Evaluation of geothermal energy extraction in Enhanced Geothermal System (EGS) with multiple fracturing horizontal wells (MFHW)

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Evaluation of geothermal energy extraction in Enhanced Geothermal System (EGS) with multiple fracturing horizontal wells (MFHW) Facheng Gong a, Tiankui Guo a, *, Wei Sun b, Zhaomin Li a, Bin Yang c, Yimei Chen a, Zhanqing Qu a a b c

School of Petroleum Engineering, China University of Petroleum (East China), Qingdao, China National Engineering Research Center for Coalbed Methane Development, Beijing, China SINOPEC Shengli Oilfield, Dongying, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 9 June 2019 Received in revised form 3 November 2019 Accepted 25 November 2019 Available online xxx

The deep geothermal energy produced from Enhanced Geothermal System (EGS) has a great development prospect because of enormous potential and environmental friendliness. EGS process involves a complex thermal-hydraulic process, and fractures in EGS are main channels for fluid flow and heat transfer, the understanding of which is crucial to the sustainable utilization of geothermal reservoirs. In this paper, a 3D thermal-hydraulic coupled numerical model is proposed to describe the interaction of fluid flow and heat transfer. Besides, the EGS with multiple fracturing horizontal wells (MFHW) is adopted to evaluate the effect of multiple hydraulic fractures on geothermal energy extraction performance. The MFHW with multiple stimulated fractures could increase fluid flow path and heat exchange area significantly, thereby enhance the heat recovery ability. Firstly, we analyzed the evolution of temperature and flow fields in EGS and compared the MFHW EGS with conventional vertical EGS. Secondly, the effects of fracturing parameters, including the fracture number, fracture length, and fracture conductivity, on heat extraction performance were investigated. Finally, the cost for drilling and hydraulic fracturing in MFHW EGS was calculated. The results indicate that MFHW EGS has a higher cumulative thermal production and a better heat extraction performance than that of conventional vertical EGS. For the optimization of hydraulic fracture parameters, the cumulative thermal production firstly increases and then decreases as the fracture number increases, the cumulative thermal production curve exists an inflection point of fracture number. Longer fracture length and higher fracture conductivity could enhance the cumulative thermal production, but the output growth slows down gradually. Considering economic cost, the best fracture parameters for MFHW EGS in this paper are the fracture number of 7, the fracture length of 300 m, and the fracture conductivity of 350 mm2
cm, respectively. The research provides a better study for multiple fracturing horizontal wells (MFHW) EGS and helps to optimize fracture parameters and geothermal reservoir management, which is conductive to improve the geothermal energy efficiency. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Geothermal energy Enhanced geothermal system Multiple fracturing horizontal wells Fracturing parameters Heat extraction performance

1. Introduction The geothermal energy as a renewable resource has the advantage of enormous potential and environmental friendliness, which is the future direction of energy development [1]. Especially the deep geothermal energy, stored in Hot Dry Rock (HDR) in depth of over 3 km and temperature of over 150  C, has a great

* Corresponding author. E-mail address: [email protected] (T. Guo).

development prospect. Due to the low permeability of a HDR reservoir, the hydraulic fracturing treatment is usually conducted to create a system of open, connected channels for fluid flow and heat exchange, which is called Enhanced Geothermal System (EGS) [2]. Since the Fenton Hill project in the 1970s [3], a large number of geothermal projects have been carried out all over the world, including Rosemanowes in the United Kingdom, Hijiori and Ogachi in Japan, Soultz in France, and Cooper Basin in Australia. Statistically, the global power capacity is expected to reach 17 GW by 2023. However, there are still some challenges needed to be discussed in EGS, and this paper mainly investigates the following aspects.

https://doi.org/10.1016/j.renene.2019.11.134 0960-1481/© 2019 Elsevier Ltd. All rights reserved.

