Performance Comparison of H2O and CO2 as the Working Fluid in Coupled Wellbore/Reservoir Systems for Geothermal Heat Extraction

CO₂ is considered as a novel heat-transmission fluid for extracting geothermal energy from enhanced geothermal systems (EGS), attributed to its high compressibility, expansivity and low viscosity in comparison to water. In order to compare the performance of CO₂ and H₂O as the working fluid in EGS, a classical five-spot model based on the geologic and geothermal conditions at the Songliao Basin, China, was constructed. Results obtained from the coupled wellbore/reservoir model revealed that the net heat extraction and flow rate are greater for CO₂ than for H₂O at a fixed operation pressure difference between the injection and production wellheads. However, the wellhead temperature is far lower for CO₂ than for H₂O due to the strong Joule–Thomson effect of CO₂ in the wellbore. Moreover, a stronger pressure change in the wellbore is observed by using CO₂, attributed to the gravity and high flow velocity of CO₂; this pressure change induces a drop in the frictional pressure. For CO₂, the enthalpy change in the wellbore is mainly contributed by the gravitational potential, while for H₂O, it is contributed by the gravitational potential and lateral heat exchange. The heat extraction performance depends on the operation pressure difference and injection temperature for H₂O-based EGS, while it depends on the wellhead pressures of both the injection and production wells as well as the injection temperature for CO₂-based EGS. A high operation pressure is favorable for improving the heat extraction performance (especially the production temperature) for CO₂. With the temperature drop limitation at the downhole of the production well, the heat extraction performance is better by using H₂O than that by using CO₂ as the working fluid. However, the low-power consumption for maintaining fluid circulation demonstrates the application potential of CO₂-based EGS.

1 Introduction

Geological sequestration of carbon dioxide (CO₂) in geological formations has been recognized as a technically feasible method to control or slow down the climate change trend (White et al., 2003; Orr, 2004; Metz et al., 2005; Goodman et al., 2013; IPCC 2014). It is recently considered as a novel heat-transmission fluid instead of H₂O for extracting geothermal energy from EGS, which can simultaneously achieve energy extraction and CO₂ geological sequestration (Brown D., 2000; Mohan et al., 2013; Xu R. et al., 2015; Pan F. et al., 2017; Wang et al., 2018; Shi et al., 2018; Bongole et al., 2019; Singh et al., 2020; Cui et al., 2021). CO₂ could perform better than H₂O, because of 1) large buoyancy force caused by a density difference between cold and hot CO₂, leading to the natural thermosiphon; 2) strong mobility, which can yield large flow velocities for a given pressure gradient; 3) low reactivity, which reduces or eliminates scaling problems caused by the water-rock geochemical reaction (Brown, 2000).

Although there is no commercial project with CO₂ as the working fluid for extracting deep geothermal energy, a number of numerical simulations were conducted to examine the feasibility and heat mining performance. Pruess (2006) used TOUGH2 to simulate the heat extraction performance of CO₂-based EGS and demonstrated that the mass flows and net heat extraction rate generated by CO₂ are higher than that generated by H₂O, by four times and 50%, respectively. Furthermore, Pruess (2008) conducted three-dimensional simulations to investigate the production behavior and revealed that production wells should be open only in a limited vertical interval near the reservoir top to avoid thermal breakthrough due to the large contrast in the CO₂ density. To consider fluid flow and heat transfer in wellbores, Atrens et al. (2010) conducted a simple calculation with pipe flow and the first law of thermodynamics for wellbores and a lumped-parameters model for reservoirs and showed that compared to water, CO₂ is less effective for extracting energy under conditions similar to those utilized for past EGS trials (Murphy et al., 1999). Following the same calculation method, Zhang et al. (2013) compared the thermodynamic performance for CO₂-based EGS and H₂O-based EGS systems, indicating that CO₂-based EGS produces more power in reservoirs with a low recoverable thermal energy, and operation parameters should be optimized to match the actual CO₂-based EGS condition. Recently, the calculation for the effect of impurities on CO₂-based EGS revealed that the system efficiency decreases with the increase in the impurity fractions (Zhang et al., 2016).

