Investigation of the Klinkenberg effect on gas flow in coal matrices: A numerical study

The Klinkenberg effect may significantly impact gas flow behavior, especially in low permeability materials (e.g., coal matrices). The estimation of permeability in coal matrices with respect to the Klinkenberg effect has significant implications for the production of coal bed methane (CBM), impacting factors such as production rates and reservoir issues. In our study, a coal permeability model consisting of seepage and the stress field is constructed. This model considers the stress-strain equation, porosity dynamic evolution equation, and permeability equation with Klinkenberg effects. The primary focus was that the Klinkenberg effect, which is linked to variable porosity in coal, was treated as a dynamic parameter affecting the permeability of the coal matrix. A numerical model, based on the COMSOL software package, was employed for this coal permeability model. A physical experiment was used to validate the numerical simulations. The results show that Klinkenberg effect-based permeability now has an improved agreement with the physical experiment. The Klinkenberg effect is influenced by the stress magnitude, gas pressure distribution, and boundary conditions. Specifically, an increase in effective stress induced by the reduction of the gas pressure improves the compressive deformation of the coal matrix, thereby changing the porosity and permeability of the coal seam. The Klinkenberg effect affects gas pressure permeability. Under fixed boundary conditions for a small change in outlet conditions, the gas pressure gradient is significantly reduced; however, under the inlet conditions, the gas pressure gradient increases.