Transport in Porous Media

, Volume 78, Issue 1, pp 11–35 | Cite as

Modeling Transverse Dispersion and Variable Density Flow in Porous Media

  • H. M. NickEmail author
  • R. Schotting
  • M. Gutierrez-Neri
  • K. Johannsen
Open Access


A two-dimensional numerical model is used to study the nonlinear behavior of density gradients on transverse dispersion. Numerical simulations are conducted using d 3 f, a computer code for simulation of density-dependent flow in porous media. Considering a density-stratified horizontal flow in a heterogeneous porous media, a series of simulations is carried out to examine the effect of the density gradient on macro-scale transverse dispersivity. Changing salt concentration significantly affects fluid properties. This physical behavior of the fluid involves a non-linearity in modeling the interaction between salt and fresh water. It is concluded that the large-scale transport properties for high density flow deviate significantly from the tracer case due to the spatial variation of permeability, described by statistical parameters, at the local-scale. Indeed, the presence of vertical flow velocities induced by permeability variations is responsible for the reduction of the mixing zone width in the steady state in the case of a high density gradient. Uncertainties in the model simulations are studied in terms of discretization errors, boundary conditions, and convergence of ensemble averaging. With respect to the results, the gravity number appears to be the controlling parameter for dispersive flux. In addition, the applicability and limitations of the nonlinear model of Hassanizadeh (1990) and Hassanizadeh and Leijnse (1995) (Adv Water Resour 18(4):203–215, 1995) in heterogeneous porous media are investigated. We found that the main cause of the nonlinear behavior of dispersion, which is the interaction between density contrast and vertical velocity, needs to be explicitly accounted for in a macro-scale model.


Heterogeneity Porous media Density contrast Solute transport Macro-dispersivity 



We wish to thank Majid Hassanizadeh, Rainer Helmig, and Robert Zimmerman for their scientific feedback and comments. We thank IWR in Heidelberg for using their cluster.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution,and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2008

Open AccessThis is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • H. M. Nick
    • 1
    • 2
    Email author
  • R. Schotting
    • 2
  • M. Gutierrez-Neri
    • 2
  • K. Johannsen
    • 3
  1. 1.Department of Earth Sciences and EngineeringImperial CollegeLondonUK
  2. 2.Environmental Hydrogeology Group, Department of Earth SciencesUniversity of UtrechtUtrechtThe Netherlands
  3. 3.The Bergen Center for Computational ScienceBergenNorway

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