The Similar Structure Method for Solving the Model of Fractal Dual-Porosity Reservoir

Abstract

This paper proposes a similar structure method (SSM) to solve the boundary value problem of the extended modified Bessel equation. The method could efficiently solve a second-order linear homogeneous differential equation’s boundary value problem and obtain its solutions’ similar structure. A mathematics model is set up on the dual-porosity media, in which the influence of fractal dimension, spherical flow, wellbore storage, and skin factor is taken into cosideration. Researches in the model found that it was a special type of the extended modified Bessel equation in Laplace space. Then, the formation pressure and wellbore pressure under three types of outer boundaries (infinite, constant pressure, and closed) are obtained via SSM in Laplace space. Combining SSM with the Stehfest algorithm, we propose the similar structure method algorithm (SSMA) which can be used to calculate wellbore pressure and pressure derivative of reservoir seepage models clearly. Type curves of fractal dual-porosity spherical flow are plotted by SSMA. The presented algorithm promotes the development of well test analysis software.

A Mathematical Model for the Analysis of the Pressure Transient Response of Fluid Flow in Fractal Reservoir

“…SCMS of the boundary value problems of Airy equation, Weber equation, Euler hypergeometric equation, and composite first Weber system were studied [24][25][26][27][28]. SCMS in fractal dual-porosity reservoir and dual-permeability reservoir were presented [29][30][31].…”

New Method of Solving the Seepage Model for the Multilayer Composite Reservoir with the Double Porosity

“…In 2004, Shunchu Li and Minhui Jia [8] put forward an important method which solved a class of differential equation, namely similar construction method, just as any a real number can be expressed by continued fraction. In the next years, many studies [9][10][11][12][13][14][15][16][17][18][19] have been carried out for some boundary value problems of the special differential equation. On the basis of above research, considering the influence of well bore storage and skin effect, this paper firstly built the seepage model for the multilayer composite reservoir with the double porosity.…”

Similar Constructive Method of Solution for the Nonlinear Percolation Model in Composite Reservoir

“…The new method that we named as The Similar Constructive Method is put forward for solving such BVP. Finally, solutions for the dimensionless reservoir flow pressures in the interior region, outer region, and the bottom hole flow pressure in Laplace space were obtained using the Similar Constructive Method [16][17][18][19][20][21]. The Similar Constructive Method provides a convenient and efficient solution to the nonlinear spherical seepage flow model the nonlinear percolation problem of composite reservoir.…”