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

Digital images of porous media often include features approaching the imageresolution length scale. The behavior of numerical methods at low resolution istherefore important even for well-resolved systems. Westudy the behavior of theShan-Chen (SC) and Rothman-Keller (RK) multicomponent lattice-Boltzmannmodels in situations where the fluid-fluid interfacial radius of curvature and/orthe feature size of the medium approaches the discrete unit size of the com-putational grid. Various simple, small-scale test geometries are considered, anda drainage test is also performed in a Bentheimer sandstone sample. We findthat both RK and SC models show very high ultimate limits: in ideal condi-tionsthemodelscansimulatestaticfluidconfigurationwithacceptableaccuracyin tubes as small as three lattice units across for RK model (six lattice unitsfor SC model) and with an interfacial radius of curvature of two lattice unitsfor RK and SC models. However, the stability of the models is affected whenoperating in these extreme discrete limits: in certain circumstances the modelsexhibit behaviors ranging from loss of accuracy to numerical instability. We dis-cuss the circumstances where these behaviors occur and the ramifications forlarger-scale fluid displacement simulations in porous media, along with strate-gies to mitigate the most severe effects. Overall we find that the RK model, withmodern enhancements, exhibits fewer instabilities and is more suitable for sys-tems of low fluid-fluid miscibility. The shortcomings of the SC model seem toarise predominantly from the high, strongly pressure-dependent miscibility ofthe two fluid components.Australian Research Council,Grant/Award Number: FT100100470;National Computational Infrastructure;Oak Ridge National Laboratory,Grant/Award Number:DE-AC05-00OR2272