Comment on “A natural gradient experiment on solute transport in a sandy aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process” by E. A. Sudicky

In the first part of this study, Sposito and Barry (1987) derived an ensemble-mean convectiondispersion equation (CDE) for tracer solute transport subject to a random velocity field. It was shown that the model dispersion coefficients originally presented by Dagan (1984) could be derived from the general expression for the dispersion coefficients in this mean CDE. Under the assumption of ergodicky, the Dagan model is used in this paper to predict chloride and bromide concentrations in the welldocumented Borden aquifer experiment reported by Roberts and Mackay (1986). Because of a possible influence on the solute from the upper aquifer boundary, it was appropriate to apply the twodimensional form of the model. A number of steps was necessary to reduce the three-dimensional raw data to a two-dimensional form, the main ones being integration over the vertical axis and the use of a gridding algorithm to form a two-dimensional solute concentration surface. Incomplete sampling of the solute plume during the early sampling sessions, as well as the assumptions made with respect to the data analysis, produce a rather large degree of uncertainty in the specification of the initial solute plume. These factors hinder a thorough experimental evaluation of the Dagan model. Data from some of the later sampling sessions were more complete, however, and the model predictions appeared to agree well with the field concentration data, especially in the preasymptotic region for the longitudinal dispersion coefficient. INTRODUCTION A number of field experiments and theoretical descriptions o[ solute dispersion in groundwater aquifers has demonstrated the inadequacy of using a constant dispersion coefficient in the convection-dispersion equation (CDE) for the purpose of modeling field scale solute transport [Anderson, 1979; Matheron and de Marsily, 1980; Pickens and Grisak, 1981; Sudicky et al., 1983; Da•Tan, 1984, 1986; Giiven et al., 1984; Thompson et al., 1984; Roberts and Mackay, 1986; Frind and Hokkanen, 1987; Frind et al., 1987]. One theoretical approach to overcoming this problem, although it creates significant unresolved mathematical questions itself, has been to model the solute convection velocity in an aquifer as a single realization of a random function, such that the CDE becomes a stochastic partial differential equation [Sposito et al., 1986]. This approach was adopted in the first part of the present study [Sposito and Barry, 1987] to derive a CDE for the ensemble mean concentration of a conservative solute transported in an incompressible liquid whose velocity in a porous medium is a wide-sense stationary, stochastic process parameterized by space and time coordinates. The cumulant expansion technique used to derive the mean CDE led to a general, time-dependent expression for the solute dispersion coefficients in terms of' the solute velocity autocorrelation function. This expression, by virtue of different choices of model for the autocorrelation function, could be specialized to reproduce the equations for time-depen...

Section: Discussionmentioning

confidence: 99%

On the Dagan Model of solute transport in groundwater: Application to the Borden Site

Barry¹,

Coves²,

Sposito³

1988

“…Given this sample volume and taking into account the porosity, the measured concentration is representative of an average within a sphere surrounding the point of extraction that is of the order of Sudicky's estimated vertical correlation of ln( K ) equal to 0.12. Following from Kemblowski [1988, equation (7)] or Dagan [1989a, equation (4.7.1)], the reduction of the variance of a vertically graded (averaged) process would consequently be a factor of 2 e −1 or 0.74. Sudicky [1988] uses this logic in arguing support for the use of a leading constant β = 0.74 in his model for plume spreading, as was suggested to him by Dagan.…”

Section: Metrics Characterizing the Plume Spreading Observed In The Bmentioning

confidence: 99%

“…The models of Dagan [1987] and Gelhar and Axness [1983] which Sudicky [1986] evaluated are based on the integral scale, traditionally determined by fitting model curves to sample bivariate statistics computed from large numbers of spatially distributed permeability data. Discussion of the spatial bivariate correlation of log conductivity and modeling it, including estimating its integral scale, can be found in work by Kemblowski [1988], Sudicky [1988], Woodbury and Sudicky [1991], Turcke and Kueper [1996], and Ritzi and Allen‐King [2007]. Modeling the spatial bivariate correlation is problematic.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Linking hierarchical stratal architecture to plume spreading in a Lagrangian‐based transport model: 2. Evaluation using new data from the Borden site

