The effect of hydrodynamic dispersion on reactive flows in porous media

Abstract

The shape stability of the reaction interface for reactive flow in a porous medium is investigated. Previous work showed that the Reaction-Infiltration Instability could cause the reaction zone to lose stability when the Peclet number exceeded a critical value. The new feature of this study is to include a velocity-dependent hydrodynamic dispersion. A mathematical model for this phenomenon is given in the form of a moving free-boundary problem. The spectrum of the linearized problem is obtained, and the related analysis and numerical calculations show that the onset of the instability is not eliminated by the new dispersive terms. The details of analysis show that the instability is reduced especially by the transverse dispersion.

Reactive-infiltration instabilities in rocks. Part 2. Dissolution of a porous matrix

“…It can be verified that, for a small permeability gradient Γ ≈ 1 − W 0 , (5.10) coincides with the small Péclet limit of (4.11) withω 1 given by (B 14). Equation (5.10) also agrees with (4.2) of Chadam et al (2001), after accounting for the different scaling of the variables. We next consider the same two limiting cases as in § 4.1: small velocities…”

“…to Θ L 1 (pure dispersion). Results for a weak permeability contrast are similar to figures 1 and 2 of Chadam et al (2001), after noting that they plot the growth rate against the dimensional wavenumber u rather thanũ. Figure 7(b) shows that the growth rate is sensitive to anisotropy in the dispersion; we again take Γ = 0, which is typical of carbonate dissolution (for example), and D E 1 = 0, meaning that diffusion in the fully dissolved matrix is negligible.…”

Use and misuse of large‐density asymptotics in the reaction‐infiltration instability

“…Here the reactant does not penetrate into the matrix and only the upstream length is significant, set by the balance of dispersion and convection. Thus, the thickness of the porosity front is determined by transport parameters ( D , v 0 , and ks ) and not by γ , as suggested in a number of publications [ Chadam et al ., ; Ortoleva et al ., ; Chadam et al ., ; Chadam and Ortoleva , ; Chadam et al ., ; Zhao et al ., ; Zhao , ; Zhao et al ., ].…”

“…Subsequently, in two influential papers [ Ortoleva et al ., 1987a, 1987b], they reframed their insights within a geological context. However, their papers [ Chadam et al ., ; Ortoleva et al ., ; Chadam et al ., ] also contain a crucial misconception, which they refer to as “large solid‐density asymptotics.” They deduced (incorrectly) that a large ratio of mineral to aqueous concentrations inevitably means that the interface between the dissolved and undissolved mineral is sharp.…”

Thermosolutal convection in an evolving soluble porous medium

“…A variety of models have been used in various contexts to relate such parameters to porosity (e.g. Chadam et al 2001;Zhao et al 2008;Ward et al 2015;Petrus & Szymczak 2016). We choose to follow Ritchie & Pritchard (2011) and employ the minimal assumption that the rate of mass exchange between the rock and the pore fluid should reduce to zero when either there is no rock or there are no pores.…”