A fully-coupled semi-analytical model for effective gas/water phase permeability during coal-bed methane production

Although many breakthrough efforts have been made in recent years, it is still challenging to gain a clear knowledge of the variation regularities of effective gas/water phase permeability with the pressure depletion. The reasons behind this phenomenon can be attributed to the coexistence of multiple effects and the transition of the flow behavior at different production stages. To date, the fully-coupled model for effective gas/water phase permeability in coal-bed methane (CBM) reservoirs is still lacking and is significantly necessary to be developed. Firstly, the Palmer-Mansoori (PM) model is employed to represent the variation relationship between absolute permeability and pressure. Secondly, after rigorous derivation of the gas-water two phase partial differential equations in coal seams, the relationship between pressure and saturation in infinitesimal coal is obtained, which can be solved through an iterative algorithm. Subsequently, combined with the Corey relative permeability model, the relative gas/water phase permeability can be described as a function of pressure. Finally, coupling the absolute permeability model and relative permeability model, the effective gas/water phase permeability can also be quantified as a function of pressure or saturation. And the reliability and the accuracy of the proposed model is successfully verified through comparisons with experimental data and previous model collected from published literature. Furthermore, on the basis of the proposed semi-analytical model, the effects of critical desorption pressure, gas desorption capacity, stress dependence, and matrix shrinkage on effective permeability are identified. And many implications and direct insights are achieved through the sensitive analysis process. The semi-analytical model, for the first time, incorporates nearly all known mechanisms and can achieve more accurate characterization of effective permeability during the production process. Moreover, due to the concise form and precise feature, the proposed model will serve as a simple, practical and robust tool for the development of CBM reservoirs.