Characterization of Stress-, Time-, and Temperature-Dependent Anisotropic Permeability for Deep Coal Rocks: A Strain-Driven and Multi-Mechanism Modelling Approach
Authors: Zeng Jie , Zhang Tao , Guo Jianchun , Zhao Zhihong , Qiao Hui , Liu Jishan , Chen Zhongwei , Gao Qi , Qu Hongyan 
Published: October 2024

Abstract
Considerable attention has recently been focused on gas extraction from coal formations with a depth greater than 2000 m due to the higher gas content. The successful stories of some massive hydraulic fracturing pilot projects in China confirm great exploitation potential of deep coalbed methane (CBM). However, deep coals generally have complex pore structure and exhibit strong anisotropy during the gas transport process. The increase of formation depth also generates high-temperature, high-in-situ-stress, and high-reservoir-pressure conditions. There is a matrix-fracture/cleat pressure nonequilibrium state due to the huge permeability difference between matrix and fracture/cleat systems. Accurate characterization of the above features and their impacts on permeability is an indispensable step toward precise simulation of gas transport and productivity or CO2 storage potential assessment.
In this study, a new directional stress-strain relation considering stress sensitivity, gas-adsorption/desorption-induced localized swelling/shrinkage in the matrix-fracture/cleat pressure nonequilibrium period, and thermal expansion/contraction is established. By satisfying that the gas-adsorption-induced surface energy change equals the elastic energy change of the rock, the anisotropic internal swelling/shrinkage is depicted through a mechanical-property-based internal swelling model. Therefore, the stress-, time-, and temperature-dependent intrinsic permeability of each cleat/fracture is obtained. Since the directional permeability is mainly provided by the butt cleats, face cleats, bedding planes, coal permeability in each principal direction can be described by parallel connection of permeability for two cleat/fracture systems.
The proposed model is verified by comparing with anisotropic permeability evolution experimental data. The 3-D permeability map is used to better illustrate permeability evolution by including the time dimension. During gas injection, four distinctive permeability evolution stages can be observed in each direction under a constant confining pressure condition. Initially, the permeability slightly increases due to pressure loading. Then, pressure-nonequilibrium-induced localized swelling narrows the flow channel and reduces permeability. With the weakening of pressure nonequilibrium and continuous pressure loading, the permeability rebound period appears. The permeability eventually becomes stable when the pressure equilibrium state is reached. The impacts of mechanical properties, matrix diffusivity, temperature variation, and thermal expansion coefficients are further documented. A controlling factor diagram is proposed to demonstrate the dominant realms of different mechanisms. Due to its analytical nature, this model can be easily inserted into the fully-coupled numerical simulator to predict deep coal gas production or CO2 geological sequestration performance.