A Study of a Flow Model in Dual Permeability Reservoir Based on Similar Structure Theory

The aim of the study is to further understand the rule of conversion of bottom hole pressure of a vertical well in a dual-permeability reservoir, which is about the dual permeability under different outer boundary (infinite, close, and constant value) conditions. However, there are few articles dealing with the model of a vertical well in a dual permeability reservoir under these three different outer boundary conditions. Hence, the paper proposes a model of a vertical well in a dual permeability reservoir under three outer boundary conditions. The model is solved with a Laplace space equation. We find the solution to the model that has a similar structure under three different outer boundary conditions by combining it with the similar structure theory. Therefore, we put forward a similar constructing method (SCM) that solves our model. The concrete steps of the SCM are given in this paper. At the same time, we draw the curves of the bottom hole pressure and pressure derivative using the modified Stehfest inversion formula and MATLAB software. In addition, we investigate the evolution of the pressure by changing the parameters (mobility ratio K, storability ratio $\omega$ , and crossflow coefficient $\lambda$ ). The solution to such a reservoir model obtained in this paper could be used as a basis for analyzing other typical reservoirs with vertical wells.

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