Transport in three‐dimensionally heterogeneous aquifers: 2. Predictions and observations of concentration fluctuations

Abstract

For a multidimensional finite-size impulse input, analytical solutions to the conservation equation for concentration variance Crc 2 are presented. Due to the dissipating action of local dispersion, at large times, cr c is a decreasing fraction of the mean concentration. The Cape Cod bromide tracer exhibits this decrease. The larger the log conductivity microscale is, the slower is the action of local dispersion, and the slower is the predicted rate of decrease of the ratio of cr c and the mean concentration (i.e., the coefficient of variation) with time, at large times, and vice versa. The coefficient of variation increases with distance from the center. A balance between the 2 relates it linearly to the squared gradients of rates of production and dissipation of cr c the mean concentration field, away from the center of mass. For the zero local dispersion case, rr c is an unboundedly growing multiple with time of the mean concentration. The longitudinal spatial second moment and macrodispersivities are insensitive to the inclusion/exclusion of local dispersion and therefore do not differentiate between the concentration fields for the two different cases. In contrast, 2 is singularly determined by the dissipating action the spatial-temporal evolution of rr c of local dispersion. Measurements of local dispersivities need to be made along with a characterization of hydraulic conductivity variations to assess contarninant concentrations in aquifers. KAPOOR AND GELHAR: THREE-DIMENSIONALLY HETEROGENEOUS AQUIFERS, 2

Advection-diffusion in spatially random flows: Formulation of concentration covariance

“…Under pure advection, IIc~[l, the spatially integrated concentration variance (globat variance) is non-decreasing: that follows from (b9) of Appendix B, in conjunction with (bll), and (b12)), as shown in Kapoor and Gelhar [1994b] (their equations 46 through 48). II((c-¢)7)11 provides an estimate of I1~11.…”

“…However when the diffusion coefficient was set to zero the concentration CV kept increasing without any bound just like that predicted in a classical pure advection Lagrangian result. Analysis of bromide tracer data at Cape Cod (Kapoor and Gelhar, 1994b), and subsequent numerical simulations Kitanidis, 1996, 1997) have exhibited the decrease in the CV at large times. A covariance analysis can lead to an assessment of the variance destruction term in greater detail, without the assumptions of Kapoor and Gelhar [1994a,b], and yield a better theoretical understanding of the variance problem.…”

“…If the macrodispersive flux of the covariance is included, then the concentration variance at the center of mass is not zero. In fact, the concentration variance, at the center of mass, becomes the maximum concentration variance, without local dispersion, as time progresses, if its macrodispersive flux is not dropped (contained in both Dagan, 1989;Kapoor and Gelhar 1994b). Therefore, the covariance macrodispersive flux needs to be included to obtain a qualitatively correct description of concentration fluctuations.…”

The Role of Dispersion in Radionuclide Transport - Data and Modeling Requirements: Revision No. 1

“…He cautions, however, that his results apply at large time scales of t >> l 2 /D d where l is the initial transverse dimension of the plume. Using the NTS as an example, where l may be on the order of two times the cavity radius (150 m) and local dispersion is on the order of 0.5 to 18 square meters per year (m 2 /yr) (based on D=Vα with a velocity estimate using minimum travel times of 11 to 27 years [no radionuclides in Oasis Valley yet]), distances of 24 to 40 km, and local dispersivities of 0.005 to 0.0005 m (Kapoor and Gelhar, 1994b), the times must be much greater than 1,200 to 50,000 years before the results of Fiori apply. This would suggest that work of Fiori (2001) will not apply at the NTS over the 1,000-year time scale of interest.…”

Generalized random walk algorithm for the numerical modeling of complex diffusion processes

“…First, the existence of effective diffusion coefficients (5.2) and self-averaging property (5.3) must be checked. Further, the fluctuations of concentration in individual realizations should be studied, in order to find the superior bound which delimits the "unsafe zone" [11] . Both problems are difficult to be solved and they imply high computing resources.…”