Thermo-economic analysis of a direct supercritical CO₂ electric power generation system using geothermal heat

Abstract

A comprehensive thermo-economic model combining a geothermal heat mining system and a direct supercritical CO₂ turbine expansion electric power generation system was proposed in this paper. Assisted by this integrated model, thermo-economic and optimization analyses for the key design parameters of the whole system including the geothermal well pattern and operational conditions were performed to obtain a minimal levelized cost of electricity (LCOE). Specifically, in geothermal heat extraction simulation, an integrated wellbore-reservoir system model (T2Well/ECO2N) was used to generate a database for creating a fast, predictive, and compatible geothermal heat mining model by employing a response surface methodology. A parametric study was conducted to demonstrate the impact of turbine discharge pressure, injection and production well distance, CO₂ injection flowrate, CO₂ injection temperature, and monitored production well bottom pressure on LCOE, system thermal efficiency, and capital cost. It was found that for a 100 MW_e power plant, a minimal LCOE of $0.177/kWh was achieved for a 20-year steady operation without considering CO₂ sequestration credit. In addition, when CO₂ sequestration credit is $1.00/t, an LCOE breakeven point compared to a conventional geothermal power plant is achieved and a breakpoint for generating electric power generation at no cost was achieved for a sequestration credit of $2.05/t.

Graphical abstract

Keywords

geothermal heat mining / supercritical CO₂ / power generation / thermo-economic analysis / optimization

1 Introduction

Global warming has become a concern, and carbon dioxide (CO₂) emissions due to the massive anthropogenic fossil fuel utilization is considered to be a dominant cause. However, coal and other types of fossil fuels are abundant as a result of which, it is predicated that the world coal consumption will be in the approximately same level until 2040, with decreasing consumptions in China and the US offsetting increases in India [1,2]. Consequently, CO₂ capture and sequestration is extensively studied and has been recognized as a promising method to reduce CO₂ emissions from fossil-fired power plants or industrial processes [3]. Recently, a concept of CO₂-plume geothermal (CPG) system combining CO₂ injection and production has been proposed to inject captured CO₂ into existing porous and permeable deep saline aquifers to extract geothermal heat [4]. It has been proven that CO₂ works more efficiently for extracting geothermal energy than water/brine geothermal systems due to its high mobility and larger density change with temperature. As a result, a buoyancy-driven loop is formed to minimize recompression of CO₂ and to re-inject it back to the geothermal reservoir. The CPG system utilizes existing, high-permeability, and porosity geologic reservoirs with a low permeable cap-rock. In addition, natural geothermal reservoirs that have considerably large sizes offer a large CO₂ sequestration potential. An additional benefit of CPG is that the injected CO₂ will be permanently sequestrated into the geothermal reservoir. The previous study indicates that about 7% of injected CO₂ will be permanently sequestrated in geothermal reservoirs over 30 years of production [5]. As CO₂ is injected into a geothermal reservoir, the brine initially occupying the reservoir is displaced by CO₂. A CO₂-plume then is formed, and hot sCO₂ is then produced from production wellbores with the extracted geothermal energy [4,6–9].

On the other hand, studies on the thermodynamic performance of sCO₂ power generation systems in energy applications that include solar-thermal, nuclear, and conventional fossil fuel energy, have been widely conducted. Different layouts of sCO₂ power cycles have been proposed by performing thermodynamic analyses [10–14]. However, it is difficult to estimate the cost of sCO₂ power generation systems to generate electric power as no units have been commercialized yet at the time of writing this manuscript [15–18]. Additionally, the economic analyses involving both geothermal heat mining systems and sCO₂ power cycles are also preliminary and limited [19]. In this paper, an integrated model that combines a geothermal heat mining system and a direct sCO₂ expansion power generation system is discussed (see Fig. 1). The hot CO₂/brine mixture produced from geothermal reservoirs first passes through a CO₂-H₂O separator to obtain a highly pure sCO₂ which subsequently expands through a gas turbine to generate electric power. The exhaust CO₂ next goes to a water cooler (pre-cooler in Fig. 1) to be cooled down before entering a CO₂ compressor. After coming out from the compressor, the pressurized hot CO₂ is cooled again by a water cooler (post-cooler in Fig. 1) to the preferable re-injection temperature of CO₂. The CO₂ at State 5 in Fig. 1 is re-injected back to geothermal reservoirs where it transitions to a supercritical fluid for permanent sequestration and heat mining. While the integrated thermodynamic model was established, it brings great interest to explore the economics of the power generation cost using hot sCO₂ produced from geothermal reservoirs. Economic analysis is of great importance and critical since it helps the plant owners and investors to make a decision for construction. Due to the fact that geothermal energy is considered as the low-grade heat source, the binary power cycle, such as the organic Rankine cycle and the conventional steam Rankine cycle, is not suitable to be used to generate electric power cost-effectively with the produced hot sCO₂. Previous studies from demonstrated the potential power generation options using the hot sCO₂ produced from geothermal reservoirs. It turns out that the direct sCO₂ expansion power generation system is the most efficient and cost-effective one with the identical geothermal conditions [20–22].

