Parameter sensitivity analysis and optimization strategy research of enhanced geothermal system: A case study in Guide Basin, Northwestern China

Journal Pre-proof Parameter sensitivity analysis and optimization strategy research of enhanced geothermal system: A case study in Guide Basin, Northwestern China

Liang-Liang Guo, Yong-Bo Zhang, Zhi-Chao Wang, Jian Zeng, Yan-Jun Zhang, Zhi-Xiang Zhang PII:

S0960-1481(20)30245-7

DOI:

https://doi.org/10.1016/j.renene.2020.02.058

Reference:

RENE 13079

To appear in:

Renewable Energy

Received Date:

31 October 2019

Accepted Date:

13 February 2020

Please cite this article as: Liang-Liang Guo, Yong-Bo Zhang, Zhi-Chao Wang, Jian Zeng, Yan-Jun Zhang, Zhi-Xiang Zhang, Parameter sensitivity analysis and optimization strategy research of enhanced geothermal system: A case study in Guide Basin, Northwestern China, Renewable Energy (2020), https://doi.org/10.1016/j.renene.2020.02.058

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Parameter sensitivity analysis and optimization strategy research of enhanced geothermal system: A case study in Guide Basin, Northwestern China Liang-Liang Guo a, b, *, Yong-Bo Zhang a, Zhi-Chao Wang b, Jian Zeng b, Yan-Jun Zhang c, Zhi-Xiang Zhang a a College

b Shanxi

of Water Resources Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China

Academy for Environmental Planning, Taiyuan 030002, China

c College

of Construction Engineering, Jilin University, Changchun 130026, China

Abstract Guide Basin is a potential site for enhanced geothermal system development in China. The optimal strategy is needed to maximize heat production potential and provide support for the future stimulation design. In this work, sensitivity analysis of influence factors on water flow path, production water temperature, and flow impedance is performed on the basis of hydraulic–thermal model of Guide Basin. The factors include reservoir parameters (length, width, height, permeability, and temperature) and operation parameters (injection rate, injection temperature, open hole length, and height difference of open hole). Results indicate that the main affecting factors of water flow path are stimulated reservoir permeability and injection rate. The most significant influencing factor of flow impedance is stimulated reservoir permeability. Reservoir geometry has the greatest influence on production water temperature. The stable period of production water temperature is mainly affected by reservoir geometry and the height difference of open hole. In the theoretically optimal strategy, the electrical powers of 150, 400, and 450 kg/s are 12.3, 32.7–33.3, and 36.2–37.6 MW, respectively. In the practically optimal strategy, the maximum injection rate is 80 kg/s and electrical power ranges from 0 to 1.25 MW. For future applications, the shallow reservoirs with high temperature are expected.

Keywords: Guide Basin; sensitivity analysis; enhanced geothermal system; reservoir stimulation; optimal strategy

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1 Introduction

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Increasing energy demand and awareness about global warming due to the extensive use of fossil energy sources, have led several countries to look for clean sources of renewable energy [1]. Among renewable energy sources, geothermal energy is abundant and has a long-term potential to meet world energy demand [2]. It is considered one of the most sustainable, dependable and clean sources with regard to low carbon emissions [3]. Furthermore, geothermal energy could provide a secure long-term power supply that could protect the country against economic instabilities resulting from fuel price fluctuations or supply disruptions in the future [2]. Geothermal energy can be divided into conventional hydrothermal and hot dry rock (HDR) resources according to their naturally occurring states [4]. The hydrothermal energy can be exploited by extracting the fluid contained in the geothermal reservoir. However, the spatial distribution of hydrothermal resources is highly inconsistent. Even in proven hydrothermal fields, “dry hole” is a common failure in geothermal exploration because of the high unpredictability of groundwater circulation characteristics. HDR geothermal energy is heat energy stored in subsurface hot and low-permeability crystalline rocks, which are normally located at depths of 3–10 km [2]. Energy contained in HDR resources can be extracted by stimulating the formation to form an artificially altered reservoir called enhanced geothermal system (EGS) [2, 4]. Compared with other renewable resources, HDR resources are more concentrated, are suitable for generating base-load electric power, and have nearly no pollution emission [2, 5]. In America, total EGS resource reserve within 3–10 km depth amounts to 14 million EJ (1EJ = 1018J); if we take 2% as the recoverable fraction, the recoverable EGS resource amounts to 0.28 million EJ and it is 2800 times total annual energy consumption in 2005 in the USA [2]. It is predicted EGS will provide an electric power of approximately 100,000 MW by 2050 in the USA [2]. In addition, although there certainly are environmental impacts associated with EGS developments (i.e., water pollution, land subsidence and induced seismicity), they are generally more benign than those associated with other power generation technologies, particularly fossil and nuclear. With more than 100 years of worldwide experience in geothermal operations, future EGS power plant facilities can be designed and operated to have relatively small impacts on the local and regional environment. In fact, because EGS plants have a small footprint and

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Journal Pre-proof Nomenclature Hr reservoir height, m IR flow impedance, MPa/(kg/s) Kr reservoir permeability, m2 Linj open hole length of injection well, m Lr reservoir length, m Pinj injection pressure, MPa qinj injection flow rate, kg/s Tinj injection water temperature, C Tr reservoir temperature, C

We Wr

electrical power, MW reservoir width, m

σV σH σh inj pro

vertical stress, MPa maximum horizontal stress, MPa minimum horizontal stress, MPa injection production

can operate essentially emissions-free, the overall environmental impact of EGS power facilities is likely to be positive, reducing the growth of greenhouse gas emissions while providing a reliable and safe source of electricity. China, located at the junction of three tectonic plates with a vast territory, possesses abundant deep geothermal systems [6]. In the continental China, over 99% of the geothermal heat within depths of approximately 10 km is available in HDR [7]. China has increased the investment on HDR research in recent years. In 2012, China government launched the “Key technology research of HDR thermal energy development and utilization” project. Its purpose was to master EGS-related technologies. Daqing oilfield was chosen as the study area due to the abundance of petroleum geological data [8, 9]. Since 2013, many potential HDR sites in China, such as Zhangzhou City, Hainan Northern area, Gonghe–Guide Basin (GGB), Wendeng City, and Datong City, had been found and reported. Finally, the China Geological Survey chose GGB as the future HDR field test site. GGB is located in the northeast margin of the Qinghai–Tibetan Plateau. Collision of India and Eurasia crusts created an anomalous geothermal belt in the northeastern part of the Qinghai–Tibetan Plateau. At depths over 2200 m, the temperature of the basement in GGB is higher than 150 C [10]. Many natural fractures exist in the deep granite due to the strong tectonic activity. The thickness of complete granite is roughly 44.0–94.8 m, while the thickness of the fractured granite ranges from 29.0 m to 134.5 m [10]. These pre-existing natural fractures are favorable for EGS development in GGB. In this study, we chose the Guide Basin (GDB) as the study area. A series of geological, geophysical, and drilling operations has been conducted in this area. Guo et al. found two types of geothermal systems, namely, tectonic-fault and basin-artesian types, in GDB [11]. Li et al. determined the location and stress regime of deep faults near the Zhacangsi (ZCS) 3

