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

Abstract

[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.

Horizontal spatial correlation of hydraulic and reactive transport parameters as related to hierarchical sedimentary architecture at the Borden research site

“…[43] The interpretive modeling exercise showed that the horizontal Ä autosemivariogram and the Ä-Y cross-semivariogram are defined more by the cross transitions than the cross transitions, as previously shown for the horizontal Y autocovariance [Ramanathan et al, 2010]. The cross-transition structure is, in turn, mostly defined by the proportions and the mean and variance in lengths of level II units.…”

“…The composite horizontal integral scales for the YY h À Á , ÄÄ h À Á , and ÄY h À Á models are, respectively, 1.9, 1.8, and 2.0. Note, the A-D terms in Table 3 are derived from data only at locations where k and K d measurements are both located, and not being restricted by this, Ramanathan et al [2010] used slightly more k data in defining A-D terms for a horizontal Y autocovariance model. Their A-D values have negligible differences (i.e., in the fourth and fifth significant figures) from those reported here, and give the same composite Y integral scale of 1.9 m. Note also that the data from horizontal lines of sampling at x k locations in Figure 1 do not facilitate an analysis of the study of vertical sample semivariograms (for Y or Ä).…”

“…Johnson and Dreiss, 1989;Carle and Fogg, 1996;Carle, 1996;Ritzi, 2000]. If units reoccur along lines of sampling, the structure of thet ro;ji h À Á cross-transition terms is largely determined by the variance in the length of units [Ritzi, 2000;Ritzi et al 2004;Dai et al, 2005;Ritzi and Allen-King, 2007;Ramanathan et al, 2010]. As the coefficient of variation (C v , the ratio of the standard deviation to the mean) in length of reoccurring unit types is systematically increased from zero to unity, thep ro h À Át ro;ji h À Á loses periodicity and comes to have an exponential-like and asymptotic increase toward a sill.…”

“…Lengths of naturally occurring sedimentary units commonly have an Erlangian distribution with high C v [White and Willis, 2000]. Ramanathan et al [2010] computed horizontal length statistics from the I ro ð x I Þdata using the method of White and Willis [2000] to reduce bias created by incomplete sampling of the units. These length statistics are given in Table 1.…”

“…[33] [Ritzi et al, 2004;Dai et al, 2005;Ritzi and AllenKing, 2007;Ramanathan et al, 2010]. The cross-transition model is…”