Skip to main content
SpringerLink
Log in

Stochastic Analysis of Macrodispersion in a Semi‐Confined Aquifer

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

Abstract

In this paper, the macroscopic dispersion resulting from one‐ and two‐dimensional flows through a semi‐confined aquifer with spatially variable hydraulic conductivity K which is represented by a stationary (statistically homogeneous) random process is analyzed using the spectral representation technique. Stochastic fluctuation equations of the steady flow and solute transport are solved to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of the leakage factor and input covariances describing the hydraulic conductivity in a semi‐confined aquifer bounded by a leaky layer above and an impervious stratum below. The macrodispersivity tensor is studied using some convenient forms of the log hydraulic conductivity process. The sensitivity of the resulting macrodispersivity to the input covariances is discussed along with the influence of the leakage factor for both one‐ and two‐dimensional flows. It is found that the longitudinal macrodispersivities are increased due to the presence of leakage, while the transverse macrodispersivities are reduced due to leakage.

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

  • Adams, E. E. and Gelhar, L. W.: 1992, Field study of dispersion in a heterogeneous aquifer, 2, Spatial moment analysis, Water Resour. Res. 28(12), 3293–3307.

    Google Scholar 

  • Bakr, A. A., Gelhar, L. W., Gutjahr, A. L. and MacMillan, J. R.: 1978, Stochastic analysis of spatial variability in subsurface flows, 1, Comparison of one-and three-dimensional flows, Water Resour. Res. 14(12), 263–271.

    Google Scholar 

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

    Google Scholar 

  • Boggs, J. M. and Adams, E. E.: 1992, Field study of dispersion in a heterogeneous aquifer, 4, Investigation of adsorption and sampling bias, Water Resour. Res. 28(12), 3325–3336.

    Google Scholar 

  • Boggs, J. M., Young, S. C., Beard, L. M., Gelhar, L. W., Rehfeldt, K. R. and Adams, E. E.: 1992, Field study of dispersion in a heterogeneous aquifer, 1, Overview and site description, Water Resour. Res. 28(12), 3281–3291.

    Google Scholar 

  • Curtis, G. P., Roberts, P. V. and Reinhard, M.: 1986, A natural gradient experiment on solute transport in a sand aquifer, 4, Sorption of organico and its influence on mobility, Water Resour. Res. 22(13), 2059–2067.

    Google Scholar 

  • Dagan, G.: 1984, Solute transport in heterogeneous porous formations, J. Fluid Mech. 145, 151–171.

    Google Scholar 

  • Dagan, G.: 1985, A note on higher-order correction of the head covariance in steady aquifer flow, Water Resour. Res. 21(4), 573–578.

    Google Scholar 

  • Dagan, G.: 1986, Statistical theory of groundwater flow and transport: Pore to laboratory, laboratory to formation, and formation to regional scale, Water Resour. Res. 22(9), 120S–134S.

    Google Scholar 

  • Dagan, G.: 1987, Theory of solute transport by groundwater, Ann. Rev. Fluid Mech. 19, 183–215.

    Google Scholar 

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

    Google Scholar 

  • Dagan, G.: 1994, The significance of heterogeneity of evolving scales to transport in porous formations, Water Resour. Res. 30(12), 3327–3336.

    Google Scholar 

  • Freyberg, D. L.: 1986, A natural gradient experiment on solute transport in a sand aquifer, 2, Spatial moments and the advection dispersion of nonreactive tracers,Water Resour. Res. 22(13), 2031–2046.

    Google Scholar 

  • Garabedian, S. P., LeBlanc, D. R., Gelhar, L.W. and Celia, M. A.: 1991, Large-scale natural-gradient tracer test in sand and gravel, Cape Cod, Massachustts, 2, Analysis of spatial moments for a nonreactive tracer, Water Resour. Res. 27(5), 911–924.

    Google Scholar 

  • Gelhar, L.W.: 1986, Stochastic subsurface hydrology from theory applications, Water Resour. Res. 22(9), 135S–145S.

    Google Scholar 

  • Gelhar, L. W.: 1993, Stochastic Surface Hydrology, Prentice Hall, Englewood Cliffs, New Jersey.

    Google Scholar 

  • Gelhar, L. W. and Axness, C. L.: 1983, Three-dimensional stochastic analysis of macrodispersion in aquifers, Water Resour. Res. 19(1), 161–180.

    Google Scholar 

  • Gelhar, L. W., Gutjahr, A. L. and Naff, R. L.: 1979, Stochastic analysis of macrodispersion in a stratified aquifer, Water Resour. Res. 15(6), 1387–1397.

    Google Scholar 

  • Gelhar, L.W., Welty, C. and Rehfeldt, K. R.: 1992, A critical review of data on field-scale dispersion in aquifers, Water Resour. Res. 28(7), 1955–1974.

    Google Scholar 

  • Gutjahr, A. L. and Gelhar, L. W.: 1981, Stochastic models of subsurface flow: Infinite versus finite domains and stationarity, Water Resour. Res. 17(2), 337–350.

