Abstract
The stability of convection in an anisotropic porous medium, where the solute concentration is assumed to decay via a first-order chemical reaction, is studied. This is a simplified model for the interactions between carbon dioxide and brine in underground aquifers; the instability of which is essential in reducing reservoir mixing times. The key purpose of this paper is to explore the role porous media anisotropy plays in convective instabilities. It is shown that varying the ratio of horizontal to vertical solutal diffusivites does not significantly affect the behaviour of the instability. This is also the case for changes of permeability when the diffusion rate dominates the solute reaction rate. However, interestingly, when the solute reaction rate dominates the diffusion rate a change in the permeability of the porous material does have a substantial effect on the instability of the system. The region of potential subcritical instabilities is shown to be negligible, which further supports the novel instability behaviour.
Highlights
The world’s current energy production is based primarily on fossil fuels; the combustion of which has been consistently highlighted as the biggest contributor to climate change through the increase of carbon dioxide in the atmosphere [1]
We present the numerical results relating to the key physical variables considered in the system, namely the critical solutal Raleigh number Ra, the Damköhler number Da, the ratio of horizontal to vertical solutal diffusivity ζ and λ such that 1 + λz describes the non-dimensional permeability varying in the z-direction
0 –3.0 –2.5 –2.0 –1.5 –1.0 –0.5 0 log (Da). This mirrors the general behaviour for an isotropic porous medium [4]
Summary
The world’s current energy production is based primarily on fossil fuels; the combustion of which has been consistently highlighted as the biggest contributor to climate change through the increase of carbon dioxide in the atmosphere [1]. To generate sustainable alternative renewable energy technologies to replace fossil fuels, intensive research and development is needed to overcome the deficiencies that limit existing approaches and produce novel new technological options While these longer term options are being developed, a more-immediately accessible strategy to limit the accumulation of carbon dioxide in the atmosphere is its storage in underground brinefilled aquifers [2]. Using spectral and asymptotic methods, stability analyses (and time-dependent simulations) are performed for convection in an isotropic porous medium (where the solute concentration is assumed to decay via a first-order chemical reaction) in [4]. An assessment of the onset of convection is achieved by analysing both the linear instability and nonlinear stability thresholds of the governing model. All numerical results were checked by varying the number of polynomials to verify convergence
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