Abstract: Shale exhibits inherent anisotropy and transverse isotropy as a result of its mineral composition and preferred orientation, leading to pronounced disparities in mass transfer characteristics along the directions parallel and perpendicular to the bedding planes. Multi-scale interconnected pores serve as effective conduits for shale gas transport, while the topographical heterogeneity of mineral grains at the microscopic scale induces an observable roughness on the pore walls. Establishing a comprehensive mass transfer model that integrates spatial pore distribution with mass transfer characteristics under multiple flow regimes, alongside determining the evolution laws of shale permeability, remains a critical challenge. In this study, anisotropic parameters, including TOC, pore size, surface diffusion coefficients, and stress sensitivity coefficients, were experimentally determined following oriented coring along both parallel and perpendicular directions relative to the bedding planes of the core samples. Multi-scale pore distribution and connectivity were characterized through integrated high-pressure mercury intrusion and nuclear magnetic resonance experiments, while the nanometer-scale roughness morphology was characterized using atomic force microscopy (AFM) in conjunction with a physical model of conical roughness elements. Based on the three-dimensional fractal theory, an anisotropic mass transfer model for multi-scale micro-nano pores in shale was established. This model integrates factors including multi-scale pore size distribution, connectivity, roughness, water film, stress sensitivity, and real gas effects, while coupling transport mechanisms such as viscous flow, Knudsen diffusion, surface diffusion, and desorption. The research results indicate that:(1) TOC, pore size, connectivity, roughness, surface diffusion coefficient, and stress sensitivity coefficient exhibit significant anisotropic characteristics; (2) The developed model comprehensively incorporates the anisotropic gas mass transfer characteristics of shale, with an average relative error between predictions and experimental results ranging from 3.24 % to 5.12 %. The ratio of parallel to vertical permeability reaches 17, and factors such as connectivity, roughness, pore size distribution, and tortuosity fractal characteristics exert significant influences on the mass transfer outcomes. (3) Matrix permeability is positively correlated with TOC, pore size, connectivity, and surface diffusion coefficient, with organic matter exhibiting greater sensitivity to pore size and connectivity compared to inorganic matter. Conversely, permeability is negatively correlated with roughness and the ratio of the porosity-permeability correction coefficient; increased capillary roughness further restricts the Knudsen diffusion of gas molecules.

Key words: shale gas, multi-scale pore, roughness, connectivity, anisotropy, variable pipe diameter, three-dimensional fractal, mass transfer mechanism

摘要： 页岩由于矿物含量及定向排列而具有各向异性和横观各向同性,导致平行与垂直页岩层理方向的传质特性存在显著差异。多尺度连通孔隙是页岩气的有效运输通道,矿物颗粒在微观尺度上的表面拓扑异质性致使孔隙壁面形成可观测的粗糙度。建立全面考虑孔隙空间分布和多流态传质特征的传质模型,并确定页岩渗透率演化规律等是目前亟待解决的难题。通过对岩心样品平行层理/垂直层理方向定向取样,利用实验获取有机质含量(TOC)、孔径、表面扩散系数、应力敏感系数等各向异性特性参数。利用高压压汞和核磁共振实验联合表征多尺度孔隙分布及连通性;结合原子力显微镜(AFM)与圆锥粗糙元物理模型表征纳米尺度粗糙形貌。基于三维分形理论,综合多尺度孔径分布、连通性、粗糙度、水膜、应力敏感及真实气体效应等因素,耦合黏性流、Knudsen扩散、表面扩散及解吸附效应等传输机理,建立了页岩各向异性多尺度微米—纳米孔传质模型。研究结果表明:① TOC、孔径、连通性、粗糙度、表面扩散系数、应力敏感程度系数等具有显著的各向异性特征。②模型全面考虑了页岩各向异性气体传质特性,预测与实验结果平均误差为3.24 %~5.12 %;平行与垂直方向渗透率之比达到17,其中,连通性、粗糙度和孔径分布及迂曲度分形特征对传质结果影响显著。③基质渗透率与TOC、孔径、连通性和表面扩散系数呈正相关,有机质对孔径与连通性的敏感程度大于无机质;渗透率与粗糙度、孔渗修正系数之比呈负相关,毛细管越粗糙,气体分子的Knudsen扩散越易受阻。

关键词: 页岩气, 多尺度孔隙, 粗糙度, 连通性, 各向异性, 可变管径, 三维分形, 传质机理