Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-14T13:19:58.202Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical assessment of 3D macrodispersion in heterogeneous porous media

Published online by Cambridge University Press:  21 January 2014

A. Beaudoin  and
J. R. De Dreuzy
A. Beaudoin*
Affiliation:
Institute P’, University of Poitiers, France
J. R. De Dreuzy
Affiliation:
Institute of Environmental Analysis and Water Studies, Barcelona, Spain Géosciences, University of Rennes, France
*
a Corresponding author:[email protected]
Get access

Abstract

Hydrodynamic dispersion is a key controlling factor of solute transport in heterogeneousporous media. It critically depends on dimensionality. The asymptotic macrodispersion,transverse to the mean velocity direction, vanishes only in 2D and not in 3D. Using theclassical Gaussian correlated permeability fields with a lognormal distribution ofvariance σY2, thelongitudinal and transverse dispersivities are determined numerically as a function ofheterogeneity and dimensionality. We show that the transverse macrodispersion steeplyincreases with σY2 underlyingthe essential role of flow lines braiding, a mechanism specific to 3D systems. Thetransverse macrodispersion remains however at least two orders of magnitude smaller thanthe longitudinal macrodispersion, which increases even more steeply withσY2. At moderateto high levels of heterogeneity, the transverse macrodispersion also converges much fasterto its asymptotic regime than do the longitudinal macrodispersion. Braiding cannot be thustaken as the sole mechanism responsible for the high longitudinal macrodispersions. Itcould be either supplemented or superseded by stronger velocity correlations in 3D than in2D. This assumption is supported by the much larger longitudinal macrodispersions obtainedin 3D than in 2D, up to a factor of 7 for σY2 = 7.56.

Keywords

parallel computingtransport equationpure advectionheterogeneous media3d macrodispersion
Type
Research Article
Information
Mechanics & Industry , Volume 14 , Issue 6 , 2013 , pp. 461 - 464
Copyright
© AFM, EDP Sciences 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Saffman, P.G., A theory of dispersion in a porous medium, J. Fluid Mech. 6 (1959) 321–349 CrossRefGoogle Scholar
de Dreuzy, J.-R., Carrera, J., Dentz, M., Le Borgne, T., Time evolution of mixing in heterogeneous porous media, Water Resour. Res. 48 (2012b) W06511 CrossRefGoogle Scholar
Taylor, G., Dispersion of Soluble Matter in Solvent Flowing Slowly through a Tube, Proc. Roy. Soc. London Ser. Math. Phys. Sci. 219 (1953) 186–203 CrossRefGoogle Scholar
Freeze, R.A., Stochastic-conceptual analysis of one-dimensional groundwater flow in nonuniform homogeneous media, Water Resour. Res. 11 (1975) 725–741 CrossRefGoogle Scholar
Gelhar, L.W., Axness, C.L., Three-dimensional stochastic analysis of macrodispersion in aquifers, Water Resour. Res. 19 (1983) 161–180 CrossRefGoogle Scholar
Rubin, Y., Stochastic modeling of macrodispersion in heterogeneous porous media, Water Resour. Res. 26 (1990) 133–141 CrossRefGoogle Scholar
Bellin, A., Salandin, P., Rinaldo, A., Simulation of dispersion in heterogeneous porous formations: statistics, first-order theories, convergence of computations, Water Resour. Res. 28 (1992) 2211–2227 CrossRefGoogle Scholar
Jankovic, I., Fiori, A., Dagan, G., Flow and transport in highly heterogeneous formations: 3. Numerical simulations and comparison with theoretical results, Water Resour. Res. 39 (2003) 1270 CrossRefGoogle Scholar
Lunati, I., Attinger, S., Kinzelbach, W., Macrodispersivity for transport in arbitrary nonuniform flow fields: asymptotic and preasymptotic results, Water Resour. Res. 38 (2002) 1187 CrossRefGoogle Scholar
de Dreuzy, J.-R., Beaudoin, A., Erhel, J., Asymptotic dispersion in 2D heterogeneous porous media determined by parallel numerical simulations. Water Resour. Res. 43 (2007) W10439 CrossRefGoogle Scholar
Le Borgne, T., de Dreuzy, J.-R., Davy, P., Bour, O., Characterization of the velocity field organization in heterogeneous media by conditional correlations, Water Resour. Res. 43 (2007) W02419 CrossRefGoogle Scholar
Schwarze, H., Jaekel, U., Vereecken, H., Estimation of Macrodispersion by Different Approximation Methods for Flow and Transport in Randomly Heterogeneous Media, Transport in Porous Media 43 (2001) 265–287 CrossRefGoogle Scholar
Neuman, S.P., Zhang, Y.-K., A Quasi-Linear Theory of Non-Fickian and Fickian Subsurface dispersion 1. Theoretical Analysis With Application to Isotropic Media, Water Resour. Res. 26 (1990) 887–902 Google Scholar
Attinger, S., Dentz, M., Kinzelbach, W., Exact transverse macro dispersion coefficients for transport in heterogeneous porous media, Stoch. Environ. Res. Risk Assess. 18 (2004) 9–15 CrossRefGoogle Scholar
Tompson, A.F.B., Gelhar, L.W., Numerical simulation of solute transport in three-dimensional, randomly heterogeneous porous media, Water Resour. Res. 26 (1990) 2541–2562 CrossRefGoogle Scholar
A.L. Gutjahr, Fast Fourier transforms for random field generation: New Mexico Tech project report 4-R58-2690R, New Mexico Institute of Mining and Technology, 1989
Salandin, P., Fiorotto, V., Solute transport in highly heterogeneous aquifers, Water Resour. Res. 34 (1998) 949–961 CrossRefGoogle Scholar
J.-E. Roberts, J.-M. Thomas, Mixed and hybrid methods, in Handbook of Numerical Analysis 2, Finite Element Methods -part 1, P.G. Ciarlet, J.L. Lions (eds.), Elsevier Science Publishers B.V. North-Holland, 1991 pp. 523–639,
Matheron, Eléments Pour une Théorie des milieux Poreux, Masson, Paris, 1967
N.G. Van Kampen, Stochastic Processes in Physics and Chemistry, Elsevier Science Pub Co., 1981
Pollock, D.W., Semianalytical computation of path lines for finite-difference models, Ground Water 26 (1988) 743–750 CrossRefGoogle Scholar
Wen, X.H., Gomez-Hernandez, J.J., The constant displacement scheme for tracking particles in heterogeneous aquifers, Ground Water 34 (1996) 135–142 CrossRefGoogle Scholar
A. Beaudoin, J.R. de Dreuzy, J. Erhel, H. Mustapha, Parallel Simulations of Underground Flow in Porous and Fractured Media, Proceedings of the International Conference ParCo, John von Neumann Institute for Computing, Jülich, 2005
A. Beaudoin, J.-R. de Dreuzy, J. Erhel, A comparison between a direct and a multigrid sparse linear solvers for highly heterogeneous flux computations, paper presented at European Conference on Computational Fluid Dynamics, ECCOMAS CFD, 2006
Dentz, M., Kinzelbach, H., Attinger, S., Kinzelbach, W., Temporal behavior of a solute cloud in a heterogeneous porous medium: 3. Numerical simulations, Water Resour. Res. 38 (2002) 1118 CrossRefGoogle Scholar