A coupled gas–water two-phase productivity model for oversaturated deep coalbed methane reservoirs integrated with a multi-scale main-branch-cleat fracture network

Abstract

Deep oversaturated coalbed methane (CBM) reservoirs contain abundant in situ free gas, and hydraulic fracturing forms a multi-scale complex fracture network with main fractures, branch fractures, and cleats. Most current productivity models target undersaturated shallow coal seams, neglecting the coexistence of free and adsorbed gas and simplifying fractures as planar main fractures, leading to low prediction accuracy. To address this, based on dual-porosity and dual-permeability theory, this study characterizes adsorbed gas and in situ free gas in the coal matrix and free gas and formation water in natural cleats. It considers one-dimensional linear flow of free gas and fracturing fluid in hydraulic fractures and two-dimensional radial flow of adsorbed gas, free gas, and formation water in the cleat–matrix system. A multi-region coupled model is developed for three typical fracture patterns: single main fracture-cleat, main single-branch fracture-cleat, and main multiple-branch fracture-cleat. This model fully considers the conductivity attenuation mechanism of hydraulic fractures, as well as spatial overlap and interaction among stimulated zones. The model is solved by a hybrid finite difference-embedded discrete fracture method, which realizes quantitative dynamic prediction of gas and water production over the entire well life cycle, including production ramp-up, stable production, and decline for oversaturated deep shale gas wells with complex fracture networks. Sensitivity analysis reveals the effects of cleat properties, hydraulic fracture parameters, and complex multiscale fracture morphologies on gas–water two-phase productivity. The core innovation of this study is a coupled gas–water two-phase productivity model integrating adsorbed gas, free gas, and water within the multi-scale fracture–matrix system, which overcomes the limitations of conventional models in characterizing complex fracture networks and multiphase flow. This work provides theoretical support for fracturing optimization and production regulation of horizontal wells in deep oversaturated CBM reservoirs.