Extension model of fracturing cracks of translayer horizontal well in roof of soft coal reservoir

In order to study the propagation rules of hydraulic fracturing crack formed by a horizontal well in roof to coal seam, taking the Permian-Carboniferous coal field in North China as an example, through the classical theory of fracture mechanics, damage mechanics and fluid mechanics, combined with field actual data, the modeling and verification of the space-time evolution law of the crack propagation distance and fracturing time were carried out. Firstly, considering the additional stress of perforation, the characteristics of primary fracture and the permeability characteristics of rock formation, the calculation formula of cracking pressure of vertical hydraulic fracture caused by horizontal well in roof was proposed; Then, considering the damage effect of fractured coal and rock mass, Dougill damage factor was introduced to extend the calculation model into the calculation model of extension pressure; Finally, based on the improved classical PKN model and fracturing fluid loss theory, the functional relationship between the crack propagation distance and fracturing construction time under continuous penetration conditions was established. The research results show that extension distance of the cracks can be controlled by accurately adjusting the time parameters according to above theoretical model.