This paper presents a spherical percolation model for dual-porosity media reservoir, where the quadratic-gradient term, wellbore storage and three types of outer boundary conditions: constant pressure boundary, closed boundary and infinity boundary were considered. Then a new method: Similar Constructive Method was put forward for solving this type of percolation model. And solutions of the dimensionless reservoir pressure and the dimensionless bottomhole pressure in Laplace space were obtained. It was proved that these solutions had a similar structure. The Similar Constructive Method is an elementary and algebraic method, simple and practical. And the similar structure of solutions can simplify the well test analysis software programming and analyze the reservoir parameter’s affection on pressure conveniently. The present research has a great academic significance and application value in oil-gas field development.

The paper is devoted to studying the solution for boundary value problem of composite Hermit equations. Based on the obtained solution with similar structural formula, a new method which is called as Similar Constructive Method (shortened as SCM) was put forward for solving this type of boundary value problem. The SCM is a simply and practical method, which provides convenience for solving boundary value problems of composite differential equations.

Aiming at spherical dual-porosity reservoir, an unsteady seepage model that based on the three different kinds of outer boundary (infinite, constant value and closed) conditions was established in this paper. Using the Laplace transform method, similar structure of dimensionless bottom pressure solution in the Laplace space and similar nuclear function were obtained. This is not only providing us a new road to further explore the inherent law of the solutions and compile corresponding analysis software, but also has a broad application prospects.

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.

The well testing model of nonlinear spherical percolation problems for composite reservoir is established under three different outer boundary conditions: closed boundary,constast pressure boundary,infinity boundary. the mathematical model are linearized by using variable substitution method, and then its solutions are derived by Laplace transform. According to the theory of similar structure of solutions to the differential equations, we obtain the similar structure of the solutions .The theory of similar structure is beneficial to understand the inherent laws of solutions and analyze the influence of parameters to solutions.