Research On The Productivity Model Of Shale Gas Fractured Wells Based On Multiple Migration Mechanisms

As a kind of unconventional oil and gas resource,the shale gas store and transport mechanisms differ significantly from conventional gas.In shale gas reservoirs,besides some gas storing in a free state,part of the gas also adsorbs on the surface of the pores in the matrix and fractures.As the pressure drops during the development of shale gas reservoirs,the adsorbed gas will desorb,compensating the produced free gas and mitigating the decline of the reservoir pressure.In addition,with the nanoscale pore radius(commonly,1?1000nm)in the matrix,Darcy flow,slip flow,Knudsen diffusion and the surface diffusion on the adsorbed layer can coexist during the transport of the shale gas.These differences in gas store and transport mechanisms will necessarily make the production rules of shale gas tremendously distinct from conventional gas.Accordingly,shale gas well performance will also behave in a different way.Against the situation mentioned above,shale gas well performance is analyzed and the body is as follows:(1)Three typical gas adsorption models,namely,Langmuir model,BET model and D-R model,are researched respectively.According to applicability,the best model is determined for the later computation.(2)The gas flow pattern in the nanoscale pore of shale gas reservoirs is divided according to the value of Kn number,with the mass flow in each pattern researched.On this basis,considering slip flow,Knudsen diffusion and surface diffusion,and combing the General Darcy Rule,a shale gas apparent permeability model is derived and verified.Using the model,the impact of pore radius,pressure,temperature,Langmuir pressure and Langmuir volume on gas apparent permeability is analyzed,and the relation of the contribution of Darcy flow,slip flow,Knudsen diffusion and surface diffusion to gas apparent permeability with the pore radius and pressure is also researched.(3)Applying the derived gas apparent permeability model entrenches fractured vertical and horizontal well performance model respectively,in which fractures' conductivity is finite.Through conformal transformation,the analytical solution of the well performance is obtained and verified.After that,the effect of Darcy permeability,slip factor,Knudsen diffusion coefficient,Langmuir pressure,Langmuir volume and fracture length on gas well performance is analyzed,particularly,with the number of fractures for horizontal well.(4)With transient gas flow from fracture to matrix,transient seepage differential equations for matrix and fracture system are established respectively.Through dimensionless and Laplace transformation,combining boundary conditions,the parameter delegation f(s)of the percolation differential equation in fracture system is worked out.After that,assuming fractures have infinite conductivity,considering wellbore storage and skin effect,applying Stehfest numerical inversion,furthermore,for horizontal well,combining numerical discretion,the dynamic pressure and performance curves of fractured gas well are gained and verified.(5)Shale gas flow stages are divided according to the dynamic pressure curves.Moreover,the influence of gas channeling coefficient,fracture storage ratio,adsorption constant,fracture length and the effect of non-Darcy flow(slip flow,Knudsen diffusion and surface diffusion),additionally fracture number and horizontal length for horizontal well,on the dynamic pressure curves is analyzed.Combing this analysis,the influence of these parameters on gas well performance is researched.