Similar Constructive Method Of Solution For The Model Of Nonlinear Spherical Seepage In Composite Reservoir

This paper according the model nonlinear spherical fluids flow problems in compositereservoir, studying the similar constructive method of solution. Mainly following fourrespects to research: chapter one, summarized the research status and development trend athome and abroad of the nonlinear spherical fluids flow in composite reservoir. Chapter two,solving one kind of the boundary value problems of composite normalized Bessel equations,and obtained the solutions structure similar and the similar kernel functions; After analyzed indetail and induced, based on the similar structure and the similar kernel functions of thesolutions, a new method-the similar constructive method-is put forward for solving this classof boundary value problems. This method is no longer required to profound and complicatedmathematical derivation. The similar kernel function is constructive only need two linearlyindependent solutions of the equation and by the coefficients of outer boundary condition; andthe similar structure of solution of the boundary value problems for differential equations, isrelated by the coefficients of inner boundary condition. Chapter three, is the key-point of thispaper, respectively, the model of nonlinear spherical seepage flow in composite reservoir isestablished, which take considering different kinds of cases in the inner boundary conditions(not to consider the wellbore storage or skin effect, consider the wellbore storage only,through the effective well radius to consider the skin effect only, and both consider thewellbore storage again through the effective well radius to consider the skin effect); and underthree outer boundary conditions(closed, constant pressure and infinite). The model istransformed into the boundary value problem of composite spread modified Bessel equationin Laplace space, by linearization and employing Laplace transformation. The model istransformed into the boundary value problem of spread modified Bessel equation in theLaplace space, by linearization and employing Laplace transformation. Then according to thesimilar constructive method of the chapter two to constructive the Laplace space analyticsolutions of the inner and outer zones reservoir pressures and bottom pressers. Chapter four,comparative analysis the similar structure of solutions and the similar kernel functions of fourmodels.The present study putting forward a new method of the nonlinear spherical seepage flowin composite is positive for understanding and studying the inherent laws of fluid flows.