The Research of the Seepage Regularity of Power-Law Fluid under Porosity Scale

Abstract

There are various shapes of capillary tubes in the rock, and the flow in triangles and rectangles capillary tubes has been studied very little. In this paper, the approximate solution of the distribution of the velocity in triangles capillary tubes has been obtained using variational method. The quantitative relation between pressure difference and flow rate in the two kinds of capillary tubes has been obtained by integrating in the entire capillary tubes, which is similar to Poiseuille's law. this study also applies the Pdetool tool in Matlab to solve the laminar flow of different sections in capillary flow numerically and compares the variational results and numerical results with the literature analytic solution, numerical solution and the experimental results. On the foundation of comparing the variational results, the numerical results and the literature analytic solution, numerical solution and the experimental results, we analyze the influence of the power-law index and cross-section shape on the comprehensive resistance coefficient and flow pressure relationship.