The theoretical basis of model building for coal reservoir permeability: A review and improvement

The dynamic permeability of coal reservoirs is more complicated than that of conventional reservoirs because of the natural cleat system and matrix shrinkage induced by methane desorption. Many permeability models have been built, but each model has its focus, and the theoretical basis used by them vary, which makes it difficult to compare different models. In this paper, the theoretical basis (basic equations and key relations) of widely cited models was summarized and strictly analyzed. Three limitations were found: the double effect of matrix shrinkage on permeability was not been realized, the concept of effective stress was not clear, and a reliable fracture closure equation was lacking to describe the mechanical response of cleats. Corresponding improvements have been made. Firstly, a new porosity-effective stress relation is obtained without introducing new parameters, which can describe the double effect of matrix shrinkage. Secondly, expressions of three effective stresses considering matrix shrinkage are obtained: Biot effective stress controls the bulk volume strain, pore effective stress controls the pore volume strain, and porosity effective stress controls porosity change. Thirdly, an explicit fracture closure equation is introduced to obtain the analytical permeability models considering the mechanical properties of cleats. Finally, based on the above improvements, a new permeability model system is obtained. Compared with previous models by theoretical analysis, the new models are more comprehensive in considering matrix shrinkage, more accurate in using the effective stresses, and include analytical models based on the mechanical property of cleats.