Skip to main content
SpringerLink
Log in

An Analytical Solution Evaluating Steady-State Plumes of Sequentially Reactive Contaminants

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

A steady state version of an analytical solution of the reactive flow and transport problem is derived. This solution allows a better understanding of the steady-state plume characteristics, and allows the prediction of the effectiveness of natural attenuation of sequentially reactive contaminants. The sequential reactions are assumed to be first order. Using spatial moments as compact information of plume characteristics, the total mass, plume centroids, and extents of each contaminant plume are derived as functions of dispersivity, velocity, and reaction rates. The steady-state plume centroids and extents are independent of stoichiometric coefficients. The solution is demonstrated for a four-species sequentially reactive transport in a one-dimensional column. The extension to three dimensions is easily made and does not change the basic functions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bear, J.: 1979, Groundwater Hydraulics, McGraw-Hill, New York.

    Google Scholar 

  • Beljin, M. S.: 1991, Review of three-dimensional analytical models for solute transport in groundwater system, International groundwater modeling center, Holcomb Research Institute, Butler University, IA.

    Google Scholar 

  • Borden, R. C. and Bedient, P. B.: 1986, Transport of dissolved hydrocarbon influenced by reaeration and oxygen limited biodegradation: Theoretical development, Water Resour. Res. 22, 1973-1982.

    Google Scholar 

  • Bosma, W. J. P., van der Zee, S. E. A. T. M. and van Duijn, C. J.: 1996, Plume development of a nonlinearly adsorbing solute in heterogeneous porous formations, Water Resour. Res. 32(6), 1569-1584.

    Google Scholar 

  • Buscheck, T. E. and Alcantar, C. M.: 1995, Regression techniques and analytical solution to demonstrate intrinsic bioremediation, In: R. E. Hinchee et al. (eds), Intrinsic Bioremediation, Battelle Press, Columbus, OH, pp. 109-116.

    Google Scholar 

  • Chappelle, F. H., Bradley, P. M., Lovley, D. R. and Vroblesky, D. A.: 1996, Measuring rates of biodegradation in a contaminated aquifer using field and laboratory methods, Ground Water 34(4), 691-698.

    Google Scholar 

  • Cho, C. M.: 1970, Convective transport of ammonium with nitrification in soil, Can. J. Soil Sci. 51, 339-350.

    Google Scholar 

  • Clement, T. P., Sun, Y., Hooker, B. S. and Petersen, J. N.: 1998, Modeling multi-species reactive transport in groundwater aquifers, Groundwater Monitoring and Remediation 18(2), 79-92.

    Google Scholar 

  • Dagan, G.: 1989, Flow and Transport in Porous Formations, Springer-Verlag, New York.

    Google Scholar 

  • Domenico, P. A.: 1987, An analytical model for multidimensional transport of a decaying contaminant species, J. Hydrol. 91, 49-58.

    Google Scholar 

  • Lunn, M., Lunn, R. J. and Mackay, R.: 1996, Determining analytic solutions of multiple species contaminant transport with sorption and decay, J. Hydrol. 180, 195-210.

    Google Scholar 

  • McNab, W. W. Jr. and Dooher, B. P.: 1998, A critique of a steady-state analytical method for estimating contaminant degradation rates, Ground Water 36(6), 983-987.

    Google Scholar 

  • McNab, W. W. Jr. and Narasimhan, T. N.: 1993, A multiple species transport model with sequential decay chain interactions in heterogeneous subsurface environments, Water Resour. Res. 29(8), 2737-2746.

    Google Scholar 

  • Molz, F. L., Widdowson, M. A. and Benefield, L. D.: 1986, Simulation of microbial growth dynamics coupled to nutrient oxygen transport in porous media, Water Resour. Res. 22(8), 1207-1216.

    Google Scholar 

  • Murray, W. D. and Richardson, R.: 1993, Progress toward the biological treatment of C 1 and C 2 halogenated hydrocarbon, Crit. Rev. Environ. Sci. Tech. 23(3), 195-217.

    Google Scholar 

  • Sun, Y., Petersen, J. N., Clement, T. P. and Skeen, R. S.: 1999, Development of analytical solutions for multi-species transport with serial and parallel reactions, Water Resour. Res. 35(1), 185-190.

    Google Scholar 

  • van Genuchten, M. Th.: 1985, Convective-dispersive transport of solutes involved in sequential firstorder decay reactions, Comput. Geosci. 11(2), 129-147.

    Google Scholar 

  • Waddill, D.W. and Widdowson, M. A.: 1998, Three-dimensional model for subsurface transport and biodegradation, J. Environ. Eng. 124(4), 336-344.

    Google Scholar 

  • Xu, T., Samper, J., Ayora, C., Manzano, M. and Custodio, E.: 1999. Modeling of non-isothermal multi-component reactive transport in field scale porous media flow systems, J. Hydrol. 214, 144-164.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Multiphase Environmental Research, Washington State University, Pullman, WA, 99164-2710, U.S.A., e-mail

    James N. Petersen & Yunwei Sun

Authors
  1. James N. Petersen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yunwei Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Petersen, J.N., Sun, Y. An Analytical Solution Evaluating Steady-State Plumes of Sequentially Reactive Contaminants. Transport in Porous Media 41, 287–303 (2000). https://doi.org/10.1023/A:1006680109002

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1006680109002

Search

Navigation