# Optimization Design of Multi-Factor Combination for Power Generation from an Enhanced Geothermal System by Sensitivity Analysis and Orthogonal Test at Qiabuqia Geothermal Area

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{6}EJ [1]. Located at the junction of three tectonic plates with a vast territory, China possesses abundant HDR geothermal energy. It is estimated that the HDR resource reserve within a 3~10 km depth in China’s mainland amounts to 20.9 × 10

^{6}EJ, which is larger than that of the United States [3]. If 2% of the reserve was exploited, it would be equivalent to 4400 times China’s total energy consumption in 2010 [3]. Since 2015, Chinese provincial governments have been actively investing in the exploration of HDR resources. Many potential HDR targets have been found, mainly including those in the Songliao Basin, southern Hainan, Wendeng, Datong, Zhangzhou, the Gonghe Basin, and the Subei Basin [4]. The Gonghe Basin is expected to be the first HDR pilot in China.

## 2. Methodology

#### 2.1. Governing Equation of Hydraulic-Thermal Coupled Numerical Model

_{n}is an arbitrary subdomain of the flow system; F denotes mass or heat flux; q denotes sinks and sources; and n is a normal vector on surface element dΓ

_{n}, pointing inward into V

_{n}.

_{β}is the saturation of phase β (i.e., the fraction of the pore volume occupied by phase β); ρ

_{β}is the density of phase β; and ${X}_{\beta}^{\kappa}$ is the mass fraction of component κ present in phase β.

_{R}and C

_{R}are, respectively, the density and specific heat of the rock; T is the temperature of the rock; and u

_{β}represents specific internal energy in phase β.

_{β}is the specific enthalpy in phase β.

_{β}is the Darcy velocity (volume flux) in phase β; k is the absolute permeability; k

_{rβ}is the permeability relative to phase β; and μ

_{β}denotes the dynamic coefficient of viscosity.

#### 2.2. Orthogonal Test Method

#### 2.3. Range Analysis

_{i}is the summation of the corresponding test results when the level number in each column is i; k

_{i}is the average of K

_{i}; and s is the sum of each level number in each column.

## 3. Geothermal Characteristics of the Gonghe Basin

#### 3.1. Geological Setting

^{2}. It is the third largest basin in Qinghai Province, and the Yellow River runs across the short axis of the basin (Figure 2a). The GHB is a faulted basin formed since the Cenozoic. It is located at the intersection of the East Kunlun and West Qinling orogenic belts in the Qinling-Qilian-Kunlun fold system. It is bounded by the uplift of the fault fold belt. Affected by the fault activity on the boundary of the basin, the surrounding mountain ranges have been uplifting and rising recently, and the interior of the whole basin has relatively subsided. A set of huge Cenozoic sedimentary layers are formed in the basin, mainly composed of Quaternary alluvial deposits, river-lacust deposits, and Neo-Paleogene lacustrine deposits. The base of the basin mainly consists of intrusive rocks dominated by the Triassic strata and granite diorite (zircon dating from 222 to 245 Ma). The Yanshan intrusive magmatic rocks (zircon dating from 180 to 195 Ma) are exposed on a small scale on the surface of the basin [26].

#### 3.2. Geothermal Features

^{2}, with an average of 72.58 mW/m

^{2}, which is much higher than the average heat flow in mainland China (62.53 mW/m

^{2}) [29]. It was reported from the DR3 and GR2 boreholes that the average heat flow is 119.3 mW/m

^{2}. The core record of the GR1 hole shows that the strata of the basin can be divided into the following three parts (Figure 3):

- (1)
- Part I (0~−505 m): The upper of Part I is a thin mid-late Pleistocene sand and gravel layer. Its grain gradually becomes finer downwards; the middle of Part I is mainly the lacustrine deposits of the Gonghe formation. The bottom of Part I is composed of sandy mudstone.
- (2)
- Part II (−505~−1350 m): It is composed of the Linxia formation and the Xianshuihe formation. The lithology is mainly medium-thick mudstone and medium-thick siltstone. The integrity of the mudstone is better. The sandstone particles are finer.
- (3)
- Part III (−1350~−3705 m): It is mid-late Triassic granite; the main lithology is granite and granodiorite. The radioactive heat generation rate of the granite ranges from 1.73 to 4.48 μW/m
^{3}, with an average of 3.04 μW/m^{3}, and there is no abnormal high radioactive heat generation rate.

## 4. EGS Reservoir Production Simulation Analysis

#### 4.1. Target Reservoir and Project Design

_{H}> σ

_{V}> σ

_{h}. Therefore, the stimulated EGS reservoir may be horizontal and may strip along the NE direction. Based on fracturing experience, the height and width of the created EGS reservoir are both assumed to be half its length, i.e., 300 m. Thus, the layer between the depths of 3700~4000 m is selected as the target reservoir, and the stimulated EGS reservoir geometry is assumed to be 600 m (length) × 300 m (width) × 300 m (height) (Figure 4). The natural fracture characteristics of the target reservoir are not clear; so, sensitivity studies are subsequently conducted to analyze the impact of the different fracture characteristics on productivity.

_{inj}) and the produced section (L

_{pro}) are arranged diagonally, considering the buoyancy of the high-temperature fluid (Figure 4). The local surface water (i.e., river or lake) or groundwater is used as the injected water and makeup water. It is assumed that the injected water is heated to 10 °C when it reaches the injected section of the reservoir. After surface power generation and stepped heat exchange, the circulated water is reduced to 10 °C and then pumped back into the injection well. In order to study the variation of the heat transfer effect of the EGS during a long operation, the project lifetime is set to 50 years.

#### 4.2. Power System

#### 4.3. Numerical Procedure

#### 4.4. Model Parameters and Single-Factor Sensitivity Scheme

^{−16}m

^{2}~1 × 10

^{−17}m

^{2}). After stimulation, the fracture permeability is generally increased by more than 1000 times [32]. In addition, through simulations, we found that when the fracture permeability was set as 1 × 10

^{−14}m

^{2}, the flow impedance of the reservoir still increased significantly (see Section 5.1). Therefore, the fracture permeability is assumed to be 1 × 10

^{−13}m

^{2}as the base value. Through a long time of chemical stimulation, the fractures will be subjected to continuous corrosion, and the fracture permeability also increases. In order to evaluate whether excessive fracture permeability has a positive impact on productivity, we selected 1 × 10

^{−11}m

^{2}for the simulation analysis.

_{x}/k

_{z}= 10 denotes that the fracture permeability in the z (vertical) direction is 10 times higher than that in the x (horizontal) direction.

^{−17}m

^{2}. However, some lithology may contain abundant micro-fractures or large dissolved pores, which may lead to higher permeability. Water would also flow through these pore spaces to extract heat [37]. Therefore, we studied the heat transfer effect under the condition of matrix permeability of 1 × 10

^{−14}m

^{2}.

#### 4.5. Initial and Boundary Conditions

#### 4.6. Simulation Results of Single-Factor Sensitivity Analysis

#### 4.6.1. Maximum Injection Rate under Base Case Condition

_{inj}) exceeds the reservoir minimum principal stress (σ

_{h}), the created fracture will dilate, giving rise to second reservoir growth and water losses; so, P

_{inj}must be lower than σ

_{h}. According to Ref. [33], the σ

_{h}at a depth of 3700 m in the Qiabuqia area is about 66 MPa. Thus, the maximum injection rate can be determined by the pressure criterion:

_{inj}< 66 MPa,

_{pro}> 105.36 °C,

_{pro}is the production water temperature.

_{pro}and P

_{inj}at different injection rates (q

_{inj}) over the 50 years. When q

_{inj}was 30 kg/s, the P

_{inj}slightly increased from 37.92 MPa up to 38.38 MPa after 50 years of production. Meanwhile, T

_{pro}decreased from 225 °C to a final 104 °C (down 53.8%). Within 50 years, the injection rate of 30 kg/s meets the pressure criterion and almost meets the temperature criterion. The injection pressure experienced three stages: slight rise, rapid rise, and slight rise. T

_{pro}has gone through three stages: stable, rapid decline, and slight decline. When the injection rate became large, the water was pumped out before it fully exchanged heat with the reservoir, resulting in a rapid drop in the production temperature. When the heat-supplying reservoir from the wall rock is approximately equal to that taken away by water circulation, the production temperature tends to be stable again. From the 30th year to the 50th year, T

_{pro}decreased by about 10 °C, while from the 45th year to the 50th year, T

_{pro}decreased by only about 1 °C.

_{inj}is 80 kg/s, P

_{inj}increases from the initial 38.62 MPa to 65.89 MPa in the 50th year. T

_{pro}decreased from 225 °C to the final 31 °C. Within 50 years, the injection rate of 80 kg/s meets the pressure criterion but does not meet the temperature criterion. To ensure continuous power generation for the EGS, the maximum q

_{inj}should be set to 30 kg/s.