To simultaneously consider fluid flow and heat transfer in wellbores and reservoirs, T2Well (Pan et al., 2011; Pan and Oldenburg 2014) was developed and used to evaluate the heat and flow in wells for CO₂-based EGS; the results revealed that an appropriate CO₂ flow rate is required to generate a positive electric power output for a fixed flow-rate production. Xu et al., 2015b used T2Well to numerically identify advantages and disadvantages of using CO₂ as the working fluid and revealed that a very low-temperature fluid was obtained by CO₂, which is major disadvantage for CO₂-based EGS. Luo et al. (2014) investigated dramatic variations in the supercritical CO₂ properties and thermal-hydraulic turbulence features of CO₂ in the wellbores in a doublet CO₂-EGS system based on conditions at the European EGS site at Groβ Schönebeck using the CFD code FLUENT 6.3. The result demonstrated that a CO₂ injection rate of 10 kg/s is apparently favorable for an expected geothermal utilization lifetime of 20 years Huang et al. (2014) coupled the reservoir simulator TOUGH2 (Pruess et al., 1999) with the wellbore simulator HOLA (Aunzo et al., 2011) to evaluate the potential heat extraction using H₂O in the Songliao Basin.

In this study, a classical five-spot model based on the geological and geothermal conditions of the Songliao Basin is constructed. The coupled wellbore/reservoir simulator T2Well (Pan et al., 2011; Pan and Oldenburg 2014) is employed to simulate the fully coupled thermal and hydrodynamic (TH) processes. The comparison of the performance, including net heat extraction, flow rate, and production temperature as well as the TH processes in the wellbores and reservoir between H₂O-based and CO₂-based EGS is performed. Then, sensitivity analysis to the operation parameters, including pressures of injection and production wellheads and injection temperature, is examined. Finally, the optimum results for both H₂O-based and CO₂-based EGS with the temperature drop limitation at the downhole of production well for the project lifetime are compared. The novelty of this study lies in that 1) the coupling TH processes in wellbore/reservoir system is considered and 2) the performance from the optimum results for both H₂O-based and CO₂-based EGS is compared.

2 Model Setup

2.1 Geological Setting of the Songliao Basin

The Songliao Basin, located in northeastern China, is a Mesozoic to Cenozoic continental sedimentary rhombic basin, with a length of 750 km and a width of 330–370 km. The total area of the basin is 260,000 km², comprising six primary structural units including the north plunge zone, west slope zone, northeast uplift zone, central depression zone, southeast uplift zone, and southeast uplift zone, respectively (Figure 1A). The basin was formed by rifting during the late Jurassic, and it was filled by 10-km-thick sediments. The stratigraphic sequence of the basin is dominated by Mesozoic and Cenozoic strata from the Late Jurassic to the Quaternary. The deep formations (buried depth > 2 km) of the basin include the Quantou Formation (K1q), the Denglouku Formation (K1d), the Yingcheng Formation (K1yc), the Shahezi Formation (K1sh), and the Huoshiling Formation (J3h) (Figure 1B). These deep formations are generally composed of sandstone, shale, siltstone, and volcanic and volcaniclastic rocks. The Songliao Basin is regarded as one of the most potential sites for EGS resource exploration, according to the heat flow and depth–temperature datasets (Jiang et al., 2016).

FIGURE 1

FIGURE 1. (A) Location map of the potential EGS site in the Songliao Basin (China) and (B) Stratigraphic profiles near the study area.

The average geothermal gradient of the basin is ∼3.7°C/100 m, which is one of the highest geothermal gradients among the Chinese basins. According to the MIT report on the definition of an enhanced geothermal system (EGS) (MIT, 2006), the potential depth for geothermal exploitation is between 3 and 6 km, and the acceptable temperature for EGS development is greater than 150°C. Therefore, the formations of K1yc, K1sh, and J3h are the potential candidates for EGS. The formation of K1yc in Shuangcheng Fault Depression, northeast of the central depression zone as the target formation, was selected; it is considered as the most potential site for EGS previously (Huang et al., 2014).

