A unified approach to simulation and upscaling of single‐phase flow through vuggy carbonates
A unified approach to simulation and upscaling of single‐phase flow through vuggy carbonates
复制标题
孔洞碳酸盐岩单相流模拟和升级的统一方法
DOI：
10.1002/fld.2630
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发表时间：
2012
影响因子：
1.8
通讯作者：
M. Pal
中科院分区：
文献类型：
--
作者：
M. Pal
通过溶洞多孔介质，主要是溶洞碳酸盐岩的流动的数值模拟，是一个具有挑战性的奋进。首先，由于溶洞的存在可以显著地改变介质的有效孔隙度和渗透率。其次，由于介质中多孔和自由流动区域的共存，以及在定义它们之间的确切边界时的不确定性。传统上，这种非均质系统是由耦合Darcy-Stokes方程来模拟的。然而，使用耦合Darcy-Stokes方程对通过孔洞多孔介质的流动进行数值建模提出了若干数值挑战，特别是关于多孔区域和自由流动区域之间的正确界面条件的规范。因此，一个替代的方法，一个更统一的方法来模拟流动通过多孔介质，斯托克斯-Brinkman模型，在这里提出。它是一个具有可变系数的单方程模型，可用于多孔和自由流动区域。这也使得对接口条件的要求变得多余。因此，使用Stokes-Brinkman方程有明显的好处，通过适当选择参数，可以将其简化为Stokes或Darcy方程。同时，Stokes-Brinkman方程提供了多孔和自由流动区域之间的平滑过渡，从而考虑了相关的不确定性。提出了一种Stokes-Brinkman模型的数值处理方法，作为将Stokes-Brinkman模型应用于多相流的一种途径。通过对数值压力收敛误差范数的分析，验证了数值尺度放大方法的有效性。在一系列实际数据集上对Stokes-Brinkman单方程模型进行了检验，并与传统的Darcy-Stokes耦合模型进行了比较。版权所有© 2011约翰威利父子有限公司.
Numerical modeling of flow through vuggy porous media, mainly vuggy carbonates, is a challenging endeavor. Firstly, because the presence of vugs can significantly alter the effective porosity and permeability of the medium. Secondly, because of the co‐existence of porous and free flow regions within the medium and the uncertainties in defining the exact boundary between them. Traditionally, such heterogeneous systems are modeled by the coupled Darcy–Stokes equations. However, numerical modeling of flow through vuggy porous media using coupled Darcy–Stokes equations poses several numerical challenges particularly with respect to specification of correct interface condition between the porous and free‐flow regions. Hence, an alternative method, a more unified approach for modeling flows through vuggy porous media, the Stokes–Brinkman model, is proposed here. It is a single equation model with variable coefficients, which can be used for both porous and free‐flow regions. This also makes the requirement for interface condition redundant. Thus, there is an obvious benefit of using the Stokes–Brinkman equation, which can be reduced to Stokes or Darcy equation by the appropriate choice of parameters. At the same time, the Stokes–Brinkman equation provides a smooth transition between porous and free‐flow region, thereby taking care of the associated uncertainties. A numerical treatment for upscaling Stokes–Brinkman model is presented as an approach to use Stokes–Brinkman model for multi‐phase flow. Numerical upscaling methodology is validated by analyzing the error norm for numerical pressure convergence. Stokes–Brinkman single equation model is tested on a series of realistic data sets, and the results are compared with traditional coupled Darcy–Stokes model. Copyright © 2011 John Wiley & Sons, Ltd.