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hot spring groups [12]. Lang et al. studied the thermal structure of two typical geothermal systems (ZCS and Sanhe) in GDB [13]. Li et al. summarized the geological condition and mechanism of geothermal resources in GDB [14]. The literature on shallow fault-controlled hydrothermal system is abundant, but the exploration data of deep HDR formation condition below 3000 m are limited. From 2013 to 2015, Zhang et al. conducted geophysical exploration in ZCS and clarified its deep tectonic features [15]. In 2016, ZR1 well with a depth of 3000 m was completed; temperature measurement, core extraction, and logging were conducted [13]. In 2018, Zhang conducted mechanical and thermosphysical tests on core samples (0–3600 m) taken from ZR2 well [16]. The next step of EGS development in GDB is to choose a target formation for hydraulic fracturing. Fracturing design considerably affects heat production and cost. Therefore, investigating the influence of main factors on heat production is of great guiding significance in optimizing fracturing design. The main indexes to evaluate EGS performance include power generation [8, 21] and flow impedance [2, 8]. Power generation is expected to be as high as possible, and its value depends on water production rate and temperature. Flow impedance represents the power consumption of the unit production rate for penetrating the fractured reservoir [5]. It is expected to be as low as possible. For EGS commercial standard, the flow impedance should not be greater than 0.1 MPa/(kg/s). Flow impedance depends on the mobility of geofluid, the pressure gradient between injection and production wells, and reservoir permeability. Secondary indexes, such as water production rate [17, 19], production temperature [20, 21], injection pressure [5, 21], pump power [4, 5], and energy efficiency [5, 19, 20, 21], are also considered. Water production rate depends on injection rate and water losses. Increasing the injection rate will increase the injection pressure of the circulation pump, which will consume substantial power. If the bottomhole injection pressure exceeds the reservoir minimum principal stress, then the fracture will dilate; accordingly, secondary reservoir growth and water losses will be induced [5, 9]. Production temperature is mainly affected by injection rate, injection temperature, and the heat transfer area. Decreasing injection rate or increasing injection temperature or heat transfer area will increase the production temperature. Injection pressure is mainly influenced by reservoir permeability, injection rate, and injection temperature. Increasing the reservoir permeability, decreasing the injection rate, or

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improving the injection temperature will obviously reduce the injection pressure. The internal energy consumption mainly includes the energy consumption of circulation pumps. It is mainly affected by reservoir permeability, injection rate and temperature. Increasing the reservoir permeability, decreasing the injection rate, or increasing the injection temperature will decrease the pump power. The energy efficiency of the system is defined as the ratio of the total produced electric energy to the internal energy consumption. Its main influencing factors are reservoir permeability, injection rate and temperature. Increasing the reservoir permeability, decreasing the injection rate, or increasing the injection temperature will increase the energy efficiency. Other factors, such as surrounding formation permeability (considering waterloss) [17, 22], geothermal gradient [17, 21], well spacing [5, 17, 22], reservoir volume [17, 21], open hole length [2, 17], production pressure [5, 17], and well array [18, 19], would influence the indexes mentioned above. With the increase in surrounding formation permeability, production rate decreases. Power generation is overestimated during the entire operation time if the existing water losses are ignored. Increasing the geothermal gradient will increase the production and water loss rates. The increase in well spacing will decrease the production rate. With the increase in reservoir volume, production rate first increases and then decreases, and water loss rate increases. With the increase in open hole length, production rate first increases and then keeps steady, and water loss rate first increases slowly and then keeps steady. With the increase in production pressure, production rate decreases, whereas water loss rate increases slowly. Heat extracted from near well regions does not compensate for the large pressure drop within regions. The regions near the wells should be heavily stimulated to increase the effective permeability. However, the influence of reservoir geometry parameters on heat transfer performance is rarely studied. In the design of hydraulic fracturing, how large the reservoir should be created must be determined first. Large reservoir length, width, and height are desirable. For a given formation, we cannot guarantee that all values are large. For example, the reservoir height will be restricted for a formation with high stress shield in the top and bottom boundaries; the created fracture will propagate upward and form a reservoir with a large height for a formation with a normal stress gradient. Therefore, the influence of each reservoir geometry parameters on heat performance needs to be analyzed. The water flow path through reservoirs is also rarely

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studied. For a given stimulated reservoir, injected water is anticipated to sweep as many zones as possible. It indicates that the stimulated reservoir is fully utilized to provide thermal energy. Thus, the affecting factors of water flow path should be investigated because they are also important for the well layout pattern. Furthermore, the influence of the height difference of open hole between injection and production wells is seldom studied. These factors mentioned above need to be considered in practical EGS projects. In this study, we introduce the geothermic features of GDB and ZCS. Sensitivity analysis of nine parameters is numerically performed on the basis of a 3D hydraulic–thermal model of ZCS. The nine parameters include reservoir parameters (length, width, height, permeability, temperature) and operation parameters (injection rate, injection temperature, open hole length, the height difference of open hole between injection and production wells). We mainly investigate the influence of the nine parameters on water flow path, production water temperature, and flow impedance for the EGS project. From the sensitivity analysis results, an optimal strategy for ZCS is presented, and its heat production performance is evaluated. Research conclusions can serve as reference for the stimulation and circulation test design of future EGS in ZCS.

2 Geothermal characteristics of GDB 2.1 Geologic setting GDB is located in the Eastern Qinghai Province, northwest of China (Fig. 1). It also locates in the intersection belt of Qilian, Kunlun, and Qinling fold systems. Its overall distribution is NWW and it is embosomed around by uplift mountains. Cenozoic strata are widely distributed in the basin, especially Tertiary strata, which are well developed and very thick. The igneous rocks are mainly Indosinian granites, aged between 264 and 234 Ma [13]. Granite intruded into the sand-slate of the Triassic system and formed large rock walls and plants. Magmatic uplift zone is distributed in the west and south parts (ZCS area). Deep and sandy mudstone layers play the role of heat insulation. Deep-large faults connect the deep magma chamber and carry its heat energy upward to shallow sandstone layers. The moho surface of GDB is shallow, and the depth of curie surface is approximately 20–22 km. The average basement depth is approximately 1500 m [14].

