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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.
Highlights
Mastering the law of gas migration and accumulation in coal seams, fractured rock masses and goafs are the basis for the development of coal mine gas prevention and drainage technology[1]
Based on the theory of porous media seepage and dynamic dispersion, Qi[5] established a three-dimensional stable seepage and gas concentration distribution mathematical model, and gave the Galerkin finite element solution of the mathematical model. It reveals the law of gas flow in coal to a certain extent by the above-mentioned research work, but they are all limited to one medium system and fail to fully and accurately reflect the gas flow characteristics in porous media
Kv where the Km is the permeability of the coal matrix system, the Kf is the permeability of the fracture system, the K v is the permeability of the hole system
Summary
Mastering the law of gas migration and accumulation in coal seams, fractured rock masses and goafs are the basis for the development of coal mine gas prevention and drainage technology[1]. Based on the theory of porous media seepage and dynamic dispersion, Qi[5] established a three-dimensional stable seepage and gas concentration distribution mathematical model, and gave the Galerkin finite element solution of the mathematical model. It reveals the law of gas flow in coal to a certain extent by the above-mentioned research work, but they are all limited to one medium system and fail to fully and accurately reflect the gas flow characteristics in porous media. The equivalent Darcy flow equation of large-scale space is derived based on the homogenization theory, and the simulation software is used to analyze the case to verify the correctness of the model
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