Steady Flux Regime During Convective Mixing in Three-Dimensional Heterogeneous Porous Media

Christopher Green,Jonathan Ennis-King

doi:10.3390/fluids3030058

Abstract

Density-driven convective mixing in porous media can be influenced by the spatial heterogeneity of the medium. Previous studies using two-dimensional models have shown that while the initial flow regimes are sensitive to local permeability variation, the later steady flux regime (where the dissolution flux is relatively constant) can be approximated with an equivalent anisotropic porous media, suggesting that it is the average properties of the porous media that affect this regime. This work extends the previous results for two-dimensional porous media to consider convection in three-dimensional porous media. Through the use of massively parallel numerical simulations, we verify that the steady dissolution rate in the models of heterogeneity considered also scales as k v k h in three dimensions, where k v and k h are the vertical and horizontal permeabilities, respectively, providing further evidence that convective mixing in heterogeneous models can be approximated with equivalent anisotropic models.

Highlights

Density-driven convective mixing of CO2 in a saline aquifer is a fascinating phenomena that can accelerate the dissolution of CO2 into the resident formation brine, reducing the risk of any leakage to the shallower subsurface
Numerical simulations of three-dimensional convective mixing in homogeneous but anisotropic porous media were performed for permeability anisotropies γ = 1, 0.75, 0.5 and 0.25 using the dimensionless form of the governing equations
Two models of permeability heterogeneity were considered, and in each case, it was demonstrated that the magnitude of the average flux in the steady flux regime for these models of permeability heterogeneity were well represented by anisotropic homogeneous porous models with effective permeabilities that provide an equivalent Darcy flux

Summary

Introduction

Density-driven convective mixing of CO2 in a saline aquifer is a fascinating phenomena that can accelerate the dissolution of CO2 into the resident formation brine, reducing the risk of any leakage to the shallower subsurface. Numerical and experimental studies examining the important features of density-driven convective mixing and its importance to CO2 storage in saline aquifers have appeared in the scientific literature (e.g., References [1,2,3,4,5,6,7,8,9,10,11,12,13]), see Reference [14] for a detailed review of the published scientific literature regarding convective dissolution of CO2 in saline aquifers. Diffusion-driven dissolution of CO2 into the resident brine slightly increases its density, resulting in a gravitational instability. All parameters used in this analysis and their units are described in the table of nomenclature, Table 1. Symbol Definition SI Units C D F g H kh kv

Methods

Results

Conclusion