#### 4.6.2. Production Temperature

_{pro}under different parameters over the 50 years. The curve of T

_{pro}could be divided into two stages: the stable period and the decline period. In the early stage of the EGS operation, the reservoir and wall rock contain sufficient heat; so, T

_{pro}can be equal to the reservoir temperature. This stage belongs to the stable period. As cold water is continuously injected into the reservoir, the reservoir heat is continuously extracted. T

_{pro}would enter decline period at some point. Among the seven selected parameters, P

_{f}, α, and q

_{inj}have the greatest influence on T

_{pro}. The second is the S

_{f}. While P

_{r}, λ

_{r}, and L

_{inj}all have a slight effect on T

_{pro}. The curve patterns of T

_{pro}are in accordance with previous studies of Refs. [4,8,35].

#### 4.6.3. Power Generation

_{e}, for the binary cycle with the following equation [38]:

_{e}, m

_{w}, T, h, s, P, and V denote conversion efficiency, production rate, temperature, specific enthalpy, entropy, pressure, and specific volume, respectively. The subscripts w, r, R, P, b, c, g, l, in, sf, and k denote wellhead, reference, reservoir, pinch point, boiling, condenser, gas, liquid, inlet, secondary fluid, and Kelvin, respectively. More detailed descriptions of Equation (11) can be found in Ref. [40].

_{e}under different parameters over the 50 years. The most influential factors are P

_{f}, α, and q

_{inj}. Comparing Figure 7 and Figure 8, it can be seen that except for q

_{inj}, the variation trends of W

_{e}under the other six factors are the same as the trends of T

_{pro}. Although T

_{pro}declined much more slowly when q

_{inj}decreased from 30 kg/s to 20 kg/s, the early W

_{e}at 20 kg/s is lower than that at 30 kg/s due to the flow rate limitation. In the base case condition, the W

_{e}in 50 years decreases from 2.53 MW to 0.16 MW, and the stable period is about 10 years. When q

_{inj}is 20 kg/s, the W

_{e}in 50 years is 1.69 MW~0.91 MW, and the stable period is about 13 years.

_{r}has the least influence on W

_{e}, followed by L

_{inj}and S

_{f}. If the lifetime of the EGS project is 30 years, P

_{r}also has little influence on W

_{e}, and the influence of S

_{f}should be considered. It should be noted that the q

_{inj}is set to be constant in the numerical simulations of case L

_{inj}and case S

_{f}. However, in a practical project, the longer the L

_{inj}and the smaller the S

_{f}, the more conducive they are to the increase of q

_{inj}.

#### 4.6.4. Bottom-Hole Pressure of Injection Well

_{inj}under different parameters over the 50 years. It illustrates that P

_{r}, S

_{f}, and λ

_{r}have the least influence on P

_{inj}. However, α, q

_{inj}, and L

_{inj}have great influence on P

_{inj}. P

_{f}has the greatest effect.

_{inj}slightly increased from 37.92 MPa up to 38.38 MPa after the 50-year production, increasing by 0.46 MPa (1.2%). When α become 10, the P

_{inj}increased from 37.92 MPa to 41.70 MPa over the 50 years, increasing by 3.78 MPa (9.1%). When q

_{inj}was 20kg/s, P

_{inj}increased from 32.78 MPa to 34.70 MPa, with an increase of 1.92 MPa (5.9%). P

_{inj}increased by 0.49 MPa (1.6%), from 30.70 MPa to 31.19MPa, over the 50 years when P

_{f}increased by 100 times. Among all the parameters, P

_{inj}increased the most when α become 10 due to a great decrease in vertical permeability compared to the base case. Under the same q

_{inj}, the longer the L

_{inj}, the lower the P

_{inj}. P

_{inj}among all the cases met the pressure criterion.

#### 4.6.5. Reservoir Injectivity

_{inj}, reflects the stimulation effect of the reservoir permeability. An ideal EGS typically requires an I

_{inj}greater than 10 kg/s/MPa. The higher the I

_{inj}, the easier it is for water to flow from the injection well to the pumping well at the same pressure difference. It reflects the average flow impedance of the reservoir. I

_{inj}is calculated by [1]:

_{inj}= q

_{inj}/(P

_{inj}− P

_{pro}),

_{inj}under the different parameters over the 50 years. P

_{f}, L

_{inj}, and α are the most important factors. In the base case, I

_{inj}ranged from 9.0 to 4.2 kg/s/MPa over the 50 years. In the P

_{f}case, I

_{inj}was 1028.2~584.7 kg/s/MPa over the 50 years, which was about 100 times that of the other cases. When the injection length doubled, I

_{inj}was 19.7~7.7 kg/s/MPa, which also nearly doubled. In the α case, I

_{inj}, 7.6–2.9 kg/s/MPa, was lower than that of the base case.

_{f}is directly related to S

_{f}. Assuming that the fracture is flat and smooth, a P

_{f}of 1 × 10

^{−11}m

^{2}is equivalent to the fracture aperture of 0.05 mm [41]. At present, a fracture aperture of this magnitude mainly depends on the self-supporting of the shear fracture after stimulation. Additionally, in this model, q

_{inj}has little influence on I

_{inj}. The main reason is that the P

_{f}of 1 × 10

^{−13}m

^{2}can still smoothly accommodate a 20 kg/s injection flow. If the P

_{f}decreases further, an excess q

_{inj}can cause a rapid rise in P

_{inj}, resulting in a significant decrease in I

_{inj}. Basically, I

_{inj}is mainly dependent on the overall permeability of the stimulated reservoir; so, λ

_{r}and P

_{r}have little influence on I

_{inj}.

#### 4.6.6. Pump Power

_{p}, mainly includes the energy consumption of the injection pump and that of the suction pump [1,8]. W

_{p}mainly refers to the electric energy consumed to drive water flow through the reservoir. It does not include the energy consumed by injecting water from the surface into the reservoir and pumping water from the reservoir to the surface. If the energy loss due to duct friction and water internal friction is neglected, the pump efficiency η

_{p}is 80%, and the internal energy consumption W

_{p}is Equation (13), based on [8]:

_{p}under different parameters over the 50 years. P

_{f}is the most important factor, followed by α, q

_{inj}, and L

_{inj}. Other factors have a slight impact on W

_{p}. Among them, α causes W

_{p}to be higher than that of the base case, while P

_{f}, q

_{inj}, and L

_{inj}make W

_{p}lower. In the base case, W

_{p}is 0.14~0.30 MW over the 50 years. In the α case, W

_{p}ranges from 0.16 MW to 0.43MW. In the P

_{f}case, W

_{p}is 0.001~0.002 MW. When P

_{f}increases, the reservoir has little resistance to water flow. Water can flow through the reservoir only driven by gravity; so, W

_{p}is extremely low.

#### 4.6.7. Coefficient of Performance

_{e}/W

_{p},

_{f}is the most important factor affecting η, followed by q

_{inj}, L

_{inj}, and α. The other factors are less important.

_{f}case, η is 570.19~0, which decreases the fastest mainly because W

_{e}declines too fast. Over the 50 years, the η of the α case was lower than that of the other cases because its W

_{e}declined the most, while W

_{p}increased the most. The decrease of q

_{inj}can improve system η, but the curve trend of η is almost unchanged. In the ground source heat pump industry, η is usually expected to be greater than 4. In this simulation, only the case of q

_{inj}can meet η larger than 4 during the whole 50 years. The curve patterns of η are in accordance with the previous studies of Refs. [4,8,35].

#### 4.7. Discussions of Single-Factor Sensitivity Analysis

#### 4.7.1. Effect of Reservoir Factors on Production Performance

_{f}), fracture permeability (P

_{f}), fracture permeability anisotropy (α), matrix permeability (P

_{r}), and heat conductivity (λ

_{r}).

_{f}reflects the development degree of the reservoir fractures. The smaller the S

_{f}, the more developed the fractures. More seepage channels can be selected for water flow. When the q

_{inj}is constant and S

_{f}increases from 3 m to 50 m, the flux that each fracture needs to bear increases. Thus, increasing S

_{f}leads to a drop in the produced water temperature and power generation. The larger the S

_{f}is, the more quickly the produced water temperature and power generation decrease, and their stable periods are both shortened. S

_{f}has little effect on the other four indicators. Therefore, the stratum with dense natural fractures should be selected as the target EGS reservoir in practical engineering.

