Effect of viscosity contrast on gravitationally unstable diffusive layers in porous media

Abstract

We investigate the effect of viscosity contrast on the stability of gravitationally unstable, diffusive layers in porous media. Our analysis helps evaluate experimental observations of various diffusive (boundary) layer models that are commonly used to study the sequestration of CO2 in brine aquifers. We evaluate the effect of viscosity contrast for two basic models that are characterized with respect to whether or not the interface between CO2 and brine is allowed to move. We find that diffusive layers are in general more unstable when viscosity decreases with depth within the layer compared to when viscosity increases with depth. This behavior is in contrast to the one associated with the classical displacement problem of gravitationally unstable diffusive layers that are subject to mean flow. For the classical problem, a greater instability is associated with the displacement of a more viscous, lighter fluid along the direction of gravity by a less viscous, heavier fluid. We show that the contrasting behavior highlighted in this study is a special case of the classical displacement problem that depends on the relative strength of the displacement and buoyancy velocities. We demonstrate the existence of a critical viscosity ratio that determines whether the flow is buoyancy dominated or displacement dominated. We explain the new behaviors in terms of the interaction of vorticity components related to gravitational and viscous effects.

Influence of viscosity contrast on buoyantly unstable miscible fluids in porous media

“…Daniel & Riaz 2014) to analyze the influence of viscosity contrast on the stability of a buoyantly unstable miscible layer. Two different cases are considered: (i) the upper fluid is more viscous than the lower one, and (ii) the lower fluid is more viscous than the upper one.…”

“…Moreover, the temporal evolution of the growth rates obtained for different viscosity contrasts are visually almost indistinguishable. The physical explanation for a different onset time of instability in flow with or without viscosity contrast in buoyantly unstable miscible fluids can be presented in terms of the instantaneous vorticity perturbation field as discussed by Daniel & Riaz (2014). From figure 2(b) it is identified that for all time the most unstable wavenumbers are larger in the absence of the viscosity contrast compared to the situation when the viscosity of the two fluids are different.…”

“…This results a computational domain having depth of unit size, and the Rayleigh number as a model parameter. On the other hand, in the present paper we choose the characteristic length to be the intrinsic finger length scale, which yields a unit Rayleigh number (compare (2.6) with equation (3) of Daniel & Riaz 2014). In all the computations of the present paper the depth of the computational domain is taken sufficiently large that the dynamics is unaffected by the influence of the top and bottom boundaries of the domain.…”

“…according to table 1. However, Daniel & Riaz (2014) used U, L and t as the dimensionless values for both R > 0 and R < 0 (see figures 4, 5 and 12(a), etc. of Daniel & Riaz 2014).…”

“…Note that Daniel & Riaz (2014) used the domain depth as the characteristic length scale. This results a computational domain having depth of unit size, and the Rayleigh number as a model parameter.…”