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The ZCS area is located at the southwestern edge of GDB. It is thrusted upward due to the SW–NE compression faults. Thus, ZCS possesses a shallower basement than the other area of the basin. The basement of ZCS is estimated to be 600–800 m. Many hot springs are found at the junction of NNW compression and EW tension faults. The highest temperature of the spring in ZCS is up to 93.5 °C. ZCS is chosen as the study area in this work [13, 14]. Fig. 1. Location and tectonic map of GDB. 2.2 Geothermal features In 2013, the China Geological Survey began to investigate the HDR geothermal resource potential in ZCS. The surface geophysical investigation has clarified geothermally related and hidden faults [16]. The results showed that ZCS possesses multiple thermal anomaly zones; it lies on the surface of a deep fracture, which cuts deeply into the underlying intrusive rock mass [13]. The thermal structure of ZCS is summarized as follows: (1) the heat reservoir consists of tectonic fracture and contact-metamorphic zones (granodiorite and middle-Triassic sand slate); (2) the heat insulation layers are composed of Neogene mudstone and middle-Triassic sand slate; (3) the heat channel is made up of the fracture zone inside the ZCS [13]. The neotectonic movement is active, and the regional stress field is dominated by the horizontal compression tectonic stress. High-angle thrust faults are developed. The Triassic strata and Indosinian granite are often overthrust over the Tertiary system [13, 14]. Thus, a horizontal stress regime with maximum horizontal stress (H)> vertical stress (V)> minimum horizontal stress (h) can be expected for deep formations within the ZCS. The location of ZR1 well is determined on the basis of the inversion results of geophysical exploration. The ZR1 well with a depth of 3000 m and a bottomhole temperature of 151.5 °C is completed. The measured temperature curve is shown in Fig. 2. The calculated geothermal gradient is approximately 3.5–29.1 °C/km, and the heat flow is 9.9–85.3 mW/m2. In accordance with the temperature curve and mud consumption condition, the geothermal zone can be divided into the following zones: (1) 100–1000 m: It is an aquifer with serious water and slurry leakage. Logging data show that this section is a fracture zone. It is inferred as the first hydrothermal system with a geothermal gradient of approximately 2 °C/km.

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(2) 1000–1500 m: It is the aquiclude. Its geothermal gradient is approximately 70 °C/km. It shows a good function for sealing and insulating deep heat. (3) 1500–2000 m: It is the confined aquifer. Mud thinning, water jet, and serious leakage occurred in the drilling process of this section. This part is called the second hydrothermal system with a gradient of 34 °C/km. (4) Below 2000 m: All the cores are nearly granites. Temperature gradient drops down to approximately 30 °C/km based on the measured temperature data between 2000 and 3000 m. This section is called the HDR system. The shallow zone (0–2000 m) is determined as fault-controlled convection hydrothermal system. The deep zone (below 2000 m) is a conduction-type HDR system. The hydrothermal system has been partially developed. Currently, the main objective of the China Geological Survey is to exploit the energy from the HDR system for electricity generation. Fig. 2. Logging results and temperature curves of ZR1 well. 3 Hydraulic–thermal numerical simulation of EGS 3.1 Conceptual model Fig. 3 illustrates the schematic of an EGS underground part. It consists of injection well, stimulated reservoir, and production well. Water is injected into the reservoir from the open hole of injection well. The open hole length (Linj) will influence the flow impedance and seepage pattern. Water stream flows through the reservoir driven by the pressure gradient between injector and producer. Reservoir permeability (Kr) definitely largely affects the water injection flow rate (qinj). Reservoir temperature (Tr) will influence the produced water temperature. Reservoir length (Lr), width (Wr), and height (Hr) will substantially influence the heat exchange area. The relative height difference of the open hole between injector and producer (ΔH = Hpro − Hinj) affects the pressure gradient and seepage path. Injected water temperature (Tinj) will largely influence the heat production. For simplification, Lpro is set equal to Linj. Therefore, nine parameters, namely, five reservoir parameters (Kr, Tr, Lr, Wr, Hr) and four operation parameters (Linj, ΔH, Tinj, qinj), are considered in this work. Only the stimulated reservoir part is illustrated in Fig. 3, and the surrounding rock part is not shown in the picture. Practical EGS is complicated. The model in this study makes the following major assumptions:

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(1) Two vertical well patterns are assumed. They are the foundation of multiwell and horizontal well patterns. The two wells are set in the middle of the left and right boundaries of the reservoir. (2) Water loss is ignored, that is, qinj equals to qpro. Heat extraction rate is overestimated during the entire operation time if the existing water losses are ignored [23]. (3) Mechanical and chemical processes are ignored. The mechanical process leads injection flow rate to increase first and approach steadiness with approximately 20% increase subsequently [24]. The chemical process slightly influences the injection and production flow rates [25]. Fig. 3. Schematic of an EGS underground part. 3.2 Sensitivity schemes Table 1 lists the parameter sensitivity schemes. In each case, only one parameter is changed, and the others adopt the base case value. A total of 29 scenarios are considered. The parameter range is set in accordance with the present EGS project [26-30]. The volume of stimulated reservoir ranges from 0.45E08 m3 to 2.70E08 m3. The mainly observed indicator consists of the water flow path, reservoir flow impedance, and produced water temperature. The water flow path is reflected by the cold halo shape (CHS). The CHS can intuitively reflect the heat extracted volume proportion of the reservoir and provide support for the well pattern design. The reservoir flow impedance largely influences the water circulation and electrical power consumed by the pump. The produced water temperature is a key indicator for the heat production potential. In this work, the injection open hole is fixed in the middle of the reservoir left boundary. Only the production open hole is moved to create a vertical height distance with the injection open hole. The methodological flowchart is illustrated in Fig. 4. Table 1 Parameter sensitivity schemes. Fig. 4. Methodological flowchart.

3.3 Model setup 3.3.1 Numerical simulator 9

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TOUGH2 is a numerical simulator that can model 3D multiphase, multicomponent flows in porous or fractured media [31]. In this work, we use TOUGH2-EOS1 codes to simulate the heat production performance. The TOUGH2-EOS1 codes use the integral finite difference method to solve the conservation equations of mass, momentum, and energy, and their accuracy and reliability have been widely proven [4, 5, 7, 8, 9, 10]. Theoretical background of the software is provided by Ref. [31]. The stimulated granite reservoir can be represented as equivalent porous media, and the circulating water and fractured rocks are in local thermal equilibrium. The heat production process can be accurately simulated with the TOUGH2-EOS1 codes. 3.3.2 Model grid, parameters, and initial and boundary conditions The reservoir properties are obtained from Ref. [13, 16] and summarized in Table 2. The 3D hydraulic–thermal numerical model of base case is shown in Fig. 5. The model geometry is 700 m (x) × 500 m (y) × 450 m (z). The grid system is 34 × 26 × 13. The total number of grid elements is 11492. The grid is refined in the vicinity of the wells with blocks of 5 m × 5 m × 10 m to ensure the model accuracy (Fig. 5). The heat exchange between reservoir and surrounding rock cannot be neglected because the reservoir possesses a large surface area. The injection open hole of all scenarios is set at a depth of 4000 m. EGS reservoir is usually filled with water before operation. The residual water comes from the hydraulic fracturing and long-term circulation test. The initial reservoir temperature is thereby assumed to be evenly distributed without temperature gradient. The topmost and bottommost boundaries of the surrounding cap and base rocks are no-flow for mass and heat. All models are simulated for a lifetime of 20 years. In order to reflect the change of reservoir and water temperature more precisely, the data resolution precision is set to seconds. In the simulation control part, the single value of time step is set to 100 s, enabling automatic time step adjustment. Therefore, the output data is in the hundreds. For example, in the Base case (Table 1), the actual output of temperature data is 475 during 20 years. However, for the convenience of display, in the subsequent graphs (Fig. 6-26), the data was all shown with symbol distance of 2% using Tecplot software. Fig. 5. 3D numerical model of the base case.

