Diffusion coefficients and multi-scale diffusion models of shale oil and gas
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摘要: 针对页岩油气在纳米–微米级孔缝体系中扩散机理不清、传统模型难以实现跨尺度预测的问题，通过结合高温高压扩散实验、分形理论建模与纳米限域效应，系统研究了页岩油气在多尺度孔缝介质中的扩散特征及其主控因素。结果表明，纳米限域效应导致相图内缩和临界点左移，显著削弱受限空间内的扩散能力。孔隙度与渗透率是主要结构控制因素：当孔隙度由5.68%增至10.53%时，气液扩散系数均提高约一个数量级；页理缝渗透率由1.69 ×10−15 m2增至404.88 ×10−15 m2时，扩散系数增大约3~4倍。压力升高（10~36 MPa）抑制气相扩散而增强液相扩散，温度升高（80~115 ℃）整体促进扩散。构建的分形–限域模型可准确拟合实验，并揭示有效扩散系数在纳米尺度较体相降低约10−5、裂缝扩散能力高于基质1~2个数量级，实现了多尺度扩散的结构敏感性分析与跨尺度预测。研究成果可为页岩油气扩散机理定量刻画及储层开发优化提供理论支撑。Abstract:
Objective To elucidate the diffusion mechanisms of shale oil and gas in nano- to microscale pore-fracture systems and overcome the limitations of conventional models in cross-scale prediction, this study investigates the diffusion characteristics and controlling factors of shale fluids across multiscale porous media. Methods High-temperature and high-pressure diffusion experiments were conducted on matrix and bedding-fractured core samples with varying petrophysical properties. A multiscale diffusion model was developed by coupling fractal theory, a tortuous capillary-bundle representation, and a confinement-corrected Peng–Robinson equation of state to account for pore-size distribution, tortuosity, phase saturation, and nanoscale fluid–wall interactions. Results Nanoscale confinement leads to phase-diagram contraction and a leftward shift of the critical point, substantially weakening diffusion capacity in confined spaces. Porosity and permeability are the primary structural controls: when porosity increases from 5.68% to 10.53%, gas and liquid diffusion coefficients increase by approximately one order of magnitude; when bedding-fracture permeability increases from 1.69 ×10−15 m2 to 404.88 ×10−15 m2, diffusion coefficients rise by about three to four times. Increasing pressure (10~36 MPa) suppresses gas-phase diffusion but enhances liquid-phase diffusion, whereas higher temperatures (80~115 °C) promote diffusion overall. Conclusions The proposed fractal–confinement diffusion model accurately matches the experimental results and reveals key nanoscale mechanisms, including a ~10−5 reduction in effective diffusivity relative to bulk fluids and diffusion capacities in fractures that exceed those of the matrix by one to two orders of magnitude. Significance This model enables structural-sensitivity analysis and cross-scale prediction of diffusion processes, providing theoretical support for the quantitative characterization of shale-fluid migration and the optimization of reservoir development. -
图 1 物理模拟实验流程
Figure 1. Schematic diagram of the experimental setup and workflow for physical simulation
图 2 相平衡计算流程图
zi—组分i的总体摩尔分数，无量纲；ωi—组分i的偏心因子，无量纲；Pci—组分i的临界压力，MPa；Tci—组分i的临界温度，K；Ki—组分i的气液平衡比，无量纲；NV—气相摩尔分率，无量纲；yi—组分i在气相中的摩尔分数，无量纲；fiL、fiV—组分i在液相、气相中的逸度，MPa；tol—相平衡迭代收敛容限，无量纲；其余变量符号含义同公式
Figure 2. Flowchart of phase equilibrium calculations
图 4 $\mathrm{C}_7^{+} $组分临界点参数变化曲线
Figure 4. Critical parameter shifts of the $\mathrm{C}_7^{+} $ fraction
(a) Critical pressure shift of the $\mathrm{C}_7^{+} $ fraction; (b) Critical temperature shift of the $\mathrm{C}_7^{+} $ fraction
图 5 不同孔隙度岩芯的流体扩散系数
Figure 5. Fluid diffusion coefficients in core samples with varying porosities
(a) Gas diffusion coefficients in core samples with varying porosities; (b) Liquid diffusion coefficients in core samples with varying porosities
图 6 不同页理缝的流体扩散系数
Figure 6. Fluid diffusion coefficients in bedding fractures
(a) Gas diffusion coefficients of bedding-fractured core samples with varying permeabilities; (b) Liquid diffusion coefficients of bedding-fractured core samples with varying permeabilities
图 7 不同压力下岩芯的流体扩散系数
Figure 7. Fluid diffusion coefficients in core samples under varying pressures
(a) Gas diffusion coefficients in core samples under varying pressures; (b) Liquid diffusion coefficients in core samples under varying pressures
图 8 不同温度下岩芯的流体扩散系数
Figure 8. Fluid diffusion coefficients in core samples under varying temperatures (a) Gas diffusion coefficients in core samples under varying temperatures; (b) Liquid diffusion coefficients in core samples under varying temperatures
图 12 不同孔隙度页理缝的扩散系数
Figure 12. Bedding-fracture diffusion coefficients across varying porosities
表 1 实验岩芯物性特征
Table 1. Petrophysical properties of experimental core samples
类别 岩芯编号 长度/cm 直径/cm 孔隙度/% 渗透率/×10−15 m2 基质岩芯 Q2 4.86 2.55 9.56 0.0652 Q3-2 5.07 2.53 10.53 1.1990 Q9-1 5.03 2.53 5.68 0.0129 页理缝岩芯 Q2-1 5.03 2.55 6.88 46.7000 Q2-2 4.78 2.53 8.80 404.8900 Q3-1 4.95 2.54 4.98 1.6900 
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