Similar Constructing Method for Solving the Model of the Plane Radial Flow of Dual Permeability Reservoir

Abstract

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.

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].…”