TY - JOUR
T1 - Coupled transport of multi-component solutes in porous media
AU - Shapiro, Michael
AU - Adler, Pierre M.
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 1997
Y1 - 1997
N2 - Coupled convective-diffusive transport of multicomponent solutes in spatially-periodic models of porous media is considered. Species coupling at the micro- or interstitial scale results from a first-order irreversible surface reaction on the bed elements, composing the porous medium, and from the off-diagonal terms of the microscale matrix transport coefficients. The coarse-scale long-time solute matrix properties are calculated, namely, mean effective reactivity, velocity and dispersivity. These coefficients are analyzed in several important particular cases, pertaining to reactive and nonreactive constituents. The solution scheme is illustrated by an example of two reactive solute components with diffusional coupling, flowing in a bundle of tubes model porous medium. The effective matrix axial transport coefficients are analyzed for various values of the dimensionless Damkohler number, Da, associated with the surface-reaction constant. Analytical expressions for the effective axial transport properties are obtained in cases of extreme (small and large) values of the dimensionless Damkohler numbers. The microscale molecular diffusive coupling provides for each solute constituent two diffusive pathways to the reactive tube wall: one - via the direct diffusivity component, another - via the coupling diffusivity. The macroscopic manifestation of this microscale coupling is to give rise to coupling off-diagonal terms in the effective matrix transport coefficients: positive off-diagonal terms in the reactivity matrix and negative off-diagonal terms in velocity and dispersivity matrices. From a physical viewpoint microscale coupling brings about a more uniform solute distribution within the tube cross section, which reduces the effective axial transport.
AB - Coupled convective-diffusive transport of multicomponent solutes in spatially-periodic models of porous media is considered. Species coupling at the micro- or interstitial scale results from a first-order irreversible surface reaction on the bed elements, composing the porous medium, and from the off-diagonal terms of the microscale matrix transport coefficients. The coarse-scale long-time solute matrix properties are calculated, namely, mean effective reactivity, velocity and dispersivity. These coefficients are analyzed in several important particular cases, pertaining to reactive and nonreactive constituents. The solution scheme is illustrated by an example of two reactive solute components with diffusional coupling, flowing in a bundle of tubes model porous medium. The effective matrix axial transport coefficients are analyzed for various values of the dimensionless Damkohler number, Da, associated with the surface-reaction constant. Analytical expressions for the effective axial transport properties are obtained in cases of extreme (small and large) values of the dimensionless Damkohler numbers. The microscale molecular diffusive coupling provides for each solute constituent two diffusive pathways to the reactive tube wall: one - via the direct diffusivity component, another - via the coupling diffusivity. The macroscopic manifestation of this microscale coupling is to give rise to coupling off-diagonal terms in the effective matrix transport coefficients: positive off-diagonal terms in the reactivity matrix and negative off-diagonal terms in velocity and dispersivity matrices. From a physical viewpoint microscale coupling brings about a more uniform solute distribution within the tube cross section, which reduces the effective axial transport.
KW - Convective-diffusion
KW - Coupling
KW - Macroscale matrix properties
KW - Reactive species
UR - http://www.scopus.com/inward/record.url?scp=0031138416&partnerID=8YFLogxK
U2 - 10.1023/A:1004211528251
DO - 10.1023/A:1004211528251
M3 - 文章
AN - SCOPUS:0031138416
VL - 31
SP - 357
EP - 378
JO - Journal of Engineering Mathematics
JF - Journal of Engineering Mathematics
SN - 0022-0833
IS - 2
ER -