 1. The system consists of a number of injection/production well doublets—each including one injection well (points 12), a reservoir (point 23), and a production well (point 34)—and a surface plant—consisting of a turbine (point 45), a compressor (point 67), and aircooled heat exchange equipment (points 56 and 71). The number of production and injection well doublets is increased linearly to allow sufficient total fluid flow to achieve the 50 MWe net target. Reservoir arrangements of greater complexity (for example, multiple coupled wells) are not considered in this work because the precise details regarding reservoir design and management depend decisively on the specific details and geology of a reservoir. The surface equipment is considered as a single set of operating units. Note that this analysis does not include binary power generation systems (those using a separate power conversion loop), as a result of direct power conversion being a major incentive for using CO2.9 r 2011 American Chemical Society
The results from the economic estimation provide a baseline process cost for a reference case, and a comparative analysis with other cases is used to examine the trade-offs and guide economic optimization of CO2-based EGS, in particular, the following: • thermodynamic and economic optimization of compressor usage, in particular selection of a turbine exhaust pressure; • the trade-off during site selection between achievable cooling temperatures and resource temperatures; • the trade-off between resource temperature and resource depth; • the implications of CO2 reaction or dispersion in the reservoir in conjunction with CO2 costs; • and the impact of dry-out times on economic performance. The examination of these aspects provides conclusions with regard to the economic viability of the CO2-based EGS concept, and implications for site selection and process design. The numerical dollar values for costs are shown for comparative purposes only: ‘real’ plant costs require close attention to what is included inside the estimate battery limits, among other considerations. As discussed further in section 3.1.4, modification of the costing basis can lead to a change in economic performance of (50%, but conclusions based on comparison between different operating points or designs should be preserved.
2. METHODOLOGY The economic calculations for this work are based on the thermodynamic model of the CO2-based EGS system, which has been comprehensively described elsewhere.10 That model has been modified to incorporate a compression system and additional cooling unit in the surface plant. The calculation approach is as follows: (1) Site conditions are defined, typically reservoir impedance, reservoir pressure (P3), flow pathway/geometry, depth, temperature, and injection temperature (T1). Injection temperature is the temperature achievable as a result of cooling and depends on the process arrangements (e.g. wet or dry cooling system, optimized heat exchanger design) and the local ambient conditions. Received: April 8, 2011 Revised: June 16, 2011 Published: June 21, 2011 3765
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Table 1. Reference Parameters for Site depth (m) reservoir length (m)
5000 1000
reservoir temp (°C)
225
injection temp (°C)
25
min. reservoir width (m) max. reservoir width (m)
0.73 250.73
reservoir impedance (MPa 3 s/L)
0.2
corresponding k.H (m3)
Figure 1. Conceptual diagram of the system. (2) A CO2 mass flow rate (m) is selected. (3) Injection wellhead pressure (P1) is calculated to be sufficient for the pressure at the reservoir-production well interface (P3) to be equal to the specified reservoir pressure. O Injection well flow is adiabatic: change in enthalpy is equal to the change in gravitational potential energy and kinetic energy, and change in pressure is equal to the static pressure change adjusted for pressure decline due to friction. O Reservoir flow follows Darcy’s law, with the flow path width linearly increasing from a minimum width at the wellbore to a maximum width at the midpoint of the reservoir, and with CO2 temperature increasing linearly from the bottom of the injection well to the bottom of the production well. (4) The pressure and temperature at the bottom of the production well (P3, T3) are set at the reservoir conditions. Production wellhead pressure (P4) and production wellhead temperature (T4) are calculated on the basis of mass flow rate. O Production well flow is adiabatic: change in enthalpy is equal to the change in gravitational potential energy and kinetic energy, and change in pressure is equal to the static pressure change and pressure decline due to friction. (5) A turbine exhaust pressure (P5) is selected to calculate heat and power flows in surface equipment to use as a basis for cost estimation. Turbine exhaust gases are cooled prior to the compressor so that T6 is equal to the injection temperature (T1). The number of injection/production well pairs is set sufficient that net power production WNET is greater than 50 MWe. O Net work is determined from a summation of surface plant power flows: WNET ¼ WT WC WHX1 WHX2
