## 2 Method
### Numerical Simulation for a Two-Horizontal-Well Geothermal System
#### 2.3.4 Parameters Selection  
Based on geothermal exploration findings and prior study experiences [24; 25; 26], a fundamental scenario of the Gonghe Basin in Qinghai was chosen as the research background to guide the selection of parameters. Table 1 contains the exact numerical model parameters for this instance. The model size is 400 m \(\times\) 400 m \(\times\) 400 m. The fracture aperture is settled as 0.002 m according to the literature and experience in hydrothermal geothermal systems [27]. The thermo-physical properties of matrix rock vary generally between 2-3.5 W/(mK), and 2.5 W/(mK) was employed. A geothermal examination of the Gonghe Basin in Qinghai found that the temperature can exceed 473.15 K at 3000 m below the surface and that the geothermal gradient is approximately 6-7 K/100 m [28]. As a result, the starting average temperature of the rock mass is set at 473.15 K and dispersed with a 6 K/100 m temperature gradient. According to [PERSON]'s research, the water density in a broken reservoir ranges from 857 kg/m\({}^{3}\) to 992 kg/m\({}^{3}\)[29], and in this work, the average value of 925 kg/m\({}^{3}\) is used. The fracture fluid is regarded as a porous medium, and the modified Cubic Law [30] is used to estimate the permeability of the rough fracture while taking the influence of fracture roughness on heat transfer into account:  
\[k=\frac{W^{2}}{12f} \tag{7}\]  
\[f=1+17\Big{(}\frac{a}{2W}\Big{)}^{1.5} \tag{8}\]  
where \(k\) stands for the fracture permeability after reservoir stimulation such as hydraulic fracturing; \(W\) represents the fracture aperture; \(f\) denotes the Lomize roughness coefficient, which is calculated according to Equation (8); \(a\) stands for the asperity height, and is set to be 0.0005 m according to [PERSON]'s research [31].  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Rock thermal conductivity & 2.5 W/(m\(\cdot\)K) \\ Rock specific heat & 1000 J/(kg\(\cdot\)K) \\ Rock density & 2650 kg/m\({}^{3}\) \\ Fracture permeability & 1.9 \(\times\) 10\({}^{-7}\) m\({}^{2}\) \\ Fracture height & 400 m \\ Fracture length & 400 m \\ Fracture aperture & 0.002 m \\ Asperity height & 0.0005 m \\ Injection temperature & 333.15 K \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of the reservoir rock matrix in the numerical model.  
By this method, the fracture permeability after reservoir reformation is calculated as 1.9 \(\times\) 10\({}^{-7}\) m\({}^{2}\), which was employed in the computer simulation.  
It is also taken into account how temperature affects the mechanical and physical properties of water. The calculations below illustrate that the water's density, heat conductivity, heat capacity, and dynamic viscosity are all variables [6].  
\[\rho_{f}=838.5+1.4T-3\times 10^{-3}T^{2}+3.7\times 10^{-7}T^{3} \tag{9}\]  
\[\left\{\begin{array}{c}\mu_{f}=1.4-0.02T+1.4\times 10^{-4}T^{2}-4.6\times 10^{-7} T^{3}+8.9\times 10^{-10}T^{4}\\ -9.1\times 10^{-13}T^{5}+3.8\times 10^{-16}T^{6}\ T\in[273.15,\ 413.15]\\ \mu_{f}=0.004-2.1\times 10^{-5}T+3.9\times 10^{-8}T^{2}-2.4\times 10^{-11}T^{3}\\ T\in[413.15,\ 533.15]\end{array}\right. \tag{10}\]  
\[C_{f}=12010-80T+0.3T^{2}-5.4\times 10^{-4}T^{3}+3.6\times 10^{-7}T^{4} \tag{11}\]  
\[\lambda_{f}=-0.9+8.9\times 10^{-3}T-1.6\times 10^{-5}T^{2}+7.9\times 10^{-9}T^{3} \tag{12}\]