Modeling Transverse Dispersion and Variable Density Flow in Porous Media
- 596 Downloads
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.
KeywordsHeterogeneity 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.
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.
- Dagan G.: Flow and Transport in Porous Formations. Springer, Berlin (1989)Google Scholar
- Fein E.: d 3 f—ein Programmpaket zur Modellierung von Dichtestromungen. Tech. Rep. GRS-139, GRS, Braunschweig, Germany (1998)Google Scholar
- Frolkovic, P.: Consistent velocity approximation for density driven flow and transport. In: Advanced Computational Methods in Engineering, pp. 603–611. Shakeer Publishing, Maastrict (1998)Google Scholar
- Hassanizadeh, S.M.: Experimental study of coupled flow and mass transport: a model validation exercise. In: Calibration and reliability in groundwater modelling, Proceedings of the Model Care Conference, IAHS publication No. 195, pp 241–250 (1990)Google Scholar
- Hassanizadeh, S.M., Leijnse, A., de Vries, W.J., Stapper, R.A.M.: Experimental study of brine transport in porous media. RIVM Report 728514005, Bilthoven, The Netherlands (1990)Google Scholar
- Johannsen K.: Numerische Aspekte dichtegetriebener Stroemung in poroesen Medien. Heidelberg University, Habilitationsschrift (2004)Google Scholar
- Landman, A. J.: Analysis of physical mechanisms underlying density-dependent transport in porous media. Utrecht University (2005)Google Scholar
- Landman A.J., Johannsen K., Schotting R.J.: Density-dependent dispersion in heterogeneous porous media. Part I: A numerical study. Water Resour. Res. 30(12), 2467–2480 (2007a)Google Scholar
- Landman A.J., Schotting R.J., Egorov A., Demidov D.: Density-dependent dispersion in heterogeneous porous media Part II: Comparison with nonlinear models. Water Resour. Res. 30(12), 2481–2498 (2007b)Google Scholar
- Moser, H.: Einfluß der Salzkonzentration auf die hydrodynamische Dispersion im porösen Medium. Mitteilungen des Institutes für Wasserbau u. Wasserwirtschaft. Mitteilung nr. 128, TU BerlinGoogle Scholar
- Schotting, R., Landman, A.L.: Towards a physically based theory of high-concentration-gradient dispersion in porous media. Experimental, theoretical and numerical studies. In: Ingham, D.B., et al. (eds.) Emerging Technologies and Techniques in Porous Media, NATO Science Series II, vol. 134, pp. 321–336. Kluwer Academic. Publishers, Dordrecht (2004)Google Scholar
- Starke, B.: Experimental and numerical investigations of macrodispersion of density-dependent flow and transport in stochastic porous media. PhD- Dissertation (in German), University Kassel, 199 pp (2005)Google Scholar
- Starke, B., Koch, M.: Laboratory experiments and Monte Carlo simulations to validate a stochastic theory of density-dependent macrodispersion, CMWRXVI (2006)Google Scholar
- Tompson A.F.B., Gelhar L.W.: Numerical simulation of solute transport in three-dimensional, randomly heterogeneous porous media. Water Resour. Res. 26(10), 2541–2562 (1990)Google Scholar