Why coal permeability changes under free swellings: New insights

Abstract

Coal permeability models are derived normally under three common assumptions: (1) uniaxial strain; (2) invariant total stress; and (3) local equilibrium. Experimental measurements are normally conducted under constant effective stress or free swelling conditions. The inconsistency between model assumptions and the experimental conditions determines that these coal permeability models may not be appropriate to use for the analysis of the experimental data. Based on the theory of poroelasticity, coal permeability is determined by the effective stress only. Therefore, there would be no permeability change when the effective stress remains constant. This theoretical conclusion contradicts with the “V” shape profile of coal permeability as widely observed through experiments. This study has solved the mystery of this “abnormal” behavior through a novel dual-permeability model. The model is formulated based on our previous concepts of local swelling, global swelling and their evolutions from the initial equilibrium state to the final equilibrium state. In the formulation, we define four strains: coal global strain, fracture local strain, matrix global strain, and pore local stain. Coal permeability is defined as a function of these strains. Their evolutions are determined by the effective stress transfer between the matrix system and the fracture system, and regulated by the gas diffusion process from the fracture system to the matrix system. We use the strain evolutions to define how coal permeability changes with time or gas pressure in the matrix system. We applied the new model to generate a series of coal permeability profiles from the “V” shape as observed in experiments to the “Langmuir” type. These profiles are regulated primarily by the matrix diffusivity. When the diffusivity is low, it displays the “V” shape; when the diffusivity is high, it displays the “Langmuir” shape.