Modeling and a Robin-Type Decoupled Finite Element Method for Dual-Porosity-Navier-Stokes System with Application to Flows Around Multistage Fractured Horizontal Wellbore


In this article, we present a time-dependent dual-porosity-Navier-Stokes model with four interface conditions, including Beavers-Joseph interface condition, to describe a coupling system of complex porous media and conduit networks. This system has many applications, such as the flow simulation problems for a multistage fractured horizontal wellbore with suitable boundary/interface conditions and complex geometries. For this coupling system, a decoupled finite element method is proposed based on Robin type transmission conditions. In order to avoid the iteration for the traditional domain decomposition, the interface information, which is needed for the Robin type transmission conditions at the current time step, is predicted directly from the numerical solution of the previous time steps. The stability and convergence of this Robin-type decoupled finite element method are rigorously analyzed. A series of analysis techniques are utilized to analyze various components of this complicated multi-physics problem term by term, especially for the Beavers-Joseph interface condition, the interaction terms of dual-porosity model, and the nonlinear advection of Navier-Stokes equation. Moreover, a pair of Robin parameters are considered in the scheme and analysis, and their effects on the robustness for the case with low permeability and low storativity are numerically investigated. Numerical experiments are provided to validate the convergence of the proposed algorithm and illustrate the features of the application to flow problems around multistage fractured horizontal wellbore.


Mathematics and Statistics


National Science Foundation, Grant DMS-1722647

Keywords and Phrases

Boundary/Interface Conditions; Decoupled Finite Element Method; Dual-Porosity-Navier-Stokes Model; Multistage Fractured Horizontal Wellbore

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Article - Journal

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Publication Date

01 Jan 2022