Abstract: Hydraulic fracturing technology is a way to efficiently develop multi layer superimposed coalbed reservoirs.Among the multi layer coalbed superimposed reservoirs,compared with other rock layers,the interlayer stress,interface properties,and lithology of coal layer are quite different,which will have a great impact on hydraulic fracture propagation.Therefore,aiming at the problem of hydraulic fracture longitudinal propagation,a multi layer superimposed coal layer hydraulic fracture longitudinal expansion mechanism model was developed based on the theory of pore elasticity and damage mechanics.In this approach,it assumes that the damage will only be caused when the element strain exceeds the critical strain of the rock.The element permeability is the weighted summation of initial rock permeability and fracture permeability,and the weight coefficient is a function of fracture width and element size.In the initial state,all elements except the fracture elements have no damage.The finite element numerical discretization method and Newton Raphson (NR) iterative method were used to establish the corresponding numerical solution iteration format,and the corresponding numerical calculation program was written by MATLAB.The model was used to examine the influences of in situ stresses difference,interface strength,modulus of elasticity and Poisson’s ratio of sandstone layer (cap layer),and fracturing fluid viscosity on the longitudinal propagation of hydraulic fracturing.The results demonstrate that the larger in situ stress difference,interface strength,and modulus of elasticity(sandstone layer),the higher probability of hydraulic fracture penetrates the sand coal layer interface and extends in the sandstone layer.High viscosity of the fracturing fluid will make it possible that the fracture extends through the interlayer interface to the upper and lower barriers.If the fracture propagation along the sand coal layer interface,the fracture width in the interface is much smaller than that in the coal.The pressure in the fracture that propagates along the sand coal layer interface is higher than the pressure of hydraulic fractures that cross the sand coal interface.