Lattice Boltzmann Simulations of 2-phase Flow In Porous Media
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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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Complex fluid
Length scale
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Lattice Boltzmann methods
Characterization
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Lattice Boltzmann methods
Boltzmann relation
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Lattice Boltzmann methods
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Abstract We describe the ongoing development of lattice-Boltzmann (LB) computer simulation codes to study flow in porous media at the pore scale. LB simulations have evolved over the past decade and are now used as a tool to calculate both single- and multi-phase flow properties directly at the pore scale using X-ray Micro Tomography (XMT) pore space images. We will review the development of our codes to study flow in two-dimensional micro-models, viscous fingering, chemical reactions, hydrodynamic dispersion and non-Newtonian flow. In three dimensions, we have developed our codes to calculate the flow in XMT images of the pore space, for both single- and multi-phase flow, resulting in predictions of the permeability. Very recently, we have extended the multi-phase flow model to include surfactants for reduction of the interfacial tension and wettability alteration.
Lattice Boltzmann methods
Viscous fingering
Multiphase flow
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A lattice Boltzmann description of fluid flow in heterogeneous porous media is presented which is intended for modeling flow processes which occur in liquid composite molding applications. The lattice Boltzmann method is equivalent to solving a hybrid method of the Stokes and Brinkman equations, with the Brinkman equation being implemented to model flow through porous structures, while the Stokes equation is applied to the open regions outside the porous structures. The Brinkman equation is recovered through a modification of the particle equilibrium distribution function, which reduces the magnitude of momentum at specified lattice sites, while leaving the direction of momentum unchanged. As a test of the new lattice Boltzmann model, steady transverse flow (saturated) through a square array of porous cylinders of elliptical cross section is investigated. Cell permeabilities obtained from the lattice Boltzmann simulations are in excellent agreement with a lubrication model, validating the lattice Boltzmann formulation of the Stokes and Brinkman equations.
Lattice Boltzmann methods
Boltzmann relation
Microscale chemistry
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