Modeling of gas non-isothermal desorption-diffusion in deformed coal and application in lost gas calculation

Coalbed methane (CBM) content is a crucial parameter for CBM exploitation and disaster prevention, with accurate gas loss calculation being essential for improving measurement precision. To investigate the physical response to gas loss and quantify the impact and interrelation of various factors, this study developed a comprehensive model incorporating the effects of gas diffusion, temperature, and pressure effects on porosity and coal deformation. By utilizing the OpenFOAM platform and C++ for numerical solution development and establishing an experimental system for gas loss measurement, the model's reliability was confirmed. The new model demonstrates an 8.56% average error, representing a significant improvement over traditional methods, with error reductions of 26.59% and 18.31% compared to the square root of time and power function methods, respectively. The hierarchy of gas loss is determined to be gas flow > gas-coal deformation coupling > gas-temperature coupling > gas-coal deformation-temperature coupling. Average diffusion contributions are identified as 41.43% from surface diffusion, 30.71% from Knudsen diffusion, and 27.86% from viscous flow. The factors affecting gas loss, in decreasing order of impact, are adsorption equilibrium pressure, temperature, porosity, moisture, and adsorption constants. These findings provide theoretical support for enhancing gas content measurement accuracy and techniques, significantly benefiting CBM extraction and mine safety.