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Table 2 Reservoir properties used in the simulations. 3.3.3 Performance criteria The HDR resource development of GDB is mainly for electricity generation. A binary system utilizing an organic working fluid called Organic Rankine Cycle (ORC) technology is assumed the best choice [21, 29]. Soultz project selected isobutene as the organic working medium [30]. The isobutene is also accordingly adopted in GDB. The limit for the production water temperature using this ORC system for generating electricity is [21] Tpro105.36 C,

(1)

where Tpro is the production water temperature. Below this temperature, the energy in the fluid is insufficient to generate power efficiently when using isobutene as organic working medium. Garg et al. derived a new expression for available electricity generation for the binary cycle with the following equation [32]:

,

(2)

where η, q, T, h, s, P, and V denote the conversion efficiency, production mass flow rate, temperature, specific enthalpy, entropy, pressure, and specific volume, respectively. Subscripts w, r, R, P, b, c, g, l, in, sf, and k denote the wellhead, reference, reservoir, pinch point, boiling, condenser, gas, liquid, inlet, secondary fluid, and kelvin, respectively. Detailed descriptions of Eq. (2) can be found in Ref. [32]. The flow impedance IR (MPa/(kg/s)) is calculated by: IR = (Pinj–Ppro)/q,

(3)

where q is the production rate; and Pinj and Ppro are the bottomhole pressures of the injection and production wells, respectively. IR should be lower than 0.1 MPa/(kg/s), and the temperature drop (Tdrop) should be less than 10% during the entire production period [33]. Therefore, the following two criteria should be met as much as possible: IR  0.1 MPa/(kg/s), 11

(4)

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Tdrop  0.1Tr.

(5)

4 Sensitivity simulation results and discussion 4.1 Reservoir length (Lr) Fig. 6 shows the comparison of CHS under different values of Lr in the 20th year. All CHS presents a right triangle shape in the x–z plane. This phenomenon indicates that water mainly flows downward first when it is just injected into the reservoir. When water reaches the reservoir bottom, it begins to move along the reservoir bottom toward the pumping well. The reason is that a large temperature difference (130 °C) exists between injected water and reservoir. The cold water will sink in the hot water reservoir because of relatively high density. When the values of Lr are 500 and 1000 m, the cold front penetrates through the reservoir (Figs. 6a and 6b). The maximum penetration distance of cold front is approximately 1210 m. When Lr is larger than 1210 m, its effect on CHS is minimal (Figs. 6c and 6d). Fig. 7 depicts the variation curves of IR and Tpro under different values of Lr during 20-year period. IR increases with the increase in Lr. The reason for the continual increase in IR can be explained by Darcy’s law. IR is the function of (μ/ρ), which is also the function of temperature. Previous studies have indicated that (μ/ρ) significantly increases when temperature declines [3, 29]. As heat production continues, the reservoir temperature continually declines; this condition results in the continual increase in (μ/ρ) and IR. The IR values of the four cases are all lower than 0.1 MPa/(kg/s). IR curve patterns of 2000 and 3000 m are similar, except that 3000 m case is just shifted upward. IR is proportional to Lr if short circuit does not happen. In terms of Tpro variation, the stable period and Tpro increase with the increase in Lr. Tpro of Lr = 500 m decreases rapidly during the descending period. Tpro difference in the 20th year between Lr = 500 m and Lr = 1000 m is up to 55 °C. The result is consistent with Ref. [17, 25], in which thermal break-through time increases with increasing Lr based on the assumption of unchanged production flow rate and water loss rate. However, the result in this paper shows that Lr still largely influences Tpro although short circuit happens. Large Lr is expected in the EGS. Besides, stimulating overlong reservoir is unnecessary because it will increase the cost. When optimizing well layout of practical EGS, optimal Lr should be calculated 12

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on the basis of reservoir and operation parameters.

Fig. 6. Comparison of CHS under different values of Lr in the 20th year at slice of y = 250 m. Fig. 7. Variation curves of IR and Tpro under different values of Lr during 20-year period. 4.2 Reservoir width (Wr) Fig. 8 shows the comparison of CHS under different values of Wr in the 20th year. Cold front extends from the injection well to the production well in a circular ring shape in the horizontal plane. The injected water nearly sweeps across the entire reservoir width. As Wr increases, the overall reservoir temperature decreases slowly (Fig. 8). Combination of Fig. 8 with Fig. 6 presents the water flow path in the reservoir, which indicates that the inject water begins to flow toward all directions at the same speed in the vicinity of injection well when it reaches the reservoir bottom. After the water flows away from the injection well to a certain distance, the water stream begins to move toward the pumping well driven by the hydraulic gradient. This condition results in a high heat extraction rate in the reservoir width direction. Fig. 9 presents the variation curves of IR and Tpro under different values of Wr over 20-year period. Before short circuit occurs (the time when Tpro starts to decline), minimal IR difference exists among the four cases. After that time, IR difference gradually grows, and IR increases with the decrease in Wr. IR of the four cases is smaller than 0.1 MPa/(kg/s). Fig. 9 shows that Tpro of the four cases nearly has the same stable period because their horizontal velocity component and reservoir length are the same. However, after stable period Tpro, the difference among the four cases becomes increasingly large. Tpro increases with the increase in Wr, but Tpro increment decreases with the increase in Wr. A minimal Tpro increase is predicted when Wr is beyond 900 m. Overall, large Wr is expected in the EGS. Fig. 8. Comparison of CHS under different values of Wr at slice of z = 300 m (upper) and y= 250, 350, 450, 550 m (lower) in the 20th year. Fig. 9. Variation curves of IR and Tpro under different values of Wr over 20-year period.

