A semi-analytical model for flow regime diagnosis in multi-fractured horizontal wells within deep coalbed methane reservoirs

Since 2021, significant advances have been made in the exploitation of deep coalbed methane (CBM) in China, with peak gas production rates reaching over 100,000 m3/d from wells in the Ordos basin. Despite these successes, research on gas flow mechanisms and transient pressure behavior, particularly in the context of horizontal wells and intensive stimulation, has lagged behind field developments. In this study, a “dual-porosity and dual-phase” model, which incorporates free and adsorptive gas, coal quality and excess adsorption, has been proposed to better understand gas flow dynamics during extraction from deep coal seams with multi-fractured horizontal wells. Utilizing Laplace transformation and the Gaver-Stehfest numerical inversion method, combined with boundary elements and point-source functions, a semi-analytical solution is derived. This solution identifies six distinct flow regimes under constant-rate conditions: wellbore storage flow (I), early pseudo-radial flow (II), elliptical flow (III), transitional flow (IV), desorptive gas dominatedflow (V), late pseudo-radial flow (VI). A notable “desorptive concave” response in Regime V and the presence of free gas in Regime III, are distinctive features of deep coal gas reservoirs. A comprehensive sensitivity analysis is conducted to examine the impact of various parameters on pressure responses. Eventually, a field case study validates the model, emphasizing the significant contribution of desorbed gas in Regime V. These findings offer valuable insights into the gas flow mechanisms of deep coal reservoirs and provide guidance for optimizing multi-fractured horizontal well management strategies.