ð1Þ
O Total capital cost of the system is determined from a summation of individual components: CTOT ¼ CT þ CC þ CHX1 þ CHX2 þ nW CW
ð2Þ
O Capital cost per unit of net power (Γ), the measure of merit for a given design, is calculated based on these values: Γ ¼ CTOT =WNET
ð3Þ
8.603 1011
reservoir pressure (MPa)
49.05
wellbore roughness (m)
0.0004
wellbore diameter (m)
0.231
isentropic efficiency, ηisen
0.85
6 The turbine exhaust pressure (P5) is varied until the minimum cost per kilowatt of net electricity generation capacity is found; this provides the optimal cost for the selected mass flow rate. 7 This process is then repeated for different mass flow rates until an overall economic profile across a range of flow rates (or their corresponding injection pressures) can be found for the set of constraints defined in step 1. Similar calculations are completed for different site conditions or economic assumptions. The list of site conditions considered, and the numbers used for the reference case can be found in Table 1; we use the same reference case as in previous works10 for ease of comparison. Symbol nomenclature is provided in Table 2. Reservoir length is the distance from the edge of the injection to the edge of the production well. Reservoir thickness is accounted for in the reservoir impedance term. Reservoir pressure is assumed to be equal to the hydrostatic head. We use a constant well diameter for simplicity, although past EGS well completions to date have typically included 7 and 95/8 in. sections. 2.1. Thermodynamic Calculations. Thermodynamic performance is calculated from the model based directly on the thermodynamic states of the system: _ isen ðh4 h5 Þ WT ¼ ðnW =2Þmη
ð4Þ
_ isen ðh7 h6 Þ WC ¼ ðnW =2Þm=η
ð5Þ
_ 6 h5 Þ þ ð1 ηisen ÞWT QHX1 ¼ ðnW =2Þmðh
ð6Þ
_ 1 h7 Þ þ ð1=ηisen 1ÞWC QHX2 ¼ ðnW =2Þmðh
ð7Þ
All thermodynamic properties are calculated using Helmholtz free energy equations of state for CO2, as are transport properties.12,13 All work flows are in kilowatts. The number of wells, nW, is divided by 2 to account for doublet pairs. The parasitic power consumption of the heat exchangers is calculated as a linear function of heat flow. Air-cooled heat exchangers are typically fan-forced, and while there is interest in utilizing natural-draft dry cooling as a means of reducing parasitic electricity losses, we examine only the typical implementation of fan-forced systems. The power consumption of fan-forced dry cooling can be estimated through a variety of different measures. We use values reported by the Electric Power Research Institute14 for an inlet air temperature difference of 22 °C, where a parasitic load of approximately 18.9 kWe per 1 MWth was noted. Therefore, for calculation of the parasitic power consumption by the heat exchanger fans, we use eq 8: WHX ¼ εQHX
ð8Þ
with ε taking a value of 0.0189. 3766
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Table 2. Nomenclature A
area for heat transfer
CTOT
total plant capital cost
CT
total turbine cost
CC
total compressor cost
CHX C0
total heat exchanger cost base equipment cost
D
well diameter
D0
reference case well diameter
F
heat exchange orientation factor
FM
equipment material factor
FP
equipment pressure factor
FS
additional cost factor
h k.H
enthalpy Reservoir permeability multiplied by reservoir height
m
mass flow rate
nW
number of wells
n
number of years
Pi
pressure at different points in the system (as in Figure 1)
QHX
heat exchanger heat transfer rate
Ti
temp at different points in the system (as in Figure 1)
U WNET
overall heat transfer coefficient net work
WT
turbine work
WC
compressor work
WHX
heat exchanger fan parasitic power losses
z
well depth
ΔTM
average heat transfer difference
ε
heat exchanger parasitic power factor
Γ ηisen
specific capital cost isentropic efficiency Remaining algebraic terms are cost correlation constants defined in Table 3.
2.2. Cost Estimation. Cost estimation of the different process units is discussed below. 2.2.1. Wells. Well costs are estimated on the basis of typical cost estimation methods, using an exponential increase in cost as a function of depth. This has been modified with a parabolic scalar to account for cases with increased well diameter. The relation for the cost increase due to diameter change is based on larger diameter wells drilled in New Zealand,15 where a reported change in cemented casing diameter from 95/8 to 133/8 in. increased costs by 17%. A parabolic scaling of costs in response to diameter is utilized as per our previous work,11 based on another work,16 which noted the proportionality of drilling times (and therefore expected cost) to the square of the diameter. Considerable uncertainty remains regarding estimates of geothermal well costs, both in terms of the cost relationship to depth, and in response to change in diameter. The uncertainty of the cost relationship with depth is mainly due to uncertainty in cost reduction due to maturation of geothermal drilling technologies. We adopt as our basis for well cost estimation the mathematical average of the following: • Joint Association Survey (JAS) Oil & Gas well cost average (as derived elsewhere17); • To-date cost average for EGS geothermal wells, scaled for increases in diameter.17 As the well costs are reported in 2003 USD, we scale them to 2009 USD by assuming a constant increase per annum of well costs of 9%. 