Long-Term Productivity Prediction for Hydraulically Fractured Deep Coalbed Methane Wells Considering Coal Creep Under Multiphysics Coupling

The long-term productivity of hydraulically fractured deep coalbed methane (CBM) wells is jointly governed by desorption-driven gas supply from the coal matrix, the effective-stress response and time-dependent creep of natural cleats, and the progressive degradation of hydraulic-fracture conductivity. To address the difficulty of conventional models in consistently describing the time-dependent transport capacities of natural cleats and hydraulic fractures, this study develops a productivity-prediction model for hydraulically fractured deep CBM wells that couples gas storage in the coal matrix, dynamic natural-cleat permeability, and dynamic hydraulic-fracture conductivity. Based on mass conservation, the model accounts for free- and adsorbed-gas storage, single-phase gas flow, matrix-fracture mass transfer, and wellbore production. The evolution of natural-cleat permeability incorporates effective-stress-induced closure, Langmuir desorption shrinkage, and fractional-order creep, whereas the evolution of hydraulic-fracture conductivity considers fracture compaction, elastic deformation and embedment of proppants, and creep-induced closure of the coal rock. The nonlinear coupled equations are solved using a fully implicit finite-difference scheme. The field dataset comprises daily production records from six deep CBM wells and is used only to constrain physically reasonable ranges of field parameters and provide reference production characteristics. The results indicate that effective stress primarily controls the rapid closure of flow pathways during the early production stage, while the relative contribution of coal creep increases with production time. Neglecting either coal creep or stress sensitivity leads to an overestimation of cumulative gas production over the medium and long term. The proposed model provides a physically constrained analytical framework for evaluating the long-term productivity of hydraulically fractured deep CBM wells and comparing alternative production strategies.