Miscible density fingering of chemical fronts in porous media: Nonlinear simulations

Abstract

Nonlinear interactions between chemical reactions and Rayleigh-Taylor type density fingering are studied in porous media or thin Hele-Shaw cells by direct numerical simulations of Darcy's law coupled to the evolution equation for the concentration of a chemically reacting solute controlling the density of miscible solutions. In absence of flow, the reaction-diffusion system features stable planar fronts traveling with a given constant speed v and width w. When the reactant and product solutions have different densities, such fronts are buoyantly unstable if the heavier solution lies on top of the lighter one in the gravity field. Density fingering is then observed. We study the nonlinear dynamics of such fingering for a given model chemical system, the iodate-arsenious acid reaction. Chemical reactions profoundly affect the density fingering leading to changes in the characteristic wavelength of the pattern at early time and more rapid coarsening in the nonlinear regime. The nonlinear dynamics of the system is studied as a function of the three relevant parameters of the model, i.e., the dimensionless width of the system expressed as a Rayleigh number Ra, the Damköhler number Da, and a chemical parameter d which is a function of kinetic constants and chemical concentration, these two last parameters controlling the speed v and width w of the stable planar front. For small Ra, the asymptotic nonlinear dynamics of the fingering in the presence of chemical reactions is one single finger of stationary shape traveling with constant nonlinear speed VϾv and mixing zone WϾw. This is drastically different from pure density fingering for which fingers elongate monotonically in time. The asymptotic finger has axial and transverse averaged profiles that are self-similar in unit lengths scaled by Ra. Moreover, we find that W/Ra scales as Da Ϫ0.5 . For larger Ra, tip splittings are observed.

Buoyancy-driven pattern formation in reactive immiscible two-layer systems

“…In order to characterize the nonlinear dynamics resulting from the coupling between chemical reactions and hydrodynamic flows, various types of measurements have been done during the numerical simulations (De Wit, 2004). Let us briefly enumerate them.…”

Modeling Pathways and Stages of CO2 Storage

“…The given or very similar descriptions are discussed in the literature under the terms 'density-driven flow' [10,11,14], 'variable density flow and transport' [12] or 'natural convection in porous media' [11,13]. In case of high Rayleigh numbers a very similar description is derived for 'density fingering' [14].…”

“…In case of high Rayleigh numbers a very similar description is derived for 'density fingering' [14]. Similar multiphysics formulations have been used dealing with other density related problems in aquifers, as saltwater intrusion [15,16], salination from saltdomes [17], thermal convection, etc [14,18,19,20].…”

“…The second factor in formula (14) describes an initial steep concentration gradient in vertical direction below the interface. Not very far away from the interface the concentration and disturbance become almost zero.…”

“…The fluxes are represented by the Sherwood number Sh, as introduced by equation (17). For comparison the curves for the three runs of the previous sub-section are added, which were started with oscillatory disturbances according to formula (14). Three stages, diffusion (A), early convection (B) and late convection (C) can be identified for most of the simulation runs.…”