T2Well/ECO2N is a popular software to simulate geothermal heat mining. However, it is computationally expensive, which typically requires days and even weeks to complete a 30-year span reservoir simulation. It is therefore not practical to perform a global system optimization by direct using the T2Well/ECO2N. In the study described in this paper, a correlation model was developed by the response surface methodology (RSM) for the reservoir heat mining by using simulation data from T2Well/ECO2N, which is integrated with the direct sCO₂ expansion power generation process modeled in Aspen. Based on the proposed modeling approach, a systematic cost calculation and optimization methodology was developed that combining evaluating the thermodynamic performance and calculating capital costs for the entire system. The primary objective of the optimization study is to minimize the levelized cost of electricity (LCOE) over the operating life of the geothermal plant.

2 Model descriptions

2.1 Geothermal heat mining model

In the study described in this paper, a geothermal heat mining simulation using CO₂ was conducted with the TOUGH2, a numerical simulator for the fully coupled wellbore-reservoir. This simulator, developed by the Lawrence Berkeley National Laboratory (LBNL) is a well-validated commercial software [23,24]. Similar to the previous study, a research version of the T2Well/ECO2N software was provided by the LBNL which is based on the standard TOUGH2 code [20,21,25]. This new upgraded and expanded simulator is capable of modeling an integrated system with wellbores connected to a geothermal reservoir [25,26]. The fundamentals of T2Well/ECO2N can be found in Refs. [27,28], where the phase velocities in reservoirs are controlled by 3-D multiphase Darcy’s Law. The detailed implementation of solving momentum equations can be found in Refs. [23,27].

A generic geothermal site in Mexico was selected to perform the geothermal heat mining simulation. The reservoir is initially full of water with a temperature of 225°C. The initial pressure in the reservoir from the top to the bottom of the reservoir ranges from 20 to 25 MPa with the elevation change. A linear temperature distribution ranging from 30°C to 225°C is assumed along the wellbores through the cap rock. It is also assumed the reservoir has a single porosity with a value of 0.1, the specific heat of cap rock equals 920 J/(kg∙K), and the thermal conductivity is 2.51 W/(m∙K), which can be found in Electronic Supplementary Material (ESM, Table S2). A grid independence study was also performed, whose additional details can be found in Ref. [21].

For each well-set shown in Fig. 2(a), there is one injection well located in the center of the circle and four production wells symmetrically around the injection well. Due to the symmetry of the well-set layout, one quarter of the system was modeled with the injection well at one corner of a square domain of 2000 m in length (see Fig. 2(a)). The cap rock/overburden formation extents down to the depth of 2000 m covering the 500 m thick of the porous formation in the geothermal reservoir. The temperature of the basement rock below the porous reservoir is set to be constant. The depths of the injection well and production well are 2500 m and 2150 m, respectively, which can be found in ESM (Table S1). The production well is assumed to be less deep than the injection well as CO₂ is driven by the buoyancy force to move upwards when it is moving from the injection well outwards to production wells, which is indicated in Fig. 2(b). Such an arrangement promotes purer sCO₂ coming from the production well. In a previous study, the T2Well integrated wellbore-reservoir simulations was performed with the well distance ranging from 300 to 1000 m [21]. The sCO₂ temperatures drop significantly after 5–10 years of production when the distance between the wells is less than 500 m. On the other hand, the thermosiphon effect reduces with the increase in the distance between the wells due to the occurrence of the large cumulative pressure drop, which reduces power generation by the direct expansion but requires a larger pumping power back to the geothermal reservoir. Therefore, the distance between the production well and the injection well is a critical parameter to be optimized.

The result of a base case presented in Fig. 3 was obtained with the initial inputs presented in ESM (Table S2). Specifically, a well distance of 500 m, a CO₂ injection flowrate of 120 kg/s, a CO₂ injection temperature of 30°C, and a monitored production well bottom pressure of 27 MPa for starting production were assumed. The whole well-set (i.e., the four production wells) is able to produce sCO₂ at about 100 kg/s with an injection flowrate of 120 kg/s at a steady production well head temperature of 190°C for a net 20 years of production period. In addition, a well head pressure difference is of approximate 5– 10 MPa, which offers the benefits of reducing or avoiding CO₂ recompression work to achieve high thermal efficiencies.

A quarter of the reservoir domain sketched in Fig. 2(a) is modeled, the one-fourth of the flowrate of CO₂ initially injected from fossil-fired power plants is also considered accordingly. The CO₂ production flowrate is controlled to a small value, i.e., 0.5 kg/s in the early stage of injection to pressurize the reservoir, and the production well bottom pressure is then being tracked. When the production well pressure reaches a desired value, full production starts at this constant pressure, which is assumed to be controlled by a valve. The CO₂ production flowrate increases rapidly and reaches a steady-state within five years. Therefore, the CO₂ production flowrate is assumed to be a constant value for a 20-year period steady production. In the meantime, the wellhead pressures and outlet temperatures are also in steady-state during this period, and can be treated as constant values in the following analyses, which makes it possible to build a simplified geothermal heat mining predictive model.

