Print Email Facebook Twitter An empirical theory for gravitationally unstable flow in porous media Title An empirical theory for gravitationally unstable flow in porous media Author Farajzadeh, R. Meulenbroek, B.J. Daniel, D. Riaz, A. Bruining, J. Faculty Civil Engineering and Geosciences Department Geoscience & Engineering Date 2013-01-19 Abstract In this paper, we follow a similar procedure as proposed by Koval (SPE J 3(2):145–154, 1963) to analytically model CO2 transfer between the overriding carbon dioxide layer and the brine layer below it. We show that a very thin diffusive layer on top separates the interface from a gravitationally unstable convective flow layer below it. Flow in the gravitationally unstable layer is described by the theory of Koval, a theory that is widely used and which describes miscible displacement as a pseudo two-phase flow problem. The pseudo two-phase flow problem provides the average concentration of CO2 in the brine as a function of distance.We find that downstream of the diffusive layer, the solution of the convective part of the model, is a rarefaction solution that starts at the saturation corresponding to the highest value of the fractional-flow function. Themodel uses two free parameters, viz., a dilution factor and a gravity fingering index. A comparison of the Koval model with the horizontally averaged concentrations obtained from 2-D numerical simulations provides a correlation for the two parameters with the Rayleigh number. The obtained scaling relations can be used in numerical simulators to account for the density-driven natural convection, which cannot be currently captured because the grid cells are typically orders of magnitude larger than the wavelength of the initial fingers. The method can be applied both for storage of greenhouse gases in aquifers and for EOR processes using carbon dioxide or other solvents. Subject CO2 sequestrationdensity-driven natural convectionenhanced mass transferanalytical modeling To reference this document use: http://resolver.tudelft.nl/uuid:e75b1d62-f651-4156-abd0-3b8377935226 DOI https://doi.org/10.1007/s10596-012-9336-9 Publisher Springer Embargo date 2014-01-19 ISSN 1420-0597 Source Computational Geosciences: modeling, simulation and data analysis 17(3), 515-527. (2013) Part of collection Institutional Repository Document type journal article Rights (c) Delft University of Technology Files PDF 292288.pdf 686 KB Close viewer /islandora/object/uuid:e75b1d62-f651-4156-abd0-3b8377935226/datastream/OBJ/view