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The numerical simulation of EGS are widely used for evaluating heat mining performance due to their economically reproductive and predictive ability. For EGS numerical modeling, it involves a complex thermal-hydraulic-mechanical-chemical (THMC) coupling process, including fluid flow, heat transfer, reservoir deformation and geochemical reactions [4]. Song et al. [5] established a numerical thermal-hydraulic (TH) coupling model in which the multilateral wells were adopted to analyze the heat extraction €cher et al. [6] analyzed the hydrothermal performance of EGS. Blo process during the lifetime of a deep geothermal reservoir in Germany. The results showed the complex interaction of fluid and thermal fields during geothermal energy production. Held et al. [7] established a 3D thermal-hydraulic numerical model with multiwell system based on a complex geological model of the Soultz geothermal reservoir to determine the optimal input parameter. The results showed the benefits of multi-well system. Rutqvist et al. [8] conducted thermal-hydraulic-mechanical (THM) modeling with TOUGH-FLAC for simulating geomechanical effects of cold water injection during the stimulation of the EGS. Zhao et al. [2] proposed a THM model of fractured reservoir based on Tengchong geothermal field in China. The study considered the heat exchange, heat transfer, fluid migration, rock mass deformation, and the coupling effect surrounding an EGS. Recently, studies dealing with the coupling associated with chemical interaction were also increasing [9,10]. Taron et al. [9] studied THMC (thermo-hydromechano-chemo) coupling effects in discrete fracture media where fracture permeability change as a result of changes in stress and chemical precipitation and dissolution. Besides, there existed some numerical methods to characterize fractured geothermal reservoirs. For example, the discrete fracture network model [11], the single porosity model [12] and the equivalent pipe network model [13]. Yao et al. [11] established a 3D discrete fracture network model where the fractured porous media consists of rock matrix blocks and discrete fractures. Jiang et al. [12] presented a threedimensional transient model for EGS subsurface thermohydraulic process by which the geothermal reservoir is treated as an equivalent porous medium of a single porosity. Xu et al. [13] proposed a simplified approach to simulate the coupled hydrothermal system for EGS, capable of providing a detailed prediction of fluid flow and heat transfer in geothermal reservoir based on an equivalent pipe network model. At present, the main constraint for EGS is creating sufficient connectivity within the injection and production well in the stimulated region to allow for high production rates without reducing reservoir life by rapid cooling. However, due to the technology and cost restriction, the commercial development of EGS geothermal heat mining is still in its infancy [14], and geothermal development needs improved exploitation methods. Ideally, in EGS we try to maximize the exposure to the high-temperature reservoir and afford a good opportunity for interconnection by hydraulic fracturing. EGS experience indicates that well with a large angle of inclination (sub-horizontal or horizontal well) would be appropriate for this. The inclined well system (especially the horizontal well) contains more geothermal volume than the vertical well system [15]. Besides, a series of stimulated fractures could be stimulated along the horizontal well, which could largely increase the stimulated reservoir volume and heat exchange area, thereby enhance the geothermal productivity. Above all, the multiple fracturing horizontal wells (MFHW) with a series of stimulated fractures are seen as an effective approach for geothermal heat extraction [16]. The MFHW techniques are widely used in the industry of oil and gas, especially the exploration of unconventional oil and gas reservoirs, such as shale gas, tight oil, and oil sand [17e21]. However, due to the expensive directional drilling cost, these innovative techniques are not widely used for geothermal

resource exploitation until now [22]. In this paper, we applied this technology to Enhanced Geothermal System. The schematic of EGS with MFHW is shown in Fig. 1. For this EGS, one main horizontal well is drilled to HDR, a series of multiple fractures are stimulated by hydraulic fracturing along this horizontal well. The hydraulic fractures in MFHW could promote HDR fracture network formation to create a stimulated reservoir volume (SRV). Then another horizontal well is drilled through the hydraulic fracture areas to create connected channels. The cold fluid is injected down one horizontal well, and then is heated through fractures by contacting with HDR. Finally, the hot fluid returns to the surface from another horizontal well for power generation. For the numerical simulation of horizontal well system in geothermal heat mining, scholars have launched some researches. Zeng et al. [22] evaluated electricity generation potential from the Yangbajing geothermal reservoir through three horizontal wells and analyzed geological factors affecting heat extraction performance, but his model did not add the fracture pathways in the HDR reservoir. Xia et al. [23] studied the effect of fracture spacing, injection rate on heat extraction for horizontal geothermal wells connected by fixed five hydraulic fractures. Though they evaluated performance of a horizontal conceptual EGS model, they did not talk much about the effect of fracture number on geothermal exploitation. Cui et al. [24] proposed a single horizontal well closed model without hydraulic fractures for geothermal exploitation. They argued that the cost for geothermal production of this system was lower than the doublet scheme. Although all these numerical simulation studies of horizontal well EGS model have helped in developing a better understanding of the heat extraction, few of them could consider the effect of fracture number, fracture length and fracture conductivity on geothermal heat mining. There is a lack of systemic and comprehensive research work on the evaluation of multiple fracturing horizontal wells (MFHW) EGS and fracturing parameter optimization. Hence, we proposed a three-dimensional (3D) thermalhydraulic (TH) coupled MFHW EGS model to analyze the effect of discrete fractures on the performance of geothermal heat mining based on the commercial finite element software COMSOL Multiphysics. Firstly, we analyzed the evolution of temperature and flow fields in EGS and compared the MFHW EGS with conventional vertical EGS. Secondly, the effects of fracturing parameters, including the fracture number, fracture length, and fracture conductivity, on heat extraction performance were investigated. Finally, the cost for drilling and hydraulic fracturing in MFHW EGS was calculated.

Fig. 1. The schematic of Multiple Fracturing Horizontal Wells (MFHW).

