## 4 Results and Discussion
### Gas Pressure Field and Production Rate around Single and Multiple Vertical Wells
For the reservoir with four wells, the simulation results are exhibited in Figures 21 and 22. Case 1 represents the reservoir containing the continuous small-size prop  
Figure 20: Comparison of the transient gas pressure fields when adopting three vertical extraction wells. (**a**) The left part is obtained based on the continuous model of the proppant pack. (**b**) The right part is obtained based on the discontinuous model of the proppant pillar. show that during the first 3000 days, the average reservoir pressure decreases from 10 MPa to 9 MPa for case 1, where the decrease is only 10%. Meanwhile, the average reservoir pressure decreases from 10 MPa to 3.8 MPa for case 2, where the decrease is up to 62%. The production curves indicate that the gas production rate is in the range of 100-400 m\({}^{3}\)/d for case 1. However, the gas production rate is only in the range of 10-20 m\({}^{3}\)/d for case 2. These results further confirm that the fracture propped by the large-size proppment can remarkably increase the gas production rate by enhancing the reservoir permeability. Figure 21: Result comparison of two kinds of reservoirs with different permeability when adopting four vertical extraction wells. (**a**) The average gas pressure variation in the reservoirs. (**b**) The gas production rate evolution in the reservoirs. Figure 22: _Cont._  
Compared to the single well, double wells, and three wells, the four wells plan provides the fastest pressure drop and highest production rate. Figure 22 clearly shows the variation in the reservoir pressure during the first 3000 days. Compared to case 1, case 2 provides a faster pressure drop in the reservoir. The pressure field variation affects the gas production rate curves. The faster the pressure drops, the higher the gas production rate. In conclusion, the discontinuous large-size proppant plan can provide a more efficient drainage rate. The number of wells has an important influence on reservoir pressure and gas production rate. Figure 23 shows that with the increase in the number of wells, the average gas pressure of the reservoir decreases, and the gas production rate increases. Comparing case 1 and case 2, it can be clearly seen that the gas pressure of reservoir 2 is lower and the gas production rate is higher. These results indicate that the discontinuous large-sized proppant can give a higher production rate when the other reservoir parameters are the same between reservoir 1 and reservoir 2. Under the condition of same porosity, the permeability of fracturing reservoir 1 containing large-sized proppant is higher, causing the gas production rate to be higher. Taking a single well as an example, the natural gas production rate is increased by 19.24 times (from 5.546 m\({}^{3}\)/d to 106.7 m\({}^{3}\)/d) at the initial stage of production (\(t\) = 1 d) after the use of large-sized proppant. In the later period of exploitation (\(t\) = 3000 d), the natural gas exploitation rate is increased by 17.01 times (from 3.037 m\({}^{3}\)/d to 51.65 m\({}^{3}\)/d) when adopting the large-sized proppant. Under the same conditions, increasing the number of production wells can significantly improve the drainage efficiency of natural gas. However, the increased times of the production efficiency will gradually decrease with time. Taking the reservoir containing large-sized proppant as an example, the production rate of natural gas will increase by four times (from 106.7 m\({}^{3}\)/d to 426.7 m\({}^{3}\)/d) at the initial stage of production (\(t\) = 1 d). In the later period of exploitation (\(t\) = 3000 d), the natural gas exploitation efficiency is increased by 2.12 times (from 51.65 m\({}^{3}\)/d to 106.37 m\({}^{3}\)/d) when the well number increases from one to four. Figure 15:0 Comparison of the transient gas pressure fields when adopting four vertical extraction wells. (**a**) The left part is obtained based on the continuous model of the proppant pack. (**b**) The right part is obtained based on the discontinuous model of the proppant pillar.