Numerical Simulation of Stress and Strain Due to Gas Sorption/Desorption and Their Effects on In Situ Permeability of Coalbeds
Authors: Gu F. , Chalaturnyk R.J. 
Published: March 2010

Abstract
Most past studies on coal shrinkage/swelling due to gas adsorption/ desorption were based on experiments under no constraint conditions. In this paper, the changes of stress and strain measured on one coal specimen under uniaxial compression in a vacuum and under axial constraint conditions during CO2 adsorption are presented and numerically simulated. The simulation results show that a linear elastic deformation model, suitable to isotropic continuum media but widely assumed in analytical permeability models, cannot adequately simulate the deformation behaviour of coal mass even under uniaxial compression in a vacuum. The equivalent continuum medium (ECC) model considering the discontinuities of coal mass is successfully applied to simulate the deformation behaviour of the specimen for the uniaxial compression case and the axial constraint case before the occurrence of shear failure in the specimen.
A detailed review of the analytical permeability models is presented and their limitations in application are discussed in this paper. The permeability, in situ stress, and production simulated with two representative analytical permeability models are compared with those calculated using the discontinuum medium coupled (DMC) permeability model and the coupled simulation. The results indicate that the DMC model provides better estimates of permeability and production than the analytical permeability models because it considers the influence of many factors such as the discontinuities and anisotropies that are ignored in analytical permeability models.

Introduction
A comprehensive review made by Gu and Chalaturnyk(1) indicated that the permeability of a coalbed (i.e., the permeability of cleat (fracture) since matrix is almost impermeable) is the most important parameter for pressure depletion coalbed methane production (CBM) and enhanced coalbed methane recovery (ECBM). However, the permeability of a coalbed is not constant but varies drastically during production due to the changes of stress and/ or strain which result from the alternations of in situ conditions such as pressures, gas desorption or absorption, and temperature. In general, a decrease in pressure causes an increase of effective stresses, a cleat compression or closure, and a decrease of permeability. Concurrently, the decrease in pressure initiates gas desorption from coal resulting in shrinkage of the coal matrix, the widening or expansion of cleat apertures, and an increase of permeability. Field results have shown that the permeability of a coalbed decreases with an increase of minimum effective stresses (corresponding to increasing depth)(2). Mavor and Vaughn(3) illustrated that the permeability of three wells increased 2.7 to 7 times after producing for 3 to 4 years, according to field well tests. The results of work by van der Meer and Fokker(4) indicated that the permeability of a coalbed decreased from 3.65 mD to 0.985 mD due to the injection of CO2. Due to its significant influence on production, the dynamic change of permeability must be considered in the simulations predicting and evaluating CBM and ECBM processes.
There are two types of permeability models that can be used to consider the influence of permeability changes during production in simulations.