Ramanathan

Ritzi

Allen‐King

2010

[1] A new data set collected at the well-documented Borden research site was used in order to evaluate a newly published but as yet untested idea for stochastic modeling (Ramanathan et al., 2008). The new data set reveals the stratal architecture of the Borden aquifer and allowed us to determine how the stratal architecture, at different scales, controlled the macrodispersion observed in the original natural gradient tracer test. The newly published idea for modeling uses a Lagrangian-based model for the particle displacement variance developed from independent, physically based, quantifiable univariate statistics, including the proportions and mean length of the strata. The method for defining model parameters avoids the often equivocal step of fitting sample bivariate permeability statistics. The model parameters were developed from the new data from the Borden site. The new data included geologic data in much greater abundance than permeability data. There are two scales of unit types delineated in a hierarchy of stratal architecture. Their shapes are complex, not simple layers or lenses. The method facilitated the direct use of both geologic and permeability data, which need not be collocated. The dispersion model developed from these data represents the field-measured particle displacement variance that occurred in the natural gradient tracer test well. The contributions to time-dependent macrodispersion by strata at each scale were computed and analyzed independently. This analysis revealed that macrodispersion at the Borden site is primarily controlled by the proportions, and the mean and variance in length of larger-scale strata of medium sand (M) and strata of fine sand and silt (FZ), with secondary contributions by smaller-scale strata types occurring within the larger-scale units. When sampling the pattern in the longitudinal direction, M and FZ couplets repeat at 10 m intervals on average, with a high length variance. To reach a time-constant macrodispersivity, the stratal length variability must be fully sampled by the plume. The macrodispersivity becomes asymptotic beyond an advective distance of about 60 m, corresponding to about 12 longitudinal transitions between M and FZ unit types.Citation: Ramanathan, R., R. W. Ritzi Jr., and R. M. Allen-King (2010), Linking hierarchical stratal architecture to plume spreading in a Lagrangian-based transport model: 2. Evaluation using new data from the Borden site, Water Resour.

“…The nonlinear variogram fitting procedure also revealed that considerable uncertainty can exist in the values of the geostatistical parameters, which, in turn, will lead to uncertainty in the values of effective, large‐scale transport parameters predicted by stochastic theory. Other discussions pertaining to the Borden tracer experiment and subsequent interpretations are given by Sudicky [1988a, 1988b, 1988c], Kemblowski [1988], White [1988], Molz and Güven [1988], Naff et al [1988, 1989], Dagan [1989], Zhang and Neuman [1990], Rajaram and Gelhar [1991], Ritzi and Allen‐King [2007], Woodbury and Sudicky [1992], and others.…”

Section: Introductionmentioning

confidence: 99%

Heterogeneity in hydraulic conductivity and its role on the macroscale transport of a solute plume: From measurements to a practical application of stochastic flow and transport theory

Sudicky

Illman

Goltz

et al. 2010

[1] The spatial variability of hydraulic conductivity in a shallow unconfined aquifer located at North Bay, Ontario, composed of glacial-lacustrine and glacial-fluvial sands, is examined in exceptional detail and characterized geostatistically. A total of 1878 permeameter measurements were performed at 0.05 m vertical intervals along cores taken from 20 boreholes along two intersecting transect lines. Simultaneous three-dimensional (3-D) fitting of Ln(K) variogram data to an exponential model yielded geostatistical parameters for the estimation of bulk hydraulic conductivity and solute dispersion parameters. The analysis revealed a Ln(K) variance equal to about 2.0 and 3-D anisotropy of the correlation structure of the heterogeneity (l 1 , l 2 , and l 3 equal to 17.19, 7.39, and 1.0 m, respectively). Effective values of the hydraulic conductivity tensor and the value of the longitudinal macrodispersivity were calculated using the theoretical expressions of Gelhar and Axness (1983). The magnitude of the longitudinal macrodispersivity is reasonably consistent with the observed degree of longitudinal dispersion of the landfill plume along the principal path of migration. Variably saturated 3-D flow modeling using the statistically derived effective hydraulic conductivity tensor allowed a reasonably close prediction of the measured water table and the observed heads at various depths in an array of piezometers. Concomitant transport modeling using the calculated longitudinal macrodispersivity reasonably predicted the extent and migration rates of the observed contaminant plume that was monitored using a network of multilevel samplers over a period of about 5 years. It was further demonstrated that the length of the plume is relatively insensitive to the value of the longitudinal macrodispersivity under the conditions of a steady flow in 3-D and constant source strength. This study demonstrates that the use of statistically derived parameters based on stochastic theories results in reliable large-scale 3-D flow and transport models for complex hydrogeological systems. This is in agreement with the conclusions reached by Sudicky (1986) at the site of an elaborate tracer test conducted in the aquifer at the Canadian Forces Base Borden.Citation: Sudicky, E. A., W. A. Illman, I. K. Goltz, J. J. Adams, and R. G. McLaren (2010), Heterogeneity in hydraulic conductivity and its role on the macroscale transport of a solute plume: From measurements to a practical application of stochastic flow and transport theory, Water Resour. Res., 46, W01508,