Four critical parameters that affect the thermal performance of the power cycle and consequently the system cost are the distance between injection and production wells (R), the CO₂ injection flowrate ({\dot{m}}_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,inj}}), the CO₂ injection temperature (T_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,inj}}), and the controlled production well pressure (P_bottom,prod). Parametric studies for these four input parameters have been conducted. It can be seen (Fig. 4) that these parameters have a sensitive impact on the produced hot CO₂ flowrate, the production well head temperature, the injection well head pressure, and the production well head pressure. For instance, for an increase in R as shown in Fig. 4(a), the CO₂ production temperature increases which could lead to more power being generated. However, the pressure drop of sCO₂ increases which weakens the thermosiphon effect. Therefore, an optimal distance should be determined to strike a balance between the two mutually contradictory outcomes. In addition, a case with a large value R would produce less CO₂ since more CO₂ will be trapped in reservoirs as well as escape over the production wells. This also leads to less power being generated. Similarly, the variations of {\dot{m}}_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,inj}},T_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,inj}} and P_bottom,prod have an effect on {\dot{m}}_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,prod}},T_{{\mathrm{CO}}_{\mathrm{2,}}\mathrm{prod}} and ΔP_well, which determines the thermal and economic performances of the whole system. Therefore, a global thermo-economic analysis is necessary to find an optimal set of parameters.

2.2 Response surface model of geothermal heat mining

As mentioned previously, it is not practical to conduct an optimization analysis with the computationally expensive high-fidelity model T2Well/ECO2N. To overcome this difficulty, RSM was used to build a predictive geothermal heat-mining model based on the simulation results by T2Well/ECO2N, which then can be integrated into a global optimization model. The RSM developed in the 1950s has been widely used as a statistical and mathematical technique in modeling and data analysis. The fundamentals of the RSM theory as well as other applications and analyses, can be found in Refs. [29–31].

In this particular analysis, four parameters were considered as the input variables for constructing the RSM model: the distance between the injection and production wells (R=X₁ in unit of m), the CO₂ injection flowrate ({\dot{m}}_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,inj}}=\mathrm{4}{X}_{\mathrm{2}}), the CO₂ injection temperature (T_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,inj}}=X_{\mathrm{3}}), and the applied production well bottom pressure (P_bottom,prod =X₄). The output variables were the output sCO₂ flowrate ({\dot{m}}_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,prod}}=\mathrm{4}{Y}_{\mathrm{1}}), outlet sCO₂ temperature (T_{{\mathrm{CO}}_{\mathrm{2,}}\mathrm{prod}}=Y_{\mathrm{2}}), the production well head pressure (P_head,prod = Y₃), and the injection well head pressure (P_head,inj = Y₄). The surface response models were adequately fit with a third order polynomial model which can be expressed as

(1)Y={\alpha }_{\mathrm{0}}+{\displaystyle \sum _{i=\mathrm{1}}^{\mathrm{4}}{\alpha }_{ii}{X}_i^{\mathrm{2}}}+{\displaystyle \sum _{i=\mathrm{1}}^{\mathrm{4}}{\alpha }_i{X}_i}+{\displaystyle \sum _{i=\mathrm{1}}^{\mathrm{4}}{\displaystyle \sum _{j=i+\mathrm{1}}^{\mathrm{4}}{\alpha }_{ij}{X}_i{X}_j}}+e,

where Y is a response/output, X is input variable, α stands for coefficient, and e is the error. The obtained regression coefficients and coefficients of determination (r²) can be found in ESM (Table S3). It can be observed from Table S4(ESM) that the differences between the predicted values and the simulation values are within 5% which provides sufficient accuracy for the economic and the global optimization analyses.

To demonstrate this multi effects from various variables on the focused output parameters, two most critical variables, the injection, and production well distance (R=X₁) and the CO₂ injection flowrate ({\dot{m}}_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,inj}}=\mathrm{4}{X}_{\mathrm{2}}) were selected to plot the response surfaces as depicted in Fig. 5. The results were validated in T2Well/ECO2N, which indicate that the RSM model is reliable to be integrated with the direct sCO₂ expansion power generation system models for optimization analysis of the whole power generation cycle.

2.3 Direct expansion gas turbine power system model

For natural geothermal reservoir conditions in Mexico where a typical reservoir temperature is around 225°C, a direct sCO₂ turbine expansion system is the most realistic and efficient option for generating electricity using the extracted geothermal heat by sCO₂. This system has a relatively simple infrastructure which potentially gives the low capital cost and operation and maintenance(O&M) cost [21]. Therefore, a direct sCO₂ expansion system was considered as the power generation option to convert the geothermal heat extracted by sCO₂ to electricity. Figure 6 illustrates this power generation system consisting of a CO₂-H₂O separator, an expansion turbine, a CO₂ pre-cooler, a CO₂ compressor, and a CO₂ post-cooler.

