Miscible Displacements of Reactive and Anisotropic Dispersive Flows in Porous Media

Abstract

The viscous fingering instability of miscible reactive-dispersive flows in a homogeneous porous media is investigated through nonlinear numerical simulations. In particular, the role of velocity-dependent transverse and longitudinal dispersions as well as the type and rate of auto-catalytic chemical reactions is analyzed. It is found that for a third-order auto-catalytic reaction, the higher the reaction rate, the more complex the finger structures. Furthermore, major differences between the flow development of third-order and second-order autocatalytic reactions are reported. In addition, the anisotropy and velocity dependence of the dispersion tensor are found to have a more profound effect on the fingering instability in the case of reactive flows than in the non-reactive ones. The qualitative characterization of the finger structures is explained by examining the flow velocity field and further quantified through an analysis of the average concentration and relative contact area.

Chemo-Hydrodynamic Patterns and Instabilities

“…Note that several works have analyzed VF of miscible autocatalytic fronts able to form a self-organized interface between the reactants and products of an autocatalytic front (De Wit & Homsy (1999b,a), Swernath & Pushpavanam (2007, Ghesmat & Azaiez (2009)). The reactions can modify the relative stability of the front and induce the formation of isolated droplets if the reaction is bistable.…”

Patterns due to an interplay between viscous and precipitation-driven fingering

“…Bistable autocatalytic reactions have, for instance, been shown numerically to allow for rupture of fingers into isolated droplets. [9][10][11] Nagatsu and collaborators have next performed extended experimental analysis of VF characteristics in the presence of A + B ! C type of reactions modifying in situ the viscosity of the solutions.…”

Viscous fingering of a miscible reactive A + B → C interface: a linear stability analysis

“…In the case of immiscible flows, this instability, known as the Saffman-Taylor instability, can also be modified by reactions that change the surface tension at the fluid interface (Jahoda & Hornof 2000;Fernandez & Homsy 2003). Several works have moreover addressed theoretically the coupling between VF and autocatalytic reactions (De Wit & Homsy 1999a, 1999bSwernath & Pushpavanam 2007Ghesmat & Azaiez 2009) without however corresponding experimental confirmations as autocatalytic reactions are more prone to change density rather than viscosity (De Wit 2001;De Wit et al 2003). In the context of chromatographic applications, adsorption-desorption phenomena have also been shown to influence VF patterns (Mishra, Martin & De Wit 2007).…”