Discretization limits of lattice‐Boltzmann methods for studying immiscible two‐phase flow in porous media,International Journal for Numerical Methods in Fluids

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Discretization limits of lattice‐Boltzmann methods for studying immiscible two‐phase flow in porous media
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2020-02-27 , DOI: 10.1002/fld.4822
Zhe Li _{1,

2} , James E. McClure ₂ , Jill Middleton ₁ , Trond Varslot ₃ , Adrian P. Sheppard ₁

Affiliation

Digital images of porous media often include features approaching the image resolution length scale. The behavior of numerical methods at low resolution is therefore important even for well‐resolved systems. We study the behavior of the Shan‐Chen (SC) and Rothman‐Keller (RK) multicomponent lattice‐Boltzmann models in situations where the fluid‐fluid interfacial radius of curvature and/or the feature size of the medium approaches the discrete unit size of the computational grid. Various simple, small‐scale test geometries are considered, and a drainage test is also performed in a Bentheimer sandstone sample. We find that both RK and SC models show very high ultimate limits: in ideal conditions the models can simulate static fluid configuration with acceptable accuracy in tubes as small as three lattice units across for RK model (six lattice units for SC model) and with an interfacial radius of curvature of two lattice units for RK and SC models. However, the stability of the models is affected when operating in these extreme discrete limits: in certain circumstances the models exhibit behaviors ranging from loss of accuracy to numerical instability. We discuss the circumstances where these behaviors occur and the ramifications for larger‐scale fluid displacement simulations in porous media, along with strategies to mitigate the most severe effects. Overall we find that the RK model, with modern enhancements, exhibits fewer instabilities and is more suitable for systems of low fluid‐fluid miscibility. The shortcomings of the SC model seem to arise predominantly from the high, strongly pressure‐dependent miscibility of the two fluid components.

中文翻译：

研究多孔介质中不相溶两相流的格-玻尔兹曼方法的离散极限

多孔介质的数字图像通常包含接近图像分辨率长度尺度的特征。因此，即使对于良好解析的系统，低分辨率数值方法的行为也很重要。我们研究了Shan-Chen（SC）和Rothman-Keller（RK）多分量晶格-Boltzmann模型在流体-流体界面曲率半径和/或介质特征尺寸接近离散单元尺寸的情况下的行为。计算网格。考虑了各种简单的小规模测试几何形状，并且还在Bentheimer砂岩样品中进行了排水测试。我们发现RK和SC模型都显示出很高的极限：在理想条件下，对于RK模型，模型可以模拟到最小跨度为三个晶格单元的管（对于SC模型为六个晶格单元），并且对于RK和SC模型为两个晶格单元的界面曲率半径，可以模拟静态流体配置。但是，在这些极端离散的限制下运行时，模型的稳定性会受到影响：在某些情况下，模型表现出从准确性到数值不稳定性的行为。我们讨论了这些行为发生的情况，以及在多孔介质中进行大规模流体驱替模拟的后果，以及减轻最严重影响的策略。总的来说，我们发现RK模型经过了现代改进，具有较少的不稳定性，并且更适合于低流体-流体混溶性的系统。

更新日期：2020-02-27

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