2.2 Simulation Tool

The injection and production wells play key roles in the transportation of the fluid and heat in the reservoir. Temperature and pressure would drastically vary in the wellbores, especially by using CO₂ as the working fluid (Atrens et al., 2010). In this study, the integrated wellbore-reservoir simulator T2Well (Pan et al., 2011; Pan and Oldenburg 2014) is employed to compare the fluid flow and heat transfer in the coupled wellbore/reservoir system with CO₂ and H₂O as working fluids. The governing equations are listed in Table 1. T2Well introduces a special wellbore sub-domain into the numerical grid, thereby extending the current numerical reservoir simulator TOUGH2 to simultaneously and efficiently calculate the flow in the wellbore and reservoir (Pan and Oldenburg 2014). This software is successfully employed to simulate the non-isothermal multiphase, multicomponent flow process in coupled wellbore/reservoir systems for CO₂ geological sequestration and geothermal extraction (Hu et al., 2012; Li et al., 2015; Pan et al., 2015; Rasmusson et al., 2015). The module ECO2N V2.0 (Pan L. et al., 2017) that can describe fluid property of CO₂-H₂O-NaCl systems within temperatures of up to 300°C is incorporated into T2Well for this study.

TABLE 1

TABLE 1. The governing equations solved in T2Well (Pan and Oldenburg, 2014).

2.3 Model Description

The target reservoir is located at a depth of 3800 m with a thickness of 136 m. To improve heat production, hydro-fracturing is implemented to enhance permeability in this deep granite reservoir. Therefore, the target reservoir is considered as fractured media. A model composed by the target reservoir and injection and production wellbores (Figure 2A) is employed to capture the fluid flow and heat-transfer process in the entire wellbore/reservoir system. For comparing the heat-extraction capability of two heat-transmission fluids, the classic “five-spot” well pattern is employed. The reservoir model can be simplified to a 1/8 symmetry domain due to the symmetry, which can significantly reduce the computational burden. The wells are located at two vertices of the triangle simulation zone, with a distance of 707 m (Figure 2B).

FIGURE 2

FIGURE 2. (A) Conceptual model for the heat extraction from EGS and (B) grid partition of the reservoir.

To simulate fluid flow and heat transfer in fractures and in the matrix pores, the dual-porosity multiple interacting continua (MINC) (Pruess and Narasimhan, 1982; Pruess and Narasimhan, 1985) model is employed. First, one-layer 2D irregular grids are created to represent the reservoir (Figure 2B). The grid size increases from 0.1 m near the well to 50 m outside. Second, the primary grids are partitioned into five sub-grids by using a set of volume fractions. The injection and production wells fully perforate the reservoir and extend 3,880 m up to the surface. Two 1D vertical grids comprising seventy-eight 50-m grid blocks are created for the wellbores, which are attached to the 2D reservoir grids to represent the injection and production wells.

The reservoir is assumed to be initially saturated with CO₂ or H₂O. The reservoir temperature is set to 150°C, and its pressure is ∼37.5 MPa according to the calculation with a geothermal gradient of 37°C/km and a hydrostatic pressure distribution. The model also considers the heat exchange between the fluid and the surrounding rock in the wellbore. Table 2 lists the parameters used in the model.

TABLE 2

TABLE 2. Parameters for the five-spot heat extraction problem in enhanced geothermal systems.

3 Results and Discussion

3.1 Base Case

Figure 3 shows the temperature, flow rate and net heat extraction rate in the H₂O-based and CO₂-based EGS, respectively. In the H₂O-based EGS, the fluid production rate and temperature are maintained at ∼20 kg/s and 135°C, respectively (Figure 3A). The net heat extraction rate (calculated by $G=R_{pro}{h}_{pro}-R_{inj}{h}_{inj}$, where $R$ is rate, and $h$ is enthalpy) is ∼10 MW. In the CO₂-based EGS, the stable heat extraction lasts for ∼10 years, and then the fluid production rate and temperature decrease from ∼146 kg/s to 120 kg/s and from 67 to 50°C, respectively (Figure 3B). The net heat extraction rate decreases from ∼25 to 13 MW. The H₂O-based EGS operation is more stable than that of the CO₂-based EGS. However, the net heat extraction rate for the CO₂-based EGS is 1.3–2.5 times greater than that for the H₂O-based EGS, indicating that the CO₂-based EGS can accelerate heat recovery. Compared with that of H₂O-based EGS, the high production rate due to the high CO₂ mobility (indicated by $\rho /\mu$, where $\rho$ and $\mu$ are density and viscosity, respectively) offsets the disadvantage of the low heat capacity for CO₂-based EGS.