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2. TH coupling numerical model 2.1. Model assumptions The model is focused on modeling and analyses of the subsurface thermo-hydraulic process in EGS. When establishing the numerical model, we assumed the following assumptions. (1) The discrete fracture network model is employed to characterize the fractured geothermal reservoir, which consists of discrete fractures and rock matrix block. The fractures were assumed to be uniform and isotropic with the same fracture conductivity separate from the homogeneous rock matrix. The governing equations for the fractures and the rock matrix were separate. (2) The water is used as circulating fluid. In the reservoir, the fluid temperature is lower than 493 K, and the hydraulic pressure is high, larger than 20 MPa, therefore the water does not vaporize under the operation conditions and the reservoir is saturated with single phase water. The fluid flow in the reservoir obeys Darcy’s law (3) The heat exchange between fluid and solid involves two ways: heat convection and heat conduction. The local thermal equilibrium is employed and the temperature difference between the solid phase and liquid is ignored, assuming that solid and liquid two phases reach temperature balance instantaneously, which could simplify numerical model and improve computational efficiency.

2.2. Governing equations Based on the previous assumptions, the governing equations of the numerical model of EGS with MFHW could be expressed as follows [5,13]: The fluid flow in the rock matrix is formulated by the following mass conservation equation:




v rf f



vt


 þ V, rf q ¼ Qf

(1)

where rf is the fluid density (kg/m3), f is the reservoir porosity, t is time (s), and q is Darcy velocity in matrix rock (m/s). According to Darcy’s law, q is described by Eq. (2):

q¼ 

k

mf


 V, p þ rf gz

(2)

3

conductivity differ between the solid (s) phase and the fluid (f) phase. In this study, the local thermal equilibrium is assumed, which introduced the effective specific heat capacity and the thermal conductivity calculated by a weighted volume sum defined as follows:



rCp

 eff


  ¼ f rf Cpf þ ð1  fÞ rs Cps

leff ¼ flf þ ð1  fÞls

(5) (6)

where rs and rf are the solid and fluid densities (kg/m3), Cs and Cf are the solid and fluid heat capacities [J/(kg K)], ls and lf are the solid and fluid thermal conductivities [W/(m$K)]. In this way, the heat transfer within the reservoir is formulated by one energy conservation equation as follows:



rCp

 eff


 vT þ rf Cf qVT  V, leff VT ¼ FT vt

(7)

where T is the temperature in rock (K), (rCp) eff and leff are the effective specific heat capacity and the effective thermal conductivity. Eq. (7) involves the heat convection term and heat conduction term, in which the second term on the left rf Cf qVT represents the heat convection term, where q is fluid flow velocity (m/s), and the third term V,ðleff VTÞ represents the heat conduction term. Similarly, the energy conservation equation in fractures is described as follows:


   vT df rCp eff þ df rf Cf qf VT  V, df leff VT ¼ FT vt

(8)

The term ФT in Eq. (7) and Eq. (8) indicates the heat transfer between the matrix and fractures. 2.3. Coupling effect The coupling effect in EGS refers to the mutual influence of fluid flow, heat transport and geomechanics processes in geothermal reservoirs [25]. As shown in Fig. 2, the interaction of THM coupling is as follows: (1) Influence of flow field on temperature field: when the cold fluid flows through fractures, the heat exchange between cold fluid and hot matrix disturb the balanced temperature filed; (2) Influence of temperature field on flow field: the high temperature and high pressure in EGS lead to the variation of physical

where k is the reservoir permeability (m2), mf is the fluid dynamic viscosity (Pa$s), p is fluid pressure (Pa), and rfgz represents the gravity term, in which rf is the fluid density (kg/m3), g is the gravitational acceleration (m/s2), and z is the vertical direction. The fluid flow equation in fractures is described as follows:

df


v ff rf vt


þ Vt , df rf qf ¼ Qf

(3)

The term df, the fracture width (m), is added to the equation to ensure that the dimension of the matrix is consistent with fractures, ff is the fracture porosity, Vt denotes the gradient operator restricted to the fracture’s tangential plane, Qf in Eq. (1) and Eq. (3) is the mass transfer between the matrix and fractures, and qf is Darcy velocity in fractures (m/s), which is also described by Darcy’s law.

qf ¼ 

kf

mf


 Vt , p þ rf gz

(4)

For the heat transfer process, the heat capacity and heat

Fig. 2. Full coupling diagram of the flow field, stress field and temperature field.

