Dynamic Prediction of Methane Diffusivity in Water-Bearing Coal Using a Pore-Network Model: Coupled Effects of Pressure and Water Saturation

Methane diffusivity controls matrix-to-cleat gas transfer in coalbed methane reservoirs and varies with pore structure, pressure, and water saturation. A three-dimensional pore–throat network combines steady-state Fickian transport with invasion percolation to evaluate these effects. Dynamic prediction refers to updating effective diffusivity at successive reservoir states. For the Pittsburgh and Madrid pressure series, the mean absolute relative errors are 3.3% and 2.5% across five observations per coal, and 2.9% and 2.5% for the two withheld observations. Effective diffusivity increases with coordination number and the investigated Weibull parameters within the specified network family, while the prescribed pressure response is negative. Increasing water saturation suppresses gas-connected transport, with near-zero diffusivity around 0.58 for the examined configuration. An alternating conditional expectation framework describes nonlinear structural responses, and a separate pressure–saturation relation expresses the state dependence in a compact form. The results distinguish the contributions of local mobility and gas-pathway connectivity to effective methane diffusion.