Slippage effect and the seepage mechanism considering the compaction and embedding action of proppant

Hydraulic fracturing technology is an effective method to improve the efficiency of coalbed methane drainage, but the universal embedding of proppant under stress will change the width of the fractures, which will affect the gas slippage effect and the permeability mechanism. In order to explore the gas slippage effect and coal seepage law under the background of hydraulic fracturing, the Hertzian contact theory is used to quantify the embedding depth of proppant, and the gas slippage coefficient calculation equation and permeability model of the combined effect of proppant and effective stress are constructed. The results show that under different gas pressures, the permeability of coal first decreases with the increase of effective stress and then tends to be flat. Under the constant effective stress conditions, the lower the gas pressure, the higher the permeability; multiple layers of sand are laid. The anti-reflective effect of slab is better than that of single-layer sand. Under the two paving conditions, the slippage factor b shows the same changing trend under different gas pressures, and both increase with the increase of the proppant embedding depth. The slippage factors of different forms of cracks all increase with the increase of effective stress, of which the slippage factor of spherical cracks is the largest, followed by the cylindrical cracks, and slit shape is the smallest. At the same time, the permeability of different forms of fractured coal decreases with the increase of effective stress, and the relationship between the permeability of the three forms of fractures is consistent with the relationship between the size of the slippage factor. Taking into account the effective stress and the proppant contribution to the fracture width, a fracture permeability model considering the comprehensive effects of proppant and effective stress was constructed, and its rationality was verified through publicly released test data. The conclusions obtained will help the further application of hydraulic fracturing technology in coalbed methane drainage.