4.3 Reservoir height (Hr) 13

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Fig. 10 shows the comparison of CHS under different values of Hr in the 20th year. With the increase in Hr, CHS gradually changes from a horizontal triangular shape to a steep “waterfall” shape. The projection area of CHS on the x–y plane decreases with the increase in Hr. Results indicate that the vertical velocity component is much larger than the horizontal velocity component after water enters reservoir. The increase in Hr prolongs the vertical flow path of water stream, and this condition results in a large heat exchange volume. Heat is nearly fully extracted from the lower part of the reservoir because of the downward movement of water, whereas limited heat is extracted from the upper part (above the open hole) (Figs. 10a–10d). Therefore, during reservoir stimulation, the formation that possesses upper in situ stress shielding should be selected as the target reservoir, and stimulation design should aim at making generated reservoir grow as far as possible downward. Fig. 11 presents the variation curves of IR and Tpro under different values of Hr over 20-year period. IR decreases with the increase in Hr, and IR difference among the cases is small. Hr greatly influences the produced water temperature. The stable period difference is caused by Hr difference. A large Tpro difference exists among the four cases in the 20th year. Overall, large Hr is expected in the EGS. Ref. [24] proposed that enlarged reservoir volume would not efficiently enhance heat extraction performance with fixed well spacing. However, each reservoir geometric parameter has different effect on the heat transfer. For practical EGS, it is more meaningful to study the effect of each geometric parameter than that of volume on productivity. Furthermore, our simulation results show reservoir volume has great influence on heat potential. Fig. 10. Comparison of CHS under different values of Hr at slice of y = 250 m and z = 150 m in the 20th year. Fig. 11. Variation curves of IR and Tpro under different values of Hr over 20-year period. 4.4 Injection open hole length (Linj) Fig. 12 shows the comparison of CHS under Linj = 50, 200 m in the 5th and 20th year. Figs. 12a and 12b show that, at the early operation stage, the height of CHS of Linj = 200 m is larger than that of Linj = 50 m. However, as the project operation continues, CHS difference decreases (Figs. 12c and 12d). Fig. 13 presents the variation curves of IR and Tpro under different values of Linj over 20-year period. An apparent IR 14

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difference and a small Tpro difference exist among the four cases. IR decreases with the increase in Linj due to the same injection flow rate. Accordingly, the reduced IR part is mainly the flow resistance around injection well. During the first 8 years, the four Tpro values are nearly identical. After the 8th year, Tpro increases minimally with the increase in Linj. Therefore, increasing Linj excessively is unnecessary when other parameters are fixed. Ref. [17] shows that larger Linj enhances heat extraction when Linj is less than reservoir height. The regularity of our results is consistent with Ref. [17]. However, our results shows that the effect of increasing Linj on the heat extraction is very small even though Linj is less than reservoir height. The reason may be that Ref. [17] considers the water loss to the surrounding formation in the circulation. Thus, the difference of heat extraction rate in different Linj is relatively large. In practical EGS, the size of Linj should be determined by the degree of reservoir filtration. If the filtration cannot be determined, a larger Linj is recommended. Fig. 12. Comparison of CHS under Linj = 50, 200 m at slice of y = 250 m in the 5th and 20th year. Fig. 13. Variation curves of IR and Tpro under different values of Linj over 20-year period. 4.5 Height difference of open hole between injector and producer (ΔH = Hpro − Hinj) Fig. 14 shows the comparison of CHS under ΔH = 100, 0, −100 m in the 20th year. As the location of production open hole goes downward, CHS also gradually moves down, and the thermal energy in the upper reservoir is not fully extracted. Fig. 15 shows the variation curves of IR and Tpro under different values of ΔH over 20-year period. With the increase in ΔH, IR significantly decreases. The negative IR value when ΔH = −100 m results from the positive hydraulic gradient between injection and production wells. In this scenario, water flows easily and rapidly through the reservoir, and minimal electricity is consumed in the circulating pump. However, less heat is exchanged between water and reservoir when the water flow is fast. Tpro consequently decreases with the decrease in ΔH, and the stable period of Tpro is also shortened. Overall, under the same reservoir condition, the production open hole should be set to be higher than the injection open hole as far as possible to extract considerable thermal energy from the reservoir. Nevertheless, IR should be evaluated to not exceed 0.1 MPa/(kg/s). Fig. 14. Comparison of CHS under ΔH = 100, 0, −100 m at slice of y = 250 m in the 20th year.

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Fig. 15. Variation curves of IR and Tpro under different values of ΔH over 20-year period. 4.6 Reservoir permeability (Kr) Fig. 16 shows the comparison of CHS under different values of Kr in the 20th year. With the decrease in Kr, CHS gradually changes from steep “waterfall” upward to be horizontal, and the CHS area also increases. The vertical migration of injected water weakens, whereas its horizontal migration strengthens. Low Kr evidently weakens the water flow condition; cold water cannot sink down due to high density when it flows into reservoir; instead, it moves toward production open hole driven by pressure gradient between two wells. Compared with previous results (Sections 4.1 and 4.3), as Kr increases, the controlling factors of water flow path gradually change from pressure gradient to gravity (cold water possessing higher density than that of hot water). Fig. 17 shows the variation curves of IR and Tpro under different values of Kr over 20-year period. IR increases with the decrease in Kr. IR under Kr = 1E–13 m2 is much larger than that of the other cases and higher than 0.1 MPa/(kg/s) during the entire 20 years. Comparison of IR curves of the four cases shows that Kr substantially influences IR. Tpro increases with the decrease in Kr due to the large heat exchange volume, and Tpro increment also increases. With the decrease in Kr, Tpro curve shape gradually changes from lower convex to upper convex. Overall, gradually increasing Kr in the process of reservoir stimulation will lower not only IR but also Tpro dramatically. Optimal Kr should be determined on the basis of comprehensive consideration.

Fig. 16. Comparison of CHS under different values of Kr at slice of y = 250 m in the 20th year. Fig. 17. Variation curves of IR and Tpro under different values of Kr over 20-year period. 4.7 Reservoir temperature (Tr) Fig. 18 shows the comparison of CHS under different values of Tr in the 20th year. CHS under different values of Tr is similar. The area of CHS is only slightly reduced with the increase in Tr. When Tr is proximated to Tinj temperature, CHS will gradually change to that in Fig. 16(d) due to the decline in gravity control. The temperature difference between reservoir and

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injected water (ΔT = Tr − Tinj) of the four cases in this work is higher than 100 °C. This condition results in minimal difference in CHS among them. Fig. 19 shows the variation curves of IR and Tpro under different values of Tr over 20-year period. IR decreases slightly with the increase in Tr. IR of the four cases increases slowly with the maximum value of only 0.015 MPa/(kg/s) in the 20th year. Tpro curve patterns are similar. The stable periods of the four cases are nearly the same (0–4 years). At the beginning period (4–8 years) of the decline stage, Tpro with high Tr possesses a large decline rate. Afterward (8–20 years), the Tpro values of the four cases have nearly uniform decline rate. The Tpro values of Tr = 220 C, 200 C, 180 C, 160 C decrease to 124.2 °C, 116.8 °C, 109.3 °C, and 101.8 °C in the 20th year, respectively. The decrements are 95.8 °C, 83.2 °C, 70.7°C, and 58.2 °C. A high temperature difference between reservoir and injected water indicates the produced temperature drop is large. For every 20 °C increase in Tr, Tpro in the 20th year increases by approximately 7.5 °C. For a conductive formation with a normal temperature gradient (30 °C/km), it needs to drill further downward 667 m to generate a reservoir with a temperature increment of 20 °C. Therefore, the drilling cost and requirements for the produced water temperature should be considered comprehensively to decide whether to drill deeper to search for higher-temperature reservoirs. Fig. 18. Comparison of CHS under different values of Tr at slice of y = 250 m in the 20th year. Fig. 19. Variation curves of IR and Tpro under different values of Tr over 20-year period. 4.8 Injection mass flow rate (qinj) Fig. 20 shows the comparison of CHS under different values of qinj in the 20th year. qinj greatly influences the CHS. As qinj increases, CHS gradually changes from the vertical direction to the horizontal direction, and the heat extraction volume of the upper reservoir also increases. The increase in flow rate mainly increases the water horizontal velocity. Fig. 21 shows the variation curves of IR and Tpro under different values of qinj over 20-year period. IR increases with the increase in qinj. For qinj = 90 kg/s, the maximum value of IR is only 0.018 MPa/(kg/s). Compared with Fig. 17. Fig. 21 indicates that the reservoir with permeability Kr = 1E–12 m2 can support very high qinj (> 90 kg/s). Therefore, for commercialization target (qinj >100 kg/s), the natural tight formation should be stimulated to have a permeability beyond 1E–12 m2 at least. Tpro 17

