A mathematical model for the permeability evolution of coal-bearing hydraulic propped fractures

The established dynamic evolution mathematical model of coal-bearing propped fractures had the ability to accurately predict the characteristics of coal fine migration and deposition in the entire region of the propped fractures, as well as identifying spatial–temporal variations in the porosity and permeability of the propped fractures. [Display omitted] •Coal-bearing hydraulic propped fracture permeability model was established.•Mass concentration of coal fine suspension, volume fraction of deposited coal fines and permeability were predicted.•Larger deposition coefficient and smaller dispersion coefficient caused lower permeability. The intrusion of coal fines into hydraulic propped fractures leads to permeability damage in coal seams, which restricts the production of coalbed methane. A permeability model of coal-bearing hydraulic propped fractures was established in this study based on a spherical particle stacking model and the Kozeny-Carman Equation. It was determined that the permeability evolution of the propped fractures which were correlated with the porosity of the porous media by introducing the deposition coefficient and dispersion coefficient of the coal fines. The results showed that during the continuous intrusion of the coal fines, the mass concentration of the coal fine suspension rose to a peak level, and then remain unchanged. The permeability of the propped fractures continuously decreased, and then remained in a stable state. The larger the coal fine deposition coefficient, the larger the amount of coal fines deposited in the entrance sections of the fractures, which resulted in lower quantities of coal fines entering the inner sections of the propped fractures. The lower the volume of deposited coal fines, the greater the permeability of the propped fractures. And the larger the coal fine dispersion coefficient, the easier it was for the coal fines to enter the propped fractures, caused the larger amount of the coal fines moved into the fractures. Hence the larger mass concentration of the coal fine suspension and the larger volume fraction of deposited coal fines led to the lower the porosity and permeability of the propped fractures.