Effects of pressure drop funnels model of different shapes on CBM well productivity

In order to study the effect of pressure drop funnel shapes on CBM well productivity, the change law of pressure and the shape of pressure drop funnel in different drainage stages of CBM wells were discussed, the mathematical models of pressure drop funnel were established, the concept of "desorption coefficient" and "effective desorption coefficient" for coal reservoir were proposed to quantitative study desorption effect of the coal reservoir. Taking a CBM well in the west of Guizhou as an example, the research results show that the logarithmic function model of pressure distribution of radial flow is difficult to accurately reflect the shape of pressure drop funnel at all stages. Four different types of pressure drop funnel models of logarithmic function, linear function, parabola function and elliptic function were compared and analyzed under the same desorption radius, the gas desorption volume and recovery ratio of the elliptic function model was the highest, recovery ratio reached 38%. The gas desorption volume and recovery ratio of the logarithmic function model were the lowest, and the recovery rate was less than 5%. Under the same drop funnels radius, the desorption radius and effective desorption radius of logarithmic, linear, paraboloid and elliptic function models were expanded successively, the desorption coefficient and effective desorption coefficient of the elliptic function model were the largest, when the pressure drop radius reached 140 m, the desorption radius of coal reservoir reached 135 m, the effective desorption radius reached 0.725, and the coal reservoir within the desorption radius was fully desorbed. By studying the change rule of productivity, recovery ratio and effective desorption radius under different pressure drop funnel shapes and different desorption radius, it is beneficial to master the law of reservoir pressure reduction in the process of CBM well drainage and to provide guidance for the desorption control of CBM well.