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decreases with the increase in qinj. In the decline stage, a high qinj indicates a fast Tpro drop. Considering the temperature criteria (Eq. 1), the projects under the cases of 50, 70, and 90 kg/s all have a short expected lifetime. A large Tpro decrease rate will reduce the power generation performance. Fig. 20. Comparison of CHS under different values of qinj at slice of y = 250 m in the 20th year. Fig. 21. Variation curves of IR and Tpro under different values of qinj over 20-year period. 4.9 Injection water temperature (Tinj) Fig. 22 shows the comparison of CHS under different values of Tinj in the 20th year. The change in CHS is similar in the four cases. The reason is the same as the change in CHS under different reservoir temperatures (Section 4.7). The temperature difference between reservoir and injected water (ΔT = Tr − Tinj) of the four cases in this work is higher than 100 °C. This condition results in a small difference in CHS among them although Tin is different. For most EGS projects, temperature difference (ΔT) will be greater than 100 °C. Therefore, Tinj has a limited effect on CHS in real projects. Fig. 23 shows the variation curves of IR and Tpro under different values of Tinj over 20-year period. IR increases with the decrease in Tinj due to the continuous increase in (μ/ρ). Tpro stable periods of four cases are nearly the same. During the decline stage, a low Tinj corresponds to a fast Tpro drop. The Tpro values of of Tinj = 10 C, 30 C, 50 C, 70 C decrease to 95.6 °C, 101.4 °C, 109.3 °C, and 118.9 °C in the 20th year, respectively. The decrements are 84.4 °C, 78.6 °C, 70.7 °C, and 61.1 °C. A high temperature difference (ΔT) indicates the produced temperature drop is large. For every 20 °C increase in Tinj, the Tpro values in the 20th year increase by approximately 5.8 °C, 7.9 °C, and 9.6 °C. Increasing Tinj will definitely increase Tpro; however, the increment in Tpro is small, and the increase in Tinj also requires extra energy. Determining the appropriate Tinj in accordance with the water source condition and the engineering requirement for Tpro is necessary. Fig. 22. Comparison of CHS under different values of Tinj at slice of y = 250 m in the 20th year. Fig. 23. Variation curves of IR and Tpro under different values of Tinj over 20-year period. 4.10 Summary of the simulation results We compare the maximum and minimum values under each scenario simulation results to reflect the influence degree of

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various factors on IR and Tpro. The comparison results are listed in Table 3. The following conclusions can be drawn: (1) CHS: It is mainly affected by Kr and qinj, followed by Lr, Wr, Hr, and ΔH. If cold front does not pass through to the pumping well, then Lr and Wr will not affect the CHS. The CHS is fundamentally controlled by the vertical and horizontal velocity components of the water flow through the reservoir. The velocity component is controlled by pressure gradient and gravity. (2) IR: Table 3 shows that the most significant influencing factor is Kr. Among all schemes, Kr is the only parameter that makes IR value exceed 0.1 MPa/(kg/s). The subsequent influential factors are ΔH, Linj, and Tinj. The influence degree of the other parameters is similar. (3) Tpro: It is mainly controlled by Lr, Wr, and Hr. Reservoir shape has the greatest influence on Tpro. Next is qinj. Kr, ΔH, Tinj, and Tr follow. The effect of Linj is minimal. The stable period of production water temperature is mainly affected by Lr, Wr, Hr, ΔH, Kr, and qinj. Other factors only slightly affect the length of stable period.

Table 3 Comparison of the maximum and minimum values of IR and Tpro. The value denotes the parameter value in the 20th year.

5 EGS optimization of ZCS 5.1 Theoretically optimal parameters The most ideal engineering state is that the produced flow rate is very large, the outlet temperature does not drop (or minimally), and the stable period time is very long. The injected water should sweep through the entire reservoir zones as much as possible and possess sufficient time to exchange heat with the surroundings for achieving high heat extraction efficiency. Therefore, in accordance with previous research results, the theoretically optimal strategy is determined as follows: Lr: The maximum horizontal migration distance of cold front is 1210 m, as shown in Fig. 6, under the injection rate of 30 kg/s. The optimal injection rate must be greater than 30 kg/s; thus, the optimal Lr is preliminarily set as 1500 m. 19

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Wr: Tpro increases with the increase in Wr, but Tpro increment decreases with the increase in Wr. A minimal Tpro increase is predicted when Wr is beyond 900 m. Thus, the optimal Wr is set as 900 m. Hr: It greatly influences Tpro, and large Hr is expected. However, in present EGS projects, a long reservoir is preferred over a high reservoir under certain fracturing fluid volume. Therefore, the optimal Hr is assumed as 900 m for simulation. Linj: The optimal Linj is set as 50 m because of the limited effect of Linj on Tpro. ΔH: As discussed in Section 4.3, heat is nearly fully extracted from the lower part of the reservoir because of the downward movement of water, whereas limited heat is extracted from the upper part. Thus, optimal reservoir should be generated and extended in the direction downward away the open hole. The open hole of injection and production wells are set at the top boundary of the reservoir (shown in Fig. 26). ΔH is 0 m. Kr: It very significantly influences IR. When Kr is 1E–13 m2, IR rises too fast; when Kr is 1E–11 m2, Tpro drops fast compared with that when Kr = 1E–12 m2 (Fig. 17). Therefore, the optimal stimulated reservoir should possess a permeability of 1E–12 m2. Tr: High Tr is anticipated. In the study area, the ZR1 well with a depth of 3000 m and a bottomhole temperature of 151.5 °C is completed. The ZR1well must be drilled further in the future to pursue a high heat production goal. In this work, Tr = 220 °C is selected as the optimal value, which means the ZR1 well should be drilled down to the depth of 5330 m. The initial pore pressure at the injection open hole is approximately 53.3 MPa. qinj: The optimal qinj will be determined through simulations. Tinj: As mentioned in Section 4.9, the increase in Tinj will definitely increase Tpro; nevertheless, the increment in Tpro is inconsiderable, and the increase in Tinj requires extra energy. The local shallow groundwater is selected as the injected water considering the availability. The average annual temperature of the ZCS area is 9.5 °C. In this work, the optimal Tinj is set as 10 °C. The nine parameters above are quasi-optimal parameters for research and thus have no exact value. High qinj will result in high injection pressure (Pinj), which will increase the required power for pumping the geofluid and make partial stimulated 20