    Google Scholar 

  • Gutjahr, A. L., Gelhar, L. W., Bakr, A. A. and MacMillan, J. R.: 1978, Stochastic analysis of spatial variability in subsurface flows, 2, Evaluation and application, Water Resour. Res. 14(5), 953–959.

    Google Scholar 

  • Hess, K. M., Wolf, S. H., and Celia, M. A.: 1992, Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts, 3, Hydraulic conductivity and calculated macrodispersivities, Water Resour. Res. 28(8), 2011–2027.

    Google Scholar 

  • Killey, R. W. D. and Moltyaner, G. L.: 1988, Twin Lake tracer tests: Setting, methodology, and hydraulic conductivity distribution, Water Resour. Res. 24(10), 1585–1612.

    Google Scholar 

  • LeBlanc, D. R., Garabedian, S. P., Hess, K. M., Gelhar, L. W., Quadri, R. D., Stoolenwerk, K. G. and Wood, W. W.: 1991, Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts, 1, Experimental design and observed tracer movement,Water Resour. Res. 27(5), 895–910.

    Google Scholar 

  • Lumley, J. L. and Panofsky, H. A.: 1964, The Structure of Atmospheric Turbulence, Wiley, New York.

    Google Scholar 

  • Mackay, D. M., Freyberg, D. L. and Roberts, P. V.: 1986, A natural gradient experiment on solute transport in a sand aquifer, 1, Approach and overview of plume movement, Water Resour. Res. 22(13), 2017–2029.

    Google Scholar 

  • Mackay, D. M., Bianchi-Mosquera, G., Kopania, A. A., Kianjah, H. and Thorbjarnarson, K. W.: 1994, A forced-gradient experiment on solute transport in the Borden aquifer, 1, Experimental method and moment analyses of results, Water Resour. Res. 30(2), 369–383.

    Google Scholar 

  • Moltyaner, G. L.: 1987, Mixing cup and through-the-well measurements in field-scale tracer tests and their related scales of averaging, J. Hydrol. 89, 281–302.

    Google Scholar 

  • Moltyaner, G. L. and Killey, R. W. D.: 1988a, Twin Lake tracer tests: Longitudinal dispersion, Water Resour. Res. 24(10), 1613–1627.

    Google Scholar 

  • Moltyaner, G. L. and Killey, R.W. D.: 1988b, Twin Lake tracer tests: Transverse dispersion, Water Resour. Res. 24(10), 1628–1737.

    Google Scholar 

  • Molz, F. J., Guven, O. and Melville, J. G.: 1983, An examination of scale-dependent dispersion coefficients, Ground Water 21, 715–725.

    Google Scholar 

  • Pickens, J. F. and Grisak, G. E.: 1981, Scale-dependent dispersion in a stratified granular aquifer, Water Resour. Res. 17(4), 1191–1211.

    Google Scholar 

  • Rehfeldt, K. R., Boggs, J. M. and Gelhar, L.W.: 1992, Field study of dispersion in a heterogeneous aquifer, 3, Geostatistical analysis of hydraulec conductivity, Water Resour. Res. 28(12), 3309–3324.

    Google Scholar 

  • Roberts, P. V., Goltz, M. N. and Mackay, D. M.: 1986, A natural gradient experiment on solute transport in a sand aquifer, 3, Retardation estimates and mass balance for organics solutes,Water Resour. Res. 22(13), 2047–2058.

    Google Scholar 

  • Sauty, J. P.: 1980, An analysis of hydrodispersive transfer in aquifers, Water Resour. Res. 16(1), 145–158.

    Google Scholar 

  • Strack, O. D. L.: 1989, Groundwater Mechanics, Prentice-Hall, New Jersey.

    Google Scholar 

  • Sudicky, E. A.: 1986, A natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process, Water Resour. Res. 22(13), 2069–2082.

    Google Scholar 

  • Thorbjarnarson, K.W. and Mackay, D. M.: 1994a, A forcec-gradient experiment on solute transport in the Borden aquifer, 2, Transport and dispersion of the conservative tracer, Water Resour. Res. 30(2), 385–399.

    Google Scholar 

  • Thorbjarnarson, K.W. and Mackay, D. M.: 1994b, Aforced-gradient experiment on solute transport in the Borden aquifer, 3, Nonequilibrium transport of the sorbing organic compounds, Water Resour. Res. 30(2), 401–419.

    Google Scholar 

  • Wheatcraft, S. W. and Tyler, S. W.: 1988, An explanation of scale dependent dispersivity in heterogeneous aquifers using concepts of fractal geometry, Water Resour. Res. 24(4), 566–578.

    Google Scholar 

  • Zhu, J.: 1995: Stochastic analysis and numerical simulation of groundwater flowand solute transport in semiconfined aquifers, PhD Thesis, Technical University of Nova Scotia, Halifax, Canada.

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Dalhousie University, Halifax, Nova Scotia, Canada, B3J 2X4

    Jianting Zhu & Mysore G. Satish

Authors
  1. Jianting Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mysore G. Satish
    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

Zhu, J., Satish, M.G. Stochastic Analysis of Macrodispersion in a Semi‐Confined Aquifer. Transport in Porous Media 35, 273–297 (1999). https://doi.org/10.1023/A:1006501308769

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1006501308769

Search

Navigation