Computational Geosciences

, Volume 17, Issue 3, pp 515–527

An empirical theory for gravitationally unstable flow in porous media

  • R. Farajzadeh
  • B. Meulenbroek
  • D. Daniel
  • A. Riaz
  • J. Bruining
Original Paper

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. The model 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.

Keywords

CO2 sequestration Density-driven natural convection Enhanced mass transfer Analytical modeling 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • R. Farajzadeh
    • 1
    • 2
  • B. Meulenbroek
    • 1
  • D. Daniel
    • 3
  • A. Riaz
    • 3
  • J. Bruining
    • 1
  1. 1.Delft University of TechnologyDelftThe Netherlands
  2. 2.Shell Global Solutions International B.V.RijswijkThe Netherlands
  3. 3.University of MarylandCollege ParkUSA

Personalised recommendations