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fracture close again. Therefore, Pinj should not exceed the h. On the basis of the logging data in Ref. [16], h of ZCS is inferred to be approximately 80 MPa at a depth of 5330 m. Pinj of the Soultz project has increased by approximately 4 MPa over 30 years, which can also be used as a reference value. We accordingly conduct a series of numerical simulations under different qinj and observe the changes in Pinj, IR, Tpro, and electrical power (We). The model is established and discretized in the same way as Section 3.3.2. The model geometry is 1700 m × 1200 m × 1200 m. The grid system is 43 × 24 × 17. The total number of grid elements is 17544. The total stimulated reservoir volume is 1.2E9 m3. 5.1.1 Variations in injection pressure and flow impedance After amounts of simulations, three cases under qinj of 150, 400, and 450 kg/s are chosen. When qinj is 150 kg/s, Pinj in the 20th year increases by approximately 4 MPa; when qinj is 450 kg/s, Pinj in the 20th year increases up to approximately 80 MPa; when qinj is 400 kg/s, Tpro begins to decline. The simulation results of Pinj and IR under the three cases are presented in Fig. 24. During the 20 years, IR under the three cases is small and does not exceed 0.1 MPa/(kg/s). It indicates that the reservoir with a permeability of 1E–12 m2 can withstand a flow rate of 450 kg/s without excess IR. The three Pinj curves are relatively flat over 20 years. This condition indicates that the project is running steadily and possesses good performance. Fig. 24. Variation curves of IR and Pinj under different injection flow rates. 5.1.2 Variations in produced water temperature and electrical power Fig. 25 shows the variation curves of Tpro and We under different injection flow rates. Tpro under 450 kg/s drops by nearly 1.6% (3.5 C) during 20 years, which is lower than the commercial requirements of 10%. Tpro under 400 kg/s begins to decline in the 18.5th year and decreases by approximately 1.5 C until the 20th year. No temperature decline stage exists for 150 kg/s. We of the three cases is stable. Over a 20-year period, the We values of 150, 400, and 450 kg/s are 12.3 MW, 32.7–33.3 MW, and 36.2–37.6 MW, respectively. The results show that the optimal strategy has high power generation potential. Fig. 26 shows the space variation of the reservoir temperature in the plane y = 600 m. At the beginning of 0–4 years, the injected water did not sink considerably due to the high injection rate, and the entire cold front surface could move evenly in horizontal and vertical directions toward the pumping well (Fig. 26a). As the injected water was pushed away from the

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injection well, the kinetic energy of the water gradually decreased. Therefore, under the action of gravity, the vertical velocity of the water flow gradually dominates the advantage, and the cold front starts to migrate downward. Subsequently, the water gradually moves to the pumping well at the reservoir bottom (Fig. 26b). When the water flow is close to the pumping well, it starts to move upward to the pumping hole under the pumping pressure gradient (Fig. 26c). From Fig. 26d, the heat exchange has taken place nearly in the entire reservoir, which indicates a high thermal energy extraction rate. Fig. 25. Variation curves of Tpro and We under different injection flow rates. Fig. 26. Space variation of the reservoir temperature in the plane y = 600 m. 5.2 Practically optimal parameters As discussed in Section 5.1, the theoretically optimal flow rate is 450 kg/s. However, it is a very large value. Taking Soultz project as example, its production flow rate is about 70 kg/s per well [2]. Thus, about 14 deep wells (injection and production) with a depth of 5330 m need completed in the theoretically optimal case. The initial investment is too large. For realistic and future application, we discussed on the feasibility of such study with a deep zone of 2 km in ZCS. Based on advanced fracturing technology and existing EGS projects, Lr=1000 m is relatively easy to achieve. As mentioned in Section 2.2, a horizontal stress regime (H > V > h) can be expected for deep formations in the ZCS. A horizontal reservoir may be created through hydraulic stimulation. Therefore, the Wr is set as half of Lr and Hr is assumed as 300 m for simulation. At the depth of 2 km, the reservoir initial temperature is measured as 125 C. The Linj, ΔH, Kr, Tinj and qinj are all set the same as Section 5.1. h of ZCS is inferred to be approximately 32 MPa at a depth of 2 km. The total stimulated reservoir volume is 1.5E8 m3. Sanyal and Butler [33] proposed that the stimulated volume should exceeds 1E8 m3 for EGS. Therefore, our proposed strategy still meets this requirement. The numerical model is established and simulated in the same way as Section 5.1. Fig. 27(a) shows the variation curves of Tpro and We under qinj =80 kg/s. After amounts of simulations, when qinj is 80 kg/s, the Tpro in the 20th year just declines to about 105.36 C. The stable period is about 8 years. Over a 20-year period, the We ranges from 0 to 1.25 MW. It is smaller than that of Soultz (2.8 MW).

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Fig. 27 (b) presents the simulation results of Pinj and IR under qinj =80 kg/s. The Pinj increases from 18.4 to 19.1 MPa. The IR increases from 0.03 to 0.04 MPa/(kg/s). They both meet the performance criteria. It means the reservoir is still capable of withstanding larger injection flows. To improve the electrical power further, the shallow reservoirs with higher temperature are expected.

Fig. 27. Variation curves of Tpro, We (a) and IR, Pinj (b) under qinj=80 kg/s.

6 Conclusions In this work, the geothermic features of the GDB and ZCS are introduced. Sensitivity analysis of the influence of nine parameters is numerically conducted. Then, two optimal strategies for ZCS are presented, and their heat production performance are evaluated. The main conclusions are shown as follows: (1) GDB possesses a good geothermal structure. The deep magma chamber and shallow magmatic walls and dykes are the heat sources for GDB; the widely distributed Indosinian granites are the heat reservoir; the deep and sandy mudstone layers play the role of heat insulation; the deep-large faults connect the deep magma chamber and carry its heat energy upward to the shallow sandstone layers. The ZCS area possesses the highest surface temperature of GDB. In ZCS, the shallow zone (0–2000 m) is determined as fault-controlled convection hydrothermal system. The deep zone (below 2000 m) is a conductiontype HDR system. (2) The main affecting factors of CHS are Kr and qinj. If the cold front does not pass through to the pumping well, then Lr and Wr will not affect the CHS. The CHS is controlled by the vertical and horizontal velocity components of the water flow through the reservoir. The velocity component is controlled by pressure gradient and gravity. (3) The most significant influencing factor of IR is Kr. The next influencing factors are ΔH, Linj, and Tinj. The influence degree of the other parameters is similar. (4) Tpro is mainly controlled by Lr, Wr, and Hr. Reservoir shape has the greatest influence on Tpro. The effect of Linj is 23

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minimal. The stable period of production water temperature is mainly affected by Lr, Wr, Hr, ΔH, Kr, and qinj. Other factors only slightly affect the length of stable period. (5) The simulation results of the theoretically optimal parameters for ZCS show that Tpro under 450 kg/s drops by nearly 1.6% (3.5 C) during 20 years. The We values of 150, 400, and 450 kg/s are 12.3 MW, 32.7–33.3 MW, and 36.2–37.6 MW, respectively. The space variation of reservoir temperature implies that the heat exchange has taken place nearly in the entire reservoir, which indicates a high thermal energy extraction rate. The theoretically optimal strategy has a high power generation potential. (6) The results of the practically optimal parameters for ZCS illustrate that the maximum injectable flow rate is 80 kg/s. Tpro in the 20th year just declines to about 105.36 C. The stable period is about 8 years. Over a 20-year period, the We ranges from 0 to 1.25 MW. It is smaller than that of Soultz. For future applications, the shallow reservoirs with high temperature are expected.

