Impact of kinetic mass transfer on free convection in a porous medium

Abstract

We investigate kinetic mass transfer effects on unstable density‐driven flow and transport processes by numerical simulations of a modified Elder problem. The first‐order dual‐domain mass transfer model coupled with a variable‐density‐flow model is employed to describe transport behavior in porous media. Results show that in comparison to the no‐mass‐transfer case, a higher degree of instability and more unstable system is developed in the mass transfer case due to the reduced effective porosity and correspondingly a larger Rayleigh number (assuming permeability is independent on the mobile porosity). Given a constant total porosity, the magnitude of capacity ratio (i.e., immobile porosity/mobile porosity) controls the macroscopic plume profile in the mobile domain, while the magnitude of mass transfer timescale (i.e., the reciprocal of the mass transfer rate coefficient) dominates its evolution rate. The magnitude of capacity ratio plays an important role on the mechanism driving the mass flux into the aquifer system. Specifically, for a small capacity ratio, solute loading is dominated by the density‐driven transport, while with increasing capacity ratio local mass transfer dominated solute loading may occur at later times. At significantly large times, however, both mechanisms contribute comparably to solute loading. Sherwood Number could be a nonmonotonic function of mass transfer timescale due to complicated interactions of solute between source zone, mobile zone and immobile zone in the top boundary layer, resulting in accordingly a similar behavior of the total mass. The initial assessment provides important insights into unstable density‐driven flow and transport in the presence of kinetic mass transfer.

Unstable Density-Driven Flow in Fractured Porous Media: The Fractured Elder Problem

“…The developed COMSOL model is verified based on the standard Elder problem (homogeneous domain, scenario A), by comparison with the results of Lu et al [26] which are obtained using SEAWAT-2000. The parameters used for this simulation are given in Table 1.…”

“…The domain and boundary conditions of the fractured Elder problem considered in this study are similar to the adapted Elder problem as used by Voss and Souza [17], Lu et al [26] and Post and Prommer [23]. The domain was 600 m wide and 150 m high, as in Figure 1.…”

“…For all other boundaries, a no-flow boundary condition was assigned. The density contrast between the saltwater and the freshwater was equal to 200 kg/m 3 as in Lu et al [26] and Post and Prommer [23].…”

“…To characterize free convection, we used the dimensionless Sherwood number (Sh). Sh is commonly used as an indicator for the strength of convection, and equal to the ratio of the actual mass transfer due to free convection to the rate of the mass transfer due to diffusion [3,26]. The average Sherwood number over the source zone boundary can be calculated using the concentration gradient, as follows:…”

“…Graf and Boufadel [25] extended the Elder problem for application to partially saturated systems. Lu et al [26] developed dual-domain mass transfer in the Elder problem to explore the kinetic mass transfer effects on unstable DDF.…”