Modeling and a Robin-type decoupled finite element method for dual-porosity–Navier–Stokes system with application to flows around multistage fractured horizontal wellbore
Modeling and a Robin-type decoupled finite element method for dual-porosity–Navier–Stokes system with application to flows around multistage fractured horizontal wellbore
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DOI：
10.1016/j.cma.2021.114248
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发表时间：
2022-01
影响因子：
7.2
通讯作者：
Jiangyong Hou;D. Hu;Xiaoming He;Changxin Qiu
中科院分区：
文献类型：
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作者：
Jiangyong Hou;D. Hu;Xiaoming He;Changxin Qiu
本文提出了一个包含Beavers-Joseph界面条件在内的四种界面条件的含时双孔隙度Navier-Stokes模型来描述复杂多孔介质与管道网络的耦合系统。该系统具有许多应用，例如具有合适边界/界面条件和复杂几何形状的多级压裂水平井筒的流动模拟问题。针对该耦合系统，提出了基于Robin型传递条件的解耦有限元法。为了避免传统区域分解的迭代，直接从前一个时间步的数值解中预测当前时间步Robin型传输条件所需的界面信息。严格分析了这种Robin型解耦有限元方法的稳定性和收敛性。利用一系列分析技术对这一复杂的多物理场问题的各个组成部分进行了逐项分析，特别是对Beavers-Joseph界面条件、双孔隙模型的相互作用项和Navier-Stokes方程的非线性平流项进行了分析。此外，在格式和分析中考虑了一对Robin参数，并数值研究了它们对低渗透率和低存储率情况下鲁棒性的影响。通过数值实验验证了该算法的收敛性，并说明了该算法应用于多级压裂水平井眼流动问题的特点。
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.