## 4 The Effect of Air Leakage on the Evaporation of Water from Goaf
### Influence of Measurement Point Location on the Amount of Water Evaporation  
The coordinate axes xoy are defined for the bottom surfaces of the squares in Figure 6a,b, where the broad side axis of the three-dimensional model is the x-axis, and the long side axis of the three-dimensional model is the y-axis. Then, the coordinates of each measurement point are shown in Table 3. \begin{table}
\begin{tabular}{c c c} \hline Measurement Points & x (cm) & y (cm) \\ \hline
1 & 15 & 20 \\
2 & 30 & 20 \\
3 & 45 & 20 \\ \hline
4 & 15 & 40 \\
5 & 30 & 40 \\ \hline
6 & 45 & 40 \\
7 & 15 & 60 \\
8 & 30 & 60 \\
9 & 45 & 60 \\ \hline
10 & 15 & 80 \\
11 & 30 & 80 \\
12 & 45 & 80 \\
13 & 15 & 100 \\
14 & 30 & 100 \\
15 & 45 & 100 \\ \hline \end{tabular}
\end{table} 
Table 3: Plane coordinates of each measurement point. Figure 6: Amount of moisture change at different measurement points: (**a**) Water evaporation at different measuring points; (**b**) Water evaporation rate at different measuring points. Based on the above rules and combined with Figure 3b, it can be concluded that both measurement points 12 and 15 are closest to the air inlet. However, the air flow through measurement point 12 is larger than that of measurement point 15. Different colors are used for plotting in Figure 7 to facilitate clear viewing. From Figure 7c, it can be seen that the relative humidity of the air at the air inlet is less than the relative humidity of the air at the air outlet. Therefore, the air flowing out of the goaf model will take away a large amount of moisture, so the moisture at measurement point 12 will be taken away first. Then, the evaporation rate of moisture at that place is the greatest. Additionally, most of the air flows away from the air outlet, so the moisture evaporation at measurement point 3 is only second to the moisture evaporation rate at measurement point 12. Then, the moisture evaporation rate is lower at measurement points 6, 9, 11 and 15. Combined with Figure 7a-c, the measurement points 3, 6, 9, 12 and 15 with higher moisture evaporation rates are all located in the first row, which is equivalent to the location near the working face in the goaf. Based on this rule, we also found that the water evaporation rate of the measurement points 2, 5, 8, 11 and 14 located in the second row is generally lower than that of the measurement points in the first row. The smallest evaporation rates correspond to the measurement points 4, 10 and 14, where the measurement points 4 and 14 are located in the third row. From this, we can derive the basic rule that, the closer the measuring point in the goaf is to the working face, the greater its moisture evaporation rate; the closer the measuring point in the goaf is to the location of the inlet and outlet, the greater its moisture evaporation rate. The Effect of Time and Air Leakage Volume Changes on the Relative Humidity of the Air Inlet and Outlet  
The first two components are based on the amount of air leakage, the location of the measurement point and the time taken for the moisture at the measurement point to reach equilibrium as key factors. The first two sections summarize the patterns of water evaporation and water evaporation rates within the mining area model. The following is a further in-depth analysis of the reasons for the above law. In Figure 3b, the two measurement points 16 and 18 are used to determine the relative humidity of the air at the air inlet and air return. The changes in air relative humidity at the air inlet and outlet with different air leakage volumes are shown in Figure 8a-c.  
From Figure 8a-c, the air relative humidity at the inlet and outlet shows irregular changes with time, and the change law of air relative humidity at the inlet is always consistent with the change law of air relative humidity at the outlet. The main reason for the change in the relative humidity trend with time and chaos is affected by the weather.