The mathematical model of gas flowing in porous medium based on the homogenization method

Abstract

Considered the characteristics of porous medium in the coal seam and goaf, in order to reflect the accurately influence of various porous media against the gas flow, the mathematical model of discrete multi-scale network and macroscopic flow, CFCM (Coal-Fracture-Cavity-Model), was presented. The porous medium is classified into coal matrix, fracture and hole systems based on the size, and the coal matrix system includes micro fractures and micro-porous. The coal matrix system and fracture system can be regarded as diffusion and percolation areas; hole system can be regarded as a free-flowing area. The computation model of flow field in micro-scale, small-scale and large-scale are obtained according the Fick’s diffusion law, Darcy’s permeability law and Forchheimer generalized Darcy law respectively, the homogenization method is used to analyse the mathematical model by scale upgrading and the equivalent Darcy’s fluid equation of porous medium is got to describe the characteristics of the medium in the flow field accurately. An example calculated shows that the coal matrix and fracture systems are the most influential factors of the flow field in goaf and the two systems above would prevent the diffusion of airflow. The study validates the correctness of the classification method and the model of flow equation.