_{f}on each indicator is very large. The greater the P

_{f}, the easier it is for water to pass through the reservoir. According to Darcy’s law, when the hydraulic gradient is constant, the water seepage velocity is proportional to the permeability of the reservoir. Thus, when P

_{f}is 100 times greater than that of the base case, the water velocity in the reservoir also increases significantly. The water circulation process would be completed quickly before the cold water absorbed enough heat from the reservoir. The produced water temperature and power generation dropped quickly compared to the base case, and the pump consumption and injectivity increased rapidly. Therefore, it is not advisable to acidify the EGS reservoir too much to widen the apertures of natural fractures. This is likely to lead to a rapid decline in net power generation.

_{x}/k

_{z}= 10) means that the vertical permeability is 10 times lower than that of the base case. When water flows through such fractured reservoirs, it will preferentially reach the production well in the horizontal direction. Thus, the water flow in the vertical direction is greatly restricted. Therefore, the water flow path and the heat exchange area are also smaller than that of the isotropic reservoir. Meanwhile, the water flow through the horizontal direction is greater than that of the base case. In general, the produced water temperature and power generation of an anisotropic reservoir are much lower than that of the base case. In addition, fracture permeability anisotropy increases pump energy consumption greatly.

_{r}, the larger the pores, and therefore the less heat storage per unit volume of rock. When P

_{r}increased by 100 times, the heat storage in the matrix also greatly decreased. In the dual-porous medium model, the matrix only exchanges heat with the fractures, and there is no heat exchange between the matrixes. In the early stage of the water circulation, the heat in the matrix is continuously transferred to the water flow, and the produced water temperature during this period is almost the same as that of the base case. With the continuous operation of the project, the matrix heat becomes less and less. However, the heat recharge of the wall rock to the reservoir is limited. Therefore, the produced water temperature and power generation both drop faster than that of the base case in the later stage of the project (about 24th year). P

_{r}has little effect on the other four indicators.

_{r}, the faster the heat conduction from the far field to the reservoir and from the reservoir matrix to the water flow. When λ

_{r}of the rock becomes larger, the stable period of the power generation also becomes longer, indicating that the heat of the reservoir rock is transferred to the fracture water flow more than that of the base case. When entering the descending period, the power generation drops faster than that of the base case due to the excessive extraction of heat from the rock in the early stage. At this time, the temperature difference between the wall rock and the reservoir is not very large; so, the wall rock supplies less heat to the reservoir. As the water continues to circulate, the reservoir with a large λ

_{r}will cool down faster. The heat transfer from the wall rock to the reservoir will increase, and the drop of power generation will begin to slow down. Therefore, the power generation with a large λ

_{r}is slightly higher than that of the base case in the 50th year. Therefore, rock heat conductivity may not be used as an indicator in selecting a target reservoir.

#### 4.7.2. Effect of Operation Factors on Production Performance

_{inj}) and injection rate (q

_{inj}).

_{inj}means the flow rate of a single fracture near the injection well decreases, and the water temperature will become higher. Therefore, the power generation after increasing the length of L

_{inj}is a little higher than that of the base case at first. When entering the descending period, because the heat near the injection well is extracted prematurely, the power generation drops faster than that of the base case. It makes the amount of heat supplied to the reservoir by the wall rock higher. The power generation of the extended L

_{inj}is a little larger than that of the base case in the 50th year. However, L

_{inj}has a great influence on the pump power and the coefficient of performance. The longer the L

_{inj}, the lower the pump power and the higher the coefficient of performance. Therefore, in practice, the L

_{inj}should be as long as possible.

_{inj}, the longer the heat exchange time between the water flow and the reservoir, and therefore the longer the stable period of power generation. The stable periods of power generation under q

_{inj}= 20 kg/s and q

_{inj}= 30 kg/s are 18 years and 10 years, respectively. Moreover, the smaller the q

_{inj}, the slower the drop of power generation during the descending period. q

_{inj}has a great influence on the pump power and the coefficient of performance. However, the smaller the q

_{inj}, the lower the pump power and the higher the coefficient of performance. Therefore, in practical engineering, the most appropriate q

_{inj}should be determined by comprehensive simulations.

#### 4.7.3. Main Factors Affecting Production Performance

_{sele}and V

_{base}, respectively, denote the 50-year average of each index under the selected case and the base case. Figure 13 shows the sensitivity analysis results of the different factors on each index.

_{pro}, the order of influence degree is as follows: q

_{inj}> P

_{f}> α > S

_{f}> P

_{r}> L

_{inj}> λ

_{r}. In the long run, the decrease of q

_{inj}is beneficial to the increase of T

_{pro}. The increase of S

_{f}, P

_{f}, α, and P

_{r}will result in the decrease of T

_{pro}. L

_{inj}andλ

_{r}have little effect on T

_{pro}.

_{e}, the order of influence degree is as follows: P

_{f}> α > P

_{r}> q

_{inj}> S

_{f}> L

_{inj}> λ

_{r}. In the long run, the increase of P

_{f}and α will obviously reduce W

_{e}. Although a higher temperature may be obtained when the injection flow rate decreases, the average annual power generation still decreases.

_{inj}, the order of influence degree is as follows: P

_{f}> α > q

_{inj}> L

_{inj}> λ

_{r}>P

_{r}> S

_{f}. In the long run, the increase of P

_{f}, q

_{inj}, and L

_{inj}will reduce P

_{inj}. The increase of α will obviously increase P

_{inj}.

_{inj}, the order of influence degree is as follows: P

_{f}> L

_{inj}> α > q

_{inj}> λ

_{r}> P

_{r}> S

_{f}. In the long run, the increase of P

_{f}and L

_{inj}will significantly increase I

_{inj}. The increase of α will decrease I

_{inj}.

_{p}, the order of influence degree is as follows: P

_{f}> q

_{inj}> α > L

_{inj}> λ

_{r}> P

_{r}> S

_{f}. In the long run, the increase of P

_{f}, q

_{inj}, and L

_{inj}can significantly reduce W

_{p}. The increase of α will increase W

_{p}.

_{f}> q

_{inj}> L

_{inj}> α >P

_{r}> S

_{f}> λ

_{r}. In the long run, the increase of P

_{f}, q

_{inj}, and L

_{inj}can significantly increase η. The increase of α will reduce η.

_{e}and η together determine the net generating capacity. It can be seen that only α acts in the same direction on the two indexes, while the other three parameters (P

_{f}, q

_{inj}, and L

_{inj}) act in opposite directions on them. Therefore, multi-factor combination analysis is needed to achieve the optimal combination of W

_{e}and η.

## 5. Multi-Factor Combination Analysis

#### 5.1. Orthogonal Test Scheme

_{f}is 1 × 10

^{−14}m

^{2}, the bottom-hole pressure increased rapidly from 44.1 MPa to 80.24 MPa in 6 days with the injection rate of 20 kg/s. Thus, the minimum P

_{f}was set to 5 × 10

^{−14}m

^{2}. L

_{inj}was set from 30 m to the reservoir height of 300 m. The maximum injection rate was set to 110 kg/s, exceeding the commercial flow rate of 100 kg/s. The maximum level of anisotropy was set as 1000 to consider the influence of a strong anisotropy geology condition. These four levels cover almost all possible scenarios. The orthogonal test scheme is shown in Table 7.

#### 5.2. Orthogonal Test Results

_{e}may be different in different situations. Even if both scenarios produce the same amount of electricity in the 50th year, they may produce very different amounts over the entire 50 years. So, the 50-year average of each index is needed. In addition, the initial values of some indexes, such as η and I

_{inj}, may differ greatly from the final values in the 50th year. The project may be no longer operational before 50 years. Only using the 50-year average cannot accurately represent the influence of the test. Therefore, the average annual value is mainly used for comparison, and the value at the end of the simulation is used for auxiliary judgment.

_{e}ranges from −3.47 MW to 1.46 MW; η ranges from −439.38 to 420.36; T

_{pro}ranges from 49.37 °C to 223.83 °C; I

_{inj}ranges from 1.17 to 892.88; P

_{inj}ranges from 30.61 to 68.63; and W

_{p}ranges from 0.0019 MW to 3.77 MW. It can be seen that the different combinations have great influence on the heat transfer performance, and it is difficult to meet all six indexes at the same time. For example, although the W

_{e}of test 1 is good, its η and I

_{inj}are low. For W

_{e}, the better combinations include test 7, test 1, and test 12. For η, the better combinations include test 7 and test 14. Their common characteristic is an injection rate of 20 kg/s. All six indexes of test 7 are good, indicating that the level of all the factors in scheme 7 is better combined at this time. The negative value of W

_{e}in Table 8 is because the selected organic working medium isobutene cannot generate power when its temperature is lower than 105.36 °C, as mentioned in Section 4.6.1. In the practical engineering, W

_{e}and η cannot be negative. However, in order to directly reflect the influence of each factor, their theoretical negative values are adopted this time. In addition, for test 6, the injection rate of 110 kg/s was too high for the fracture permeability of 1 × 10

^{−13}m

^{2}, resulting in a rapid increase of P

_{inj}; so, test 6 has no data. Similarly, test 3 and test 8 only run to 15.8 years and 25.2 years, respectively, due to the excessive pressure growth.