The hot pressurized sCO₂ and water/brine mixture coming from the geothermal reservoir is first separated out in a CO₂-H₂O separator before entering the direct sCO₂ expansion system at State 1. The purified sCO₂ is expanded to a pressure near its critical point (State 2 in Fig. 6) in a turbine. Subsequently, the discharged CO₂ is cooled down in a water cooler which is specifically called a pre-cooler in this analysis. At State 3, the cooled CO₂ is then compressed in a CO₂ compressor to the pressure level which is required to re-inject it back to geothermal reservoirs. A post-cooler further cools down the pressurized CO₂ before re-injecting it back to the geothermal reservoir for heat mining and permanent sequestration after State 5. The thermodynamic models and mathematical equations of different process units are presented below.

Turbine

The isentropic expansion power output and efficiency for a CO₂ turbine can be expressed as

(2)W_{\mathrm{t}}={\dot{m}}_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,prod}}\left(h_{\mathrm{1}}-h_{\mathrm{2}}\right),

(3){\eta }_{\mathrm{t,s}}={\displaystyle \frac{h_{\mathrm{1}}-h_{\mathrm{2}}}{h_{\mathrm{1}}-h_{\mathrm{2}\mathrm{s}}}},

where W_t is the turbine power in kW, h is the enthalpy of CO₂ in kJ/kg, {\dot{m}}_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,prod}} is the CO₂ production rate in kg/s, and η_t,s is turbine isentropic efficiency.

Compressor

The isentropic compression work and efficiency for a CO₂ compressor can be expressed as

(4)W_{\mathrm{comp}}={\dot{m}}_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,prod}}\left(h_{\mathrm{4}}-h_{\mathrm{3}}\right),

(5){\eta }_{\mathrm{comp,s}}={\displaystyle \frac{h_{\mathrm{4}\mathrm{s}}-h_{\mathrm{3}}}{h_{\mathrm{4}}-h_{\mathrm{3}}}},

where W_comp is the compression power in kW and η_comp,s is the compressor isentropic efficiency.

System performance

The net power output can be calculated by

(6)W_{\mathrm{net}}=W_{\mathrm{t}}-W_{\mathrm{comp}},

where W_net is the net power being generated in kW.

The cycle efficiency is defined in Eq. (7). Since partial CO₂ is permanently sequestrated in the reservoir, the total thermal energy extracted by CO₂ is based on the CO₂ production rate at the production well.

(7){\eta }_{\mathrm{power�cycle}}={\displaystyle \frac{W_{\mathrm{net}}}{Q_{{\mathrm{CO}}_{\mathrm{2}}}}}={\displaystyle \frac{W_{\mathrm{net}}}{m_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,prod}}(h_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,prod}}-h_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,inj}})}},

where η_{power_cycle} is the cycle thermal efficiency and Q_{{\mathrm{CO}}_{\mathrm{2}}} is the total thermal power extracted in kW_th.

Disregarding the underground geothermal heat mining loop, this power cycle is operating as an open cycle and Fig. 7 is a temperature-entropy (T–s) diagram, where the red curve shows the base case conditions mentioned in Section 2.1. It is a closed loop system after combining the power generation system and the underground geothermal heat mining system. Therefore, the closed loop efficiency can be calculated by Eq. (8). Based on Ref. [21], the optimal turbine discharger pressure was set to 7.5 MPa, just above the critical pressure of CO₂. In addition, the minimum CO₂ outlet temperature at the pre-cooler outlet was fixed to 31.5°C, also just above the critical temperature of CO₂. The pressure drop of CO₂ through this power generation cycle was neglected. The thermodynamic model was developed and implemented in the ASPEN Plus software [32].

3 Economic and optimization analyses

The cost analysis methods and empirical equations used here for both the geothermal heat mining system and the direct sCO₂ expansion power generation system were systematically introduced by Wang [21]. The cost for each component in the direct expansion power cycle is calculated based on the thermodynamic performance at the optimal conditions, as well as being adjusted to the cost in 2019. Moreover, the LCOE calculation methodology is introduced following the capital cost analysis.

3.1 Geothermal heat mining system cost (Well capital cost)

The geothermal heat mining system which corresponds to the well cost consists of the well drilling cost, the exploration cost, and the confirmation cost. Each geothermal well drilling cost is given by Eq. (8), which is slightly adapted and scaled up into the year of 2019 based on Ref. [19], as

(8)C_{\mathrm{well,drilling}}={\displaystyle \frac{\mathrm{1.39}}{S}}\times \left[\zeta {\left({\displaystyle \frac{D_{\mathrm{well}}}{D_{\mathrm{0}}}}\right)}^{\mathrm{2}}+(\mathrm{1}-\zeta )\right]K{\mathrm{e}}^{bz},

where C_{well,drilling} is the per-well drilling cost in 2019 in M$, D₀, which is 0.23125 m, is used as a baseline well diameter, z is the well depth (meters), and S is the well drilling successful rate. The constants used in Eq. (8) are K = 0.2865, b = 6.657 × 10⁻⁴, and \zeta = 0.6662 [19].

