Advertisement

Transport in Porous Media

, Volume 30, Issue 1, pp 87–112 | Cite as

Three-Dimensional Analytical Models for Virus Transport in Saturated Porous Media

  • Youn Sim
  • Constantinos V. Chrysikopoulos
Article

Abstract

Analytical models for virus transport in saturated, homogeneous porous media are developed. The models account for three-dimensional dispersion in a uniform flow field, and first-order inactivation of suspended and deposited viruses with different inactivation rate coefficients. Virus deposition onto solid particles is described by two different processes: nonequilibrium adsorption which is applicable to viruses behaving as solutes; and colloid filtration which is applicable to viruses behaving as colloids. The governing virus transport equations are solved analytically by employing Laplace/Fourier transform techniques. Instantaneous and continuous/periodic virus loadings from a point source are examined.

virus transport analytical modeling multidimensional systems nonequilibrium adsorption filtration virus inactivation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abramowitz, M. and Stegun, I. A.: 1972, Handbook of Mathematical Functions, Dover, New York.Google Scholar
  2. Armon, R. and Kott, Y.: 1994, The health dimension of groundwater contamination, in: U. Zoller (ed.), Groundwater Contamination and Control, Marcel Dekker, New York, pp. 71-85.Google Scholar
  3. Bales, R. C., Li, S., Maguire, K. M., Yahya, M. T., Gerba, C. P. and Harvey, R. W.: 1995, Virus and bacteria transport in a sandy aquifer, Cape Cod, MA, Ground Water 33(4), 653-661.Google Scholar
  4. Bales, R. C., Li, S., Yeh, T.-C. J., Lenczewski, M. E. and Gerba, C. P.: 1997, Bactriophage and microsphere transport in saturated porous media: Forced-gradient experiment at Borden, Ontario, Water Resour. Res. 33(4), 639-648.Google Scholar
  5. Batu, V.: 1989, A generalized two-dimensional analytical solution for hydrodynamic dispersion in bounded media with the first-type boundary condition at the source, Water Resour. Res. 25(6), 1125-1132.Google Scholar
  6. Batu, V.: 1993, A generalized two-dimensional analytical solute transport model in bounded media for flux-type finite multiple sources, Water Resour. Res. 29(8), 1125-1132.Google Scholar
  7. Batu, V. and van Genuchten, M. T.: 1990, First-and third-type boundary conditions in two-dimensional solute transport modeling, Water Resour. Res. 26(2), 339-350.Google Scholar
  8. Bellin, A., Rinaldo, A., Bosma, W. J. P., van der Zee, S.E.A.T.M. and Rubin, Y.: 1993, Linear equilibruim adsorbing solute transport in physically and chemically heterogeneous porous formations, 1, Analytical solutions, Water Resour. Res. 29(12), 4019-4030.Google Scholar
  9. Berg, G.: 1977, Viruses in the environment: Criteria for risk, in: B. P. Sagik and C. A. Sorber (eds.), Risk Assessment and Health Effects of Municipal Wastewater and Sludges, Proceedings, Univ. Texas, San Antonio, pp. 216-229.Google Scholar
  10. Birgersson, L. and Neretnieks, I.: 1982, Diffusion in the matrix of granitic rock field test in the Stripa mine, Part 1, SKBF/KBS Teknish Rapport, 82-08, Royal Inst. Technol., Stockholm, Sweden.Google Scholar
  11. Brock, T. D. and Madigan, M. T.: 1991, Biology of Microorganisms, 6th edn, Prentice-Hall, Englewood Cliffs, p. 874.Google Scholar
  12. Buddemeier, R. W. and Hunt, J. R.: 1988, Transport of colloidal contaminants in groundwater radionuclide migration at the Nevada test site, Applied Geochem. 3, 535-548.Google Scholar
