mass transport: 2. Analysis of uncertainty in prediction

Abstract

The first paper in this series presented a description of a stochastic modeling concept for mass transport. In this paper we extend that analysis to consider a more realistic set of. transport conditions in a groundwater basin with geologic layering, hydraulic anisotropy, spatial variations in porosity, and geochemical retardation. Uncertainties in transport predictions can be characterized by frequency distributions formed on the time of arrival of mass at the water table, on the exit location, and on the quantity of mass arriving at the water table as a function of time. Results show that transport is highly sensitive to porous medium heterogeneities. Considerable uncertainty is possible in predicting the spatial and temporal distribution of mass. Porous medium parameters capable of changing both the magnitude and direction of advective transport are of primary importance in influencing predictive ability. Most important in this respect are the arrangement of units with different mean hydraulic conductivities, the standard deviation and spatial continuity of hydraulic conductivity, and the hydraulic anisotropy. In certain geologic systems, patterns of contaminant migration can be predicted with more certainty. Features such as layering and hydraulic anisotropism can constrain the flow of mass to specific directions, thus limiting the size of the region through which mass is likely to spread. Depending upon the relative time scales of the release function and the transport process, lack of information about the timing and concentrations added at the source may cause greater uncertainty than the heterogeneity. 1979] there now are sets of mathematical tools to tackle this problem.

Density-dependent dispersion in heterogeneous porous media Part I: A numerical study

“…1, but for small initial solute source sizes compared to the correlation scale, travel times need to be extremely large to reach the asymptotic limit. (3) Results differ greatly between individual porous medium realizations having the same stochastic parameters (Smith and Schwartz [37]). Therefore, to make predictions of solute concentrations in field situations (single realizations), not only ensemble averaged results are needed but also a measure of the deviation (uncertainty).…”

A Model of Quality Distribution in Groundwater With Reference to Natural Tritium Concentration

“…When both the specific discharge through a unit area in the vertical section and the concentration of tritium in pore water are separated into the spatial mean and the spatial fluctuation, the convective flux of tritium averaged over the vertical section includes a term which is the average of product of fluctuations in both the specific discharge and the concentration. This term, which represents just the above mentioned dispersion caused by the inhomogeneity of flow field, corresponds to the so-called macro-dispersion (e. g., Freeze, 1975;Bear, 1979;Smith and Schwartz, 1981).…”

“…Actually, the problem on the tritium distribution in groundwater flow systems has been left unsolved theoretically. Recently the problem on solute transport in inhomogeneous media has been investigated with stochastic modeling by several hydrologists (e. g., Freeze, 1975;Gelhar, et al, 1975;Smith and Schwartz, 1981;Dagan, 1982). In the present paper, a theoretical approach to the problem on the spatial distribution and time variation of tritium concentrations in an unconfined aquifer with a uniform input of tritium from precipitation will be made by investigating how far the influence of the dispersion due to inhomogeneity of media on the tritium distribution extends.…”

A stochastic analysis of pollutant movement in groundwater

“…In a series of three articles. Smith and Schwarz (1980, 1981a, 1981b determined that the major cause of dispersion in solute transport in porous media on a macroscopic scale was heterogeneity in hydraulic conductivity, not primarily a mechanical mixing process as represented in the advective-dispersive equation.…”

“…Anderson concluded that dispersion was not a mixing process in field studies where large distances are traversed by the pollutant. Smith and Schwarz (1981a) Smith and Schwarz (1981b) concluded their analyses by investigating the effect of the amount of field data available on uncertainty in prediction. They concluded that field data significantly decrease uncertainty in transport prediction only in a small area around the location of the data and that considerable data collection is required to significantly decrease prediction uncertainty.…”