Mathematical Geology

, Volume 31, Issue 7, pp 771–791 | Cite as

Transverse Dispersion of a Kinetically Sorbing Solute

  • A. K. Mishra
  • A. Gutjahr


A recursion formulation for the transverse spreading of a solute is developed, and under conditions of steady flow in a stratified aquifer, the transport of a linearly sorbing solute undergoing nonequilibrium sorption is studied. The effect of spatial variability in the velocity field and the sorption kinetics are modeled to see the combined effect of the two processes on the spreading of the solute injected at a point in the aquifer. The main result of this work is a transport model based on a discrete formulation that includes local dispersion and leads to nonasymptotic behavior in the spreading of the plume in a direction normal to the mean flow velocity.

transverse dispersion solute steady flow stratified aquifer nonequilibrium sorption spatial variability velocity field sorption kinetics recursion 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Andricevic, R., and Foufoula-Georgiou, E., 1991, Modeling kinetic non-equilibrium using the first twomoments of the residence time distribution: Stochastic Hydrology and Hydraulics, v. 5, p. 155–171.Google Scholar
  2. Cushman, J. H., 1991, Diffusion in fractal porous media: Water Resources Res., v. 27, no. 4, p. 643–644.Google Scholar
  3. Cushman, J. H., and Ginn, T. R., 1993, Nonlocal dispersion in media with continuously evolving scales of heterogeneity: Transport in porous media: v. 13, p. 123–138.Google Scholar
  4. Dagan, G., 1989, Flow and transport through porous formations: Springer-Verlag, New York.Google Scholar
  5. Dagan, G., and Cvetkovic., V., 1993, Spatial moments of a kinetically sorbing plume in a heterogeneous aquifer: Water Resources Res., v. 29, no. 12, p. 4053–4061.Google Scholar
  6. Deng, F. W., Cushman, J. H., and Dellur, J. W., 1993, A fast Fourier transform stochastic analysis of the contaminant transport problem: Water Resources Res., v. 29, no. 9, p. 3241–3247.Google Scholar
  7. Gelhar, L. W., Gutjahr, A. L., and Naff, R. L., 1979, Stochastic analysis of macrodispersion in a statified aquifer: Water Resources Res., v. 15 no. 6, p. 1387–1397.Google Scholar
  8. Gutjahr, A. L., Fast Fourier transform for random field generation, 1989, Technical Report Contract Number 4–58–2690R, New Mexico Institute of Mining and Technology, Project Report for Los Alamos National Laboratory Grant.Google Scholar
  9. Hu, B. X., Deng, F., and Cushman, J. H., 1995, Nonlocal reactive transport with physical and chemical heterogeneity: Linear nonequilibrium sorption with random Kd: Water Resources Res. v. 31, p. 2239–2252.Google Scholar
  10. Hu, B. X., and Cushman, J. H., 1997, Comparison of nonlocal-eulerian to lagrangian moments for transport in an anisotropic heterogeneous aquifer with deterministic linear nonequilibrium sorption: Water Resources Res., v. 33, no. 4, p. 891–896.Google Scholar
  11. Koch, D. L., and Brady, J. F., 1987, Nonlocal dispersion in porous media: Nonmechanical effects: Chemical Engineering Science, v. 42, p. 1377–1392.Google Scholar
  12. Mishra, A. K., 1997, Reactive transport in chemically and physically heterogeneous porous media: Effect of non-equilibrium linear sorption: unpublished doctoral dissertation, New Mexico Institute of Mining and Technology, Socorro, New Mexico.Google Scholar
  13. Mishra, A. K., Gutjahr, A., and Rajaram, H., 1998, Transport with spatially variable kinetic sorption: Recursion formulation, Adv. Water Resources, in press.Google Scholar
  14. Neuman, S. P., 1993, Eulerian-Lagrangian theory of transport in space-time nonstationary velocity field: Exact nonlocal formalism by conditional moments and weak approximations: Water Resources Res., v. 29 no. 3, p. 633–645.Google Scholar
  15. Quinodoz, H. M., and A. J. Valocchi, 1993, Stochastic analysis of the transport of kinetically sorbing solutes in aquifers with randomly heterogeneous hydraulic conductivity: Water Resources Res., v. 29, no. 9, p. 3227–3240.Google Scholar

Copyright information

© International Association for Mathematical Geology 1999

Authors and Affiliations

  • A. K. Mishra
    • 1
  • A. Gutjahr
    • 2
  1. 1.Department of Earth and Environmental ScienceNew Mexico Institute of Mining and TechnologySocorro
  2. 2.Department of MathematicsNew Mexico Institute of Mining and TechnologySocorro

Personalised recommendations