  13. Chrysikopoulos, C. V.: 1995, Three-dimensional analytical models of contaminant transport from nonaqueous phase liquid pool dissolution in saturated subsurface formations, Water Resour. Res. 31(4), 1137-1145.Google Scholar
  14. Chrysikopoulos, C. V. and Sim, Y.: 1996, One-dimensional virus transport in homogeneous porous media with time dependent distribution coefficient, J. Hydrol. 185, 199-219.Google Scholar
  15. Chrysikopoulos, C. V., Voudrias, E. A. and Fyrillas, M. M.: 1994, Modeling of contaminant transport resulting from dissolution of nonaqueous phase liquid pools in saturated porous media, Transport in Porous Media 16(2), 125-145.Google Scholar
  16. Elimelech, M., Gregory, J., Jia, X. and Williams, R. A.: 1995, Particle Deposition and Aggregation: Measurement, Modeling and Simulation, Butterworth-Heinemann, Oxford, Great Britain.Google Scholar
  17. Gerba, C. P. and Keswick, B. H.: 1981, Survival and transport of enteric bacteria and viruses in groundwater, Stud. Environ. Sci. 17, 511-515.Google Scholar
  18. Goltz, M. N. and Roberts, P. V.: 1986, Three-dimensional solutions for solute transport in an infinite medium with mobile and immobile zones, Water Resour. Res. 22(7), 1139-1148.Google Scholar
  19. Gradshteyn, I. S. and Ryzhik, I. M.: 1980, Table of Integral, Series, and Products, Academic Press, New York.Google Scholar
  20. Greenberg, M. D.: 1978, Foundations of Applied Mathematics, Prentice-Hall, Englewood Cliffs.Google Scholar
  21. Grosser, P. W.: 1984, A one-dimensional mathematical model of virus transport, Paper presented at the Second International Conference on Ground-Water Quality Research, Tulsa, OK., Mar. pp. 26-29.Google Scholar
  22. Haridas, A.: 1984, A mathematical model of microbial transport in porous media, PhD Dissertation, Univ. of Delaware.Google Scholar
  23. Harvey, R. W. and Garabedian, S. P.: 1991, Use of colloid filtration theory in modeling movement of bacteria through a contaminated sandy aquifer, Environ. Sci. Technol. 25(1), 178-185.Google Scholar
  24. Hassani, S.: 1991, Foundations of Mathematical Physics, Allyn and Bacon, Boston.Google Scholar
  25. Hunt, B.: 1978, Dispersive Sources in uniform groundwater flow, J. Hydraul. Div. Am. Soc. Civ. Eng. 104(HY1), 75-85.Google Scholar
  26. IMSL: 1991, IMSL MATH/LIBRARY user's manual, ver. 2.0, IMSL, Houston.Google Scholar
  27. Kahaner, D., Moler, C. and Nash, S.: 1989, Numerical Methods and Software, Prentice-Hall, Englewood Cliffs.Google Scholar
  28. Keswick, B. H. and Gerba, C. P.: 1980, Viruses in groundwater, Environ. Sci. Technol. 14, 1290-1297.Google Scholar
  29. Kreyszig, E.: 1993, Advanced Engineering Mathematics, 7th edn, Wiley, New York.Google Scholar
  30. Lapidus, L. and Amundson, N. R.: 1952, Mathematics of adsorption in beds, VI. The effect of longitudinal diffusion in ion exchange and chromatographic columns, J. Phys. Chem. 56, 984-988.Google Scholar
  31. Leij, F. J. and Dane, J. H.: 1990, Analytical solutions of the one-dimensioal advection equation and two-or three-dimensional dispersion equation, Water Resour. Res. 26(7), 1475-1482.Google Scholar
  32. Leij, F. J., Skaggs, T. H. and van Genuchten, M. Th.: 1991, Analytical solutions for solute transport in three-dimensional semi-infinite porous media, Water Resour. Res. 27(10), 2719-2733.Google Scholar
  33. Leij, F. J., Toride, N. and van Genuchten, M. Th.: 1993, Analytical solutions for nonequilibrium solute transport in three-dimensional porous media, J. Hydrol. 151, 193-228.Google Scholar