Acknowledgements

This work was supported by the Natural Science Foundation of China (No. 41807195); Applied Basic Research Foundation of Shanxi Province (CN) (No. 201801D221049); China Postdoctoral Science Foundation (No. 2019M661053); China Scholarship Council (No.201906935007).

Conflict of Interests The author(s) declare(s) that there is no conflict of interests regarding the publication of this article.

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Liang-Liang Guo: Conceptualization, Methodology, Software, Writing-Original draft preparation. Yong-Bo Zhang: Visualization, Investigation. Zhi-Chao Wang: Supervision. Jian Zeng: Data curation. Yan-Jun Zhang: Software, Validation. Zhi-Xiang Zhang: Writing-Reviewing and Editing.

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Declaration of interests  The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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Fig. 1. Location and tectonic map of GDB.

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Fig. 2. Logging results and temperature curves of ZR1 well.

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Fig. 3. Schematic of an EGS underground part.

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Fig. 4. Methodological flowchart.

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Fig. 5. 3D numerical model of the base case.

Fig. 6. Comparison of CHS under different values of Lr in the 20th year at slice of y = 250 m.

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Fig. 7. Variation curves of IR and Tpro under different values of Lr during 20-year period.

Fig. 8. Comparison of CHS under different values of Wr at slice of z = 300 m (upper) and y= 250, 350, 450, 550 m (lower) in the 20th year.

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Fig. 9. Variation curves of IR and Tpro under different values of Wr over 20-year period.

Fig. 10. Comparison of CHS under different values of Hr at slice of y = 250 m and z = 150 m in the 20th year.

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Fig. 11. Variation curves of IR and Tpro under different values of Hr over 20-year period.

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Fig. 12. Comparison of CHS under Linj = 50, 200 m at slice of y = 250 m in the 5th and 20th year.

Fig. 13. Variation curves of IR and Tpro under different values of Linj over 20-year period.

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Fig. 14. Comparison of CHS under ΔH = 100, 0, −100 m at slice of y = 250 m in the 20th year.

Fig. 15. Variation curves of IR and Tpro under different values of ΔH over 20-year period.

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Fig. 16. Comparison of CHS under different values of Kr at slice of y = 250 m in the 20th year.

Fig. 17. Variation curves of IR and Tpro under different values of Kr over 20-year period.

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Fig. 18. Comparison of CHS under different values of Tr at slice of y = 250 m in the 20th year.

Fig. 19. Variation curves of IR and Tpro under different values of Tr over 20-year period.

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Fig. 20. Comparison of CHS under different values of qinj at slice of y = 250 m in the 20th year.

Fig. 21. Variation curves of IR and Tpro under different values of qinj over 20-year period.

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Fig. 22. Comparison of CHS under different values of Tinj at slice of y = 250 m in the 20th year.

Fig. 23. Variation curves of IR and Tpro under different values of Tinj over 20-year period.

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Fig. 24. Variation curves of IR and Pinj under different injection flow rates.

Fig. 25. Variation curves of Tpro and We under different injection flow rates.

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Fig. 26. Space variation of the reservoir temperature in the plane y = 600 m.

Fig. 27. Variation curves of Tpro, We (a) and IR, Pinj (b) under qinj=80 kg/s.

Journal Pre-proof Highlights     

Nine influencing factors of heat performance are numerically investigated. Reservoir geometry has the greatest influence on production water temperature. The affecting factors of water flow path are determined. The effects of the length and location of open hole are considered. Optimal system attains an electric power of 36.2–37.6 MW and a flow rate of 450 kg/s.

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Table 1 Parameters sensitivity schemes. Parameters

Lr /m

Wr /m

Hr /m

ΔH /m

Linj /m

Kr /m2

Tr /℃

qinj /kg/s

Tinj /℃

Base case Other cases

500 1000 2000 3000 -

300 500 700 900 -

300 500 700 900 -

0 100 50 –50 –100

50 100 150 200 -

10E-12 10E-10 10E-11 10E-13 -

180 160 200 220 -

30 50 70 90 -

50 10 30 70 -

Table 2 Reservoir properties used in the simulations. Parameters

Value 2560 kg/m3 0.023 3E–16 m2

Rock density Rock porosity Rock permeability (Kx= Ky = Kz) Rock thermal conductivity Rock specific heat Reservoir porosity Injection specific enthalpy (base case) Productivity index (base case)

3.12 W/(mK) 0.823 kJ/(kgK) 0.1 243.56 kJ/kg 5.3E–12 m3

Table 3 Comparison of the maximum and minimum values of IR and Tpro. The value denotes the parameter value in the 20th year. IR/ MPa/(kg/s) Parameters

Lr /m Wr /m Hr /m Linj /m ΔH/m Kr/m2 Tr/C qinj/(kg/s) Tinj/C

Max.

Min.

Case

Value

Case

Value

𝑽𝐚𝐥𝐮𝐞(𝐌𝐚𝐱.) 𝑽𝐚𝐥𝐮𝐞(𝐌𝐢𝐧.)

3000 300 300 50 100 1E-10 160 90 10

0.0190 0.0156 0.0156 0.0156 0.0480 0.0001 0.0159 0.0188 0.0290

500 900 900 200 -100 1E-13 220 30 70

0.0156 0.0130 0.0130 0.0060 -0.014 0.1500 0.0150 0.0156 0.0127

1.22 1.20 1.20 2.60 -3.43 1500.00 1.06 1.21 2.28

Tpro /C Max.

Min.

Case

Value

Case

Valu e

𝑽𝐚𝐥𝐮𝐞(𝐌𝐚𝐱.) ― 𝑽𝐚𝐥𝐮𝐞

3000 900 300 200 100 1E-13 220 30 70

180.0 158.3 109.3 111.2 126.0 124.7 124.2 109.3 118.9

500 300 900 50 -100 1E-10 160 90 10

109.3 109.3 165.1 109.3 97.9 95.1 101.8 62.2 95.6

70.70 49.00 55.80 1.90 28.07 29.56 22.42 47.12 23.22