In this paper, the well depths for injection wells, production wells, and re-injection wells are fixed due to the underground location of the reservoir. Therefore, the only parameter that needs to be considered to minimize the well drilling cost is the well diameter which is correlated to the mass flowrate of CO₂ in the wellbore. It has to be mentioned that the well diameter variation does not significantly affect the geothermal heat mining simulation based on Ref. [25]. Therefore, the effects of well diameter were not considered. However, it is critical to the well cost estimation and the optimization analysis. Thus, the variation of well diameter is accounted in the economic and optimization analyses.

Equation (9) is the continuity equation which states that the well diameter is determined by the CO₂ mass flowrate in the well.

(9){\dot{m}}_{\mathrm{inj/prod/reinj}}={\displaystyle \frac{\mathrm{1}}{\mathrm{4}}}\mathrm{\pi }{D}_{\mathrm{well}}^{\mathrm{2}}\rho v,

where {\dot{m}}_{\mathrm{inj/prod/reinj}} is the mass flowrate of CO₂ in injection, production, and re-injection wells in unite of kg/s, D_well is the well diameter, ρ and v are CO₂ density and velocity, in units of kg·m⁻³ and m·s⁻¹ respectively. Given that the maximum CO₂ in the wellbore velocity of 3 m·s⁻¹ based on the previous experiment conducted for CO₂ flowing through pipelines [33,34] and derived from Eq. (9), D_well can be expressed as a function of the mass flowrate as Eq. (10). Since the density of CO₂ along the wellbore is varying, the minimum well diameter is achieved where the minimum CO₂ density reaches.

(10)D_{\mathrm{well,min}}\mathrm{}=\sqrt{{\displaystyle \frac{\mathrm{4}{\dot{m}}_{\mathrm{inj/prod/reinj}}}{\mathrm{3}\mathrm{\pi }{\rho }_{\min }}}}.

Furthermore, the total minimum well cost for one well-set illustrated in Fig. 2(a) can be expressed as Eq. (11) which includes the total drilling cost, the exploration cost, and the confirmation cost.

=\min (C_{\mathrm{inj,drilling}}+\mathrm{4}\times C_{\mathrm{prod,drilling}}

(11)

3.2 Direct sCO₂ expansion power generation system cost

Supercritical CO₂-based power generation systems were not commercialized in 2020. In addition, no actual cost data are available for the cycle components as well as the O&M costs for sCO₂-based power plants. Therefore, estimating methods for the purchase cost of the equipment used in sCO₂-based power cycles are introduced and summarized in this section. However, the purchase cost of all the components needed for building a plant cannot represent the actual total cost of a plant. It is necessary to take into account factors reflecting materials, pressure levels, contingencies, and other possible costs which can affect the capital cost of constructing a power plant. In the present paper, factorial cost estimation techniques are presented. A well-known cost estimation method, the bare module factor method, is capable of taking into account the effects of operating pressures and materials on capital costs which are critical to a direct sCO₂ expansion power generation system. Moreover, the factors for other components are also available, such as shell tube heat exchangers, turbines, compressors, which were adopted in this paper. The costs for the major equipment illustrated in Fig. 6, including compressors, turbines, tube-shell heat exchangers, cooling water chiller, and CO₂-H₂O separators were estimated. The cost calculation correlations and factors can be found in ESM.

3.3 LCOE calculation

The objective function for the global optimization considering both power generation systems and geothermal heat mining systems is introduced in this section.

To meet the nominal power plant size, more than one well-set would be required to produce a sufficient amount of hot sCO₂ flow from geothermal reservoirs (Fig. 8). For each well-set, an additional injection well for re-injection to permanently sequestrate CO₂ is necessary. In this analysis, to be conservative, the re-injection well would be drilled for each well-set. However, one re-injection well can serve more than one well-set with a reasonable injection flowrate.

The total capital cost of the sCO₂ turbine expansion system using the hot produced sCO₂ from geothermal reservoirs includes the power generation system cost and the well cost, which have been presented in Sections 3.1 and 3.2 in detail. The layout consists of one power plant and the required number of well-sets. Accordingly, the total capital cost is expressed as Eq. (12).

(12)C_{\mathrm{totcapital}}=C_{\mathrm{totcaptital,powersystem}}+N_{\mathrm{wellset}}\times C_{\mathrm{wellset,min}}.

Other baseline conditions being considered for cost estimation and optimization analysis are listed in Table 1, including loan period, capacity factor, and financial factors, etc. According to geothermal heat mining with 20 years of steady CO₂ production, a loan period of 20 years with a capacity factor of 0.75, which is typical for a geothermal based power plant, was considered [2]. For the heat exchanger (HX) design of sCO₂-based power cycles, an HX effectiveness of 0.85 was used to obtain the required heat transfer area. Since the CO₂ sequestration credit is not considered in the present paper, which mitigates the cost of the carbon capture process, the counted CO₂ sequestration credit for the present paper may vary. Thus, sensitivity analyses were performed with the CO₂ credit ranging from 0 to 5 $/t for the final LCOEs.

