A Fully Coupled Gas–Water–Solids Mathematical Model for Vertical Well Drainage of Coalbed Methane

The coupling relationship between the deformation field, the diffusion field, and the seepage field is an important factor in fluid transport mechanisms in the long-term coalbed methane (CBM) exploitation process. A mathematical model of gas–water two-phase fluid–structure coupling in a double-porosity medium in coal reservoirs is established in this paper. Taking Hancheng Block, a typical production block in Qinshui Basin, as the geological background critical desorption pressure, reservoir permeability anisotropy is considered in the model. COMSOL Multiphysics (COMSOL_6.0) was used to create the model. The accuracy and rationality of the model were verified by comparing field production data with the results of the simulation. Using the simulation, the influence law of various reservoir geological characteristics parameters (Langmuir strain constant, ratio of critical desorption pressure to reservoir pressure of coal seam (CDPRP), elastic modulus, initial water saturation, Langmuir pressure, etc.) on CBM productivity, reservoir pressure, and permeability ratio was discussed, and a thorough analysis of the factors affecting productivity was obtained using the orthogonal test method. The findings of this study indicate that the change in permeability is the result of the superposition effect of many factors. Different stages of drainage have different primary regulating factors. Rock skeleton stress has a consequence on coal matrix permeability in the early drainage stage, and coal matrix shrinkage is primarily impacted in the later drainage stage. Besides the initial water saturation, other reservoir geological parameters (e.g., CDPRP, Langmuir volume, Langmuir strain constant, elastic modulus) have a strong relationship with productivity. When the value of coal geological parameters increases, the degree of productivity release is higher (as the initial water saturation increases, the production decreases correspondingly). Different coal and rock parameters have varying levels of impact on the drainage stage of CBM wells. The influences of the CDPRP, Langmuir volume, Langmuir strain constant, and elastic modulus on gas production are mainly concentrated in the initial and intermediate drainage stages and begin to fall off during the last drainage stage. Per the multi-factor analysis, the main coal–rock parameters affecting the productivity release are the Langmuir strain constant, followed by the CDPRP and other parameters. The analysis findings can offer theoretical guidance for CBM well selection and layer selection and enhance the block’s overall CBM development level. The improved productivity prediction model for CBM, which is based on fluid–structure coupling theory, can offer a new technical benchmark for CBM well productivity prediction.