Analysis of Analytical Models Developed under the Uniaxial Strain Condition for Predicting Coal Permeability during Primary Depletion

The stress-dependent permeability of coal during coalbed methane production has been extensively studied both experimentally and theoretically. However, how permeability changes as a function of stress variation is somewhat unclear to date, and currently used analytical models fail to accurately predict permeability evolution with gas depletion. Considering that the role played by changes in in situ stress in permeability evolution is critical, a comprehensive theoretical study was first conducted, through which it was found that coal permeability is determined by mean effective stress. Moreover, the influence of matrix shrinkage on cleat deformation and then coal permeability was overestimated by currently used models, leading to inaccuracy of the predicted permeability. By taking both mean effective stress and the influence of matrix shrinkage on cleat deformation into account, a new permeability model was developed under the uniaxial strain condition in order to precisely estimate permeability evolution during gas depletion. An in-depth investigation and comparison among four commonly-used permeability models, the Palmer and Mansoori (P&M) model, Improved P&M model, Shi and Durucan (S&D) model, and Cui and Bustin (C&B) model, was then conducted. It was experimentally verified that a good match can be achieved between the lab data and the results predicted by the proposed model. Permeability variation of coalbed reservoirs associated with gas depletion is a consequence of two opposing effects: mechanical compaction and matrix shrinkage. In comparison, it was found that the coefficients of these two effects incorporated in those four models have a significant impact on permeability variation; and the accuracy of the values of initial cleat porosity and cleat compressibility, the bridges connecting permeability, and those two effects in analytical models, is extremely critical to permeability estimations. This study can shed light on improving the accuracy of analytical coal permeability models and the prediction of gas production.