Advertisement

Impact of Small-Scale Spatial Variability upon the Transport of Sorbing Pollutants

  • Albert J. Valocchi
  • Hernán A. M. Quinodoz
Conference paper
Part of the NATO ASI Series book series (volume 32)

Abstract

It is now widely recognized that groundwater aquifers exhibit significant three-dimensional, small-scale variability in their hydraulic properties and that this variability controls the migration and dispersion of contaminants at the field scale. Quantitative study of the impact of small-scale variability upon field-scale transport has been a central theme of groundwater research in recent years; this research has been motivated by a host of important questions. How can properties measured on small samples in the laboratory be extrapolated to larger scales? Are fundamental constitutive relations derived from studies at the laboratory scale valid at field scales? How can we quantify the inherent uncertainty in our information on spatially varying soil properties? What is the effect of this uncertainty upon the reliability of model predictions?

Keywords

Hydraulic Conductivity Heterogeneous Porous Medium Heterogeneous Aquifer Spatial Moment Pore Water Velocity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. ASCE Task Committee on Geostatistical Techniques (1990) Review of geostatistics in geo-hydrology. I: basic concepts. J Hydraul Eng 116:612–632.CrossRefGoogle Scholar
  2. Bahr JM (1989) Analysis of nonequilibrium desorption of volatile organics during a field test of aquifer decontamination. J Contam Hydrol 4:205–222.CrossRefGoogle Scholar
  3. Bear J (1979) Hydraulics of groundwater, McGraw-Hill, New York.Google Scholar
  4. Bellin A, Valocchi AJ, Rinaldo A (1991) Double peak formation in reactive solute transport in one-dimensional heterogeneous porous media. Quaderni del dipartimento IDR 1/1991, Dipartimento di Ingegneria Civile ed Ambientale, Università degli Studi di Trento.Google Scholar
  5. Black TC, Freyberg DL (1987) Stochastic modeling of vertically averaged concentration uncertainty in a perfectly stratified aquifer. Water Resour Res 23:997–1004.CrossRefGoogle Scholar
  6. Brenner H (1980) A general theory of Taylor dispersion phenomena, Physicochem Hydrodyn 1:91–123.Google Scholar
  7. Brenner H, Adler PM (1982) Dispersion resulting from flow through spatially periodic porous media, II, Surface and intraparticle transport, Philos Trans R Soc London Ser A 307:149–200.CrossRefGoogle Scholar
  8. Chrysikopoulis CV, Kitanidis PK, Roberts PV (1991 submitted) Macrodispersion of sorbing solutes in heterogeneous porous formations with spatially periodic retardation factor and velocity field. Water Resour Res.Google Scholar
  9. Chrysikopoulis CV, Kitanidis PK, Roberts PV (1992) Generalized Taylor-Aris moment analysis of the transport of sorbing solutes through porous media with spatially-periodic retardation factor. Transport in Porous Media 7:163–185.CrossRefGoogle Scholar
  10. Cvetkovic VD, Shapiro A (1990) Mass arrival of sorptive solute in heterogeneous porous media. Water Resour Res 26:2057–2068.CrossRefGoogle Scholar
  11. Dagan G (1986) Statistical theory of groundwater flow and transport: Pore to laboratory, laboratory to formation, formation to regional scale. Water Resour Res 22:120s–134s.CrossRefGoogle Scholar
  12. Dagan G (1989) Flow and transport in porous formations. Springer-Verlag, Berlin.Google Scholar
  13. Dagan G (1990) Transport in heterogeneous porous formations: spatial moments, ergodicity, and effective dispersion, Water Resour Res 26:1281–1290.CrossRefGoogle Scholar
  14. Dagan G (1991) Dispersion of a passive solute in non-ergodic transport by steady velocity fields in heterogeneous formations. J Fluid Mech 233:197–210.CrossRefGoogle Scholar
  15. Dagan G, Nguyen V (1989) A comparison of travel time and concentration approaches to modeling transport by groundwater, J Contam Hydrol 4:79–92.CrossRefGoogle Scholar
  16. Dagan G, Neuman SP (1991) Nonasymptotic behavior of a common Eulerian approximation for transport in random velocity fields, Water Resour Res 27:3249–3256.CrossRefGoogle Scholar
  17. de Marsily G (1986) Quantitative hydrogeology, Academic Press, Orlando Florida.Google Scholar
  18. Ene H (1990) Applicatiopn of the homogenization method to transport in porous media. In: Cushman JH (ed) Dynamics of fluids in hierarchical porous media. Academic Press, London, p 223–241.Google Scholar