A capital recovery factor method is adopted to convert the present value into a stream of equal annual payments of over 20 years’ loan period at a specified discount rate. The total installed cost based on the capital recovery factor above can be converted into an annual fixed cost considering capital amortization and tax and insurance costs alternatively. An annual payment is calculated using

(13)\mathrm{APF}={\displaystyle \frac{i{\left(\mathrm{1}+i\right)}^n}{{\left(\mathrm{1}+i\right)}^n-\mathrm{1}}},

where APF is the annual payment factor, i is the annual interest rate, and n is the period of the loan in years, which equals the plant life in this paper. Based on the information listed in Table 1, an APF of 0.07358 is obtained. Moreover, the annual fixed cost with the APF, the taxes and the insurance factor of 1.5%, and the total capital cost of the power system can be calculated by

(14)

Besides the plant capital cost, the O&M is another part of LCOE. A typical O&M estimating method for geothermal power generation was used. The O&M cost of the conventional hydrothermal geothermal power generation was adapted and adjusted to 2019 for a sCO₂-based geothermal plant which can be expressed as [35]

(15)

where C_{fixed O&M} is the fixed O&M cost per kWh and W is the plant capacity in MW_e.

Typically, LCOE is calculated for a power generation unit using its total cost to build and O&M costs divided by the total power output over its lifetime (see Eq. (16)).

(16)\mathrm{LCOE}={\displaystyle \frac{\mathrm{Lifetime\; cost}\left(\$\right)}{\mathrm{Lifetime\; power\; generation\; (kWh)}}}.

Two methods, the “discounting” method and the “annuitizing” method, are commonly used to calculate LCOE [36]. In this analysis, the “annuitizing” method is used. The present value of the stream of costs over the loan period is calculated using the calculation techniques discussed above to convert to an equivalent annual cost. Then, the annual equivalent annual cost is divided by the overall annual electric power being generated over the loan period, as expressed in Eq. (17).

(17)

where F_capacity is the plant capacity factor of 0.85 in this paper, {\dot{m}}_{{\mathrm{tot,CO}}_{\mathrm{2}}\mathrm{,inj}} is the total CO₂ injection mass flowrate during operation in kg/s, and b_{{\mathrm{CO}}_{\mathrm{2}}} is the credit for CO₂ sequestration in $/t CO₂ being sequestrated. Since the produced sCO₂ after being used for power generation will then be re-injected back underground for permanent sequestration, the initial CO₂ injection flowrate would be considered to calculate the CO₂ sequestration benefit.

4 Cost analysis results and optimization

A base case analysis with the parameter values presented in Table 2 was performed for the LCOE optimization. It needs to be mentioned that the compressor inlet temperature of 31.5°C is also the optimal value associated with the turbine inlet temperature and pressure in this paper based on Ref. [21]. Therefore, the CO₂ pre-cooler outlet temperature which is also the inlet temperature at the CO₂ compressor inlet is predetermined and is fixed at 31.5°C. In addition, the wet cooling technique was selected and the cooling water inlet temperature of 20°C is fixed. In the base case analysis, the credit of CO₂ sequestration is not counted.

Besides the four geothermal heat mining simulation parameters, i.e., R,{\dot{m}}_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,inj}},T_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,inj}} and P_bottom,prod, the turbine discharge pressure of the power cycle, P_t,dis was also considered as a variable for the optimization analysis. The turbine discharge pressure not only determines the amount of power being generated, but also significantly affects the CO₂ compressor performance. Therefore, this parameter is critical to the system thermal performance which influences the LCOE. Equation (18) shows the formulation of the optimization problem with the LCOE as the objective function. Suitable ranges of the design variables are specified as the lower and the upper bound constraints.

(18)\begin{array}{l}\mathrm{minimize\; LCOE}(R,{\dot{m}}_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,inj}},T_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,inj}},P_{\mathrm{bottom,prod}},P_{\mathrm{t,dis}})\hfill \\ \mathrm{subject\; to\; }\mathrm{500}\le R\le \mathrm{800},\mathrm{m}\hfill \\ \mathrm{}\mathrm{120}\le {\dot{m}}_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,inj}}\le \mathrm{300}\mathrm{,\; kg/s}\hfill \\ \mathrm{}\mathrm{30}\le T_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,inj}}\le \mathrm{80}\mathrm{,}°\mathrm{C}\hfill \\ \mathrm{}\mathrm{24}\le P_{\mathrm{bottom,prod}}\le \mathrm{30},\mathrm{MPa}\hfill \\ \mathrm{7}\mathrm{.5}\le P_{\mathrm{t,dis}}\le \mathrm{9}\mathrm{,\; MPa}.\hfill \end{array}

The process of the LCOE optimization flowchart is presented in Fig. 9. Sequential quadratic programming (SQP) was employed and implemented in ASPEN Plus to obtain the minimal LCOE as well as conducting a parametric study for the design parameters considered in the optimization analysis [37].