FIGURE 3

FIGURE 3. Key performance parameters for (A) the H₂O-based and (B) CO₂-based EGS from simulations.

In the H₂O-based EGS, downhole pressures are maintained at 40.6 and 36.0 MPa in the injection and production wells, respectively (Figure 4A). The downhole temperatures are maintained at 33 and 150°C in the injection and production wells, respectively (Figure 4A). On the other hand, in CO₂-based EGS, the downhole pressures and temperatures in the production well are stable for the first 10 years, followed by an increase from 36.6 to 38.9 MPa and a decrease from ∼150 to 106°C, respectively. The downhole temperature in the injection well is stabilized at 48°C, but the pressure increases from 44.0 to 45.3 MPa. These fluctuations correspond to the change in flow rate. The downhole pressure in the injection well is determined by the flow process in the wellbore under a fixed wellhead pressure. The decrease in the flow rate results in a pressure loss related to the wellbore roughness. Pressure and temperature distributions satisfy the relative stable condition after a fluid injection of 0.03–0.04 years (Figure 5). In this short period, the downhole pressure in the injection well for the H₂O-based EGS increases from 37.5 to 40.6 MPa, while the pressure increases to 44.0 MPa for the CO₂-based EGS. There are about 1.1 and 4.5 MPa contributed by the change in density from the wellbore for the H₂O-based and CO₂-based EGS, respectively. This result is related to the fact that the density of CO₂ is more sensitive to temperature. In the production well, the average fluid temperature generally increases due to the upward flow of the hot fluid from the reservoir. The downhole pressures decrease by 1.5 and 0.9 MPa at the start of production for the H₂O-based and CO₂-based EGS, respectively. This is because that the temperature redistribution in the production well results in a decrease in density. With the heat in the reservoir is gradually extracted, and the fluid temperature in the production wellbore decreases for the CO₂-based EGS, thereby increasing the pressure (Figure 5).

FIGURE 4

FIGURE 4. Downhole pressure and temperature for (A) the H₂O-based and (B) CO₂-based EGS.

FIGURE 5

FIGURE 5. Evolution of pressure and temperature distributions in the wellbore: (A) pressure and (B) temperature for H₂O in the injection well, (C) pressure and (D) temperature for H₂O in the production well, (E) pressure and (F) temperature for CO₂ in the injection well, (G) pressure and (H) temperature for CO₂ in the production well.

Fluid pressure profiles (Figure 6) reveal that strong pressure gradients are observed near the injection well. The pressure in the reservoir for the CO₂-based EGS increases with the production due to the decrease in temperature, thereby increasing the pressure at the downhole of the production well. Finally, the decrease in temperature and increase in pressure lead to a decrease in the flow rate and net heat extraction rate (Figure 3B). The temperature-decrease zone extends to ∼230 m after the production of 5 years for the H₂O-based EGS (Figure 6A), while it extends to ∼300 m for the CO₂-based EGS (Figure 6B). After the production of 30 years, they extend to 660 m (Figure 6A) for H₂O and the production well for CO₂ (Figure 6B), and the downhole temperature in the production well decreases to 100°C for CO₂ (Figure 6B). Heat extraction within a zone of 180 m away from the injection well is completed after the production of 30 years for the H₂O-based EGS (Figure 6A), while the zone reaches to ∼260 m for the CO₂-based EGS (Figure 6B).

FIGURE 6

FIGURE 6. Pressure and temperature profiles along a line from the injection well to the production well in the reservoir for (A) H₂O-based and (B) CO₂-based EGS.

Based the governing equations in Table 1, the change in the pressure along the wellbore is contributed by the gravity and well frictional term, while it is contributed by the frictional term in the reservoir. The gravitational contribution to the pressure gradient is dominant. In the CO₂-based EGS, the gravitational contribution accounts for 91 and 82%–89% in the injection and production wells, respectively (Figure 7A). The proportion of the well frictional term in the production well is greater than that in the injection well, attributed to the small density under the conditions of a high temperature and a high flow velocity in the production well. In the H₂O-based EGS, the well frictional term is neglected due to a small value resulting from a low flow velocity. (Figure 7B). The reservoir frictional term is greater for the CO₂-based EGS than for the H₂O-based EGS, because the pressure gradient in the reservoir only depends on the downhole pressure difference between injection and production wells determined by the flow process in the wellbores.

