Relating reactive solute transport to hierarchical and multiscale sedimentary architecture in a Lagrangian-based transport model: 2. Particle displacement variance
This series of papers addresses the transport of sorbing solutes in groundwater. In part 2, plume dispersion, as quantified by the particle displacement variance, X11R(t), is linked to hierarchical sedimentary architecture using a Lagrangian-based transport model. This allows for a fundamental understanding of how dispersion arises from the hierarchical architecture of sedimentary facies, and allows for a quantitative decomposition of dispersion into facies-related contributions at different scales within the hierarchy. As in part 1, the plume behavior is assumed to be controlled by linear-equilibrium sorption and the heterogeneity in both the log permeability, Y=ln(k), and the log distribution coefficient, Ξ=ln(Kd). Heterogeneity in Y and Ξ arises from sedimentary processes and is structured by the consequent sedimentary architecture. Our goal is to understand the basic science of the dispersion process at this very fundamental level. The spatial auto and cross covariances for the relevant attributes are linear sums of terms corresponding to the probability of transitioning across stratal facies types defined at different scales. Unlike previous studies that used empirical relationships for the spatial covariances, here the model parameters are developed from independent measurements of physically quantifiable attributes of the stratal architecture (i.e., proportions and lengths of facies types, and univariate statistics for Y and Ξ). Nothing is assumed about Y- Ξ point correlation; it is allowed to differ by facies type. However, it is assumed that Y and Ξ variance is small but meaningful, and that pore-scale dispersion is negligible. The time-dependent spreading rate is a function of the effective ranges of the cross-transition probability structures (i.e., the ranges of indicator correlation structures) for each relevant scale of stratal hierarchy. As in part 1, the well-documented perchloroethene (PCE) tracer test at the Borden research site is used to illustrate the model. The model was parameterized with univariate statistics for Y, Ξ of (PCE), and proportions and lengths of lithologic facies types defined at two scales within a two-level hierarchical classification, as given by Ritzi et al. (). The model gives a viable explanation for the observed PCE plume dispersion, and thus X11R(t) can be explained by the process of linear equilibrium sorption and the heterogeneity in k and Kd. The results quantitatively show that the k- Kd cross correlation, though small, and varied by facies type, can significantly impact the particle displacement variance. Furthermore, by quantitatively decomposing the dispersion into facies-related contributions, we gain the fundamental insight that that the time-dependent rate of spreading is mostly defined by the cross-transition probability correlation structure imparted by the proportions and sizes of the larger-scale facies types.
& Dai, Z.
(2015). Relating reactive solute transport to hierarchical and multiscale sedimentary architecture in a Lagrangian-based transport model: 2. Particle displacement variance. Water Resources Research, 51, 1601-1618.