The minimal LCOE of $0.177/kWh was obtained with the overall cycle thermal efficiency of 15.13%. For this 100 MW_e capacity plant, 20 well-sets are required to provide enough geothermal energy. As presented in Table 3, the set of optimal values of R,{\dot{m}}_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,inj}},T_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,inj}}, and P_bottom,prod are 500 m, 120 kg/s, 30°C, and 30 MPa, respectively for the base case. The optimal turbine discharge pressure is 8.07 MPa which is slightly above CO₂ critical pressure. It can be seen that the optimal R,{\dot{m}}_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,inj}}\mathrm{and}{T}_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,inj}}is achieved at their boundaries. For the well distance and the CO₂ injection flowrate, 500 m is the lowest value with the lowest CO₂ injection flowrate to avoid the temperature drop of CO₂ during the entire 30 years including 20 years’ steady full production. If the CO₂ injection flowrate increases, the distance of the well needs to be increased to prevent the produced CO₂ temperature from dropping significantly. However, a long well distance can cause a large pressure drop during CO₂ migration underground which reduces the thermosiphon effect. These sensitivity analyses are covered in the following parametric study. Without considering CO₂ credits, the minimal LCOE is still high compared to the current power generation options [2]. It is necessary to take into account the CO₂ sequestration benefit for this novel application to make it sustainable, applicable, and cost-effective.

The effects of two essential factors, plant capacity and CO₂ sequestration credit, on LCOE are presented as follows.

Power plant capacity

The power plant capacity is significantly affected by the total produced sCO₂ flowrate. When the produced CO₂ flowrate increases from 628.01 kg/s to 3140.06 kg/s, the plant capacity changes from 30 MW_e to 150 MW_e. Consequently, to be able to handle a larger amount of CO₂, more geothermal wells and larger size plants can result in higher capital costs. Figure 10 shows the LCOE decreases with the increase of the plant capacity, while the capital costs increases. The well capital cost and the plant capital cost are in the same magnitude regardless of the plant capacity. Furthermore, the natural condition limitations of geothermal reservoirs are also factors that should be considered when the plant size increases in addition to the economic perspective.

CO₂ sequestration credit

As a critical benefit of this application, the CO₂ from fossil-fired power plants is partially sequestrated when flowing through the geothermal reservoir for heat mining. Besides, the produced sCO₂ after power generation is re-injected back to a new reservoir for permanent sequestration.

It needs to be mentioned that the CO₂ credits gained in the first couple of years before full production are not counted into the LCOE in this analysis. This part of the benefit can also be an advantage for the system to be profitable at the early stage of operation, even during the construction phase of the power generation.

Excluding CO₂ transportation and storage costs, the electricity production price ranges from $0.04/kWh to $0.09/kWh for fossil-fired power plants with carbon capture. If no CO₂ capture is equipped, the electricity production price can range from $0.03/kWh to $0.06/kWh. Accordingly, the estimated cost of CO₂ due to capture ranges from $37/t to $74/t for a PC plant and $29/t to $51/t for an NGCC plant [38]. The new 45Q tax code in the US offers a $50/t credit for saline CO₂ sequestration which was introduced in 2017 [39]. Any new fossil-fuel power plant or carbon-dioxide producing industry that commences construction before 2024 is eligible for tax credits for up to 12 years (a time cap on the credits). It can be seen in Fig. 11 that the difference between the $50/t credit offered by 45Q and the costs of a PC/NGCC plant capture cost in some cases is enough to exceed the breakeven points mentioned previously, which means with CO₂ tax credits, the power generation technology proposed in this paper are competitive with conventional geothermal power plants.

5 Parametric study

The turbine discharger pressure P_t,dis and four geothermal heat mining model inputs, i.e., R,{\dot{m}}_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,inj}},T_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,inj}}, and P_bottom,prod were considered for the parametric study. The other input parameters and operating conditions are identical to those of the base case.

Although the turbine discharge pressure is above 7.5 MPa in the optimization analysis, the 6 to 9 MPa pressure range has been selected to conduct the parametric study for the turbine discharge pressure. Figure 12 presents the LCOE, the change of system thermal efficiency, and the net power output per well-set along with the turbine discharge pressure. The maximum net power output is achieved when the turbine discharge pressure reaches 7.62 MPa which is consistent with the previous thermodynamic study [21]. The minimal LCOE is obtained at the turbine discharger pressure of 8.07 MPa which is not necessary to be the same as the maximum net power output. The curve of the LCOE and the system thermal efficiency indicate that the two are highly correlated and influenced by the turbine discharge pressure.

Figures 13(a) and 13(b) show the parametric study of the well distance. As the well distance is over 650 m, the well-set number required could increase significantly to maintain a certain level of CO₂ production due to the fact that less CO₂ is produced with a large production and injection wells distance, which leads to a tremendous increase of the capital costs and LCOE (see Fig. 13(a)). More CO₂ is passing over the production wells and a larger pressure drop cumulates when the well distance is increasing (see Fig. 13(b)). To collect more CO₂ at a large well distance, a different well layout, such as more production wells distributing around the injection well, must be investigated and the thermo-economic analysis is necessary to be performed.

