Desorption funnel model based on composite pressure drop propagation in gas production stage of coalbed methane

In the development of coalbed methane, the reasonable expansion speed of pressure drop directly affects the effective desorption range and the ability to maintain stable production continuously. Currently, the existing pressure drop propagation models either only adopt the gas pressure propagation formula throughout the gas production stage or neglect the pressure fluctuations in the early stage of gas production, which does not conform to the actual situation. Formulas for calculating the gas saturation at different times and different radii are established. On this basis, a composite model of the combined propagation of water pressure and gas pressure is established. Furthermore, a desorption funnel expansion model that takes into account the dynamic changes of relative permeability and gas saturation over time and space is established, and the pressure drop propagation law applicable to the whole process of gas production is obtained. It is found that during the stage of simultaneous production of gas and water, the damage caused by stress sensitivity to permeability is lower than the positive effect produced by the matrix shrinkage effect. Moreover, the decline amplitude of the bottom hole flowing pressure can be determined according to the highest point of the Rg value curve of the boundary line, so as to maintain a relatively high desorption efficiency. The model in this paper can characterize the impact of the dynamic changes of gas and water on the expansion of the desorption funnel and can evaluate the changes of parameters such as reservoir pressure drop and relative permeability more accurately, laying a foundation for adjusting production measures.