Evolution and Prediction of Deep Coal–Rock Fracture Conductivity with Energy-Based Breakage Criterion of Proppant

It is of great significance to clarify the evolution law and control mechanism of fracture conductivity in different production stages for the efficient development of coalbed methane. However, research on fracture conductivity in coal–rock remains limited, and the existing models are inadequate for predicting fracture conductivity with a consideration of staged proppant crushing. To address this gap, long-term conductivity tests were conducted on deep coal–rock under varying closure pressures and proppant gradation ratios. Within a coupled computational fluid dynamics and discrete element method (CFD-DEM) framework, a particle substitution scheme was integrated with the energy-based breakage model (Tavares breakage model) to develop a fracture conductivity predictor that incorporates proppant crushing and captures the time-dependent kinetics of proppant breakage during fracture conductivity evaluation. The model’s predictions align well with the experimental data, with an average error of less than 5%. The results indicate that fracture conductivity evolution can be delineated into three stages according to particle-breakage characteristics, (i) proppant pack compaction, (ii) the primary crushing of coarse proppant grains, and (iii) the secondary crushing of proppant fines, and the contributions of these three stages to the total conductivity loss are approximately 60%, 30%, and 10%, respectively. At a low closure pressure, fracture conductivity varies markedly among proppant packs with different particle sizes; once the closure pressure exceeds 40 MPa, the proppant pack enters the fines-breakage stage, and the conductivity differences among various particle size blends become marginal. Furthermore, a semi-empirical prediction model incorporating a composite crushing factor (CCF) was developed based on the Kozeny–Carman relationship, enabling a rapid evaluation of fracture conductivity in deep coal–rock fractures. Overall, these results provide a practical basis for fracture conductivity prediction and hydraulic fracturing parameter optimization in coal–rock reservoirs.