粗糙裂隙煤岩的分形多场渗流模型及数值模拟

A fractal multi⁃field model and numerical simulation of rough coal rock fractures

煤体裂隙分布特性对气体聚集、运移及产出具有至关重要的影响。基于多孔介质分形理论,构建了一种新的跨学科分析模型,定量表征了煤岩裂隙粗糙程度,并将煤岩渗透率定义为它的函数,进而与煤体变形、吸附效应及气体压力耦合,实现了多物理场耦合作用下裂隙粗糙程度及分形行为对气体渗流、煤岩应力和渗透率影响的定量分析。研究表明:提出的4个分形参数能够很好地表征粗糙裂隙数目、长度、迂曲度及粗糙程度;当煤岩物性参数保持不变时,渗透率与裂隙迂曲度分形维数成反比,与裂隙分形维数成正比;相较于其他微观参数,迂曲度分形维数的改变对煤岩渗透率及气体压力的影响最大。研究结果可为相关工程项目提供一种全新的评估抽采率及开采安全性的跨学科方法。

Topological characteristics of coal rock fractures have a crucial impact on gas accumulation,migration,and production.Based on the fractal theory of porous media,a new interdisciplinary analysis model was constructed to quantitatively characterize the roughness of coal rock fractures.Meanwhile,the permeability of coal rock was defined by a function of fracture roughness.In this way,the influences of fracture roughness and fractal behaviour on gas seepage,coal rock stress and coal rock permeability un⁃der the coupling of multiple physical fields(coal deformation,gas adsorption,and gas pressure)were quantitatively analysed.The research results demonstrate that the proposed four fractal parameters can ef⁃fectively characterize the number,length,tortuosity,and roughness of rough cracks.When the physical parameters of coal rock remain unchanged,its permeability is inversely proportional to the fractal dimen⁃sion of fracture tortuosity and directly proportional to the fractal dimension of fractures.Compared to the other microscopic parameters,changes in the fractal dimension of fracture tortuosity have the greatest impact on coal rock permeability and gas pressure.This study provides a new interdisciplinary method for evaluating extraction rates and mining safety in related engineering projects.