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characteristics of the working fluid; (3) Influence of temperature field on stress field: the change of temperature field affects the inherent physical and mechanical properties of matrix. Besides, thermal stress created by temperature gradient disturbs the original stress field; (4) Influence of stress field on temperature field: heat energy will be generated during the rock deformation, in addition, the thermal conductivity will be affected by matrix deformation; (5) Influence of flow field on deformation field: the effective stress will be impacted by porous pressure evoked by fluid injection; (6) Influence of stress field on flow field: the change of stress field leads to the contraction and expansion of matrix, so the permeability of matrix and fractures changes. In this paper, we neglected the rock thermoelastic and poroelasticity effect and considered the thermal-hydraulic coupling in EGS. On the one hand, the cold fluid is injected into the hot rock, extracts heat from the high-temperature rock and influences the reservoir original temperature distribution. On the other hand, the temperature field, in turn, affects the flow field. The change of working fluid temperature during geothermal extraction influences the fluid physical properties and the fluid flow. In this paper, we use water as the working fluid because it is generally available and has a high heat capacity. Under hightemperature conditions in the thermal reservoir, the physical properties of water are the functions of temperature. When the fluid temperature is between 273 and 533 K, the water properties are described as follows [26]:

rwater ¼ 838:5 þ 1:4T  3:0  103 T 2 þ 3:7  107 T 3

(9)

mwater ¼ 0:004  2:1  105 T þ 3:9  108 T 2  2:4  1011 T 3 ; T2½413; 533

(10)

Cp;water ¼ 12010  80  T þ 0:3  T 2  5:4  104 T 3 þ 3:6  107 T 4 (11)

lwater ¼  0:87 þ 0:009T  1:6  105 T 2 þ 7:9  109 T 3

Fig. 3. Schematic diagram of a single-fracture conceptual model.

Tðx; tÞ ¼ T0

2

3  .
! ðls xÞ rw Cpw df x 6 7 U t  þ ðTin  T0 Þerfc4 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 5
   uf 2 uf uf t  x ls rs Cps

(13)

where Cpw and Cps are the water and rock heat capacities [J/(kg K)], ls is the solid thermal conductivity [W/(m$K)], rw and rs are the water and fluid densities (kg/m3), df is the fracture width (m). In Eq. (13), erfc is the residual error function; U is the unit step function. The values of parameters for the numerical and analytical models are listed in Table 1. The numerical solution of the single fracture TH coupled model was obtained with COMSOL and compared with the analytical solution, as shown in Fig. 4. Fig. 4(a) illustrates the temperature distribution along the fracture at various times (t ¼ 10, 50, and 100 d, where unit d represents day), while Fig. 4(b) shows the temperature variation with time at three different positions (x ¼ 30, 50, and 80 m) in the fracture. Fig. 4 shows that the numerical model fits well with the analytical solution, indicating that the presented mathematical model and computation method are both feasible. 3. MFHW EGS model case

(12) We implemented Eq. (9) to Eq. (12) to calculate the dynamic change of fluid properties. The water hydraulic and thermal properties are both related to temperature. The fluid flow extracts the heat energy stored in the hot rock, and heat exchange directly affects the fluid flow. The interaction between the two processes is a strong coupling relationship.

3.1. Model description In this study, we established an idealized three-dimensional (3D) MFHW EGS model based on typical HDR geothermal field in which the values of the geometrical and physical parameters are referenced from the values employed in the previous studies [3,5,28]. The deep reservoir is mainly within fractured granite that has characteristics of brittle shearing and is covered by intensely impermeable granite. There is a molten crust mass at a depth of 5e15 km and the molten mass is just the heat source for the

2.4. Model validation Before further investigation, it is necessary to verify the accuracy of the proposed model. The analytical solution of the water temperature within the fracture was used to verify the accuracy of the discrete fracture TH coupled model and the feasibility of the computation method. The geometric model of heat transfer within the single fracture is shown in Fig. 3. In the 2D single fracture model, the rock matrix and the fracture extend to infinity in the y directions. The initial rock temperature is Ti, and the water is injected into the fracture with a constant temperature Tin and a fluid velocity uf to extract heat from the rock matrix. According to Lauwerier’s [27] analytical solution, the water temperature within the fracture along the x-axis at time t is expressed as follows:

Table 1 Values of numerical simulation parameters. Property

Value

Initial temperature T0 Injection temperature Tin Rock Density rs Rock specific heat capacity ls Rock thermal conductivity Cps Water velocity uf Water viscosity mf Water density rw Water specific heat capacity Cpw Fracture width df

353 K 303 K 2700[kg/m3] 1000[J/(kg$K)] 3[W/(m$K)] 0.02 [m/s] 1  103 [Pa$s] 1000[kg/m3] 4200[J/(kg$K)] 5  103 [m]

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(a) Temperature distribution along the fracture

5

(b) Temperature variation with time

Fig. 4. Comparison between the numerical and analytical results.

