This paper applies stochastic methods to the analysis and prediction of solute transport in heterogeneous saturated porous media. Partial differential equations for three unconditional ensemble moments (the concentration mean, concentration covariance, and velocity concentration cross covariance) are derived by applying perturbation techniques to the governing transport equation for a conservative solute. Concentration uncertainty is assumed to be the result of unmodeled small-scale fluctuations in a steady state velocity field. The moment expressions, which describe how each moment evolves over time and space, resemble the classic deterministic advection-dispersion equation and can be solved using similar methods. A solution procedure based on a Galerkin finite element algorithm is illustrated with a hypothetical two-dimensional example. For this example the required steady state velocity statistics are obtained from an infinite domain spectral solution of the stochastic groundwater flow equation. The perturbation solution is shown to reproduce the statistics obtained from a Monte Carlo simulation quite well for a natural log conductivity standard deviation of 0.5 and moderately well for a natural log conductivity standard deviation of 1.0. The computational effort required for a perturbation solution is significantly less than that required for a Monte Carlo solution of acceptable accuracy. Sensitivity analyses conducted with the perturbation approach provide qualitative confirmation of a number of results obtained by other investigators for more restrictive special cases. 215 216 GRAHAM AND McLAUGHLIN.' STOCHASTIC SUBSURFACE SOLUTE TRANSPORT examples include studies by Freeze [1975], Sagar [1978], Smith and Freeze [1979a, b], Bakr et al. [1978], Gutjahr and Gelhar [1981], Dettinger and Wilson [1981], Dagan [1982a, b], Townley and Wilson [1985], and McLaughlin and Wood [1988a, b]. The application of derived head statistics to Bayesian estimation is discussed by Dagan [1982b-!, Hoeksema and Kitanidis [1985], and Gutjahr and Wilson [1985].The basic concepts used in the above studies of groundwater flow extend naturally to solute transport. In this case, the ensemble concentration moments may be derived from velocity statistics which may, in turn, be derived from the ensemble moments of the hydraulic conductivity field. Much of the research in stochastic solute transport has emphasized evaluations of concentration statistics and related macrodispersivity coefficients for the special case of onedimensional flow through perfectly layered random media [Gelhat et al., 1979;Matheron and de Marsily, 1980; Gelhat et al., 1981;Black and Freyberg, 1987]. Our interest here is in more general multidimensional problems similar to the one investigated by Smith and Schwartz [1980, 1981]. They used Monte Carlo techniques to investigate solute transport in a finite two-dimensional domain with a spatially correlated hydraulic conductivity field. The synthetically generated concentration distributions obtained in this study were v...

No abstract

The coupled transport process through an integrated soil-groundwater system is quantified for kinetically sorbing solute that originates from a time dependent source at the soil surface and is transported by steady random velocity. The derived expressions of ensemble mean solute breakthrough at some arbitrary control plane normal to the mean flow direction involve probability density functions (pdfs) of advective solute travel time through the unsaturated and the saturated zone of the transport domain. A nonstationary travel time pdf is derived for the saturated zone, to account for possible effects of flow nonuniformity due to recharge of water from the unsaturated zone. Nonuniform mean flow in the saturated zone decreases the relative influence of spatial variability within that zone on the ensemble mean solute breakthrough curve. Factors such as the longitudinal extent of the solute source and the unsaturated zone variability become more important for the spreading of the expected solute breakthrough as the degree of flow nonuniformity in the saturated zone increases. This implies that possible far-field simplifications based on the assumption that the transport process in an integrated soil-groundwater system is dominated by the transport conditions in the saturated zone may not be valid in cases with significant groundwater recharge from the unsaturated zone. 1981; Small and Mular, 1987; van der Zee and van Riemsdijk, 1987; Jury and Gruber, 1989; Destouni and Cvetkovic, 1991; Russo, 1993], or plume migration and solute breakthrough in the saturated zone resulting from point sources or sources that are distributed normal to the mean flow direction in that zone [Groundwater contamination, however, may often be the result of sources that are located at the soil surface, such as agricultural fields, waste deposits, or accidental spills. The transport domain of interest in these cases is the integrated soil-groundwater system. The unsaturated zone then acts as a source of water and solute for the transport process in the saturated zone. The solute flux from the unsaturated and into the saturated zone is the mechanism that couples the transport processes in the two subsurface systems. A general framework for quantifying the statistics of solute flux in heterogeneous porous formations was presented by Dagan et al. [1992]. This framework has been used for describing solute transport in both the unsaturated [Destouni, 1992, Copyright 1995 by the American Geophysical Union. Paper number 95WR01330. 0043-1397/95/95WR-01330505.00 1993a, b; Russo, 1993] and the saturated [Cvetkovic et al., 1992] zone and has been extended to reactive solute transport by Cvetkovic and Dagan [1994]. The framework is based on a Lagrangian representation of the transport process, in which molecular diffusion and local dispersion within the mobile water are neglected. Under these conditions, the solute flux statistics can be quantified at an arbitrary control plane (CP) normal to the mean flow direction as functions of the one-and two-particle...

The purpose of the present study was to conduct a comprehensive field-scale investigation to evaluate the effectiveness of the in situ cosolvent flushing technique for enhanced remediation of aquifers contaminated with residual NAPLs. Limitations or difficulties related to larger-scale applications were 2673

No abstract