#### 5.3. Discussions of Multi-Factor Combination Analysis

#### 5.3.1. Effect of Main Factors on Production Performance

_{e}), pump power (W

_{p}), and the coefficient of performance (η). Injection pressure is allowed to grow as long as it is not so high as to exceed the strength capacity of the pump and pipeline. In order to further explore which factor plays a dominant role in the multi-parameter combination, we sorted out the results in Table 8 according to W

_{e}, W

_{p}, and η (Figure 14).

_{e}varies greatly even though it is for the same level. This means that even when the fracture permeability is selected to the optimal value, the resulting W

_{e}may be very low if the other parameters do not match the fracture permeability. The variation range of η at the same level may be very different, indicating that a different fracture permeability may have a great impact on η. The W

_{p}of the other three levels, except that of level 1, does not change much. Considering the three indicators, the best cases at levels 1~4 are G1, G3, G4, and G2, respectively. From level 1 to level 4, W

_{e}, η, and W

_{p}do not increase or decrease as the fracture permeability increases, indicating that it is not necessary to increase fracture permeability too much in the actual reservoir stimulation. Depending on other parameters, even small fracture permeability can generate significant W

_{e}(i.e., G1 at level 1 and G3 at level 2). However, when the fracture permeability is low (level 1), W

_{p}is higher in most cases than that at the other levels, and overall η is higher than that at the other levels. When fracture permeability is large (level 4), W

_{e}is also small. Therefore, the overall fracture permeability should not be too low or too high.

_{e}varies greatly even though it is for the same level, indicating that fracture permeability anisotropy does not dominate. If the values of the other factors do not match, productivity will also be affected. With the increase in fracture permeability anisotropy (from level 1 to level 4), there is no obvious increase or decrease of each indicator. Even if the anisotropy is very large, it is possible to obtain larger W

_{e}as long as the other parameters are well matched. Considering the three indicators, the best cases at level 1~4 are G1, G4, G2, and G3, respectively. It also shows that even though the actual fracture permeability anisotropy varies greatly, we only need to find other parameters matching it. It is not necessary to stimulate the reservoir permeability to be isotropic.

_{e}varies greatly even though it is for the same level. The injected section length does not dominate. The fluctuation of the three indicators of level 1 is relatively small. This means that when the injected section length is small, the other parameters have difficulty playing a large role. At this time, if the injected section length is not increased, the EGS production performance cannot be improved. The three indicators at level 3 and level 4 fluctuate greatly, indicating more possibility of combination with the other factors. Therefore, in practical engineering, the injected section length should be larger. Ref. [42] shows that a larger L

_{inj}enhances heat extraction when L

_{inj}is less than the reservoir height. The regularity of our results is consistent with Ref. [42].

_{e}and η obviously decrease as injection rate increases (from level 1 to level 4), regardless of whether the other factors are matched. The lower the injection rate, the lower the W

_{p}. Moreover, as the injection rate increases, W

_{e}and η drop rapidly to negative values. It indicates that the produced water temperature drops too fast with the increase in the injection rate. All three indicators of level 1 are the best of the four levels. Thus, the injection rate determines in all factors, and the smaller the better. Therefore, in practical engineering, special attention should be paid to the value of the injection rate, which should not be too large.

#### 5.3.2. Order of Main Factors and Optimal Combination

_{pro}, the order of influence degree is as follows: q

_{inj}> P

_{f}> α > L

_{inj}. This result is consistent with that of the single-factor sensitivity analysis.

_{e}, the order of influence degree is as follows: q

_{inj}> P

_{f}> α > L

_{inj}. In comparison with the result of the single-factor sensitivity analysis, only the order of q

_{inj}and P

_{f}has changed.

_{inj}, the order of influence degree is as follows: q

_{inj}> P

_{f}> α > L

_{inj}. In comparison with the result of the single-factor sensitivity analysis, only the order of q

_{inj}and P

_{f}has changed.

_{inj}, the order of influence degree is as follows: L

_{inj}> P

_{f}> α > q

_{inj}. In comparison with the result of the single-factor sensitivity analysis, only the order of L

_{inj}and P

_{f}has changed.

_{p}, the order of influence degree is as follows: P

_{f}> q

_{inj}>α > L

_{inj}. This result is consistent with that of the single-factor sensitivity analysis.

_{f}> q

_{inj}> L

_{inj}> α. This result is consistent with that of the single-factor sensitivity analysis.

_{e}and η. According to Table 9, the better level combination of these two indicators is A

_{2}B

_{3}C

_{1}D

_{1}and A

_{2}B

_{2}C

_{3}D

_{1}, respectively. From the orthogonal results listed in Table 8, the optimal combination is test 7 (A

_{2}B

_{3}C

_{4}D

_{1}). The comparison of these three combinations and the results are shown in Figure 15. The W

_{e}of A

_{2}B

_{3}C

_{1}D

_{1}, A

_{2}B

_{2}C

_{3}D

_{1}, and A

_{2}B

_{3}C

_{4}D

_{1}over the 50 years are 1.69 MW~1.04 MW, 1.69 MW~0.68 MW, and 1.69 MW~1.11 MW. Between 0 and 42.3 years, the W

_{e}of A

_{2}B

_{3}C

_{1}D

_{1}was consistently higher than that of A

_{2}B

_{3}C

_{4}D

_{1}. The η of A

_{2}B

_{3}C

_{1}D

_{1}, A

_{2}B

_{2}C

_{3}D

_{1}, and A

_{2}B

_{3}C

_{4}D

_{1}over the 50 years are 12.53~1.70, 14.59~12.70, and 120.26~35.26. Although the W

_{e}of A

_{2}B

_{3}C

_{1}D

_{1}is overall higher than that of A

_{2}B

_{3}C

_{4}D

_{1}, the η of A

_{2}B

_{3}C

_{1}D

_{1}is much lower than that of A

_{2}B

_{3}C

_{4}D

_{1}. Thus, considering W

_{e}and η comprehensively, the optimal scheme is A

_{2}B

_{3}C

_{4}D

_{1}. Based on the above results, this indicates that the optimal EGS reservoir should have moderate fracture permeability and moderate fracture permeability anisotropy; the injected section length should be large; and the injection rate should be moderate.

#### 5.3.3. Optimal Scheme Considering Fracture Permeability Anisotropy

_{e}and T

_{pro}increase first and then decrease, while P

_{inj}and W

_{p}keep growing. So, η decreases downwards. All the cases in Table 10 comply with the temperature and pressure criteria. If permeability anisotropy can be controlled during reservoir stimulation, the optimal strategy is still test A

_{2}B

_{3}C

_{4}D

_{1}(α = 100). If permeability anisotropy is not controlled, the 50-year average W

_{e}, η, and I

_{inj}with A

_{2}C

_{4}D

_{1}are likely to be 1.23 MW~1.46 MW, 11.42~67.50, and 14.28~20.92, respectively. In addition, it can be seen that the 6 indicators of these 4 tests in Table 10 are all good and are all better than that of the 15 tests, except test 7 in Table 8. Therefore, this proves that the optimization combinatorial scheme of EGS can be achieved through the orthogonal test and range analysis.

#### 5.3.4. Optimal Scheme Considering Injection Rate

_{e}− W

_{p}) under different injection rates based on test A

_{2}B

_{3}C

_{4}D

_{1}, as shown in Figure 16. The results show that with the decrease in the injection rate, the stable period of net power generation gradually lengthens. The decreasing rate of the net power generation during the descending period also slows down. However, in the initial period, the net power generation is still higher when the injection rate is higher. Thus, the net power generation at 30 kg/s is greater than that at 20 kg/s up to 34.2 years. The net power generation at 20 kg/s was consistently greater than that at 15 kg/s for the entire 50 years. The intersection of the two curves occurred 50 years later. The net power generation at 10 kg/s is almost constant over a 50-year period. Therefore, the choice of optimal injection rate also depends on the life of the project. The injection rate should not be excessive if the EGS project life is required to be longer.