2009 USD are used for all cost calculations to make results more relevant
to current pricing structures. This equates to a rise in costs of 67.7% from 2003 to 2009. The function we use for well cost estimation is therefore eq 9: " # 2 D n CW ¼ 1:09 0:6662 þ 0:3338 Kebz ð9Þ D0 where n is the number of years from 2003 to 2009, per-well cost CW is calculated in millions of 2003 USD, D0 is 0.23125 m, z is the well depth, and K and b are parameters given in Table 3. Effect of cost uncertainty and variability is shown in section 3.1.4. 2.2.2. Turbine. Our earlier assessments incorporated a cost estimation method for CO2 turbines that accounted for the higher density of CO2 as the turbine fluid compared to typical power conversion fluids.9,11 The equation to calculate the cost for the turbine is given in eq 10: C0T ¼ 3:5 RWTβ Fγ5
ð10Þ
where C0T is the base cost of the turbine, WT is the turbine work output,
R and β and γ are constants, and F5 is the turbine exhaust density (see Figure 1). This equation was fitted to the costs of steam turbines and CO2 turbines estimated in the previous work.9 Cost estimation for CO2 turbines is complex and a number of other approaches could be used, including rigorous turbine design or estimation using different equipment comparisons (e.g., other gas expanders, axial compressors). We use eq 10 as it relatively simply links fluid density to turbine size, as has been encountered with other organic fluids.18 The values for the parameters used in this fit are given in Table 3. Total cost in 2009 USD for the turbine is given in eq 11: CT ¼ 525:7=575:4 FS C0T
ð11Þ
CT is the cost of the turbine updated to represent 2009 USD, and FS is an additional factor to account for material, additional piping, control, freight, labor, and other overheads. Turbine costs are given in the previous work in 2008 USD;11 they are updated to 2009 USD by the ratio of Chemical Engineering Plant Cost Indices (CEPCI) for the relevant years: 2008 = 575.4; 2009 = 525.7.19 2.2.3. Compressor. The centrifugal compressor cost is based on standard compressor costing methods.20 Equations 12 and 13 were used to estimate compressor cost: CC ¼ 525:7=397 2:8FS C0C
C0C
¼
8 < 10ðR1 þ R2
ð12Þ
log WC þ R3 ½log WC 2 Þ
: WC =3000 10ðR1 þ R2
9 WC < 3000 =
,
log 3000 þ R3 ½log 30002 Þ
,
WC g 3000 ; ð13Þ
Note that the factor of 2.8 in eq 12 is to account for material (carbon steel), compressor type (centrifugal), as well as additional piping, freight, labor, etc. Carbon steel is appropriate, as water condensation does not occur under the pressure and temperature conditions, for suitably low water content in CO2 from the production well. Uncondensed water dissolved in CO2 will not instigate corrosion.21 Additionally, C0C is reported in 2001 USD, so it is updated to 2009 USD based on the ratio of CEPCI for the relevant years: 2001 = 397; 2009 = 525.7.19 2.2.4. Heat Exchangers. The base costs of the air-cooled heat exchangers are estimated from standard costing methods.20 Costing is based on air-cooled heat exchangers; in some cases, water cooling will be available. In these cases, the cost of cooling systems will be significantly reduced. The cost of heat exchangers is estimated from eq 14: CHX ¼ 525:7=397ðB1 þ B2 FM FP ÞFS C0HX
ð14Þ
where CHX is the heat exchanger cost, B1 and B2 are constants for an equipment type, FM is the material factor (for stainless steel), FP is the 3767
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Table 3. Calculation Parameters constant
value
equation
justification
units
ηisen
0.85
4, 5, 6, 7
see text
ε
0.00825
8
14
K
0.2865
9
see text
2009 USD
b
6.657 104
9
see text
m1
D0
0.23125
9
see text
m
R
1.066
10
9
USD kW0.5439 m0.4416 kg0.1472
β γ
0.5439 0.1472
10 10
FS
1.7
11, 12, 14
20
R1
2.2897
13
20
R2
1.3604
13
20
R3
0.1027
13
20
B1
0.96
14
20
B2
1.21
14
20
extrapolated. The resulting extrapolation is eq 17:
FM K1
2.9 4.0336
14 15
20 20
FP ¼ 0:939P0:04759
K2
0.2341
15
20
K3
0.0497
15
20
The result of this is shown in Figure 2. The base area for heat exchange, used as a basis for costing, is given by eq 18:
9 9
C1
0.1250
16
20
C2
0.15361
16
20
C3
0.02861
16.
20
F
0.91
18
see text
U ΔTlm
300 11
18 18
see text see text
Figure 2. Pressure factor for air-cooled heat exchanger versus pressure.
