Dissolution patterns and mixing dynamics in unstable reactive flow

Abstract

We study the fundamental problem of mixing and chemical reactions under a Rayleigh‐Taylor‐type hydrodynamic instability in a miscible two‐fluid system. The dense fluid mixture, which is generated at the fluid‐fluid interface, leads to the onset of a convective fingering instability and triggers a fast chemical dissolution reaction. Contrary to intuition, the dissolution pattern does not map out the finger geometry. Instead, it displays a dome‐like, hierarchical structure that follows the path of the ascending fluid interface and the regions of maximum mixing. These mixing and reaction hot spots coincide with the flow stagnation points, at which the interfacial mixing layer is compressed and deformed. We show that the deformation of the boundary layer around the stagnation points controls the evolution of the global scalar dissipation and reaction rates and shapes the structure of the reacted zones. The persistent compression of the mixing layer explains the independence of the mixing rate from the Rayleigh number when convection dominates.

Critical Dynamics of Gravito-Convective Mixing in Geological Carbon Sequestration

“…Third, diffusion is further promoted by the nature of Rayleigh-Taylor fluid dynamics: downward motion of (growing) dense fingers and subsequent upwards displacement of fresh lighter brine increase the surface area of the CO 2 dissolution front. The evolution of mixing rates is controlled by the competition between the advective stretching mechanism and such lateral compositional diffusion12. Following the onset of the previous regime, fast advective downward transport of fingers exceeds the diffusive rate of CO 2 dissolution at the top.…”

“…Higher initial spreading ends in an earlier convective-shutdown regime in bimodal heterogeneities once the fingers reach the lower boundary and the domain starts to be saturated with CO 2 . This phenomenon has been studied in both numerical simulations and experiments as a late-time reduction of mixing rates1251.…”

“…In this work, we focus on solubility trapping, which can be enhanced when gravitational instabilities (fingering) are triggered by a local increase in brine density as CO 2 dissolves into brine in the top of an aquifer. This Rayleigh-Taylor-type instability12 is sometimes referred to as gravito-convective mixing and involves both diffusive and advective motion of dissolved CO 2 , with advection being the dominant driving force. Whether the interface between CO 2 -bearing brine and fresh brine becomes gravitationally unstable depends on the ratio of advection to molecular diffusion (Rayleigh or Péclet numbers).…”

“…Whether the interface between CO 2 -bearing brine and fresh brine becomes gravitationally unstable depends on the ratio of advection to molecular diffusion (Rayleigh or Péclet numbers). When a fingering instability is triggered, dissolved CO 2 is mixed throughout the aquifer at advective time-scales, which can be much faster than diffusive transport121314. This improves the storage capacity of a given aquifer and decreases the leakage risk in case of cap rock failure.…”

Effect of diffusing layer thickness on the density-driven natural convection of miscible fluids in porous media: Modeling of mass transport

“…Two main configurations (De Paoli et al 2016;Hewitt et al 2013) were considered in previous studies depending on the boundary condition at the bottom boundary, namely, the so-called "one-sided" cell, in which the Neumann boundary condition (i.e., no concentration gradient) is imposed at the bottom boundary (Pau et al 2010;Neufeld et al 2010;Slim 2014;Xu et al 2006;De Paoli et al 2017), and the so-called "two-sided" cell, in which the Dirichlet boundary condition (i.e., constant concentrations) is imposed at the top and bottom boundaries (Otero et al 2004;Hewitt et al 2012;Wen et al 2013). Based on theoretical analyses (Coskuner and Bentsen 1990;Hassanzadeh 2013, 2015;Rapaka et al 2008) , numerical simulations Ghesmat et al 2010;Hassanzadeh et al 2007;Hewitt et al 2012Hewitt et al , 2013Hidalgo and Carrera 2009;Hidalgo et al 2015;Otero et al 2004;Pau et al 2010;Riaz et al 2006;Shahraeeni et al 2015;Wen et al 2012;Xie et al 2011), and laboratory experiments including the construction of a nonlinear density profile of a mixture of miscible fluids (Backhaus et al 2011;Faisal et al 2015;Huppert and Neufeld 2014;Hidalgo et al 2012;Neufeld et al 2010;Wang et al 2016), mass transport is modeled as a function of Rayleigh number, because the time required for the shift in trapping mechanism scales with mass flux. In the Rayleigh-Taylor model, Rayleigh-Taylor instability (Kolditz et al 1998) occurs on the interface that separates a lighter fluid from a heavier one located above it, and the fluids convectively mix with each other (Manickam and Homsy 1995;…”