#### 5.3.5. Well Layout Mode

^{8}m

^{3}. Sanyal and Butler [43] proposed that the stimulated volume should exceed 1 × 10

^{8}m

^{3}for the EGS. The EGS reservoir volume needs to be increased further. If the created EGS reservoir is too long, a large flow resistance needs to be overcome in order to drive water through the reservoir. Considering the symmetry of hydraulic fracturing, the triplet-well straight-line mode with one injector and two producers is recommended according to case A

_{2}B

_{3}C

_{4}D

_{1}(Figure 17). Well spacing is 600 m, and the total EGS reservoir volume reaches 1.08 × 10

^{8}m

^{3}. During reservoir stimulation, fractures mostly extend parallel to the direction of maximum principal stress. Thus, the direction of the well connection line is set in the same direction as the maximum principal stress in the study area (N51°). The injection rate is 40 kg/s and the flow rate from each production well is 20 kg/s. In actual engineering, more fluid may need to be injected to compensate for the fluid loss. The 50-year average of W

_{e}, η, and I

_{inj}with this triplet-well mode can reach 2.46 MW~2.92 MW, 11.42~67.50, and 14.28~20.92, respectively.

#### 5.3.6. Optimal Scheme Considering Injection Water Temperature

_{2}B

_{3}C

_{4}D

_{1}.

_{pro}and W

_{e}(Figure 18a). During the decline stage, a high injection temperature causes a slow drop of T

_{pro}and W

_{e}. Increasing the injection temperature will definitely increase T

_{pro}and W

_{e}; however, the increase in the injection temperature also requires extra energy. The appropriate injection temperature should be determined in accordance with the water source condition and the engineering requirement.

_{inj}and W

_{p}both decrease. P

_{inj}is the function of (μ/ρ), which is also the function of temperature. As heat production continues, the reservoir temperature continually declines; (μ/ρ) significantly increases when the temperature declines (Figure 18d). The higher injection temperature causes the production temperature to drop more slowly. Thus, P

_{inj}and W

_{p}both increase slowly when the injection temperature is higher (Figure 18b,c). Finally, I

_{inj}and η are both improved according to Equations (12) and (14).

#### 5.3.7. Space Variation of Reservoir Temperature Field

_{2}B

_{3}C

_{4}D

_{1}with an injection temperature of 70 °C. As can be seen from the profile, with the cold water gradually injected into the reservoir, the cold front continues to move towards the pumping well. Generally, the density of the injected cold water is large; so, its downward speed is high under the gravity drive. Because the water injection section and pumping section are located at the same depth in this study, the vertical diffusion velocity of the cold halo is nearly the same as the horizontal diffusion velocity (Figure 19a–e). Thus, the cold front almost uniformly moves horizontally from the injection well to the pumping well, and the heat extracted from the whole reservoir is sufficient. It can be seen from Figure 19f that after 50 years of operation, the lateral influence range of thermal extraction on wall rock is about 99 m on each side and that of the injection well and pumping well sides is 148 m and 24 m, respectively. Cooling does not affect the boundary of the model in this simulation, indicating that the size and boundary conditions of this model are reasonable.

## 6. Conclusions

- (1)
- The Gonghe Basin possess a good geothermal structure. The molten layer in the depth interval of 15~35 km may be the heat source. The widely distributed huge-thick high-temperature granite formation is an ideal target reservoir for HDR. The cap rocks are mainly mudstone and sandstone, which have the characteristics of low heat conductivity. The complex geological structure has produced many deep large faults, which can serve as heat conduction channels. Therefore, there has formed a relatively shallow high-temperature HDR reservoir in the Gonghe Basin.
- (2)
- For single-factor sensitivity analysis, when q
_{inj}was constant, the increase of S_{f}had a slight influence on T_{pro}and W_{e}. P_{f}had the greatest influence on the production performance among all the factors. For the condition with α = 10, W_{e}declined the fastest, while W_{p}rose the fastest, resulting in the lowest η. The increase of P_{r}had a slight influence on T_{pro}and W_{e}in the later stage of the project. λ_{r}was the least influential of all the parameters. Increasing L_{inj}had little influence on T_{pro}and W_{e}but had great influence on P_{inj}and W_{p}. When q_{inj}decreased, the early W_{e}decreased due to the flow rate limitation although T_{pro}declined much more slowly. Meanwhile, W_{p}decreased and η increased significantly. Therefore, the biggest influence factor on the W_{e}value was the overall permeability of the fractured reservoir. For η, P_{f}was the most important factor, followed by q_{inj}, L_{inj}, and α. - (3)
- The four factors of fracture permeability, fracture permeability anisotropy, injected section length, and injection rate had the greatest influence on the EGS production. For the multi-factor sensitivity analysis, the order of influence degree on W
_{e}was q_{inj}> P_{f}> α > L_{inj}. The order of influence degree on η was P_{f}> q_{inj}> L_{inj}> α. On the whole, the rank results of the orthogonal test are almost the same as those of single-factor sensitivity. - (4)
- Different factor combinations have great influence on the heat transfer performance. The multi-factor and multi-level combination optimization is needed and the optimization scheme of the EGS can be achieved through the orthogonal test and range analysis.
- (5)
- For reservoir stimulation, the stratum with dense natural fractures should be selected as the target EGS reservoir. It is not advisable to acidify the EGS reservoir too much to widen the apertures of natural fractures. This is likely to lead to a rapid decline in net power generation. Fracture permeability anisotropy will increase pump energy consumption, but this adverse effect can be greatly reduced if the other parameters are well matched. Matrix permeability and heat conductivity may not be used as an indicator in selecting a target reservoir.
- (6)
- For project operation, the injected section length should be as long as possible. The injection rate plays a major role in all factors. Special attention should be paid to the value of the injection rate, which should not be too large. The appropriate injection temperature should be determined in accordance with the water source condition and the engineering requirement. If a commercial rate (100 kg/s) is to be obtained, the permeability of the reservoir fracture network needs to be stimulated to be higher. Meanwhile, in order to ensure that the production temperature is both high and stable, it is necessary to further increase the volume of the EGS reservoir.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

C_{R} | Rock specific heat, J/(kg·K) | h_{β} | Specific enthalpy in phase β, J/kg |

F | Mass or heat flux, kg/m^{2} or W/m^{2} | t | Time, s |

I_{inj} | Injectivity, kg/s/MPa | u_{β} | Specific internal energy in phase β, J/kg |

L_{inj} | Injected section length, m | α | Fracture permeability anisotropy |

M | Mass or energy per volume, kg/m^{3} or J/m^{3} | Φ | Porosity |

P_{f} | Fracture permeability, m^{2} | φ | Sensitivity |

P_{inj} | Bottom-hole pressure of injection well, MPa | κ | Mass components |

P_{r} | Matrix permeability, m^{2} | η | Coefficient of performance |

q_{inj} | Injection rate, kg/s | η_{e} | Conversion efficiency |

R | Range | η_{p} | Pump efficiency |

S_{f} | Fracture spacing, m | λ_{r} | Heat conductivity, W/(m·K) |

S_{β} | Saturation of phase β | ρ_{R} | Rock density, kg/m^{3} |

T | Temperature, °C | ρ_{β} | Density of phase β, kg/m^{3} |

T_{pro} | Production water temperature, °C | v_{β} | Darcy velocity in phase β, m/s |

V_{n} | Subdomain of the flow system | μ_{β} | Dynamic coefficient of viscosity, Pa·s |