A ¼ QHX =UFΔTM
W m2 K1 K
pressure factor, and C0HX is the cost for the heat exchanger made from carbon steel operating at ambient pressure. Stainless steel is selected as the construction material, as it is possible that some trace water and carbonic acid will condense during cooling. The constants are given in Table 3. The base cost for carbon steel equipment is given by eq 15: 8 9 < 10ðK1 þ K2 log A þ K3 ½log A2 Þ , A < 10000 = 0 CHX ¼ 2 : A=10000 10ðK1 þ K2 log 10000 þ K3 ½log 10000 Þ , A g 10000 ; ð15Þ where K1, K2, and K3 are constants for the heat exchanger type, and A is the area over which heat exchange occurs in the heat exchanger. The constants are given in Table 3. For heat exchange areas greater than 10,000 m2, multiple parallel units are used (rather than scaling up the size), so there is no cost reduction from economies of scale. Pressure factors are given by eq 16: FP ¼ 10ðC1 þ C2
log P þ ½C3 log P2 Þ
ð16Þ
where C1, C2, and C3 are constants for the heat exchanger type, and P is the design pressure (in bar) of the equipment. The values of these constants are given in Table 3. The range of pressure factor estimation given in the literature20 is limited to below 100 bar for air-cooled heat exchangers. As some design pressures for the CO2 thermosiphon may be slightly above this range, a small extrapolation of these pressure factors is used. The extrapolation is derived from the fit of a power law to the higher-pressure region (i.e., 50100 bar) of the pressure-factor calculation, which is then
ð17Þ
ð18Þ
Design of a CO2-based power plant would include economic optimization of the heat exchange/cooling system. This would involve an iterative optimization of heat exchange tube materials, geometry and fins, as well as air flow and fan design, based on site constraints and the trade-offs between capital cost, ongoing parasitic power consumption, and CO2 pressure drop within the cooling system. Because heat exchanger design is well-understood but also involves a complex set of trade-offs, we do not include it in this analysis. Instead, we calculate economic performance based on heat exchanger parameters representative of a near-optimal design. Precise optimization of the heat exchangers would provide performance benefits, but they are of second order importance to this study (see section 3.1.4 for a discussion of the sensitivity of economic performance to heat exchanger costs). Relevant heat exchanger design parameters are discussed below. Heat flow, Q, is defined for both cooling systems by the equations specified in section 2.2. The three parameters U, F, and ΔTM are therefore critical to the economic efficiency of the heat exchange system. For this analysis, we use a value for F, the temperature difference correction factor, of 0.91, which is an estimate for a single-tube-pass aircooled heat exchanger.22 This value would increase toward unity with the addition of additional tube rows, but for the purpose of this assessment, we assume a conservatively simple design. For the average temperature difference ΔTM, we assume a value of 11 K. This is comparable to typical minimum approach temperature differences for air-cooled heat exchangers of 814 K.22 This value is therefore taken as a conservative but representative value for the average temperature difference for an optimized air-cooled heat exchanger. Values for the overall heat exchange coefficient, U, are typically determined experimentally. As values for the optimized heat exchange between CO2 and air are not readily available, we use values for U for heat exchange between air and fluids with similar convective heat transfer coefficients to that for CO2. CO2 has reported convective heat exchange coefficients typically in the range of 24 kW 3 m2 3 K1, although this increases substantially for conditions near the critical point, reaching values greater than 18 kW 3 m2 3 K1.23,24 The typical range is similar to that of the convective heat transfer coefficients reported for cooling and condensation of light hydrocarbons: 26 kW 3 m2 3 K1.25 3768
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Figure 3. Net work, turbine power, compressor power, and specific capital cost as a function of injection pressure for the reference case.
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Figure 4. Power flows in the surface plant versus exhaust pressure, for the optimum injection pressure for one well doublet in the reference scenario.
Typical overall heat transfer coefficient, U, values reported for light hydrocarbon condensation are 250 to 350 W 3 m2 3 K1.26 Therefore, we adopt a value for U for CO2 of 300 W 3 m2 3 K1. Variation in these values is incorporated into the discussion of cost sensitivity in section 3.1.4.
3. RESULTS 3.1. Reference Case. For the initial consideration, we examine the reference case with parameters as specified in Table 3. 3.1.1. Single Doublet Operation. First we examine results for the case of a single well doublet. For a single doublet, the thermodynamic and economic performance can be seen in Figure 3, as a function of the injection pressure (P1). Note here that as we examine only a single doublet, the WNET is not 50 MWe but a much lower value; for the cases considering 50 MWe, sufficient identical parallel doublets are calculated to produce sufficient power output, which is developed in section 3.1.3 and onward. Figure 3 shows that there are both thermodynamic and economic optimums for the system. These optimums are not very sensitive to the injection pressure (i.e., (1 MPa from the optimum will result in only relatively small variations in performance). The economic and thermodynamic optimums are for similar injection pressures but are not identical due to an economic incentive toward minimizing equipment size. 3.1.2. Turbine Exhaust Pressure Optimization. Exhaust pressure can be selected to optimize thermodynamic, or more importantly, economic performance. The results discussed from section 3.1.1 are given for optimized exhaust pressures. If we examine the range of performance at different exhaust pressures for a single injection pressure, we can see the manner in which the system behaves in response to changing the turbine exhaust pressure parameter. Figure 4 shows the response to turbine exhaust pressure of power loads for the turbine, compressor, heat exchangers, and overall net work produced for the optimum injection pressure from Figure 3 (13.8 MPa). Figure 4 shows a clear thermodynamic performance optimum, corresponding to an exhaust pressure of 8.4 MPa. In the region near this pressure, at the injection temperature (35 °C), there is a rapid change in density. The peak in performance at these thermodynamic conditions is due to a change in the gradient
Figure 5. Cost per kilowatt versus exhaust pressure at 15 °C, 35 °C, and 55 °C.
