Theoretical Analysis And Numerical Computation Of Fluid-solid Coupling Nonlinear Seepage In Shale Gas Horizontal

The rock mechanical properties of shale determine the complexity of the fracture network structure formed by reservoir volume fracturing and the strength of fluid-solid coupling during shale gas production.Considering the influence of the de formation of pore-fracture medium on shale gas seepage,the seepage law of shale gas can be revealed more deeply,so as to establish a more accurate production model.For the fluid-solid coupling nonlinear seepage problem of the fractured shale horizontal well,this paper systematically studies the experimental analysis of the mechanical properties of shale,the shale gas seepage law in multi-scale porous medium and the numerical calculation of production for horizontal well,etc.The main contents and results of this research are as follows:(1)The mechanical properties of shale such as tensile strength,elastic modulus and f'racture toughness are determined by Brazilian disc test.First,the complex function method for elastic plane problem is used to obtain the series solutions of the stress and displacement in the disc under arbitrarily symmetric distributed load.For the pre-cracked disc,the expression of stress intensity factor at crack tip is given.Then,the influence of the contact pressure and friction on the test results is studied.In addition,the effect of the initial nonlinear elastic of shale is considered in the determination of contact pressure.Based on the generalized variational principle and load increment method,the distribution of contact pressure is calculated and consistent with the result in experiment.(2)For the fractured shale horizontal well,the fluid-solid coupling mechanism is analyzed during shale gas production.Considering the effect of proppant imbedding an equivalent intrinsic permeability model of the fracture network is established,which takes into account the initial geostress,fracture orientation and the number of proppant layers,etc.Considering the effect of elastic deformation of porous media,a modified model of intrinsic permeability for matrix is given.Considering the Fick and Knudsen diffusion effects for free gas,and the surface diffusion effect for adsorbed gas,an equivalent permeability model for shale gas flowing in multi-scale porous is established.Finally,the influence of the fluid-solid coupling and the nonlinear effects on shale gas seepage is analyzed numerically.(3)For the fractured shale horizontal well.non-uniform distribution models of equivalent porosity and intrinsic permeability are proposed basing on the reservoir characteristics and the energy attenuation trend during fracturing.Then,a three-dimensional mathematical model of non-uniform,nonlinear and unsteady seepage flow of shale gas is established,and a corresponding the semi-analytical numerical simulation method is developed.Compared with the production data in the literature,the applicability of the mathematical model in this study and the correctness of the semi-analytical numerical simulation method are verified.(4)The productions of the actual shale gas production wells in southwest China are simulated and predicted.In addition,the influence of initial geostress,the number of proppant layers,elastic modulus,Biot coefficient and other parameters in fluid-solid coupling,as well as the effects of Knudsen diffusion,surface diffusion and desorption on the production of fractured shale horizontal well are numerically analyzed.