  19. Frankel I, Brenner H (1989) On the foundations of generalized Taylor dispersion theory. J Fluid Mech 204:97–119.CrossRefGoogle Scholar
  20. Freyberg D (1986) A natural gradient experiment on solute transport in a sand aquifer, 2. Spatial moments and the advection and dispersion of nonreactive tracers. Water Resour Res 22:2031–2046.CrossRefGoogle Scholar
  21. Garabedian SP (1987) Large-scale dispersive transport in aquifers: field experiments and reactive transport theory. Ph.D. dissertation, Massachusetts Institute of Technology, Cambridge MA.Google Scholar
  22. Gelhar LW (1986) Stochastic subsurface hydrology from theory to applications. Water Resour Res 22:135s–145s.CrossRefGoogle Scholar
  23. Goltz M, Roberts PV (1987) Using the method of moments to analyze three-dimensional diffusion-limited solute transport from temporal and spatial perspectives. Water Resour Res 23:1575–1585.CrossRefGoogle Scholar
  24. Graham W, McLaughlin D (1989) Stochastic analysis of nonstationary subsurface transport, 2, conditional moments. Water Resour Res 25:2331–2355.CrossRefGoogle Scholar
  25. Guven O, Molz F, Melvill JG (1984) An analysis of dispersion in a stratified aquifer, Water Resour Res 10:1337–1354.CrossRefGoogle Scholar
  26. Hess K (1989) Use of a borehole flowmeter to determine spatial heterogeneity of hydraulic conductivity and macrodispersion in a sand and gravel aquifer, Cape Cod, Massachussets. In: Molz FJ, Melville JG, Guven O (eds) Proceedings of the conference on new field techniques for quantifying the physical and chemical properties of heterogeneous aquifers. National Water Well Association, Dublin OH, p 497-508.Google Scholar
  27. Kabala ZJ, Sposito G (1991) A stochastic model of reactive solute transport with time-varying velocity in a heterogeneous aquifer. Water Resour Res 27:341–350.CrossRefGoogle Scholar
  28. Keller RA, Giddings JC (1960) Multiple zones and spots in chromatography. J Chromatog 3:205–220.CrossRefGoogle Scholar
  29. Kinzelbach W (1987) The random walk method in pollutant transport simulation. In:Custodio E, et al. (eds) Groundwater flow and quality modeling. D Reidel, Dordrecht, p 227–245.Google Scholar
  30. Kitanidis, P.K. (1990) Effective hydraulic conductivity for gradually varying flow. Water Resour Res 26:1197–1208.CrossRefGoogle Scholar
  31. LeBlanc DR, Garabedian SP, Hess KM, Gelhar LW, Quadri RD, Stollenwerk KG, Wood WW (1991) Large-scale natural gradient test in sand and gravel, Cape Cod, Massachusetts, 1, experimental design and observed tracer movement. Water Resour Res 27:895–910.CrossRefGoogle Scholar
  32. MacQuarrie KTB, Sudicky EA (1990) Simulation of biodegradable organic contaminants in groundwater, 2, Plume behavior in uniform and random flow fields. Water Resour Res 26:223–240.Google Scholar
  33. Mantoglou A, Wilson J (1982) The turning bands method for simulation of random fields using line generation by a spectral method. Water Resour Res 18:1379–1394.CrossRefGoogle Scholar
  34. McQuarrie DA (1963) On the stochastic theory of chromatography. J Chem Phys 38:437–435.CrossRefGoogle Scholar
  35. Neuman SP (1990) Universal scaling of hydraulic conductivities and dispersivities in geologic media. Water Resour Res 26:1749–1758.CrossRefGoogle Scholar
  36. Neuman SP, Zhang YK (1990) A quasi-linear theory of non-Fickian subsurface dispersion, 1, Theoretical analysis with application to isotropic media. Water Resour Res 26:887–902.Google Scholar
  37. Nkedi-Kizza P, Biggar JW, Selim HM, van Genuchten M Th, Wierenga PJ, Davidson JM, Nielsen DR (1984) On the equivalence of two conceptual models for describing ion exchange during transport through an aggregated oxysol, Water Resour Res 20:1123–1130.CrossRefGoogle Scholar
  38. Quinodoz HAM, Valocchi AJ (1990) Macrodispersion in heterogeneous aquifers: numerical experiments. In: Moltyaner G (ed) Transport and mass exchange processes in sand and gravel aquifers: field and modelling studies. Atomic Energy of Canada Limited, Chalk River Ontario, p 455-468.Google Scholar
  39. Quinodoz HAM, Valocchi AJ (1992 submitted) Stochastic analysis of the transport of kinetically adsorbing solutes in randomly heterogeneous aquifers. Water Resour Res.Google Scholar