of compression work required; at lower turbine exhaust pressures, compressor work increases rapidly, reducing net power produced, while, at higher turbine exhaust pressures, the compressor work is low, but power produced through the turbine continues to decline. Heat exchanger load is relatively constant, leading to constant parasitic power consumption. The economic optimum corresponds very closely to the thermodynamic optimum, with some bias toward minimizing equipment sizes (the economic performance optimum is at 8.63 MPa). The similarity between economic optimum and thermodynamic optimum was found to extend across all the surface plant cases we examined. The optimum exhaust pressure to select for the process was found to be strongly dependent on achievable cooling temperature (which depends on ambient temperature). The economic performance at the optimum injection pressure versus exhaust pressure is shown in Figure 5 for three different cooling temperatures. As seen in Figure 5, the optimum exhaust pressure to maximize economic performance changes as surface temperature changes. This is predominantly due to the thermodynamic behavior of the system: at lower temperatures, the region of rapid increase in fluid density is also at a lower pressure. At lower temperatures, the optimum for performance is also more sharply defined, as the 3769
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Figure 6. Optimum exhaust pressure versus temperature for different reservoir temperatures and depths.
change in fluid density is more rapid. The very sharp minimum visible for 15 °C corresponds to moving the compressor inlet from the gas side of the liquid vapor envelope to the fluid side (and a step change in compressor fluid density), drastically reducing compressor costs. The optimum conditions for plant optimization—that is, exhaust pressure as a function of surface temperature (effectively compressor inlet conditions)—can be plotted for a range of surface temperature conditions, for a variety of reservoir temperatures and reservoir depths (i.e., different site conditions). This plot is shown in Figure 6, with an additional line denoting the liquidvapor saturation curve. Figure 6 allows determination of the optimum exhaust pressure for a variety of different site conditions. As can be seen in Figure 6, the optimum exhaust pressure tracks very closely to the liquidvapor saturation curve until the critical point. At temperatures above the critical point (where the liquidvapor saturation curve ends), the optimum exhaust pressure tends to follow the trend seen below the critical point. For temperatures below and near the critical point, there is only a small deviation from this line: the sharp change in thermodynamic performance from operating a condensing cycle leads to an economic optimum. As temperature rises above the critical point, the optimum in thermodynamic performance becomes less defined, and so too does the economic optimum (this can also be seen in Figure 6 for 55 °C). This leads to a wider spread of optimum exhaust pressure points at higher temperature for the range of different reservoir conditions, as the economic optimum is less dependent on closely matching the thermodynamic optimum. Typically, a near-optimum performance point for turbine exhaust pressure for a CO2-based EGS power plant can be selected on the basis of Figure 6. The exact optimum can then be refined on the basis of the reservoir conditions for the site, as well as the economic conditions for the project. Operating at the critical point may require specially designed equipment as a result of rapid thermodynamic property change. 3.1.3. Scale-up to 50 MW. To examine the effect of scaling the plant size up to larger facility sizes, we examine the change in performance as we move from a single well doublet to a 50 MWe plant and then to a 300 MWe plant. The minimum capital expenditure per kilowatt (from Figure 3) for a single doublet and for increases in plant size is plotted versus net capacity in Figure 7.
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Figure 7. Cost per kilowatt versus nominal plant capacity.
Figure 8. Cost components of the plant for the (A) reference case, (B) favorable performance case, and (C) unfavorable performance case.