geothermal field. The reservoir has an average temperature of about 500 K and a geothermal gradient of 50 K/km. This model consists of an SRV, an HDR reservoir enclosing the SRV, one horizontal injection well, one horizontal production well, and multiple vertical hydraulic fractures, as shown in Fig. 5. The HDR reservoir is confined by nonconductive overburden and underlying layers that provide hydraulic and thermal insulation to trap fluid and heat. The HDR reservoir is a 3000  3000  1000 m cube located at a depth of 2500e3000 m. The SRV is located in the middle of the HDR, and the size is 1200 m  1000 m  300 m. The injection well and horizontal well are located at the center of the SRV cross section., and the horizontal lengths and well depths of two wells are 1000 m and 3000 m, respectively. The injection wells are 350 m away from the front of the SRV and the production wells are 350 m away from the back of the SRV. The multiple hydraulic fractures are stimulated along the horizontal injection well, and the production well is drilled through the multiple fractures. Therefore, a closed loop including injection well, fractures and production well is formed. As for geothermal reservoir with dense fractures, the discrete fracture model is usually employed. The hydraulic fractures in EGS are the main channel for fluid flow and heat exchange, and working fluid usually circulate through one or several dominating flow channels from the injection well to production well. Based on this, the multiple hydraulic

fractures in the model are simplified to a set of equidistant fracture planes of rectangular shape consisting of zones with higher permeability and porosity than the surrounding reservoir, giving rise to highly conductive zones connecting two wells. Besides, the planar fractures could simplify the physical model and reduce the compute workload. Fig. 5 shows the fracture configuration of an idealized MFHW EGS model. In this model, the fracture number, fracture length and fracture conductivity are 4, 300 m and 350 mm2 cm, respectively. In the following study, these three parameters are varied to study the effects on the performance of EGS. For the other matrix and fracture properties, the key parameters are listed in Table 2. 3.2. Initial and boundary conditions In this paper, the initial and boundary conditions are set as follows: For the flow field, the operation during EGS thermal exploration is under constant pressure difference. The pressures of injection and production wells are fixed at 40 and 20 MPa, respectively. The reservoir is initially filled with water, and the initial pressure of the reservoir is set as 30 MPa. Because the overburden and underlying layers could be seen as impermeable compared with HDR and SRV, the top and bottom boundaries are set as no-flow conditions. For the side boundaries, the fluid flow occurred mainly in the fractures within the SRV area, which shows that the side boundary effect could be ignored. So we impose Dirichlet condition at side boundaries, where the initial reservoir pressure is utilized.

Table 2 Matrix and fracture parameters in EGS.

Matrix Parameters

Fracture Parameters

Fig. 5. The schematic of the geological model.

Property

Value

Permeability Porosity Density Specific heat capacity Thermal conductivity Hydraulic fracture height Hydraulic fracture porosity Density Specific heat capacity Thermal conductivity

1  1015[m2] 0.01 2800[kg/m3] 4200[J/(kg$K)] 3[W/(m$K)] 200[m] 0.2 1200[kg/m3] 800[J/(kg$K)] 2[W/(m$K)]

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For the temperature field, the Dirichlet boundary condition is used for the fluid injection temperature fixed at 293 K. The initial temperature of the reservoir increases linearly from the top to the bottom boundary with the reference temperature of 473 K at the depth of 2500 m (top boundary) and a geothermal gradient of 50 K/ km. The top and bottom boundaries are set as thermal insulation conditions because of the nonconductive overburden and underlying layers. The reservoir is large enough to make sure the temperature of side boundaries did not change during heat mining. So the temperatures at the side boundaries are constant set as the initial reservoir temperature.

Table 3 Model results for different mesh numbers. Number of meshes

Production temperature/K

Computational time/s

13909 33576 71787 112411 154568 208540

467.78 470.71 475.52 475.77 475.85 475.36

20 42 150 289 421 548

absolute tolerance is regarded as the convergence criterion of the numerical solutions and is set as 103.

3.3. Model mesh and solution 3.4. Performance parameters Reservoir domain is discretized by a collection of nodal points referred to as finite element mesh. In the 3D geothermal reservoir, the discrete hydraulic fractures are integrated as 2D boundary faces, and the wells are set as cylinders. We use the tetrahedral meshes in the 3D rock matrix and triangular meshes in 2D fracture faces. This approximation increases computational efficiency and saves us from meshing the actual fractures. Increase in the number of grids can provide a better representation of the actual reservoir. However, this comes at the cost of increased time for initialization, running, and processing. So an appropriate mesh refinement is critical. The grids in SRV area are refined in order to improve simulation precision as this area includes the fractures and wellbore zones which are highly sensitive to small changes (pressure and temperature). Fig. 6 shows the detailed mesh scheme consisting of horizontal wells, fractures, SRV and HDR. The mesh-independent test is conducted to ensure the simulation results are mesh-independent. Table 3 shows the production temperature and computational time for different mesh numbers. It can be observed that the average production temperature within 50 years remains stable at 475 K when the mesh number exceeds 71787. Therefore, considering the computational time and precision, the succeeding simulations are conducted with a mesh number of approximately 70000. In this paper, the COMSOL Multiphysics simulator is used for numerical solution to study the flow rate and heat exchange in geothermal reservoir. The feature of this simulator is that it includes self-defining partial differential equation module and uses the finite element method (FEM) to solve the governing equations automatically. For the thermal-hydraulic coupling, we combine heat transfer module with subsurface flow module in COMSOL. For the discrete fractures in EGS, these fractures are set as interface units, which can be realized by the fracture module in COMSOL. An implicit scheme (Backward Differentiation Formula) is used for time discretization. The total heat production period of 50 years is investigated. The time step is set as 1 year in the first 10 years and 10 years for the last 40 years with 15 time points overall. An

Fig. 6. The numerical mesh scheme.