W_{e} | Power generation, MW | σ_{H} | Maximum horizontal stress, MPa |

W_{p} | Pump power, MW | σ_{V} | Vertical principal stress, MPa |

z | Depth, m | σ_{h} | Minimum horizontal stress, MPa |

## References

- Tester, J.; Livesay, B.; Anderson, B.; Moore, M.; Bathchelor, A.; Nichols, K.; Blackwell, D.; Petty, S.; DiPippo, D.; Toksoz, M.; et al. The Future of Geothermal Energy: Impact of Enhanced Geothermal Systems (EGS) on the United States in the 21st Century; An Assessment by an MIT-Led Interdisciplinary Panel; Massachusetts Institute of Technology: Cambridge, MA, USA, 2006. [Google Scholar]
- Li, S.; Wang, S.; Tang, H. Stimulation mechanism and design of enhanced geothermal systems: A comprehensive review. Renew. Sustain. Energy Rev.
**2022**, 155, 111914. [Google Scholar] [CrossRef] - Wang, J.; Hu, S.; Pang, Z.; He, L.; Zhao, P.; Zhu, C.; Rao, S.; Tang, X.; Kong, Y.; Luo, L.; et al. Estimate of geothermal resources potential for hot dry rock in the continental area of China. Sci. Technol. Rev.
**2012**, 30, 25–31. (In Chinese) [Google Scholar] - Zhang, Y.; Zhang, Y.J.; Zhou, L.; Lei, Z.H.; Guo, L.L.; Zhou, J. Reservoir stimulation design and evaluation of heat exploitation of a two-horizontal-well enhanced geothermal system (EGS) in the Zhacang geothermal field, Northwest China. Renew. Energy
**2022**, 183, 330–350. [Google Scholar] [CrossRef] - Hofmann, H.; Babadagli, T.; Zimmermann, G. Hot water generation for oil sands processing from enhanced geothermal systems: Process simulation for different hydraulic fracturing scenarios. Appl. Energy
**2016**, 113, 524–547. [Google Scholar] [CrossRef] - Barenblatt, G.; Zheltov, I.; Kochina, I. Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks. J. Appl. Math. Mech.
**1960**, 24, 1286–1303. [Google Scholar] [CrossRef] - Warren, J.E.; Root, J.P. The Behavior of Naturally Fractured Reservoirs. Soc. Pet. Eng. J.
**1963**, 228, 245–255. [Google Scholar] [CrossRef] [Green Version] - Zeng, Y.; Su, C.Z.; Wu, N.Y. Numerical simulation of heat production potential from hot dry rock by water circulating through two horizontal wells at Desert Peak geothermal field. Energy
**2013**, 10, 92–107. [Google Scholar] [CrossRef] - Suzuki, A.; Fomin, S.A.; Chugunov, V.A.; Niibori, Y.; Hashida, T. Fractional diffusion modeling of heat transfer in porous and fractured media. Int. J. Heat Mass Transf.
**2016**, 103, 611–618. [Google Scholar] [CrossRef] - Gong, F.; Guo, T.; Sun, W.; Li, Z.; Yang, B.; Chen, Y.; Qu, Z. Evaluation of geothermal energy extraction in Enhanced Geothermal System (EGS) with multiple fracturing horizontal wells (MFHW). Renew. Energy
**2020**, 151, 1339–1351. [Google Scholar] [CrossRef] - Zhou, D.J.; Tatomir, A.; Niemi, A.; Tang, C.F.; Sauter, M. Study on the influence of randomly distributed fracture aperture in a fracture network on heat production from an enhanced geothermal system (EGS). Energy
**2022**, 250, 123–781. [Google Scholar] [CrossRef] - Pandey, S.N.; Chaudhuri, A.; Kelkar, S. A coupled thermo-hydro-mechanical modeling of fracture aperture alteration and reservoir deformation during heat extraction from a geothermal reservoir. Geothermics
**2017**, 65, 17–31. [Google Scholar] [CrossRef] - Soltani, M.; Kashkooli, F.M.; Souri, M.; Rafiei, B.; Jabarifar, M.; Gharali, K.; Nathwani, J.S. Environmental, economic, and social impacts of geothermal energy systems. Renew. Sustain. Energy Rev.
**2021**, 140, 110–750. [Google Scholar] [CrossRef] - Guo, T.; Gong, F.; Wang, X.; Lin, Q.; Qu, Z.; Zhang, W. Performance of enhanced geothermal system (EGS) in fractured geothermal reservoirs with CO
_{2}as working fluid. Appl. Eng.**2019**, 152, 215–230. [Google Scholar] [CrossRef] - Huang, W. Heat extraction performance of EGS with heterogeneous reservoir: A numerical evaluation. Int. J. Heat Mass Transf.
**2017**, 13, 645–657. [Google Scholar] [CrossRef] [Green Version] - Guo, B.; Fu, P.; Hao, Y.; Peters, C.A.; Carrigan, C.R. Thermal drawdown-induced flow channeling in a single fracture in EGS. Geothermics
**2016**, 61, 46–62. [Google Scholar] [CrossRef] [Green Version] - Asai, P.; Panja, P.; McLennan, J.; Deo, M. Effect of different flow schemes on heat recovery from Enhanced Geotherm al Systems (EGS). Energy
**2019**, 175, 667–676. [Google Scholar] [CrossRef] - Patterson, J.R.; Cardiff, M.; Feig, K.L. Optimizing geothermal production in fractured rock reservoirs under uncertainty. Geothermics
**2020**, 88, 101–906. [Google Scholar] [CrossRef] - Wu, X.T.; Li, Y.C.; Tang, C.A. Fracture spacing in horizontal well multi-perforation fracturing optimized by heat extraction. Geothermics
**2022**, 101, 102–376. [Google Scholar] [CrossRef] - Fisher, A. A mathematic examination of the methods of determining the accuracy of an observation by the mean error and by the mean square error. Mon. Not. R Astron. Soc.
**1920**, 80, 758–770. [Google Scholar] [CrossRef] [Green Version] - Han, Y.S.; He, J.T.; Lu, Y.T. Sensitivity of the properties of the graduated compression stocking and soft tissues on the lower limb-stocking interfacial pressure using the orthogonal simulation test. Med. Eng. Phys.
**2021**, 95, 84–89. [Google Scholar] [CrossRef] - Lin, R.; Diao, X.Y.; Ma, T.C.; Tang, S.H.; Chen, L.; Liu, D.C. Optimized microporous layer for improving polymer exchange membrane fuel cell performance using orthogonal test design. Appl. Energy
**2019**, 254, 113–714. [Google Scholar] [CrossRef] - Xie, J.X.; Wang, J.S. Performance optimization of pinnate horizontal well in geothermal energy utilization with orthogonal test. Appl. Therm. Eng.
**2022**, 209, 118–321. [Google Scholar] [CrossRef] - Yu, L.K.; Wu, X.T.; Hassan, N.S.; Wang, Y.D.; Ma, W.W.; Liu, G. Modified zipper fracturing in enhance d geothermal system reservoir and analyzed heat extraction optimization via orthogonal design. Renew. Energy
**2020**, 161, 373–385. [Google Scholar] [CrossRef] - Pruess, K.; Oldenburg, C.; Moridis, G. TOUGH2 User’s Guide, Version 2.0; Lawrence Berkeley National Laboratory: Berkeley, CA, USA, 1999. [Google Scholar]
- Pruess, K.; Faybishenho, B.; Bodvarsson, G.S. Alternative concepts and approaches for modeling flow and transport in thick unsaturated zones of fractured rocks. J. Contam. Hydrol.
**1999**, 38, 281–322. [Google Scholar] [CrossRef] - Wu, L.; Liu, J.; Zhou, J.; Zhang, Q.; Song, Y.; Du, S.; Tian, W. Evaluation of tar from the microwave co-pyrolysis of low-rank coal and corncob using orthogonal-test-based grey relational analysis (GRA). J. Clean. Prod.
**2022**, 337, 130–362. [Google Scholar] [CrossRef] - Gao, J.; Zhang, H.J.; Zhang, S.Q.; Chen, X.B.; Cheng, Z.P.; Jia, X.F. Three-dimensional magnetotelluric imaging of the geothermal system beneath the Gonghe Basin, Northeast Tibetan Plateau. Geothermics
**2018**, 76, 15–25. [Google Scholar] [CrossRef] - Zhang, C.; Jiang, G.; Shi, Y.; Wang, Z.; Wang, Y.; Li, S.; Jia, X.; Hu, S. Terrestrial heat flow and crustal thermal structure of the Gonghe-Guide area, northeastern Qinghai-Tibetan plateau. Geothermics
**2018**, 72, 182–192. [Google Scholar] [CrossRef] - Zhang, S.Q.; Li, X.F.; Song, J.; Wen, D.G.; Li, Z.W.; Li, D.M.; Cheng, Z.; Fu, L.; Zhang, L.; Feng, Q.; et al. Analysis on Geophysical Evidence for Existence of Partial Melting Layer in Crust and Regional Heat Source Mechanism for Hot Dry Rock Resources of Gonghe Basin. Earth Sci.
**2021**, 46, 1416–1436. [Google Scholar] - Genter, A.; Fritsch, D.; Cuenot, N.; Baumgärtner, J.; Graff, J.J. Overview of the current activities of the European EGS Soultz project: From exploration to electricity production. In Proceedings of the Thirty-Fourth Workshop on Geothermal Reservoir Engineering Stanford University, Stanford, CA, USA, 9–11 February 2009. SGP-TR-187. [Google Scholar]
- U.S. Department of Energy. Geothermal Technologies Program 2013 Peer Review; U.S. Department of Energy: Washington, DC, USA, 2013.
- Lei, Z.H.; Zhang, Y.J. Investigation on the effect of symmetrical multi-well layout on geothermal energy extraction from a fractured granitic reservoir: A case study in the Gonghe Basin, Northwestern China. Energy Rep.
**2021**, 7, 7741–7758. [Google Scholar] [CrossRef] - Huang, X.X.; Zhu, J.L.; Niu, C.K.; Li, J.; Hu, X.; Jin, X.P. Heat extraction and power production forecast of a prospective enhanced geothermal system site in Songliao Basin. China Energy
**2014**, 75, 360–370. [Google Scholar] [CrossRef] - Zhang, Y.J.; Li, Z.W.; Yu, Z.W.; Guo, L.L.; Jin, X.P.; Xu, T.F. Evaluation of developing an enhanced geothermal heating system in northeast China: Field hydraulic stimulation and heat production forecast. Energy Build.
**2015**, 88, 1–14. [Google Scholar] [CrossRef] - Zoback, M.D. Reservoir Geomechanics, 1st ed.; Cambridge University Press: Cambridge, UK; New York, NY, USA, 2007; p. 464. [Google Scholar]
- Hofmann, H.; Weides, S.; Babadagli, T.; Zimmermann, G.; Moeck, I.; Majorowicz, J.; Unsworth, M. Potential for enhanced geothermal systems in Alberta, Canada. Energy
**2014**, 69, 578–591. [Google Scholar] [CrossRef] - Garg, S.K.; Combs, J. A reformulation of USGS volumetric “heat in place” resource heat in place” resource estimation method. Geothermics
**2015**, 55, 150–158. [Google Scholar] [CrossRef] - NIST. Thermophysical Properties of Fluid Systems. 2010. Available online: http://webbook.nist.gov/chemistry/fluid/ (accessed on 1 January 2022).
- Guo, L.L.; Zhang, Y.B.; Zhang, Y.J.; Yu, Z.W.; Zhang, J.N. Experimental investigation of granite properties under different temperatures and pressures and numerical analysis of damage effect in enhanced geothermal system. Renew. Energy
**2018**, 126, 107–125. [Google Scholar] [CrossRef] - Li, Z.W.; Feng, X.T.; Zhang, Y.J.; Xu, T.F. Feasibility study of developing a geothermal heating system in naturally fractured formations: Reservoir hydraulic properties determination and heat production forecast. Geothermics
**2018**, 73, 1–15. [Google Scholar] [CrossRef] - Cheng, W.L.; Wang, C.L.; Nian, Y.L.; Han, B.B.; Liu, J. Analysis of influencing factors of heat extraction from enhanced geothermal systems considering water losses. Energy
**2016**, 115, 274–288. [Google Scholar] [CrossRef] - Sanyal, S.K.; Butler, S.J. An analysis of power generation prospects from enhanced geothermal systems. In Proceedings of theWorld Geothermal Congress, Antalya, Turkey, 24–29 April 2005; pp. 1–6. [Google Scholar]

