A model of coupling the stress equilibrium and fluid continuity equations is proposed and implemented to solve numerical simulation problem of the hydraulic fracturing propagations. The mechanism of critical stress criterion of crack propagation is also introduced. The pressure descent distribution function on the fracture face along the fracture length is deduced and the corresponding user subroutines are developed and also embedded into ABAQUS. The complex factors of geology such as in-situ stress distribution

mechanical properties

fracturing fluid properties etc. are included in the present model. Several conclusions are drawn from the simulation results. It is viable to solve problems of hydraulic fracturing propagations in the permeable reservoirs with the finite element analysis software(ABAQUS). The concept of critical width is proposed; the critical width can be used to judge a hydraulic fracture is treated as a porous passage or as a fluid flow fracture passage. The obtained conclusions are of much significance for the perforation parameter optimization and design of hydraulic fracturing treatments.