### Analysis of the Main Influencing Factors and Classification of Water Production Types  
The degree of impact of the aforementioned factors that influence the average water production of coalbed methane wells varies. Consequently, water production is a complicated variable with various levels and influencing factors. At present, due to the limitations of various objective conditions, the available data on the factors affecting average water production is very limited, belonging to a poor information system. Additionally, the existing limited data contain both known and unknown information. Therefore, the key factor influencing the average water production is a typical grey system, which can be investigated and studied through grey system theory. Important content of grey system theory is grey correlation analysis. The correlation between diverse factors within a system and its key behaviors can be quantitatively measured through grey correlation analysis, consequently identifying the primary influential factors that impact the key behaviors of the system. When two factors in a system exhibit similar changing trends, they are deemed to be strongly correlated (with a high degree of correlation). The detailed calculation process was referred to in references [37; 43; 44].  
The correlation degree was calculated and ranked in order of magnitude (Table 4). The order of factors that influence water production, from strongest to weakest, is as follows: sand-muud ratio > porosity > fractal dimension of fault > fracture fractal dimension \(D\) value > groundwater sealing coefficient > groundwater stability index > total water content of coal seams.  
Using average water production as the classification standard, a classification of low water production was established under multi-influence factors (Table 5). The average water production is divided into low-production wells (<10 m\({}^{3}\)/d), middle-production wells (10-20 m\({}^{3}\)/d), and high-production wells (>20 m\({}^{3}\)/d). When considering the values at the boundaries of each parameter, which correspond to an average water production of 10 m\({}^{3}\)/d (as shown in Figures 6-12), certain thresholds can indicate the potential for drainage and gas production. A sand-muud ratio less than 1.5, a total water content less than 20,000 m\({}^{3}\), a fault fractal dimension less than 0.6, a fracture fractal dimension \(D\) value less than 1.78, a groundwater stability index exceeding 3.7, a porosity less than 5.5%, and a sealing coefficient greater than 160 all suggest low water production and well drainage and gas production potential.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline Factors Influencing & Sand-Mud & \multirow{2}{*}{Porosity} & \multicolumn{4}{c}{Fracture} & \multirow{2}{*}{Groundwater} & \multirow{2}{*}{Groundwater} & \multirow{2}{*}{Total Water} \\ Average Water & & & & & & & \\ Production & & & & & & \\ \hline Correlation degree & 0.792 & 0.777 & 0.768 & 0.764 & 0.762 & 0.758 & 0.744 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Correlation degree of influencing factors.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline Water & Sand-Mud & \multirow{2}{*}{Total Water} & \multirow{2}{*}{Fault Fractal} & \multirow{2}{*}{Groundwater} & \multirow{2}{*}{Groundwater} & \multirow{2}{*}{Groundwater} \\ Production Type & Ratio & & & & & \\ \hline Low production & \textless{}1.5 & \textgreater{}20,000 m\({}^{2}\) & \textless{}0.6 & \textless{}1.78 & \textgreater{}3.7 & \textless{}5.5\% & \textgreater{}160 \\ Middle production & 1.5–3.5 & 20,000–40,000 m\({}^{3}\) & 0.6–0.8 & 1.78–1.82 & 3.2–3.7 & 5.5–7.5\% & 80–160 \\ High production & \textgreater{}3.5 & \textgreater{}40,000 m\({}^{3}\) & \textgreater{}0.8 & \textgreater{}1.82 & \textless{}3.2 & \textgreater{}7.5\% & \textless{}80 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Classification of production well patterns for coalbed methane wells.