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A. Bakr, L. Gelhar, A. Gutjahr, J. Macmillan (1978)
Stochastic analysis of spatial variability in subsurface flows: 1. Comparison of one‐ and three‐dimensional flowsWater Resources Research, 14
Warren Warren, Skiba Skiba (1964)
Macroscropic dispersionSoc. Petrol. Eng. J.
R. Stallman (1972)
Subsurface Waste Storage--the Earth Scientist's Dilemma, 75
Simpson Simpson (1978)
A note on the structure of the dispersion coefficientGeol. Soc. Amer. Abstr. Program, 10
James Smith (1978)
A stochastic analysis of steady-state groundwater flow in a bounded domain
E. Holley, Y. Tsai (1977)
Comment on ‘Longitudinal dispersion in natural channels’ by Terry J. DayWater Resources Research, 13
A. Scheidegger (1954)
Statistical Hydrodynamics in Porous MediaJournal of Applied Physics, 25
Scheidegger Scheidegger (1964)
Statistical hydrodynamics in porous mediaAdvan. Hydrosci., 1
T. Day (1977)
Reply [to “Comment on ‘Longitudinal dispersion in natural channels’ by Terry J. Day”]Water Resources Research, 13
D. Tang, G. Pinder (1977)
Simulation of groundwater flow and mass transport under uncertaintyAdvances in Water Resources, 1
J. Bear (1975)
Dynamics of Fluids in Porous MediaSoil Science, 120
L. Smith, R. Freeze (1979)
Stochastic analysis of steady state groundwater flow in a bounded domain: 2. Two‐dimensional simulationsWater Resources Research, 15
F. Schwartz (1977)
Macroscopic dispersion in porous media: The controlling factorsWater Resources Research, 13
S. Ahlstrom, H. Foote, R. Arnett, C. Cole, R. Serne (1977)
Multicomponent mass transport model: theory and numerical implementation (discrete-parcel-random-walk version)
Conventional modeling of mass transport in groundwater systems usually involves use of the dispersion‐convection equation with large values of porous medium dispersivity to account for macroscopic dispersion. This work describes a modeling concept which accounts for macroscopic dispersion not as a large‐scale diffusion process but as mixing caused by spatial heterogeneities in hydraulic conductivity. The two‐dimensional spatially autocorrelated hydraulic conductivity field is generated as a first‐order nearest‐neighbor stochastic process. Analysis of a variety of hypothetical media shows that over finite domains a population of tracer particles convected through this statistically homogeneous conductivity field does not have the normal distribution and does not yield the constant dispersivity that classic theory would predict. This problem occurs because of insufficient spatial averaging in the macroscopic velocity field by the moving tracer particles. Our analyses suggest that the diffusion model for macroscopic dispersion may be inadequate to describe mass transport in geologic units. Sensitivity analysis with the model has shown that features of transport, such as first arrival of a tracer, are dependent on porous medium structure and that even when the statistical features of porous media are known, considerable uncertainty in the model result can be expected.
Water Resources Research – Wiley
Published: Apr 1, 1980
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