煤体双重孔隙瓦斯双渗流模型及无因次解算

Mathematical model and dimensionless numerical simulation of methane flow in a dual-porosity and dual-permeability coal seam

考虑瓦斯在煤层中的解吸、放散与渗流,利用达西定律分别描述煤基质与裂隙内的瓦斯运移,以煤基质与裂隙之间的传质通量为桥梁,发展煤体双重孔隙瓦斯双渗流模型,推导无因次模型,并运用有限差分法进行编程解算。结果表明:瓦斯压力、含量在裂隙内的下降速度要远大于煤基质;基质空间内瓦斯压力及含量的分布具有非均匀性及非稳态性;增大裂隙渗透性或煤层瓦斯压力,或减小煤壁表面瓦斯压力,均能导致瓦斯涌出速度的增大;煤体游离瓦斯含量对瓦斯涌出速度影响较小。结合潘一矿煤层瓦斯参数,对比模拟结果和实测数据,验证了煤体双重孔隙瓦斯双渗流模型的正确性。

Considering the three stages of methane flow in coalseam including desorption, migration and seepage, Darcy＇s law was employed to describe gas migration in coal matrix and fracture, and the gas mass transfer flux between coal matrix and fracture was served as a coupling term to develop a mathematical model of methane flow in a dual-porosity, dual-permeability coal seam and its dimensionless model. The finite difference method was applied to develop a numerical solution for the model. The numerical results show that the decline rate of gas pressure and content in fracture is much faster than that in coal matrix. The gas pressure distribution and gas content in coal matrix are heterogeneous and unsteady over time. A higher permeability of fracture, a higher original gas pressure in coal, or a lower gas pressure outside coal wall, lead to a higher gas emission rate. The dual-porosity and dual-permeability model for methane flow in coal seam is validated to be correct by comparing the simulated results and the field data from Panyi mine.