Numerical Investigation of the Influence of Hydrodynamic Dispersion on Solutal Natural Convection

Abstract

We investigate numerically the effect of hydrodynamic dispersion on convective dissolution of carbon dioxide in saline aquifers. Solutions of the transport equations were used to describe the dissolution process in the aquifer and provide a systematic parametric analysis of the influence of dispersion on two important measures of convective dissolution, the wavenumber, and dissolution flux. The results suggest that dispersion decreases the dissolution rate and reduces the finger wavenumber. Based on the simulated results, new empirical scaling laws that predict the dissolution rate and wavenumber were developed. The application of the new laws to two storage sites shows that the currently available predictions overestimate the dissolution rates by ∼30%. We have identified some discrepancies between published scaling laws that were obtained for the dissolution rate. While most numerical studies identify a linear scaling, experimental investigations often suggest a sublinear behavior. Our findings resolve the controversy by suggesting that dispersion, which was not considered in these past numerical studies, is the reason for the apparent sublinear scaling.

Towards the understanding of convective dissolution in confined porous media: thin bead pack experiments, two-dimensional direct numerical simulations and physical models

“…Motivated by the observations of coarsening fingers in figure 11(b), we assume a diffusive growth for δ with an effective diffusivity of dU, namely (7.14) with β being a fitting parameter. Note that the effective diffusivity dU determined here coincides with the effective longitudinal dispersion usually considered for bead packs (Liang et al 2018;Tsinober, Shavit & Rosenzweig 2023). We now substitute the expressions obtained in (7.12) and (7.14) into the definition (7.13), together with the evolution of the mixing length h = 2Ut and the wavelength measured from the simulations λ/d = α √ t/(d/U), as in figure 11.…”

Convective mixing in porous media: a review of Darcy, pore-scale and Hele-Shaw studies

“…2.2.1) is also important to determine the flow character. As a result, the parameters space for convective porous media flows with dispersion is controlled by at least three parameters: Ra, Ra d and r. In order to quantify the relative importance of molecular diffusion to transverse dispersion, one can introduce the parameter [84,118]…”

“…With specific reference to granular media, additional simplifications allow a further characterisation of the flow in the parameter's space. Considering that the longitudinal dispersivity can be approximated [29,118] as α L = D L /U ≈ d, we can rewrite Eq. (35) as…”

“…A possible complementary approach with respect to the formulation used by Wen et al [84] and Liang et al [26] is proposed by Dhar et al [123], where the dispersive Fig. 13 Range of parameters space explored with simulations [84,117,118] and experiments [19,26] with dispersion. The configuration (one-sided-OS or Rayleigh-Bénard-RB) is indicated.…”

“…In this parameters space, ∆ sets the flow behaviour: diffusiondominated [∆ < O( 1 Rayleigh number is replaced by a parameter quantifying the strength of longitudinal dispersion compared to molecular diffusion. More recently, Tsinober et al [118] performed simulations in one-sided configuration. They modelled fluids with constant viscosity and linear density-concentration profiles, and derived a linear correlation between Sh and Ra, where the prefactor is a function of molecular to dispersive Rayleigh-Darcy numbers,Ra/Ra d .…”