FIGURE 7

FIGURE 7. Pressure changes along the flow path for (A) the CO₂-based and (B) H₂O-based EGS based on simulations. Arrow upward denotes an increase, otherwise it denotes a decrease.

The enthalpy change along the flow path is mainly contributed by the gravitational potential energy, lateral heat exchange with the surroundings in the wellbores, and heat exchange with the reservoir. The enthalpy change contributed by the gravitational potential energy is dominant in the wells for the CO₂-based EGS (Figure 8A). In the early stage, a heat of ∼184 kJ per kilogram CO₂ is extracted by CO₂ from the reservoir, which decreases to 108 kJ in the late stage due to the decrease in the reservoir temperature. For the H₂O-based EGS, the contributions to the enthalpy change by the gravitational potential and lateral heat exchange are similar in the wells (Figure 8B). A heat of 490 kJ per kilogram H₂O is extracted by H₂O (Figure 8B). Hence, H₂O exhibits a high heat-carrying capacity due to its high heat capacity. To obtain the same heat extraction rate as H₂O, the CO₂ mass rate should be 2.6 times of that of H₂O.

FIGURE 8

FIGURE 8. Enthalpy changes along the flow path for (A) the CO₂-based and (B) H₂O-based EGS based on simulations. In both cases, the reference state (zero enthalpy) is chosen as (T, P) = (20°C, 10 MPa). Arrow upward denotes an increase, otherwise it denotes a decrease.

Figure 9 shows the state change of pressure–temperature–enthalpy diagram along the flow path. The CO₂-based EGS is significantly affected by the Joule–Thomson effect of CO₂, which reduce the temperature in the production well (Figure 9B). The disadvantage can be weakened in the CO₂-based EGS under high-pressure conditions.

FIGURE 9

FIGURE 9. State (P, T, E) change along the flow path for (A) the H₂O-based and (B) CO₂-based EGS.

3.2 Sensitivity Analysis to Operation Conditions

Operation conditions (i.e., injection pressure and temperature as well as production pressure) exhibit a key effect on the EGS performance. To examine the effect, sensitivity analysis to these key parameters (Table 2) is performed. The parameters that are not listed in Table 3 are the same as the base case.

TABLE 3

TABLE 3. Parameters used in sensitivity analysis based on the base case.

3.2.1 Effect of the Injection and Production Pressures

Compared to the base case, the results of Case 1 and Case 2 (Figures 10A–C) reveal that the increase in the operation pressure for the CO₂-based EGS leads to a slight decrease in the net heat extraction rate and mass-flow rate, albeit clearly increase of the production temperature. This is related to the fact that the increase in the operation pressure would shift the curve upward in Figure 9B, indicative of the decreased Joule–Thomson effect. The comparison of the base case, Case 3, and Case 4 ((Figures 10A–C) reveals that the increase in the operation pressure difference leads to the increase in the net heat extraction rate and mass-flow rate and weakly decreases the wellhead temperature. The results of Case 5 and Case 6 demonstrate that the CO₂-based EGS can run under a negative pressure difference (Pinj − Ppro < 0), indicating that CO₂ can circulate without the need for external pumping. The phenomenon is attributed to the high compressibility and expansivity of CO₂. The simulated results for the H₂O-based EGS (Figures 10D–F) reveal that the net heat extraction rate and mass-flow rate are only related to the operation pressure difference.

FIGURE 10

FIGURE 10. Performance of (A) net heat extraction rate, (B) mass-flow rate, (C) temperature for the CO₂-based EGS, (D) net heat extraction rate, (E) mass-flow rate, and (F) temperature for the H₂O-based EGS.

3.2.2 Effect of Injection Temperature

Effects of the injection temperature on the performance of CO₂-based and H₂O-based EGS are different. For the CO₂-based EGS, the high injection temperature leads to the low downhole pressure in the injection well, thereby decreases the pressure gradient in the reservoir and ultimately reduces the mass-flow rate and net heat extraction (Figure 11A). The slight temperature difference is observed in the late stage of heat extraction, which is related to the different temperature decrease rates in the reservoir. For the H₂O-based EGS, the effect of injection temperature on the flow viscosity is superior to the effect of pressure gradient. Therefore, a high injection temperature leads to a high mass-flow rate (Figure 11B). However, the net heat extraction rate is inverse because the additional heat from the production is less than that from the injection.

