Journal of Fluid Mechanics


Pore-scale mass and reactant transport in multiphase porous media flows

A. Parmigiania1 c1, C. Hubera2, O. Bachmanna3 and B. Choparda1

a1 Computer Science Department, University of Geneva, CH-1227 Carouge, Switzerland

a2 School of Earth and Atmospheric Sciences, Georgia Institute of Technology, GA 30332, USA

a3 Department of Earth and Space Sciences, University of Washington, WA 98195, USA


Reactive processes associated with multiphase flows play a significant role in mass transport in unsaturated porous media. For example, the effect of reactions on the solid matrix can affect the formation and stability of fingering instabilities associated with the invasion of a buoyant non-wetting fluid. In this study, we focus on the formation and stability of capillary channels of a buoyant non-wetting fluid (developed because of capillary instabilities) and their impact on the transport and distribution of a reactant in the porous medium. We use a combination of pore-scale numerical calculations based on a multiphase reactive lattice Boltzmann model (LBM) and scaling laws to quantify (i) the effect of dissolution on the preservation of capillary instabilities, (ii) the penetration depth of reaction beyond the dissolution/melting front, and (iii) the temporal and spatial distribution of dissolution/melting under different conditions (concentration of reactant in the non-wetting fluid, injection rate). Our results show that, even for tortuous non-wetting fluid channels, simple scaling laws assuming an axisymmetrical annular flow can explain (i) the exponential decay of reactant along capillary channels, (ii) the dependence of the penetration depth of reactant on a local Péclet number (using the non-wetting fluid velocity in the channel) and more qualitatively (iii) the importance of the melting/reaction efficiency on the stability of non-wetting fluid channels. Our numerical method allows us to study the feedbacks between the immiscible multiphase fluid flow and a dynamically evolving porous matrix (dissolution or melting) which is an essential component of reactive transport in porous media.

(Received November 22 2010)

(Reviewed April 08 2011)

(Accepted June 11 2011)

(Online publication September 30 2011)

Key Words:

  • multiphase flow;
  • porous media;
  • solidification/melting


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