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科学通报  2015 

自仿射粗糙割理中流体渗流的分形定律

DOI: 10.1360/N972015-00140, PP. 2036-2047

Keywords: 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

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Abstract:

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.

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