Coalbed methane (CBM), as an unconventional natural gas, is an important alternative energy source for China’s oil and gas resources. To improve the extraction rate of coalbed methane, the lattice Boltzmann method (LBM) was used to investigate the flow patterns of coalbed methane during the extraction process. A systematic exploration was conducted on how parameters such as extraction pressure, borehole diameter, borehole depth, and coal seam boundaries influence the extraction rate of coalbed methane. The study findings revealed that when extracting with a single borehole, the extraction rate of coalbed methane exhibits a peak value as the extraction pressure fluctuates. Specifically, when the extraction pressure is relatively low, the extraction rate increases with the rise in extraction pressure. However, once the extraction pressure surpasses a certain threshold, the extraction rate begins to decline. Additionally, the extraction rate of coalbed methane tends to increase with the enlargement of the borehole diameter, yet after the borehole diameter reaches a certain value, the extraction rate stabilizes, indicating the existence of an optimal borehole diameter. The extraction rate also rises with the increase in borehole depth, but when the depth reaches 2 m, the change in extraction rate becomes minimal. Based on engineering practice, it is recommended to select a borehole depth between 1 m and 2 m. Moreover, the rougher the boundary of the extraction reservoir, the lower the extraction rate of coalbed methane. When employing dual-borehole extraction, the extraction rate initially increases and then decreases with the increase in the distance between borehole centers. The optimal range for the distance between borehole centers is found to be between 1.0 m and 2.5 m. Ultimately, quantitative relationships were established between extraction pressure and extraction rate when the extraction pressure remains constant. Additionally, quantitative relationships were determined between borehole geometric dimensions (diameter and depth) and extraction rate when the extraction pressure is held constant. Furthermore, quantitative relationships were also established between borehole diameter and extraction pressure and extraction rate when the borehole depth is kept constant. These findings have enabled the determination of the optimal ranges for borehole diameter, depth, extraction pressure, and borehole spacing, thereby providing a basis for guiding the extraction of coalbed methane.