Coupling of transient matrix diffusion and pore network models for gas flow in coal

Processes of sorption and diffusion play a critical role in the analysis and simulation of coal seam gas (CSG) reservoirs since most of the gas reserves are held by the coal matrix. Thus, it is essential to understand the displacement of gas in coal matrix and fractures. This can be formulated in terms of sorption and diffusion processes inside the matrix and advective flow in the cleats. The multi-scale porous structure and multi-physics nature of gas flow in coal complicate numerical modelling of these phenomena. A novel approach is developed to solve this problem by coupling conventional pore network modelling (PNM) with transient diffusion flow. The coupling is undertaken for each pore network throat separately by utilising the Finite Volume Method and Fick's second law of diffusion. The Langmuir isotherm is employed to describe sorption processes within the coal matrix and to link the concentration and pressure values when coupling the diffusion model with PNM. The proposed approach provides the possibility to account for the transient nature of gas transport across the different scales, while limiting the number of unknowns in the simulation to an effective diffusivity parameter. Our results demonstrate that steady-state pore network models can be effectively coupled with a transient phenomenon such as Fick's diffusion allowing to estimate the diffusive constitute of the matrix to the total gas flow in coal over time. The obtained gas sorption capacity and its release rate can then be used to accurately estimate the timedependent production profile of CSG reservoirs.