FIGURE 11

FIGURE 11. Effect of injection temperature on the performance for (A) the CO₂-based and (B) H₂O-based EGS.

3.3 System Optimization for Heat Extraction

EGS stable operation requires a minimal temperature drop and the maximal net heat extraction during the development period. For the comparison of CO₂ with H₂O, a target temperature drop is set as 20°C at the bottom of the production well after 30 years. For a specific EGS site, the most easily optimized parameter is the wellhead pressure. To prevent the damage of the reservoir by high pressure, the maximal pressure in the reservoir is limited to the value of 1.5 times of the initial pressure (56.25 MPa). Considering the strong Joule–Thomson effect of CO₂ in the wellbore, the wellhead pressure in the production well should be as high as possible to obtain the maximal temperature in the CO₂-based EGS. Based on a simple calculation method for the pressure and temperature distribution proposed by Atrens et al. (2010), the estimated maximal allowed wellhead pressures in the production and injection wells for the CO₂-based EGS are ∼25 and 20 MPa, respectively. The pressure differences from 1 to 15 MPa with an interval of 1 MPa are used in the simulation for the system optimization of the H₂O-based EGS. For CO₂, the negative pressure differences (e.g., $P_{inj}-P_{pro}\le 0$) are only considered based on the previous simulated results. The injection pressures ranging from 11.7 to 19.7 MPa with an interval of 2 MPa and the negative pressure differences ranging from -5 to 0 MPa with an interval of 1 MPa. A total of 30 models are operated for the system optimization of the CO₂-based EGS.

The optimal pressure difference is ∼10 MPa for a temperature drop limitation of 20°C for the H₂O-based EGS (Figure 12). The corresponding net heat extraction rate, flow rate, and production temperature are 22.9 MW, 47.4 kg/s, and 124°C, respectively. For CO₂, the numerical result reveals that the negative pressure difference should not be greater than 5.0 MPa. Otherwise, the driving force is not always sufficient to drive CO₂ to the wellhead. The net heat extraction and flow rate at the low operation pressure are greater than that at the high operation pressure, but the wellhead temperature exhibits an inverse relationship (Figure 13). Under the temperature drop limitation, when the injection pressure increases from 11.7 to 19.7 MPa, the production wellhead temperature increases from 76 to 86°C (Figure 14). The corresponding flow rate and net heat extraction slightly increase. The negative pressure differences change from −4.1 MPa to −2.1 MPa, indicating that a large driving force is required at the high operation pressure. The optimal pressures for the CO₂-based EGS are the maximal limited pressure of 19.7 MPa (implying that the operation pressure is as high as possible) at the injection well and 21.8 MPa at the production well. The corresponding net heat extraction rate, flow rate, and production temperature are 16.3 MW, 105.4 kg/s, and 86°C, respectively. Clearly, the heat extraction performance using CO₂ is worse than that using H₂O under the temperature drop limitation. However, the negative pressure difference for CO₂ may lead to lower power consumption to maintain fluid circulation. Moreover, the low reactivity between CO₂ and formation can prevent scaling and formation plugging, and large amounts of CO₂ could be stored by heat extraction. These features make CO₂ competitive with H₂O for heat extraction.

FIGURE 12

FIGURE 12. Effect of pressure difference on performance for the H₂O-based EGS.

FIGURE 13

FIGURE 13. Effect of pressure difference on performance for the CO₂-based EGS at the wellhead pressure of (A) 11.7 MPa, (B) 15.7 MPa, and (C) 19.7 MPa in the injection well.

FIGURE 14

FIGURE 14. Effect of injection pressure on performance with the temperature drop limitation for the CO₂-based EGS.

4 Concluding Remarks

CO₂ is recently considered as a competitive working fluid in comparison to H₂O for extracting heat from hot dry rocks. A coupled wellbore/reservoir simulation is conducted to comprehensively compare the performance of both fluids. The following major conclusions are drawn:

(1) At a fixed wellhead pressure difference, the net heat extraction and flow rate are greater for CO₂ than those for H₂O due to a large pressure gradient in the reservoir and high density gradient within CO₂-base system, but the wellhead temperature is far lower in CO₂-base system than that in H₂O-base system due to the strong Joule–Thomson effect of CO₂ in the wellbore.