  40. Robin MJL, Sudicky EA, Gillham RW, Kachanoski RG (1991) Spatial variability of strontium distribution coefficients and their correlation with hydraulic conductivity in the CFB Borden aquifer. Water Resour Res 27:2619–2632.CrossRefGoogle Scholar
  41. Rubin Y (1991) Transport in heterogeneous porous media: prediction and uncertainty. Water Resour Res 27:1723–1738.CrossRefGoogle Scholar
  42. Sardin M, Schweich F, Leij FJ, van Genuchten MTh (1991) Modeling the nonequilibrium transport of linearly interacting solutes in porous media: a review. Water Resour Res 27:2287–2307.CrossRefGoogle Scholar
  43. Schaefer W, Kinzelbach W (1992 in press) Stochastic modeling of in situ bioremediation in heterogeneous aquifers. J Contam Hydrol.Google Scholar
  44. Semprini L, Roberts PV, Hopkins GD, McCarty PL (1990) Afield evaluation of in-situ biodegradation of chlorinated ethenes: part 2, results of biostimulation and biotransformation experiments. Ground Water 28:715–727.CrossRefGoogle Scholar
  45. Shapiro M, Brenner H (1988) Dispersion of a chemically reactive solute in a spatially periodic model of a porous medium, Chem Eng Sci 43:551–571.CrossRefGoogle Scholar
  46. Sudicky EA (1986) A natural gradient tracer experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process. Water Resour Res 22:2069–2082.CrossRefGoogle Scholar
  47. Sudicky EA, Huyakorn P (1991) Contaminant migration in imperfectly known heterogeneous groundwater systems. In: Reviews of Geophysics, Supplement, April, p. 240-253.Google Scholar
  48. Taylor GI (1921) Diffusion by continuous movements, Proc London Math Soc 2:196–212.Google Scholar
  49. Taylor GI (1953) The dispersion of matter in a solvent flowing slowly through a tube, Proc R Soc London Ser A 219:189–203.Google Scholar
  50. Tompson AFB, Dougherty DE (1988) On the use of particle tracking methods for solute transport in porous media. In: Celia MA, et al. (eds) Computational methods in water resources, Vol. 2, Numerical methods for transport and hydrologic processes. Elsevier, Amsterdam, p 227-232.Google Scholar
  51. Tompson AFB, Gelhar LW (1990) Numerical simulation of solute transport in three-dimensional, randomly heterogeneous porous media, Water Resour Res 26:2541–2562.CrossRefGoogle Scholar
  52. Tompson AFB, Ababou R, Gelhar LW (1989) Implementation of the three-dimensional Turning Band random field generator. Water Resour Res 25:2227–2244.CrossRefGoogle Scholar
  53. Valocchi AJ (1988) Theoretical analysis of deviations from local equilibrium during sorbing solute transport through idealized stratified aquifers. J Contam Hydrol 2:191–207.CrossRefGoogle Scholar
  54. Valocchi AJ (1989) Spatial moment analysis of the transport of kinetically adsorbing solutes through stratified aquifers. Water Resour Res 25:273–279.CrossRefGoogle Scholar
  55. Valocchi AJ (1990a) Use of temporal moment analysis to study reactive solute transport in aggregated porous media. Geoderma 46:233–247.CrossRefGoogle Scholar
  56. Valocchi AJ (1990b) Numerical simulation of the transport of adsorbing solutes in heterogeneous aquifers. In: Gambolati G, et al. (eds) Computational methods in subsurface hydrology. Springer-Verlag, Berlin, p. 373–382.Google Scholar
  57. Valocchi AJ, Quinodoz HAM (1989) Application of the random walk method to simulate the transport of kinetically adsorbing solutes. In: Abriola LM (ed) Groundwater contamination, IAHS Publ. No. 185, p 35-42.Google Scholar
  58. van der Zee SEATM, van Riemsdijk WH (1987) Transport of reactive solutes in spatially variable soil systems. Water Resour Res 23:2059–2069.CrossRefGoogle Scholar
  59. van Genuchten MTh (1985) A general approach for modeling solute transport in structured soils. In: Hydrology of rocks of low permeability. Proceedings of the 17th international congress. Intl Assoc Hydrogeol 17:513–526.Google Scholar
  60. Vomvoris E, Gelhar LW (1990) Stochastic analysis of the concentration variability in a three-dimensional, randomly heterogeneous porous media. Water Resour Res 26:2591–2602.Google Scholar
  61. Wood WW, Kraemer TF, Hearn P (1990) Intragranular diffusion: an important mechanism influencing solute transport in clastic aquifers? Science 247:1569–1572.PubMedCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Albert J. Valocchi
    • 1
  • Hernán A. M. Quinodoz
    • 1
  1. 1.Department of Civil EngineeringUniversity of IllinoisUrbanaUSA

Personalised recommendations