To evaluate the heat extraction performance of MFHW EGS, four parameters, namely production temperature, production flow rate, production thermal power, and cumulative thermal production, are defined as evaluation indexes [29]. The production temperature (Tout) is the average temperature along the production well [11], which is calculated as follows:

Tout ¼

P u T d þ uw Tw L Pf f f uf df þ uw L

(14)

where u is the fluid velocity, T is the fluid temperature, the subscript f and w denote the fracture and wellbore, L is the well length, df is the fracture width. The production flow rate (Q) is the average mass flow rate:

Q¼

X

2pruf df rf þ 2pruw Lrf

(15)

where r is the well radius, and rf is the fluid density. The production thermal power (P) is the average thermal energy reflecting the heat extraction efficiency [5]. This parameter is calculated as follows:

P¼

X


 2pruf df rf Cf Tf  Tin þ 2pruw Lrf Cf ðTw  Tin Þ

(16)

where Cf is fluid heat capacity, and Tin is the temperature of the injection fluid. The cumulative thermal production (C) refers to the integral of production thermal power over time:

C¼

X

PðtÞdt

(17)

4. Result analysis 4.1. Temperature and flow fields Fig. 7 shows the evolution of temperature field, press field and velocity field in the SRV region, and the corresponding times are 1, 10, and 50 years. From the temperature field, it can be observed that with the time increasing, the blue low-temperature region propagated from the injection well to the production well along the fractures indicating that the heat energy in the thermal reservoir was gradually extracted. After 50 years, the cold front reached the injection well, and most heat energy of SRV region was extracted. The existence of fractures in MFHW significantly increase the stimulated reservoir volume and heat exchange areas, thereby enhance the heat extraction efficiency. In press field we can see that the pressures of the injection and

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Fig. 7. The temperature field, press field, velocity field with different time.

production wells are fixed at 40 and 20 MPa, and the fluid flows from the horizontal injection well to the horizontal production well under differential pressure. The pressure changed sharply near the injection and production wells, and most of the pressure was consumed near the wellbore. This result agrees with the study by Zhao et al. [2]. Affected by the lower pressure of production well, the lower pressure propagated to the formation leading to a drop of reservoir pressure. From the velocity field, it can be observed that the flow velocity in fractures is in the order of 102 m/s, shown in the red areas, while that in the matrix is 108 m/s. The flow velocity is much larger than that in the reservoir matrix, indicating the fact that the fractures are the main channels for fluid flow, and the fluid flow is confined to the SRV region. This result agrees with the study by Song et al. [5]. Besides, the velocity in fractures declined with time. The reason is that when the reservoir temperature declined the fluid viscosity and flow resistance increased, which led to a decrease of fluid velocity.

two wells. The well length is 200 m, and the fracture length is 1200 m, which is equal to the total length of four fractures in MFHW. The geometrical parameters of the two EGS are set as the same as those in Table 2. Fig. 9 shows the production temperature and flow rate curves of MFHW and vertical EGS. The production temperature of vertical EGS declines from 500 to 450 K, while that of MFHW decreased

4.2. Comparisons of MFHW EGS and vertical EGS In order to evaluate the heat extraction performances of MFHW geothermal system, we compared it with conventional vertical doublet geothermal system. The schematics of vertical EGS is shown in Fig. 8. For the vertical EGS, there are two vertical wells located diagonally in the area of SRV and one fracture connecting

Fig. 8. The schematics of vertical EGS.

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Fig. 9. The production temperature cures (left) and the production flow rate cures (right) for MFHW and vertical EGS.

more significantly, dropping from 500 to 390 K. As the cold front propagates from the injection well to the production well, the flow resistance increases, and the flow rate decreases. A significant flow rate drawdown can be seen in both EGS. The MFHW EGS with a large number of fractures is prone to thermal break and the temperature at production well is lower than that of vertical EGS. However, due to the existence of multiple fractures, the MFHW EGS produces more flow rate than that of vertical EGS. Combined with these two factors (temperature and flow rate), MFHW EGS performs better than vertical EGS in thermal energy extraction, as shown in Fig. 10. The production thermal power curve of MFHW is above vertical EGS. At 50 years, the cumulative thermal production for MFHW EGS is about 4  107 J, while that for vertical EGS produces is about 3  107 J. 5. Fracture parameters optimization The hydraulic fracture parameters of MFHW have a significant effect on heat extraction performance. In this part, we discussed the sensitivity analysis of fracture parameters, including the fracture number, the fracture length, and the fracture conductivity. 5.1. Fracture number The fracture number is a critical index for hydraulic fracturing design in the oil reservoir exploitation. In order to evaluate the