(2) In the wellbore, the pressure change is mainly affected by gravity. For CO₂, the frictional pressure drop accounts for 9–18% due to the high flow velocity. The enthalpy change is mainly contributed by the gravitational potential for CO₂, while it is mainly contributed by the gravitational potential and lateral heat exchange for H₂O.

(3) The heat extraction performance for H₂O depends on the pressure difference at the wellheads and injection temperature, while the performance of CO₂-based system depends on the pressure and temperature at the wellhead of injection well and production well. A high running pressure is favorable for improving the heat extraction performance (especially the production temperature) for CO₂. A high injection temperature cannot increase the net heat extraction.

(4) With the constraint of temperature drop of 20°C at the bottom of the production well, the heat extraction performance by using H₂O as the working fluid is better than that by using CO₂. The optimal pressure difference is ∼10 MPa for H₂O. The corresponding net heat extraction rate, flow rate, and production temperature are 22.9 MW, 47.4 kg/s, and 124°C, respectively. The optimal pressures for the CO₂-based EGS are the maximal limited pressure of 19.7 MPa (implying that the operation pressure is as large as possible) at the injection wellhead and 21.8 MPa at the production wellhead. The corresponding net heat extraction rate, flow rate, and production temperature are 16.3 MW, 105.4 kg/s, and 86°C, respectively.

The present results are limited to the given conditions and parameters. However, the numerical experiments provide a critical insight into the hydrodynamic and heat-transfer processes for the H₂O-based and CO₂-based EGS considering the coupled wellbore/reservoir systems. The critical evaluation of modeling results can provide a reference to design the H₂O-based and CO₂-based EGS. In future studies, the realistic fracture network after fracturing should be considered in the model.

Data Availability Statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

Author Contributions

HL contributed to all of the study.

Funding

This study was supported by the National Natural Science Foundation of China (Grant Nos. 41602255 and 51809259).

Conflict of Interest

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s Note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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Nomenclature

$A$ wellbore cross-sectional area

$C_R$ specific heat of the rock

$C_0$ profile parameter account for the effect of local gas saturation and velocity profile over the pipe cross-section

$F^{\kappa }$ mass or heat flux of component $\kappa$

$f$ apparent friction coefficient

$g$ or $g$ gravitational acceleration

$h_{\beta }$ specific enthalpy of phase $\beta$

$k$ absolute permeability

$k_{r\beta }$ relative permeability of phase $\beta$

$M^{\kappa }$ mass or energy per volume of component $\kappa$

$P$ pressure

$P_{\beta }$ fluid pressure in phase $\beta$

$q^{\kappa }$ sinks and sources of component $\kappa$

$q^{\text{'}}$ wellbore heat loss/gain per unit length of wellbore

$S_G$ gas phase saturation

$S_{\beta }$ saturation of phase $\beta$

$t$ time

$T$ temperature

$u_d$ drift velocity of gas

$u_G$ gas phase velocity

$u_L$ liquid phase velocity

$u_m$ mixture velocity (velocity of mass center)

$u_{\beta }$ or $u_{\beta }$ velocity of phase $\beta$

$U_{\beta }$ specific internal energy of phase $\beta$

$V_n$ subdomain of the flow system

$X_{\beta }^{\kappa }$ mass fraction of component $\kappa$ present in phase $\beta$

$z$ one-dimensional coordinate along the length of the wellbore

$\Gamma$ perimeter of the wellbore cross-section

${\Gamma }_n$ closed boundary surface of $V_n$

$\gamma$ a quantity caused by slip between the two phases

$\theta$ incline angle of the wellbore

$\lambda$ thermal conductivity

${\mu }_{\beta }$ viscosity of phase $\beta$

${\rho }_G$ gas phase density

${\rho }_m$ mixture density

${\rho }_m^{\ast }$ profile-adjusted average density

${\rho }_R$ grain density of the rock

${\rho }_{\beta }$ density of phase $\beta$

$\varphi$ porosity