Numerical Simulation of Stress and Strain Due to Gas Sorption/Desorption and Their Effects on In Situ Permeability of Coalbeds

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.

Empirical and numerical approaches for geomechanical characterization of coal seam reservoirs

“…The joint shear and normal stiffness for the bedding planes, face and butt cleat were set to 40.0 GPa/m (Gu and Chalaturnyk, 2006). The joint friction and dilation angles were set equal for all joints and were 25°and 5.0°r espectively.…”

Modeling anisotropic permeability of coal and its effects on CO 2 sequestration and enhanced coalbed methane recovery

“…The currently published permeability models can be generally classified into two types: analytical permeability models, mainly based on geomechanics theory combined with empirical or semi-empirical analysis (Gray, 1987;Harpalani and McPherson, 1985;Palmer, 2009;Puri and Seidle, 1991;Durucan, 2004, 2010;Shi et al, 2014;Somerton, 1975) and coupled permeability models, which include continuum medium coupled (CMC) model and discontinuum medium coupled (DMC) model. Gu and Chalaturnyk (2006) compared these models and suggested that the DMC model provides better estimates of permeability and production than analytical models because it includes the influences of many factors, such as discontinuity and anisotropy.…”

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

“…Of the existing models, the most commonly used are the ones presented by Palmer and Mansoori [12] (P&M model), Shi and Durucan [13] (S&D model), and Cui and Bustin [14] (C&B model). Gu and Chalaturnyk [15] and Palmer [16] have reviewed commonly used analytical permeability models, and made a classification based on whether a model is strainbasedor stress-based. For the strain-based models, the coal/rock strain is the cause for any change in flow behavior; In CBM reservoirs, gas desorption-induced matrix shrinkage and mechanical compaction induced by an increase in effective stress with gas depletion are the two factors influencing the volumetric strain of the coal matrix, and in turn, changes in cleat porosity and cleat permeability.…”

“…Gu and Chalaturnyk [15] offered a distinction based on whether a model is strain-based or stress-based. The original P&M model and improved P&M model are based on the change in volumetric strain due to the desorption of methane, thus resulting in changes in cleat porosity and permeability.…”