**Figure 2.**Location of Gonghe Basin (

**a**). Distribution of geothermal wells and faults in the Qiabuqia area (

**b**).

**Figure 4.**Schematic of EGS (

**left**); operation diagram of surface ORC system (

**right up**); conceptual model of stimulated EGS reservoir (

**right down**).

**Figure 6.**Evolutions of T

_{pro}and P

_{inj}at different injection rates (q

_{inj}) over the 50 years.

**Figure 14.**Variations of W

_{e}, W

_{p}, and η at four levels of different factors based on the results in Table 8. G1–G4 represent the results of the four tests at each level: (

**a**) fracture permeability; (

**b**) fracture permeability anisotropy; (

**c**) injected section length; and (

**d**) injection rate.

**Figure 15.**Simulation results of three combinations of A

_{2}B

_{3}C

_{1}D

_{1}, A

_{2}B

_{2}C

_{3}D

_{1}, and A

_{2}B

_{3}C

_{4}D

_{1}.

**Figure 16.**Comparison of net power generation (W

_{e}− W

_{p}) under different of injection rates based on test A

_{2}B

_{3}C

_{4}D

_{1}.

**Figure 17.**Schematic diagram of optimal well layout designed according to case A

_{2}B

_{3}C

_{4}D

_{1}.

**Figure 18.**Comparison of production index under different injection temperature in the 50th year based on test A

_{2}B

_{3}C

_{4}D

_{1}. The production index include T

_{pro}and W

_{e}(

**a**), I

_{inj}and P

_{inj}(

**b**), η and W

_{p}(

**c**), and production water density, ρ

_{water}(

**d**).

**Figure 19.**Profiles of space variations of reservoir temperature fields over 50 years (y = 350 m) (

**a**–

**e**) and the temperature plan in the 50th year (z = 350 m) (

**f**). The results are based on test A

_{2}B

_{3}C

_{4}D

_{1}with injection temperature of 70 °C.

Level | Factor | ||
---|---|---|---|

A | B | C | |

Level l | a1 | b1 | c1 |

Level 2 | a2 | b2 | c2 |

Level 3 | a3 | b3 | c3 |

Test Number | Factor | ||
---|---|---|---|

A | B | C | |

1 | a1 | b1 | c1 |

2 | a1 | b2 | c2 |

3 | a1 | b3 | c3 |

4 | a2 | b1 | c3 |

5 | a2 | b2 | c1 |

6 | a2 | b3 | c2 |

7 | a3 | b1 | c2 |

8 | a3 | b2 | c3 |

9 | a3 | b3 | c1 |

Wells | Depth, z (km) | Measured Temperature, T (°C) |
---|---|---|

GR1 | 0.1~1.0 | T = 66.061z + 18.467 (R^{2} = 0.9958) |

1.1~2.8 | T = 40.289z + 48.992 (R^{2} = 0.9967) | |

2.9~3.6 | T = 57.738z − 5.0238 (R^{2} = 0.9861) | |

GR2 | 0.1~3.0 | T = 50.154z + 33.795 (R^{2} = 0.9996) |

DR3 | 0.1~1.4 | T = 72.879z + 14.198 (R^{2} = 0.9988) |

1.5~2.9 | T = 44.357z + 55.081 (R^{2} = 0.996) | |

DR4 | 0.1~0.5 | T = 7z + 77.3 (R^{2} = 0.9423) |

0.6~1.5 | T = 8.303z + 99.782 (R^{2} = 0.91) | |

1.6~3.1 | T = 44.456z + 46.466 (R^{2} = 0.9983) |

Lithology | Depth (km) | Heat Conductivity (W/(m·K)) |
---|---|---|

Mudstone | 0.20~1.40 | 1.25~1.99 (average is 1.58) |

Igneous Rock | 1.50–3.63 | 2.10–3.17 (average is 2.53) |

Items | Parameters | Base Case Value | Selected Case Value |
---|---|---|---|

Reservoir | Fracture spacing, S_{f} | 3 m | 50 m |

Fracture permeability (k_{x} = k_{y} = k_{z}), P_{f} | 1 × 10^{−13} m^{2} | 1 × 10^{−11} m^{2} | |

Fracture permeability anisotropy, α (α = k _{x}/k_{z}, k_{x} = k_{y}), | 1 | 10 | |

Matrix permeability, P_{r} | 1 × 10^{−17} m^{2} | 1 × 10^{−14} m^{2} | |

Matrix porosity | 0.025 | No changed | |

Matrix density | 2360 kg/m^{3} | No changed | |

Heat conductivity, λ_{r} | 2.0 W/(m·K) | 3.5 W/(m·K) | |

Specific heat | 754.4 J/(kg·K) | No changed | |

Initial pressure | P = 4 × 10^{−7}–10,000z (Pa) | No changed | |

Initial temperature | 225 °C | No changed | |

Operation | Injected section length, L_{inj} | 60 m | 120 m |

Injection rate, q_{inj} | 30 kg/s | 20 kg/s | |

Injection water temperature | 10 °C | No changed | |

Injection water specific enthalpy | 78.77 kJ/kg | No changed | |

Productivity index | 5.4 × 10^{−12} m^{3} | No changed | |

Production bottom-hole pressure | 30 MPa | No changed |

Level | Factors | |||
---|---|---|---|---|

A | B | C | D | |

Fracture Permeability, P_{f} (m^{2}) | Fracture Permeability Anisotropy, α | Injected Section Length, L_{inj} (m) | Injection Rate, q_{inj} (kg/s) | |

1 | 5 × 10^{−14} | 1 | 30 | 20 |

2 | 1 × 10^{−13} | 10 | 120 | 50 |

3 | 1 × 10^{−12} | 100 | 210 | 80 |

4 | 1 × 10^{−11} | 1000 | 300 | 110 |

Test Number | Factors | |||
---|---|---|---|---|

A | B | C | D | |

Fracture Permeability, P_{f} (m^{2}) | Fracture Permeability Anisotropy, α | Injected Section Length, L_{inj} (m) | Injection Rate, q_{inj} (kg/s) | |

1 | A1 (5 × 10^{−14}) | B1 (1) | C1 (30) | D1 (20) |

2 | A1 (5 × 10^{−14}) | B2 (10) | C2 (120) | D2 (50) |

3 | A1 (5 × 10^{−14}) | B3 (100) | C3 (210) | D3 (80) |

4 | A1 (5 × 10^{−14}) | B4 (1000) | C4 (300) | D4 (110) |

5 | A2 (1 × 10^{−13}) | B1 (1) | C2 (120) | D3 (80) |

6 | A2 (1 × 10^{−13}) | B2 (10) | C1 (30) | D4 (110) |

7 | A2 (1 × 10^{−13}) | B3 (100) | C4 (300) | D1 (20) |

8 | A2 (1 × 10^{−13}) | B4 (1000) | C3 (210) | D2 (50) |

9 | A3 (1 × 10^{−12}) | B1 (1) | C3 (210) | D4 (110) |

10 | A3 (1 × 10^{−12}) | B2 (10) | C4 (300) | D3 (80) |

11 | A3 (1 × 10^{−12}) | B3 (100) | C1 (30) | D2 (50) |

12 | A3 (1 × 10^{−12}) | B4 (1000) | C2 (120) | D1 (20) |

13 | A4 (1 × 10^{−11}) | B1 (1) | C4 (300) | D2 (50) |

14 | A4 (1 × 10^{−11}) | B2 (10) | C3 (210) | D1 (20) |

15 | A4 (1 × 10^{−11}) | B3 (100) | C2 (120) | D4 (110) |

16 | A4 (1 × 10^{−11}) | B4 (1000) | C1 (30) | D3 (80) |

**Table 8.**Orthogonal test results. V

_{End}and V

_{Ave.}denote the value at the end of simulation and the average annual value of each index, respectively.

