Time‐dependent macrodispersion for solute transport in anisotropic heterogeneous aquifers

Abstract

The expected values of the spatial second‐order moments of a solute body transported by groundwater are derived for flow through heterogeneous formations of a stationary random anisotropic structure. They are based on a general formulation, which reduces to most existing results in the literature as particular cases. Detailed results are given for the spatial variance as a function of time in the case of axisymmetric anisotropy, average flow parallel to the plane of isotropy, first‐order approximation in the log conductivity variance σY2, and high Peclet numbers. These results fill the gap existing between the studies of Dagan (1982, 1984), on one hand, and those of Gelhar and Axness (1983) and Neuman et al. (1987), on the other. A preliminary investigation of the higher‐order effects in σY2 suggests that the use of the first‐order approximations is warranted, at present, only for σY2 ≪ 1. The impact of the errors of estimation of the parameters on which transport depends is briefly analyzed.

Effective Parameters, Effective Processes: From Porous Flow Physics to In Situ Remediation Technology

“…The recent hydrogeology literature abounds with efforts to derive macroscopic solute dispersion from the underlying advective and mixing processes in random fields (Sahimi et al, 1986a, b;Dagan, 1988). Most work in this area has been limited to solute transport in single-phase flow.…”

Measurement of anisotropic hydraulic conductivity in unconsolidated sands: A case study from a shoreface deposit, Oyster, Virginia

“…It has been generally recognized that the spreading of contaminant plumes in the subsurface is controlled by the spatial distribution of hydraulic conductivity [Gelhat and Axeness, 1983;Dagan, 1988]. In sedimentary deposits, structures such as grain fabric, bedding, and laminations have been shown to affect the magnitude of hydraulic conductivity (K) as well as its anisotropy [Mast and Potter, 1963].…”

Comment on “A note on the recent natural gradient tracer test at the Borden site” by R. L. Naff, T.‐C. Jim Yeh, and M.W. Kemblowski

“…For some reason, Naff et al [1988] have not considered these measurements in their analysis. The two main findings set forth by Sudicky [1986] and Freyberg [1986] Dagan [1988] shows that for threedimensional structures, X22 and X33 tend to constant values, which are quite small for the values of tr 2 r and Ih inferred by Sudicky [1986]. Even if one supplements X22 and X33 by the linearly growing terms related to pore-scale dispersion or the cross terms in the latter and in tr2r of Gelhat and Axness [1983] or Neuman et al [1987], the figures are still much smaller than the measured X22.…”

“…In particular, this is true for a two-dimensional transport model [Dagan, 1982[Dagan, , 1984[Dagan, , 1987Freyberg, 1986] or a three-dimensional one for a anisotropic log conductivity covariance [Gelhar and Axness, 1983]. This writer completely agrees with the authors reasoning and herein are some additional arguments, based on recent publications.In a theoretical study of the statistical moments of the solute particles displacements [Dagan, 1988] …”

“…In a theoretical study of the statistical moments of the solute particles displacements [Dagan, 1988] …”