Gas sorption-induced coal deformation is one of the primary geomechanics effect in coalbed methane (CBM) engineering. Coal is known to have transversely isotropic properties because of its cleat structure. We propose a new theoretical approach to modeling the strain behavior of bulk coal by including sorption-induced matrix shrinkage/swelling strain, cleat volume strain and matrix mechanical strain resulting from changes in pore pressure, and external stresses. The new model framework can define the apparent bulk coal volume with respect to the variation in gas pressure. To validate the model, unconstrained gas flooding experiments were conducted with helium, methane and carbon dioxide injections. The experimental data agreed well with the modeled strain evolution results under hydrostatic conditions and at the injection pressure conditions. The results show that the degree of anisotropy is ~ 1.6 for helium injection, comparing the strains perpendicular to and parallel to the bedding plane. The results demonstrate that the volumetric strains closely correlate to the sorption capability of coal. The maximum volumetric strain induced by carbon dioxide injection can reach ~ 2.05% as gas pressure increases up to ~ 5.43 MPa, which is ~ 2.77 times that of the methane-induced volumetric strain of ~ 0.74% at a gas pressure of ~ 5.45 MPa. The proposed model can be simplified to be equivalent to the commonly extended Langmuir-type strain model at relatively low gas pressure for bulk coal with low cleat porosity. The proposed model can also successfully cover the volumetric response of bulk coal for high pressures that range beyond 13 MPa. A sensitivity study shows that Young’s modulus, Poisson’s ratio, and the degree of anisotropy affect the volumetric responses differently at various pressure stages, but the effects are always distinct for high-pressure injections. The proposed model framework can be coupled into a coal dynamic permeability model for defining the permeability evolution—which is important for gas production predictions for CBM wells.

中文翻译：

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使用横向各向同性方法模拟吸附气体的煤基质表观应变

气体吸附引起的煤变形是煤层气（CBM）工程中的主要地质力学效应之一。众所周知，煤由于其割理结构而具有横向各向同性的特性。我们提出了一种新的理论方法，通过包括吸附引起的基质收缩/膨胀应变、割理体积应变和由孔隙压力和外部应力变化引起的基质机械应变来模拟散装煤的应变行为。新的模型框架可以定义相对于气体压力变化的表观散装煤体积。为了验证该模型，通过注入氦气、甲烷和二氧化碳进行了无约束气驱实验。实验数据与流体静力条件和注入压力条件下的模拟应变演化结果一致。结果表明，氦注入的各向异性程度约为 1.6，比较垂直和平行于层理平面的应变。结果表明，体积应变与煤的吸附能力密切相关。随着气压增加至约 5.43 MPa，由二氧化碳注入引起的最大体积应变可达到约 2.05%，这是在约 5.45 MPa 的气压下甲烷引起的约 0.74% 的体积应变的约 2.77 倍。对于具有低割理孔隙度的散装煤，所提出的模型可以简化为在相对较低的气压下等效于普遍扩展的朗缪尔型应变模型。所提出的模型还可以成功地涵盖范围超过 13 MPa 的高压下散装煤的体积响应。敏感性研究表明，杨氏模量，泊松比和各向异性程度对不同压力阶段的体积响应有不同的影响，但对高压注射的影响总是不同的。所提出的模型框架可以耦合到煤动态渗透率模型中，用于定义渗透率演化——这对于 CBM 井的天然气产量预测很重要。