  34. Li, S.: 1993, Modeling biocolloid transport in saturated porous media, PhD Dissertation, Univ. of Arzona, Tucson.Google Scholar
  35. Matthess, G. and Pekdeger, A.: 1981, Concepts of a survival and transport model of pathogenic bacteria and viruses in groundwater, Sci. Tot. Environ. 21, 149-159.Google Scholar
  36. Mitchell, J. K.: 1976, Fundamentals of Soil Behavior, Wiley, New York.Google Scholar
  37. Park, N., Blanford, T. N. and Huyakorn, P. S.: 1992, VIRALT: A Modular Semi-Analytical and Numerical Model for Simulating Viral Transport in Ground Water, International Ground Water Modeling Center, Colorado School of Mines, Golden, CO.Google Scholar
  38. Penrod, S. L.: 1995, The deposition kinetics of Bacteriophage MS2 and λ, Master Thesis, Univ. of California, Irvine, CA.Google Scholar
  39. Roberts, G. E. and Kaufman, H.: 1966, Table of Laplace Transforms, W. B. Saunders, Philadelphia, PA.Google Scholar
  40. Sim, Y. and Chrysikopoulos, C. V.: 1995, Analytical models for one-dimensional virus transport in saturated porous media, Water Resour. Res. 31(5), 1429-1437. (Correction: Water Resour. Res. 32(5), p. 1473, 1996.)Google Scholar
  41. Sim, Y. and Chrysikopoulos, C. V.: 1996a, One-dimensional virus transport in porous media with time dependent inactivation rate coefficients, Water Resour. Res. 32(8), 2607-2611.Google Scholar
  42. Sim, Y. and Chrysikopoulos, C. V.: 1996b, Parameter sensitivity of macroscopic virus transport in porous media with temporally variable inactivation, in: H. J. Morel-Seytoux (ed.), Sixteenth Annual American Geophysical Union Hydrology Days, Fort Collins, CO., pp. 455-466.Google Scholar
  43. Stumm, W.: 1977, Chemical interaction in particle separation, Environ. Sci. Technol. 11, 1066-1070.Google Scholar
  44. Taylor, D. H. and Bosmann, H. B.: 1981, The electrokinetic properties of reovirus type 3: Electrophoretic mobility and zeta potential in dilute electrolytes, J. Colloid Interface Sci. 83, 153-162.Google Scholar
  45. Tim, U. S. and Mostaghimi, S.: 1991, Model for predicting virus movement through soils, Ground Water 29(2), 251-259.Google Scholar
  46. van Dujin, C. J. and van der Zee, S.E.A.T.M.: 1986, Solute transport parallel to an separating two different porous materials, Water Resour. Res. 22(13), 1779-1789.Google Scholar
  47. Vilker, V. L., Frommhagen, L. H., Kamda, R. and Sundaram, S.: 1978, Application of ion exchange/adsorption models to virus transport in percolating beds, AIChE Symp. Ser. 74(178), 84-92.Google Scholar
  48. Vilker, V. L.: 1981, Simulating virus movement in soils, in: I. K. Iskandar (ed.), Modeling Waste Renovation; Land Treatment, Wiley, New York, pp. 223-253.Google Scholar
  49. Yates, M. V. and Yates, S. R.: 1988, Modeling microbial fate in the subsurface environment, Crit. Rev. Environ. Control 17(4), 307-344.Google Scholar
  50. Yates, M. V. and Ouyang, Y.: 1992, VIRTUS: A model of virus transport in unsaturated soils, Appl. Environ. Microb. 58(5), 1609-1616.Google Scholar
  51. Zelikson, R.: 1994, Microorganisms and viruses in groundwater, in: U. Zoller (ed.), Groundwater Contamination and Control, Marcel Dekker, New York, pp. 425-436.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Youn Sim
    • 1
  • Constantinos V. Chrysikopoulos
    • 1
  1. 1.Department of Civil and Environmental EngineeringUniversity of CaliforniaIrvineU.S.A.

Personalised recommendations