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

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.

Experimental and Simulation Study on Validating a Numerical Model for CO2 Density-Driven Dissolution in Water

“…The setup of our study has a thickness d of only 1 cm, resembling a Hele-Shaw type of cell. We therefore use a definition of the Rayleigh number as it is used in porous-media applications [12] with the permeability k (in m 2 ) representing a resistance to advection and a porosity equal to one. For flow between parallel plates, the permeability can be derived as k = b 2 /12, where b is the distance between the plates; in our case, 1 cm.…”

“…The Rayleigh number is thus a criterion for the onset time of a convective fingering and also for the characteristic wave length of the fingers. Again following Green and Ennis-King (2018) [12], Pau et al (2010) [11] or Emami-Meybodi et al (2015) [28], who review the literature on convective dissolution of CO 2 in saline aquifers, we may estimate for the onset time based on linear stability analysis:…”

“…Therefore, more pragmatic approaches avoid the resolution of the fingers and employ effective rates, dependent on permeability; density difference as a function of CO 2 concentration and brine salinity; and fluid viscosity [11]. An overview is given, for example, in the paper of Green and Ennis-King (2018) [12].…”

6. Multiphase Multicomponent Reactive Transport and Flow Modeling

“…The density of fluids should then be accurately modeled to predict the onset time and convective fluxes, and to estimate convective dissolution trapping. Farajzadeh et al (2007) Several studies were carried out, which involved mathematical and numerical stability analyses of convective mixing for homogeneous and heterogeneous media, with and without capillary transition zones (Lindeberg and Wessel-Berg 1997;Xu et al 2006;Hesse et al 2008;Pau et al 2010;Elenius et al 2012Elenius et al , 2015Li and Jiang 2014); for an anisotropic medium (Ennis-King and Paterson 2005); in open and closed systems (Riaz et al 2006;Wen et al 2018) and 3D heterogeneous domains (Green and Ennis-King 2018). At present, there is insufficient information as to the influence of gases other than CO 2 on convective mixing.…”

Bounding of Flow and Transport Analysis in Heterogeneous Saturated Porous Media: A Minimum Energy Dissipation Principle for the Bounding and Scale-Up

“…Complex materials with heterogeneous spatial distributions govern subsurface flow and contaminant transport [1]. In models, it is difficult to represent accurately these complexities and so modelers use more uniform material representations to represent the actual complex distributions.…”