Abstract

On the basis of the laws of conservation and the principles of thermodynamics, a mathematical model of the flow of a two-phase granular fluid is proposed. One of the phases is the viscoplastic granular Bingham fluid; the other phase is a viscous Newtonian fluid. The equations for flows in the Hele–Shaw cell are analyzed asymptotically, i.e., when the flat-channel width is much less than its length. The correlations between the phase flow rates and the pressure gradient leading to equations of filtration for a two-phase granular viscoplastic fluid are constructed. The criterion is found for the initiation of motion of a granular phase in a porous medium. It is established that, depending on the shear-yield stress, such a phase does not flow if either the pressure gradient or the channel thickness is small. The phase flow rates are analyzed numerically at various input parameters such as the phase viscosities, phase resistivities, ultimate shear stress, etc. The factors slowing down the penetrating motion of the solid phase into the porous medium are revealed.

中文翻译：

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裂缝附近粘塑性岩石的行为：数学建模

摘要

根据守恒定律和热力学原理，建立了两相颗粒流体流动的数学模型。相之一是粘塑性粒状宾厄姆流体；另一相是粘性牛顿流体。对Hele-Shaw单元中的流动方程进行渐进分析，即当平通道宽度远小于其长度时。构造了相流速和压力梯度之间的相关性，从而建立了两相颗粒状粘塑性流体的过滤方程。发现了用于在多孔介质中开始粒相运动的标准。可以确定的是，取决于剪切屈服应力，如果压力梯度或通道厚度较小，则这种相不会流动。