Similar Constructive Method For Solving The Model Of The Seepage In Multilayered Reservoir

From the perspective of mathematical theory research, we solve the boundary value problem of variant Bessel equation and the boundary value problem of generalized Bessel equations first, with carefully studying the solving progress, we can find that the solution of the boundary value problems can be simplified into the continued fraction form (the similar structure), and then we can summarize a new method to solve the boundary value problem of variant Bessel equation and the boundary value problem of generalized Bessel equations——The Similar Constructive Method, and gives the detailed steps of the method.In this paper, the fractal theory is introduced into the seepage flow mechanics, and through the systematically studied on the seepage situation of the (fractal) multilayer reservoir, the seepage flow model that under different inner and outer boundary conditions can be established respectively. Firstly, with using the Laplace transform method, the seepage mathematical model can be converted into the boundary value problem of variant Bessel equation and the boundary value problem of generalized Bessel equations. Secondly, construct the solution of all kinds of model with using the similar constructive method respectively. Finally, in the same basic seepage equation and inner boundary conditions, after careful analysis we find that the expressions of the solution under different outer boundary conditions are consistent, and the different similar kernel function can be obtained in the special boundary conditions. The similar structure of solution is helpful to prepare the well test analysis software, draw the corresponding curves, and be mastered by the well test workers to use.