Test Number | Index | ||||||
---|---|---|---|---|---|---|---|

Power Generation, W_{e} | Coefficient of Performance, η | Production Temperature, T_{pro} | Injectivity, I_{inj} | Bottom-Hole Pressure, P_{inj} | Pump Power, W_{p} | ||

1 | V_{End}V _{Ave.} | 1.00 1.45 | 2.38 3.63 | 176.46 208.11 | 1.13 1.17 | 30.69 30.61 | 0.42 0.40 |

2 | V_{End}V _{Ave.} | −1.60 0.33 | −0.88 0.21 | 52.87 110.62 | 1.79 2.12 | 60.27 55.82 | 1.81 1.54 |

3 | V_{End}V _{Ave.} | −1.24 0.49 | −0.28 0.20 | 77.53 110.07 | 1.96 2.32 | 74.69 68.63 | 4.38 3.77 |

4 | V_{End}V _{Ave.} | −3.35 −1.44 | −1.01 −0.37 | 54.78 81.09 | 5.01 5.62 | 55.83 53.46 | 3.30 2.99 |

5 | V_{End}V _{Ave.} | −2.62 −0.36 | −1.55 0.13 | 51.67 93.97 | 4.68 5.42 | 49.62 46.90 | 1.69 1.48 |

6 | V_{End}V _{Ave.} | - | - | - | - | - | - |

7 | V_{End}V _{Ave.} | 1.11 1.46 | 35.26 51.99 | 183.40 208.79 | 17.43 19.28 | 33.65 33.44 | 0.03 0.03 |

8 | V_{End}V _{Ave.} | −0.86 0.67 | −0.31 0.57 | 222.41 223.83 | 1.22 1.69 | 74.70 64.89 | −0.86 0.67 |

9 | V_{End}V _{Ave.} | −4.96 −3.74 | −20.56 −16.04 | 32.41 49.37 | 45.66 48.45 | 36.71 36.00 | 0.24 0.22 |

10 | V_{End}V _{Ave.} | −2.29 -0.88 | −24.98 −7.97 | 57.69 84.32 | 95.71 110.12 | 34.60 34.12 | 0.09 0.08 |

11 | V_{End}V _{Ave.} | −1.27 0.88 | −2.08 2.80 | 62.2 126.6 | 4.39 5.15 | 45.92 42.59 | 0.61 0.50 |

12 | V_{End}V _{Ave.} | 0.43 1.14 | 5.55 12.41 | 132.38 185.98 | 2.65 3.63 | 38.82 36.93 | 0.16 0.11 |

13 | V_{End}V _{Ave.} | −1.68 −0.91 | −377.26 −439.38 | 50.34 73.60 | 897.44 892.88 | 33.10 32.92 | 0.0038 0.0038 |

14 | V_{End}V _{Ave.} | 0.05 0.52 | 18.77 420.36 | 104.76 140.23 | 22.34 22.90 | 32.68 32.58 | 0.0024 0.0019 |

15 | V_{End}V _{Ave.} | −4.28 −1.71 | −25.12 −6.44 | 41.83 77.13 | 40.07 41.85 | 36.94 35.94 | 0.17 0.15 |

16 | V_{End}V _{Ave.} | −3.17 −0.88 | −2.67 0.05 | 39.48 83.07 | 6.04 7.23 | 53.71 48.87 | 1.19 0.99 |

**Table 9.**Range analysis results of the orthogonal test. For simplicity, only all k

_{i}values of W

_{e}and η are listed in the table. The other indexes only give R and rank results.

Index | Value | Factors | |||
---|---|---|---|---|---|

A | B | C | D | ||

W_{e} | k_{1} | 0.21 | −0.89 | 0.48 | 1.26 |

k_{2} | 0.59 | −0.01 | −0.03 | 0.24 | |

k_{3} | −0.53 | 0.28 | −0.52 | −0.41 | |

k_{4} | −0.75 | −0.01 | −0.44 | −2.30 | |

R | 1.34 | 1.17 | 0.10 | 3.56 | |

Rank | 2 | 3 | 4 | 1 | |

Better level | A_{2}B_{3}C_{1}D_{1} | ||||

η | k_{1} | −112.92 | 0.92 | 2.16 | 124.52 |

k_{2} | 137.53 | 17.56 | 4.00 | −108.95 | |

k_{3} | 12.14 | 0.22 | 101.27 | −1.8975 | |

k_{4} | 5.59 | −6.35 | −98.93 | −7.62 | |

R | 250.45 | 23.92 | 200.21 | 233.47 | |

Rank | 1 | 4 | 3 | 2 | |

Better level | A_{2}B_{2}C_{3}D_{1} | ||||

T_{pro} | R | 82.02 | 45.69 | 27.31 | 125.04 |

Rank | 2 | 3 | 4 | 1 | |

I_{inj} | R | 238.41 | 232.21 | 252.46 | 213.49 |

Rank | 2 | 3 | 1 | 4 | |

P_{inj} | R | 15.30 | 13.85 | 12.04 | 16.82 |

Rank | 2 | 3 | 4 | 1 | |

W_{p} | R | 1.96 | 0.66 | 0.54 | 1.45 |

Rank | 1 | 3 | 4 | 2 |

Test | W_{e} | η | T_{pro} | I_{inj} | P_{inj} | W_{p} | |
---|---|---|---|---|---|---|---|

A_{2}B_{1}C_{4}D_{1} (α = 1) | V_{End} | 0.97 | 69.29 | 173.07 | 19.63 | 33.03 | 0.014 |

V_{Ave.} | 1.23 | 64.74 | 192.28 | 20.92 | 33.03 | 0.019 | |

A_{2}B_{2}C_{4}D_{1} (α = 10) | V_{End} | 1.02 | 63.75 | 177.18 | 19.29 | 33.1 | 0.016 |

V_{Ave.} | 1.35 | 67.50 | 201.02 | 20.69 | 33.07 | 0.02 | |

A_{2}B_{3}C_{4}D_{1} (α = 100) | V_{End} | 1.11 | 35.26 | 183.4 | 17.43 | 33.65 | 0.03 |

V_{Ave.} | 1.46 | 51.99 | 208.79 | 19.28 | 33.44 | 0.03 | |

A_{2}B_{4}C_{4}D_{1} (α = 1000) | V_{End} | 1.01 | 6.20 | 174.88 | 12.35 | 38.83 | 0.163 |

V_{Ave.} | 1.37 | 11.42 | 202.77 | 14.28 | 37.06 | 0.12 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhao, Y.; Shu, L.; Chen, S.; Zhao, J.; Guo, L.
Optimization Design of Multi-Factor Combination for Power Generation from an Enhanced Geothermal System by Sensitivity Analysis and Orthogonal Test at Qiabuqia Geothermal Area. *Sustainability* **2022**, *14*, 7001.
https://doi.org/10.3390/su14127001

**AMA Style**

Zhao Y, Shu L, Chen S, Zhao J, Guo L.
Optimization Design of Multi-Factor Combination for Power Generation from an Enhanced Geothermal System by Sensitivity Analysis and Orthogonal Test at Qiabuqia Geothermal Area. *Sustainability*. 2022; 14(12):7001.
https://doi.org/10.3390/su14127001

**Chicago/Turabian Style**

Zhao, Yuan, Lingfeng Shu, Shunyi Chen, Jun Zhao, and Liangliang Guo.
2022. "Optimization Design of Multi-Factor Combination for Power Generation from an Enhanced Geothermal System by Sensitivity Analysis and Orthogonal Test at Qiabuqia Geothermal Area" *Sustainability* 14, no. 12: 7001.
https://doi.org/10.3390/su14127001