自仿射粗糙割理中流体渗流的分形定律  

Fractal seepage law characterizing fluid flow through a single rough cleat composed of self-affine surfaces

作　　者：金毅[1,2,3] 郑军领[1] 董佳斌[1] 黄存捍[1] 李翔[1] 吴影[1] 

机构地区：[1]河南理工大学资源与环境学院,焦作,454003 [2]中原经济区煤层页岩气河南省协同创新中心,焦作454003 [3]河南省生物遗迹及成矿过程重点实验室,焦作454003

出　　处：《科学通报》2015年第21期2036-2047,共12页Chinese Science Bulletin

基　　金：国家自然科学基金(41102093;41472128);山西省煤层气联合研究基金(41072153)资助

摘　　要：耦合分形理论、裂隙流控制方程及孔隙尺度下数值模拟技术,详细分析了煤储层单割理中端面几何对流体运移的控制作用.首先,依据流阻成因及作用方式,确立了割理端面几何对流体运移的多重效应模式及其所对应的物理参数,依次为水文弯曲度、局部粗糙度因子以及端面曲折率.在此基础上,利用割理端面几何的自仿射属性,构建了观测尺度为割理开度时的分形裂-渗方程.其中,水文弯曲度和端面曲折率表现出不同的尺度不变特征,而局部粗糙度因子则具有长程平稳的特点.最后,利用格子Boltzmann方法于孔隙尺度下模拟了粗糙割理中煤层气的运移规律,结果表明:参数物理意义明确的新裂-渗方程解析值同数值模拟渗透率之间是高度一致的;在粗糙割理中,流速剖面的分布是一种正态分布而非抛物线模型;端面几何除了摩擦作用外还会引起涡流效应,并且同其局部特征直接相关,这会加剧压力的损失.The surfaces geometric controlling effects on fluid flow through a single cleat in coal reservoir were investigated in detail, by coupling the fractal theory, governing equation of fracture flow and numerical simulations. At first, we proposed a multiple-effect fracture-permeability model according to the resistant ways on the fracture flow from the surface geometries, in which, apart from the stationary local roughness effect, the hydraulic tortuosity and surface tortuosity are physically taken into consideration. Based on the new proposed model, a fractal fracture-permeability equation was established according to the self-affine property of the cleat＇s internal surfaces, with the observed scale being its mean aperture. The new fractal fracture-permeability model indicates that： the effects from hydraulic and surface tortuosities are both scaling-invariant to the mean aperture, but they possess different tortuous fractal dimension; while the local roughness effect is stationary at long range. The performance of the new fractal fracture-permeability model were verified by lattice Boltzmann methods, and the numerical experiments show that： in a rough cleat, the velocity profile is a skewed or norm distribution model other that the parabolic one; except for the frictional effect, the surface rough geometry will bring about eddy effect, that will speed up the loss of pressure due to the counterpresssure distribution near the rough surfaces.

关 键 词：自仿射端面 赫斯特指数 格子BOLTZMANN模型 分形裂-渗方程 水文弯曲度 端面曲折率 

分 类 号：O357.3[理学—流体力学]