Theoretical Investigation And Numerical Computation Of Nonlinear Unsteady Percolation In Shale Gas Reserviors

Different from conventional natural gas reservoirs,for the extraordinarily low porosity and the permeability in shale,the classical Darcy linear seepage mechanism is no longer applicable.In addition,the pore-fracture system in the artificial modification zones is very complex which caused by hydraulic fracturing,so that the seepage problems of shale gas need to consider the nonlinear effects(including desorption,slip and diffusion),complicated media(hydraulic fractures-microfractures-matrix),anisotropic characteristics and stress-sensitive effects,etc.Therefore,the establishment of mathematical model for nonlinear seepage problem and the development of numerical methods for the analysis and prediction of shale gas wells have important scientific research value.Under the framework of continuum mechanics,this paper systematically studies the nonlinear seepage of shale gas.The mathematical description of the macro distribution characteristics of hydraulic fracture network is given,the inhomogeneous equivalent continuous distribution models of porosity and intrinsic permeability in the whole flow zones are proposed,also,the mathematical model with consideration of inhomogeneity,unsteady and nonlinear seepage problem is established,and the semi-analytical numerical method to predict the production is developed.The specific research contents are as follows:(1)For the hydraulic fractured shale vertical well,this study generalized the partition homogeneous models of porosity and intrinsic permeability into the equivalent inhomogeneous distribution models which can be used in the whole gas production zones,namely,proposed the Gaussian distribution mathematical models of porosity and intrinsic permeability.By applying the Beskok-Karniadakis seepage model which considers the slip and diffusion effects and desorption effect,the mathematical model for this problem is established,that is,the initial-boundary value problem of the nonlinear partial differential equation.In the spatiotemporal discrete region,the generalized pseudo-pressure function and mass source function are introduced,and by use of approximate Boltzmann transformation,the iteration scheme formula for numerical discretizing pressure field is obtained.The influence of nonlinear effects,such as desorption,slip and diffusion on cumulative gas production are mainlyanalyzed,and the pressure dependent effects of viscosity and compressibility factor on shale gas production rate are discussed.(2)For the hydraulic fractured shale horizontal well,on the basis of macrofracture-microfracture-matrix homogeneous partition models of porosity and intrinsic perpeability permeability,the macroscopic two-dimensional inhomogeneous continuous distribution Gaussian models of equivalent porosity and intrinsic permeability are proposed which can be applied to the whole flow zones.The two-dimensional mathematical model of inhomogeneous,nonlinear and unsteady seepage of shale reservoir fracturing is established,and the corresponding semi-analytical numerical method is developed.By means of two-dimensional approximate Boltzmann transformation in the spatiotemporal discrete region,the initial-boundary value problem of the nonlinear partial differential equation is converted into the equation in integration form,and then,the iterative format of the pressure field is given by applying the numerical integration.The influences of permeability parameters,nonlinear effects and the distribution of fracture network of the shale horizontal well on the gas production are analyzed and discussed.(3)Due to the bedding structure of shale,the anisotropic seepage effect and stress sensitivity effect are considered.For the hydraulic fractured shale horizontal well,the inhomogeneous continuous medium models of the macroscopic three-dimensional Gaussian distribution for the equivalent porosity and the isotropic equivalent permeability are proposed,then the anisotropy,inhomogeneity,nonlinearity and unsteady three-dimensional mathematical model for the seepage in shale fractured horizontal well seepage problem is established.The approximate Boltzmann transformation in the spatiotemporal discrete region is extended to three dimensional transverse isotropic situation,and further the semi-analytical numerical simulation method is developed.The effects of shale anisotropy,stress sensitivity and different fracture parameters on gas production rate are investigated.(4)The calculation and prediction of the actual shale gas production well in southwest China are simulated,and the numerical simulation results are compared with the actual recorded data which illustrates the availability of the present theoretical mathematical model and computation method.In addition,the influences of the length parameters of adjacent fractures in the shale gas horizontal well are analyzed.