impact of the number of fractures on heat extraction performance, we compared different fracture numbers from 3 to 8. The fractures are evenly distributed on the 1000 m horizontal well, corresponding to the fracture spacing from 250 to 111 m. For other fracture parameters, the fracture length is 300 m, and the fracture conductivity is 350 mm2 cm. Fig. 11 show the heat extraction performance of different fracture numbers. The significant production temperature drawdown can be seen for a total heat extraction period of 50 years. The temperature drops faster with the increase of fracture number. The production temperature drops from 500 to 400 K with fracture number of 3, while the temperature drops from 500 to 360 K with 8 fractures. The flow rate increases with the increase of the fracture number at first, then it begins to decline when the number of fractures exceeds 7. The fracture spacing becomes smaller with the increase of fracture number, and the interference among fractures intensifies. Besides, the geothermal reservoir temperature drops faster with a large number of fractures leading to the increase of flow resistance. Thereby the flow rate curve of 8 fractures is down below that of 7 fractures. Figs. 12 and 13 shows the change of thermal power and cumulative thermal production with different fracture numbers. When the number of fractures is 7, the cumulative thermal production at 50 years reaches a peak of 5.2  107 GJ. When the fracture number exceeds 7, the production temperature drawdown increases and the production flow rate decreases, both of them affect the

Fig. 10. The production thermal power cures (left) the cumulative thermal production cures (right) for MFHW and vertical EGS.

Please cite this article as: F. Gong et al., Evaluation of geothermal energy extraction in Enhanced Geothermal System (EGS) with multiple fracturing horizontal wells (MFHW), Renewable Energy, https://doi.org/10.1016/j.renene.2019.11.134

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Fig. 11. The production temperature cures (left) and the production flow rate cures (right) with different fractures numbers.

Fig. 12. The production thermal power cures (left) and the cumulative thermal production cures (right) with different fractures numbers.

geothermal production simultaneously, leading to a decline of cumulative thermal production. Blindly increasing the number of fractures will not promote geothermal exploitation, instead will increase production cost. For a specific WHFW EGS, there exists a relatively optimal number of fractures. In this study, the fracture number of 7, corresponding to a fracture spacing of 125 m, is the best arrangement with an output heat of 5.2  107 GJ. 5.2. Fracture length

Fig. 13. The optimization graph of the fracture number.

The fracture length refers to the radial distance from the wellbore to the out tip of a fracture propagated by hydraulic fracturing. It is one crucial factor influencing the production dynamics of horizontal wells. Due to the difference of in-situ stress distribution and the need to connect the natural fractures dense zones, the hydraulic fracture length may be different in geothermal exploitation. So it is necessary to analyze the effect of fracture length on geothermal heat mining. In this study, we set the fracture number as 7, the fracture conductivity as 350 mm2 cm, and compared different cases in which the fracture length is 100, 200, 300, 400, 500 m, respectively. Figs. 14 and 15 show heat extraction performance with different

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Fig. 14. The production temperature cures (left) and the production flow rate cures (right) with different fracture lengths.

fracture lengths. It can be observed that the fracture length has a significant impact on production temperature. When the fracture length is 100 m, the heat exchange time between fluid and rock reduces, and the temperature decreases significantly, dropping from 500 to 330 K. When the fracture length is 500 m, the fluid could be in full contact with HDR, and the temperature remains at a relatively high level. The flow rate curves of different fracture lengths are almost overlapping, which indicates the fracture length has little influence on the flow rate. Fig. 16 shows the change in cumulative thermal production with fracture lengths. When the fracture length is relatively small, the cumulative thermal power increases linearly. However, after the fracture exceeds 300 m, the fracture interference is more and more serious, and the growth of cumulative thermal production slows down. There exists an optimal fracture length for an EGS with MFHW when considering the economic cost. In this study, the optimal fracture length for this specific MFHW EGS is 300 m. 5.3. Fracture conductivity The fracture conductivity is the product of the fracture permeability and the fracture width. Proppants are always injected into the fracture together with the fracturing fluid to achieve long term

conductivity. The type of proppants selected and proppants concentration are two factors that determine the fracture conductivity [30]. The practice shows that the fracture conductivity is one of the most sensitive factors affecting productivity for MFHW in fossil exploitation [31]. For a MFHW EGS, it is also necessary to study the effect of fracture conductivity on heat extraction performance. In this study, we set the fracture number as 7, the fracture length as 300 m, and compared different cases with the fracture conductivity of 50, 100, 150, 200, 250, 300, 350, 400, 450, 500 mm2 cm, respectively. Fig. 17 shows the production temperature and flow rate curves. Production temperature drawdown and the flow rate increase with the increase of fracture conductivity. Fig. 18 shows the production thermal power and cumulative thermal production cures. For the cumulative thermal production, the cumulative production increases logarithmically with conductivity. When the conductivity reaches 350 mm2 cm, the rise of thermal output slows down. The contribution of fracture conductivity to yield increase is not unlimited. Considering economic cost, the best fracture conductivity in this geothermal case is set as 350 mm2 cm (see Fig. 19). 6. Cost analysis Planning and exploiting an EGS is a considerable capital

Fig. 15. The production thermal power curves (left) and the cumulative thermal production curves (right) with different fracture lengths.