Figures 13(c) and 13(d) show the influences of the injection flowrate. The results indicate the capital costs and the system thermal efficiency are not sensitive to the CO₂ injection flowrate for one well-set. The reason for this is that the fixed plant capacity requires a similar amount of sCO₂ even if the input parameter changes. When the CO₂ injection flowrate per well-set increases from 120 kg/s to 300 kg/s, the LCOE still increases from $0.177/kWh to $0.200/kWh even though the total CO₂ production flowrate increase from 2.1 t/s to 2.9 t/s. The reason for this is that fewer well-sets are needed for the high CO₂ injection flowrate per well-set case, leading to a lower LCOE. However, the smaller thermosiphon effect can offset it with less power being generated. Therefore, the number of well-sets varies to meet the requirement of sCO₂ amount. In addition, one of the ways to implement this application in a smaller land area or a reservoir is to increase the CO₂ injection flowrate per well-set to reduce the number of well-sets.

Figures 13(e) and 13(f) show the impact of the CO₂ injection temperature. The curves indicate that the LCOE varies not significantly with the change of CO₂ injection temperature. On the contrary, it considerably affects both the geothermal heat mining system and the thermal performances of the power generation system. The lower the temperatures of CO₂ at the injection/re-injection wellheads are, the smaller pressures are required for the injection process. Consequently, the biggest thermosiphon effect is obtained at the lowest CO₂ injection temperature. Figure 13(f) shows that the wellhead pressure differences are 8.5 and 3.7 MPa when the CO₂ injection temperatures are 30°C and 80°C respectively. The minimal LCOE is achieved at the lowest CO₂ injection temperature even if the system thermal efficiency is low.

Figures 13(g) and 13(h) show the effects of the onset production pressure. The pressurizing period is decided by monitoring the pressure at the production well. In the simulations, the pressure at the well bottom is monitored as an indicator for the time to begin the full production. To reach a higher production pressure, a higher pressurizing period is required. Consequently, the full production starting time points for the cases with the monitored production well bottom pressure of 24 and 30 MPa are 2.5 and 7.5-year respectively. However, the high monitored production well pressure means that the CO₂-plume is forming for a long period of time which leads to a high CO₂ portion of the CO₂/bring mixture. Consequently, a smaller pressure drop occurs for the high CO₂ portion flow which leads to a large thermosiphon effect.

6 Conclusions

In this paper, a thermo-economic analysis and an optimization were performed for utilizing captured CO₂ from fossil-fired power plants to extract geothermal heat to generate electric power by a comprehensive model because the direct turbine expansion not only directly converts the enthalpy to electric power with less loss, but also takes advantage of the CO₂ thermosiphon effect to end up with large net power output. However, due to the direct contact with geothermal fluid which potentially contains corrosive substance for many devices in the process, high anti-corrosive and expensive materials are indispensable to build turbines, compressors, and HXs, which were also considered in the economic analysis in this paper.

LCOE was selected as the objective to perform the optimization. For a base case with the capacity of 100 MW_e, the minimal LCOE of $0.177/kWh was obtained. The optimal values of an injection and production well distance of 500 m, a CO₂ injection flowrate of 120 kg/s, a CO₂ injection temperature of 30°C, a monitored production well bottom pressure of 30 MPa, and a turbine discharge pressure of 8.07 MPa were acquired in their operating condition ranges to get the minimal LCOE. It is noted that 20 well-sets are needed to generate 100 MW_e and be able to permanently sequestrate CO₂ at 2.4 t/s. To demonstrate the benefits of such an application, the CO₂ sequestration credit was taken into account. Compared to a conventional geothermal steam power plant, the LCOE of direct sCO₂ expansion system reaches the breakeven point with a CO₂ credit of $1.00/t. Furthermore, when it is $2.05/t, the direct sCO₂ expansion system can generate electricity at no cost. The other conclusion remarks can be made as follows:

The CO₂ production flowrate and the thermosiphon effect during the geothermal heat mining are two major factors impacting the economic and thermal performance of the direct sCO₂ expansion power generation system. The total produced CO₂ flowrate dominates the plant capacity. The produced CO₂ flowrate increases from 628.01 kg/s to 3140.06 kg/s when the plant capacity changes from 30 to 150 MW_e.

The minimal LCOE is always achieved at the largest thermosiphon effect that occurs in the reservoir. However, the thermosiphon effect does not dominate the economic performance of the system.

The LCOE decreases when the plant capacity increases. For instance, direct sCO₂ expansion power plants with capacities of 30 MW_e and 150 MW_e can have a minimal LCOEs of $0.191/kWh and $0.172/kW, respectively. However, more well-sets are needed to produce more CO₂ to provide sufficient thermal energy for a larger capacity plant, which is subject to the geothermal reservoir size or geological conditions.

The injection and production well distance significantly affect both well capital cost and plant capital cost. The shortest well distance without significant production temperature decreasing is the optimal value for the well pattern considered in this paper.

The capital costs and the thermal performance of the system are not sensitive to the change of CO₂ injection flowrate per well-set with a fixed plant capacity. When the CO₂ injection flowrate per well-set increases from 120 to 300 kg/s, the LCOE still increases by 13.1% even though the total CO₂ production flowrate increase by 36.5%. The reason for this is that fewer well-sets are needed for the high CO₂ injection flowrate per well-set case, leading to a lower LCOE but it is offset by the smaller thermosiphon effect due to the large pressure drop occurring through the reservoir which results in less power being generated.

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