Abstract Permeability of shale and coal is a main controlling factor for gas migration and is sensitive to effective stress, sorption/desorption-induced internal swelling/shrinkage (swelling/shrinkage at fracture/pore surfaces), and gas rarefaction effects. The dependence of gas permeability on effective stress and rarefaction effects has been extensively studied. However, the impacts of anisotropic strains and their time-dependent evolution (creep deformation) on permeability variation were still not fully understood, which makes it difficult to accurately predict permeability evolution and simulate gas transport, especially for deep coal. To fill this knowledge gap, a modified sugar-cube conceptual model that captures the structural anisotropy of coal and shale is used to develop a generic fully anisotropic strain-driven permeability model incorporating anisotropic creep deformation, directional internal matrix swelling/shrinkage, and gas rarefaction effects. The time-dependent creep deformation is described by the Nishihara quasi-static rheological model with elastic, viscoelastic, and visco-plastic strain elements. Unlike previous studies where anisotropic internal swelling/shrinkage is ignored or simulated by simply using three sets of independent Langmuir pressure and swelling strain constants, a mechanical-property-based swelling model is used to truly couple directional internal swelling/shrinkage strain with mechanical anisotropy according to the energy balance theory. The Beskok-Karniadakis model is employed to accurately characterize full-Knudsen-number-ranged gas rarefaction effects. The proposed permeability model is verified against coal permeability measurement data. Analyses results indicate that the permeability evolution in each direction shows unique features depending on the anisotropic structure, directional internal swelling, and mechanical properties. The permeability reduction contributed by three-stage creep deformation can be larger than 90%. Internal swelling strain variation in all directions also exhibits a noticeable impact on the magnitude of permeability, which is more obvious at the third stage. The overall influence of the gas rarefaction phenomenon turns heavier as time increase due to the continuous narrowing of flow channel. Due to its analytical feature, the proposed model is suitable for different permeability measurement conditions, including constant effective stress, constant confining pressure, and constant average pore pressure conditions. It can be easily incorporated into a more complex and realistic Multiphysics framework for field-scale simulation and well production prediction.
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.
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