Method for determining the flowback rate of fracturing fluid considering gel degradation during hydraulic fracturing

Fracturing flowback plays a vital role in coalbed methane (CBM) reservoir development, but field flowback rates are still commonly selected based on operational experience and are therefore difficult to generalize across wells. To move beyond a field-application description, this study develops a mechanics-based and parameterized framework for estimating the allowable flowback-rate window after hydraulic fracturing. The model incorporates the post-break viscosity of the fracturing fluid and formulates the critical particle-mobilization condition from the force balance acting on coal fines and proppant before and after fracture closure. Instead of calibrating an empirical correlation for a single block, the method uses measurable or literature-constrained inputs, including particle size and density, fluid density and viscosity, fracture pressure differential, wetting-phase saturation, and contact-mechanics coefficients. Field parameters from two CBM wells are used as demonstrative cases to implement the workflow and to examine whether the calculated operating window is consistent with realistic field flowback-rate magnitudes. The calculated critical proppant flowback velocity ranges from 3.6 to 498 m³/day before fracture closure and 36-890 m³/day after closure, while the minimum velocity required to mobilize coal fines increases with particle size. Sensitivity analysis identifies particle radius, post-closure pressure differential, particle density, fluid viscosity, and wetting-phase saturation as the dominant controlling factors. Larger and denser particles increase the required flowback velocity, whereas higher fluid viscosity reduces it by enhancing drag. Capillary forces promote particle mobilization, while friction becomes the primary resisting force after fracture closure. Because no new laboratory flowback experiment is conducted in this work, the model is not claimed to be fully experimentally validated; instead, its reliability is supported by transparent parameterization, literature-constrained coefficients, order-of-magnitude comparison with reported flowback rates, and systematic sensitivity analysis. The proposed workflow provides a transferable screening tool for selecting flowback rates that balance early cleanup efficiency and long-term fracture conductivity in CBM and other propped-fracture operations.