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investment, including the cost of well drilling, the hydraulic fracturing and ground power generation facility, hence the geothermal exploitation calls for the proper planning, design and development. For an MFHW geothermal system, the cost for geothermal production consists of three parts, including the well drilling, the hydraulic fracturing, and ground power generation facility. In this paper, we only consider the cost of drilling and hydraulic fracturing, which can be calculated by Eq. (18):


C ¼ nwell  ðlv  cv þ lh  ch Þ þ nfra  cope þ lfra  cfra

(18)

where nwell is the well number, lv is the well vertical length (m), cv is the cost of drilling in the vertical segment, which is set in 30 $/m, lh is the well horizontal length (m), ch is the cost of horizontal segment, which is set as 50 $/m referring to previous drilling experience [32], nfra is the fracture number, cope is the cost of fracturing operation in one fracture, which is set as 1  105 $, lfra is the fracture length (m), and cfra is the cost of material per meter fracture ($/m), which can be calculated as follows: Fig. 16. The optimization graph of the fracture lengths.

cfra ¼ conprop  hfra  cprop þ Vfluid  cfluid

(19)

where conprop is the proppant concentration (kg/m2), hfra is the

Fig. 17. The production temperature cures (left) and the production flow rate cures (right) with different fracture conductivities.

Fig. 18. The production thermal power cures (left) and the cumulative thermal production cures (right) with different fracture conductivities.

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fracture length and fracture conductivity, the growth of thermal production slows down, the optimal fracture length and fracture conductivity are 300 m and 350 mm2 cm, respectively. (4) For an MFHW system with the fracture number of 7, the fracture length of 300 m and the fracture conductivity of 350 mm2 cm, the cost for drilling and hydraulic fracturing is estimated at 2.98  106 $. (5) The MFHW geothermal system could enhance the conductivity between injection and production well, increase stimulated reservoir volume and heat exchange area significantly, which is proved an efficient method for geothermal energy extraction. The proposed model provides an alternative MFHW EGS method for geothermal exploitation, and the numerical results of fracture parameters analysis have an instructive significance for hydraulic fracturing treatment in EGS.

Fig. 19. The optimization graph of the fracture conductivity.

fracture height (m), cprop is the cost of proppant set as 100 $/t, the Vfluid is the fracturing fluid volume (m3), which is the proppant volume divided by sand ratio (usually 20%), and cfluid is the cost of fracturing fluid set as 10 $/m3. In this paper, the well number is 2 with vertical length of 3000 m and horizontal length of 1000 m. The fracture height is 200 m. According to the sensitivity analysis of fracture parameters, the best fracture parameters are the fractures number of 7, the fracture length of 300 m, and fracture conductivity of 350 mm2 cm. The fracture conductivity of 350 mm2 cm can be achieved with the proppant concentration of 30 kg/m2. The fracture parameter values above are added to Eq. (18) and Eq. (19) to calculate the cost for geothermal production, and the final result is about 2.98  106 $.

Author contributions section Facheng Gong: Conceptualization, Methodology, Software. Tiankui Guo: Supervision. Wei Sun: Resources, Funding acquisition. Zhaomin Li: Writing- Reviewing and Editing. Bin Yang: Writing- Reviewing and Editing. Yimei Chen: Software, Validation. Zhanqing Qu: Software, Visualization. Declaration of competing interest 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. Acknowledgements

7. Conclusions In this paper, we presented a three-dimensional (3D) thermalhydraulic coupled model to analyze the performance of MFHW EGS. We analyzed the temperature and flow fields comprehensively and compared the MFHW EGS with conventional vertical EGS. Besides, the sensitivity studies of fracturing parameters, including the fracture number, fracture length, fracture conductivity, were investigated. We got the conclusions as follows: (1) The temperature field shows that the low-temperature zone propagates along the fractures. The velocity field indicates that the velocity in fractures is in 6 orders of magnitude higher than that in the matrix, which shows the fractures are the main channels for heat exchange and fluid flow. In the press field, most pressure is consumed near the wellbore, we could reduce the energy loss by improving the skin factor around the wellbore. (2) The MFHW EGS has a better heat extraction performance than that of conventional vertical EGS. At 50 years, the cumulative thermal production for MFHW EGS is about 4  107 J, while that for vertical EGS produces is about 3  107 J. (3) For the sensitivity analysis of fracture parameters, blindly increasing the fracture number, the fracture length, and the fracture conductivity will not promote geothermal exploitation, instead will increase production cost. In this paper, the cumulative thermal power curve exists an inflection point with the fracture number of 7. With the increase of

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