Upscaling of gas transport in shale matrix based on homogenization theory

Abstract

The shale matrix is composed of organic matrix with free gas and adsorbed, and inorganic matrix with only free gas. The gas transport mechanism in two different shale matrix is different. The conventional numerical model did not consider the different gas transport mechanism in the shale matrix and the influence of the distribution of the organic matter. In this paper we established a upscaled shale matrix model with considering these mechanisms. In the microscale region, the Knudsen diffusion and viscous flow of free gas and surface diffusion of adsorbed gas is considered in the microscale model of organic matrix, while only Knudsen diffusion and viscous flow of free gas is considered in the microscale model of inorganic matrix. We calculated the production and pressure of shale matrix have different organic matrix distribution and same TOC content in the microscale region while have same parameters in the macroscale model, the result shows that the macro-scale equations solved directly without homogenization process have the same pressure and production while with upscaling process the solved pressure and production are different in these macro-scale models.