A seepage model of producing at a constant rate, based on the three outer boundary (infinite, closed, constant value) conditions and regardless of the well-bore storage and skin effects, is established for the problem of the plane radial flow of dual permeability reservoirs. Firstly, we get dimensionless model by introducing the dimensionless variables. Second, we obtain a boundary value problem of ordinary differential equation in the Laplace space by using the Laplace transformation. Finally, we prove that the solution to the boundary value problem has similar structural formula. Therefore a new method for solving such seepage model is obtainedSimilar Constructive Method (shortened as SCM). And then, according to the modified numerical inversion formula of Stehfest, we draw the curves of bottom-hole under the three kinds of outer boundary conditions by using MATLAB.

Based on the similar structure theory, we conduct rigorous mathematical derivation and proof for the boundary value problem of a class of differential equation . We put forward a new algorithm------Similar Structure Algorithm to solve such boundary value problems. The similar structure algorithm only includes arithmetic and logical operation, hence it can be oriented towards computer. According to the similar structure algorithm, an example is given to conduct a simulation experiment by the application of computer software at the end of the paper. And we also observe and analysis the variational laws of the laboratory result by changing the coefficient of the boundary condition.

The similar structure of solution for the boundary value problem of second order linear homogeneous differential equation has been studied. Based on the analysis of the relationship between similar structure of solution, its kernel function, the equation and boundary conditions, similar constructive method (shortened as SCM) of solution is obtained. According to the SCM, the similar structure of solution and its kernel function are constructed for the mathematical model of homogeneous reservoir which considers the influence of bottom-hole storage and skin effect under the infinite outer boundary condition. The SCM is a new and innovative way to solve boundary value problem of differential equation and seepage flow theory, which is especially used in Petroleum Engineering.