Figure 7 shows that there is a large initial reduction in unit costs for moving from a doublet to a larger, multiwell power plant, but the effect becomes less pronounced at larger plant sizes. This is because large geothermal power plant costs are relatively insensitive to economies of scale: the wells and air-cooled heat exchanger fan bays and to a degree the compressors, which represent a large component of the facility costs, increase in number as energy output size goes up, and so they scale linearly with cost. Turbine costs do provide some benefit from economies of scale. 3.1.4. Cost Breakdown and Uncertainty. For the 50 MWe plant used as the reference case, the overall cost components are given in Figure 8. Also shown in Figure 8 are breakdowns of the costs of different equipment components for the same plant design basis under a set of more favorable costing assumptions and under a set of less favorable assumptions. This is not intended to be an extended sensitivity study on the effects of component costs, as they are mostly self-evident, but it may provide an indication of the overall variability due to costing assumptions. The changes used for these different cases are detailed in Table 4. As shown in Figure 8, the total cost of the plant is very sensitive to the economic calculation basis. The substantive part of the 3770
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Table 4. Modified Performance Characteristics parameter
higher
lower
performance
performance
units
ΔTlm
14
8
K
U
400
200
W m2 K1
K
0.1099
0.4786
$
b
7.804 104
6.132 104
m1
R
1.066
1.3189
USD kW0.5439 m0.4416 kg0.1472
β γ
0.5439 0.1472
0.5353 0
differences is due to the well cost, where if typical oil and gas well costs are assumed, the total plant capital expenditure is reduced by 25%. Changes to the heat exchanger costing assumptions will also impact the overall price of the plant, but by a relatively modest percentage, which justifies the approach of not undertaking optimization calculations for those systems. 3.2. Design Optimization: Well Diameter. Here we briefly revisit the trade-off of increasing well diameter on increased costs and increased performance using better cost estimation data, as discussed in section 2.2.1. This balance has been examined previously,11 favoring larger well sizes than currently contemplated. Figure 9 shows the cost per kilowatt of a 50 MWe plant for different well diameters. Figure 9 suggests that given the cost data we have used for this analysis, there is continued justification for increasing well diameters to improve the performance of CO2-based EGSs. Performance continues to be more limited by wellbore considerations than by flow in the fluid in-reservoir. It also indicates that, at least for the reference case, there is unlikely to be a net economic benefit from increasing the well diameter beyond 0.3 m (1200 ). Larger diameters are likely to be more favorable for hotter resources, for more permeable resources, or for lower overall drilling costs. 3.3. Site Considerations/Optimizations. Sites for CO2based EGS should be selected to maximize economic performance. For H2O-based EGS, the primary site considerations are reservoir temperature, depth, and permeability. For CO2-based EGS, reservoir temperature and depth are important, but performance is altered less by permeability,10 assuming a permeability representative of past EGS projects can be achieved. For CO2-based EGSs, economic performance is substantially benefitted by lower injection temperatures, due to an increase in density in the injection well leading to a higher static pressure increase in the wellbore, which leads to greater flow throughput.10 Additionally, both compressor inlet temperature and the injection temperature are assumed to be set by a minimum approach temperature to ambient (defined by detailed heat exchanger optimization, but explored in this work over the range 814 K). Therefore, the economic performance of CO2based EGSs is sensitive to injection temperature, reservoir temperature, and depth. Site selection should take into account the relative effects of these key characteristics on performance. We assess the relative importance of these characteristics by examining the economic performance of CO2-based EGSs for different reservoir temperatures and injection temperatures for a constant depth of 5000 m in section 3.3.1 and for different reservoir temperatures and depths for a constant injection temperature of 35 °C in section 3.3.2.
Figure 9. Capital cost per kWe of net power produced versus injection pressure for well diameters of 0.23125 m, 0.3 m, and 0.4 m.
Figure 10. Contours of capital cost in 2009 USD per kilowatt of capacity as a function of injection temperature and reservoir temperature.
3.3.1. Ambient Temperature versus Reservoir Temperature. A contour plot of cost per kilowatt as a function of injection temperature and reservoir temperature for a reservoir depth of 5000 m is shown in Figure 10. Figure 10 shows how the economic performance of CO2based EGSs increases for lower injection temperatures and higher reservoir temperatures. The capital cost remains constant when injection pressure and reservoir temperature change together at a ratio of approximately 1:3. The interpretation is that every degree lower injection temperature (i.e., lower ambient temperature, since these are coupled by the approach temperature of the heat exchangers) has an equivalent value of 3 degrees of higher reservoir temperature. Comparatively, on a simple economic basis, a site in an area with a high ambient temperature, say 30 °C, compared to a temperate site, say 20 °C ambient, would need to have reservoir temperatures about 30 °C hotter to compensate. 3.3.2. Reservoir Temperature versus Depth. Deeper wells generally access higher resource temperatures, leading to higher power generation per well, but they also incur greater well costs. To properly optimize power plant design, it is necessary to select the optimum depth for economic performance. For a defined site, this depends on the local temperaturedepth relationship. 3771
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Table 5. Levelized Cost of Electricity Parameters parameter
value
capacity factor
90%
inflation rate
3%
operating costs
1¢ 3 kWh1
interest rate
8%
equity rate
15%
equity proportion
50%
debt proportion
50%
debt payback period plant lifetime
10 yrs 30 yrs
depreciation schedule
MAR ACH 15 year accelerated
operating cost escalation rate
1%
tax rate
38%
Figure 11. Contours of cost in 2009 USD per kilowatt of capacity as a function of reservoir temperature and reservoir depth.
