Abstract
On the basis of similar structure of solutions of ordinary differential equation (ODE) boundary value problem, the similar construction method was put forward by solving problems of fluid flow in porous media through the homogeneous reservoir. It is indicate that the pressure distribution of dimensionless reservoir and bottom hole in Laplace space, which take on the radial flow, also shows similar structure, and the internal relationship between the above solutions were illustrated in detail.
Highlights
Due to the permeability of porous media, reservoir engineers could simulate fluid flow by using media such as ground rock, filters and catalyst beds as well, it is useful to those researches who are interested in the behavior of porous media in different engineering applications
Over the past six years, for some second-order homogeneous ordinary differential equation (ODE) [1-14], and some second-order homogeneous linear partial differential equations (PDE) in Laplace space [15-21] as well as some mathematical models of fluids flow in porous media [22-34], the right smart evolution had been obtained on the study of the similar structure of their solutions
The previous studies are separate, since the similar structure of solutions merely deduced from one certain model of the differential equation boundary value problem, and that was apparently gone against the analysis of the internal relationship between solutions of different models
Summary
Due to the permeability of porous media, reservoir engineers could simulate fluid flow by using media such as ground rock, filters and catalyst beds as well, it is useful to those researches who are interested in the behavior of porous media in different engineering applications. Over the past six years, for some second-order homogeneous ODE [1-14], and some second-order homogeneous linear partial differential equations (PDE) in Laplace space [15-21] as well as some mathematical models of fluids flow in porous media [22-34], the right smart evolution had been obtained on the study of the similar structure of their solutions. The previous studies are separate, since the similar structure of solutions merely deduced from one certain model of the differential equation boundary value problem, and that was apparently gone against the analysis of. In section two, we provide the theoretical background materials of the similar structure of solutions for solving the modified Bessel equation boundary value problem. 2. The Similar Structure of Solutions of the Modified Bessel Equation Boundary Value Problem. Quite similar to solve the ODE boundary value problem, by Equations (9) and (11) have the following similar structure form of solution y
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