Next Article in Journal
Flow and Heat or Mass Transfer in the Chemical Process Industry
Next Article in Special Issue
CO2 Injection Effect on Geomechanical and Flow Properties of Calcite-Rich Reservoirs
Previous Article in Journal
Genetic Algorithm Based Optimization of Wing Rotation in Hover
Previous Article in Special Issue
Steady Flux Regime During Convective Mixing in Three-Dimensional Heterogeneous Porous Media
Article Menu

Export Article

Open AccessArticle
Fluids 2018, 3(3), 60;

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)
Full-Text   |   PDF [2199 KB, uploaded 28 August 2018]   |  


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

Graphical abstract

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).

Share & Cite This Article

MDPI and ACS Style

Hadji, L. A Simple Analytical Model for Estimating the Dissolution-Driven Instability in a Porous Medium. Fluids 2018, 3, 60.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Metrics

Article Access Statistics



[Return to top]
Fluids EISSN 2311-5521 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top