For a generic overview of the optimization between temperature and depth, it is necessary to examine a broad range of values for temperature and depth. Figure 11 shows contours of cost per kilowatt of capacity for a 50 MWe CO2-based EGS power plant as a function of reservoir temperature and depth. All reservoir pressures are equivalent to hydrostatic pressure at the specified depth; permeability does not vary with depth, and injection temperature is 35 °C. As shown in Figure 11, the capital cost decreases monotonically as reservoir temperature increases at constant depth. At a constant reservoir temperature, variation of capital cost with depth has a minimum at depths between 2000 and 3000 m. This is distinctly different from the behavior of H2O-based EGSs, where deeper reservoirs of similar temperature and geological conditions are always less economically favorable. The nonlinear behavior of CO2-EGS costs in response to depth is not intuitive. It occurs because the CO2-based EGS relies on high densities in the reservoir for low in-reservoir pressure drops, and large well lengths to provide a large net buoyant force from the difference in densities between injection and production wells.10 If CO2 is used to extract heat from a very shallow reservoir (of reference impedance), much more of the energy extracted is used to push the low density CO2 through the reservoir instead of being converted to net electrical power generation, which leads to higher costs per-unit of power. 3.4. Time-Dependent Economic Performance. There are two CO2-based EGS features that do not affect capital costs but will affect economic performance because of their impacts over the lifetime of the power plant. These features are dry-out time and sustained fluid losses in the reservoir. To encompass the time-dependent behavior of these features, their impact on levelized cost of energy (LCoE) is assessed. Changes in resource temperature are neglected for transparency and simplicity. The costing methodology discussed in section 2 provides an estimate of the capital cost of the power plant. This is translated into a levelized cost of electricity by the same approach used by MIT in a report on nuclear power.27 A detailed description of the method can be found in that source. The assumptions used for that model are given in Table 5. In the scenarios we examine, we assume that the capital expenditure occurs in equal portions over two years and that no power is produced during that time. The plant life refers to the
Figure 12. Levelized cost of electricity as a function of dry-out time.
operating life (i.e., does not include those initial two years of capital expense/construction). 3.4.1. Dry-out Time. Dry-out time is unique to CO2-based EGSs and represents the time required to displace initial reservoir fluids such that produced CO2 is sufficiently water-free to directly drive a turbine.6 It can be represented in an economic model as a delay after construction before the power plant starts generating electricity and, therefore, revenue. During the dry-out period, water would be removed from produced fluids either by physical separation after cooling or using desiccants (e.g., zeolite, alumina). Power could potentially be generated during this period with a binary power cycle. We assume the reference case system and examine the effect on LCoE of delaying power generation for up to five years after construction of the power plant. The results are shown in Figure 12. It is apparent from Figure 12 that, for the reference case, the levelized cost of electricity under the assumptions in Table 5 will be approximately 24¢ 3 kWh1. LCoE increases as dry-out time increases in a slightly nonlinear manner whereby larger dry-out times are increasingly more detrimental. 3.4.2. Fluid Loss and CO2 Sequestration. Fluid loss is present for water-based systems but is more complex for the CO2-based EGS. Short-term H2O-based EGS trials have reported steady state fluid losses sustained over months of operation as high as 30%.28 These losses are particularly pertinent to CO2-based EGS because of their potential to contribute to sequestration of CO2. 3772
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Figure 13. Levelized cost of electricity as a function of CO2 cost for different steady state fluid loss rates.
To examine the impact of fluid losses, we assess LCoE as a function of the price of CO2 for two scenarios: fluid losses of 5% and 10%, sustained over the lifetime of the power plant. Price for CO2 represents the cost of supplying CO2 at the boundary of the power plant and could be estimated as market price for CO2 emissions minus per-tonne costs of sequestration and transport of the CO2 to the geothermal site. Negative values represent a payment for the service of CO2 sequestration. Figure 13 shows the LCoE versus CO2 cost for the two scenarios. Figure 13 shows that a value associated with CO2 can significantly impact the LCoE for the CO2-based EGS power system. Expenses associated with procuring CO2 dramatically increase the LCoE, but income from CO2 disposal makes the concept much more economically feasible. We estimate 5% fluid losses from a 50 MW power plant would be on the order of 23 million tonnes per annum of CO2 stored underground.
