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Fluids 2018, 3(3), 60; https://doi.org/10.3390/fluids3030060

A Simple Analytical Model for Estimating the Dissolution-Driven Instability in a Porous Medium

Department of Mathematics, The University of Alabama, Tuscaloosa, AL 35487, USA
This paper is an extended version of our paper published in InterPore 10th Annual Meeting and Jubilee, New-Orleans, LA, USA, 14–17 May 2018, titled “Modeling the dissolution-driven convection as a Rayleigh–Bénard problem”.
Received: 24 July 2018 / Revised: 22 August 2018 / Accepted: 23 August 2018 / Published: 25 August 2018
(This article belongs to the Special Issue Fundamentals of CO2 Storage in Geological Formations)
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Abstract

This article deals with the stability problem that arises in the modeling of the geological sequestration of carbon dioxide. It provides a more detailed description of the alternative approach to tackling the stability problem put forth by Vo and Hadji (Physics of Fluids, 2017, 29, 127101) and Wanstall and Hadji (Journal of Engineering Mathematics, 2018, 108, 53–71), and it extends two-dimensional analysis to the three-dimensional case. This new approach, which is based on a step-function base profile, is contrasted with the usual time-evolving base state. While both provide only estimates for the instability threshold values, the step-function base profile approach has one great advantage in the sense that the problem at hand can be viewed as a stationary Rayleigh–Bénard problem, the model of which is physically sound and the stability of which is not only well-defined but can be analyzed by a variety of existing analytical methods using only paper and pencil. View Full-Text
Keywords: carbon dioxide sequestration; buoyancy-driven instabilities; Rayleigh–Taylor instability carbon dioxide sequestration; buoyancy-driven instabilities; Rayleigh–Taylor instability
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Hadji, L. A Simple Analytical Model for Estimating the Dissolution-Driven Instability in a Porous Medium. Fluids 2018, 3, 60.

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