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Upscaling pore‐scale reactive transport equations using a multiscale continuum formulation
Author(s) -
Lichtner P. C.,
Kang Q.
Publication year - 2007
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2006wr005664
Subject(s) - representative elementary volume , homogenization (climate) , continuum hypothesis , statistical physics , lattice boltzmann methods , multiscale modeling , porous medium , scale (ratio) , continuum mechanics , mechanics , physics , materials science , porosity , classical mechanics , thermodynamics , finite element method , chemistry , biodiversity , ecology , computational chemistry , quantum mechanics , biology , composite material
Reactive transport equations are solved at the pore scale using the lattice Boltzmann (LB) method, and the results are upscaled using volume averaging over a representative elemental volume and are fit to a multiscale continuum model. The multiscale continuum model accounts for local concentration gradients within diffusion‐dominated matrix domains that are coupled to the primary continuum fluid. In general it is found that a multiscale continuum formulation is required to fit the upscaled pore‐scale results. However, it is also demonstrated that in some cases, multiscale processes may be represented by a single‐continuum model employing effective parameters that are not directly measurable. Provided that sufficient resolution of the pore‐scale geometry can be obtained, the pore‐scale model can be used to determine the most appropriate form of continuum formulation (single, dual, or multiple continua) that best fits the upscaled pore‐scale simulation and, simultaneously, to provide parameters needed for constitutive relations appearing in the multiscale continuum formulation. It is suggested that a multiscale continuum approach may help explain the observed discrepancy between laboratory and field‐derived reaction rates by explicitly representing distinct transport domains through separate interacting continua which could be responsible for the formation of preferential pathways. An example is presented on the basis of a multiscale, synthetic, structured porous medium describing transport of a tracer and linear reaction kinetics.