4. DISCUSSION The results in this paper depend on the assumptions and parameters used. Uncertainty in these parameters and assumptions leads to uncertainty in results and consequently limits the conclusions that may be drawn. The effects of various assumptions and parameter choices on results and conclusions are discussed below. Well costs are highly variable and can change for individual wells due to difficulties while drilling, for a reservoir system due to geological characteristics, and for an industry depending on technology and drilling experience. For this work, a single well costdepth relationship was used, nominally representing the industry average well cost for EGSs after additional experience accumulation and technology development. The impact on economic performance of underestimating or overestimating drilling costs was assessed in section 3.1.4. The impact of well costs on optimization of system parameters is unclear. It is unlikely to substantively affect turbine exhaust pressure optimization or the importance of low injection temperatures. Different well costs will substantially alter the optimal reservoir depth, however. There is a close correspondence between thermodynamic and economic optima. This implies that, for a preliminary design of a CO2-based EGS, turbine exhaust pressure and injection pressure can be estimated from thermodynamic performance. Other
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parameters, particularly those affected by well costs (e.g., target depth), will depend primarily on economic performance and cannot be estimated from thermodynamics alone. This analysis examined a limited range of parameters. In particular, the impact of permeability, which is a significant characteristic for H2Obased systems, was not assessed. This is much less important for CO2-based EGS performance, but further research on this topic is worthwhile in order to evaluate whether that assessment remains legitimate over the full range of potential values for other site parameters. The range of the parameters assessed in this work was also quite limited and may not be suitable for extrapolation. For example, for lower temperature geothermal resources, it may become favorable to target much shallower systems than the depths examined here. The simultaneous interaction between multiple site and process parameters was not comprehensively considered. Instead the effect of changes in individual or pairs of parameters from the reference case was assessed. This means that the behavior of the system where multiple parameters are simultaneously changed from the reference case is unquantified by this work, since there may be interactions. However, we expect that the characteristic behavior presented here is representative for parameter values within bounds typically encountered for geothermal reservoirs. An isentropic efficiency of 85% was assumed for both the turbine and compressor. That value is an estimate for welldeveloped CO2 turbomachinery technology. Currently, CO2 compression is relatively well understood, but CO2 turbines are not currently commercial. Lower isentropic efficiencies will reduce thermodynamic and economic performance of the system compared to the results discussed here and bias the optimization of the system toward reduced compressor usage and higher turbine exhaust pressures. Details of reservoir development were not addressed in this work. We have assumed linear increases in the number of injection and production well doublets to achieve sufficient power output for a 50 MWe system. Favorable operation of a real system should incorporate a reservoir development plan that would account for the interaction between wells and, consequently, change the ratio of injection to production wells as the scale of the system increases. Injection is comparatively easier than fluid production,10 and so one might generally expect fewer injection wells compared to production wells. Exploiting these considerations and particular geological features of an individual reservoir is likely to result in an overall improvement in performance relative to the results reported here (for the same overall resource specifications). We have examined the economic impact of CO2 prices only from underground fluid losses. A CO2 price will also have immediate economic consequences because large quantities of CO2 will be required to displace fluids (i.e., water) that are initially in the reservoir. There is a high degree of uncertainty regarding the total volume that would be required. Preliminary calculations indicate that this may run to millions of tonnes of CO2 per well doublet for fluid displacement,6 and CO2 supply, price (or credit), and logistical considerations will dramatically affect economic performance for quantities of that magnitude. A sequestration or disposal value for CO2 would provide an immediate revenue boost for such a project, making this technology highly competitive with conventional power generation and other sequestration projects. Additional exploration of economics regarding the opportunities and issues for combined sequestration and power generation is warranted. 3773
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5. CONCLUSIONS In this work, the economics and related thermodynamics of CO2-based EGSs have been examined. Optimization of some system parameters and site considerations has been addressed. A number of conclusions can be drawn from the results: • Significant reductions in capital expenditure per unit of power capacity can be achieved from moderate increases in the scale of the power plant. • Large diameter wellbores continue to have some thermodynamic and economic justification, but on the basis of current cost information, benefits are small. This may change as the cost effects of large diameters are better understood. • Ambient temperature conditions, through their influence on the injection temperature, remain a major factor in thermodynamic and economic performance. • Including compression as part of the system design leads to substantial improvement in thermodynamic performance, resulting in a benefit to economic performance. • Near-optimal turbine exhaust pressure or compressor inlet pressure can be specified as a function of injection temperature alone. • There is an economic trade-off during site selection between surface ambient temperature (through its decisive influence on injection temperature) and reservoir temperature, whereby economic performance is approximately constant for a decrease in reservoir temperature of 3 K if injection temperature is also reduced by 1 K. • There is an optimum economic reservoir depth, around 23 km, due to thermodynamic benefits of deeper wells offsetting the additional well cost up to a point. • Capital costs of CO2-based EGSs are dominated by well costs. • If substantial fluid losses are present, system economics are dominated by CO2 price. • CO2 costs may be of significant importance even without fluid losses due to the need to displace pre-existing reservoir fluids. A generalized conclusion can also be drawn about broad economic viability. Implementation of CO2-based EGS technology relies on one of the following: • Supply of CO2 in abundance at low cost. • Utilization of an existing CO2-filled reservoir suitable for geothermal power generation. • Combination with a carbon-capture and sequestration project. Given fulfillment of one of the above, this work presents a basis for comparison of potential sites for this technology, and initial parameter estimation for plant design. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT We thank the State Government of Queensland for providing the funding that made this research possible. ’ REFERENCES (1) Pruess, K. Enhanced geothermal systems (EGS) using CO2 as working fluid—A novel approach for generating renewable energy with simultaneous sequestration of carbon. Geothermics 2006, 35, 351–367.
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