Discretization limits of lattice‐Boltzmann methods for studying immiscible two‐phase flow in porous media

Li, Zhe; McClure, James E.; Middleton, Jill; Varslot, Trond; Sheppard, Adrian P.

doi:10.1002/fld.4822

Title: Discretization limits of lattice‐Boltzmann methods for studying immiscible two‐phase flow in porous media

Journal Article · 27 February 2020 · International Journal for Numerical Methods in Fluids

DOI: https://doi.org/10.1002/fld.4822 · OSTI ID:1602090

^[1]; McClure, James E. ^[2]; Middleton, Jill ^[3]; Varslot, Trond ^[4]; Sheppard, Adrian P. ^[3]

Department of Applied Mathematics The Australian National University Canberra Australian Capital Territory, Advanced Research Computing Virginia Tech Blacksburg Virginia
Advanced Research Computing Virginia Tech Blacksburg Virginia
Department of Applied Mathematics The Australian National University Canberra Australian Capital Territory
Thermo Fisher Scientific FEI Company Trondheim Norway

Summary 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.

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Sponsoring Organization:: USDOE

Grant/Contract Number:: NONE; AC05-00OR22725

OSTI ID:: 1602090

Journal Information:: International Journal for Numerical Methods in Fluids, Journal Name: International Journal for Numerical Methods in Fluids Journal Issue: 9 Vol. 92; ISSN 0271-2091

Publisher:: Wiley Blackwell (John Wiley & Sons)Copyright Statement

Country of Publication:: United Kingdom

Language:: English

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