Relating reactive solute transport to hierarchical and multiscale sedimentary architecture in a Lagrangian-based transport model: 1. Time-dependent effective retardation factor

This series of papers addresses the transport of reactive solutes in groundwater. In part 1, the time-dependent effective retardation factor, R approximate to eff(t), of reactive solutes undergoing equilibrium sorption is linked to hierarchical stratal architecture using a Lagrangian-based transport model. The model is based on hierarchical expressions of the spatial covariance of the log distribution coefficient, =ln?(Kd), and the spatial cross covariance between and the log permeability, Y=ln?(k). The spatial correlation structure in these covariance expressions is the probability of transitioning across strata types of different scales, and they are parameterized by independent and quantifiable physical attributes of sedimentary architecture including univariate statistics for Y, , and the proportions and lengths of facies. Nothing is assumed about Y- point correlation; it is allowed to differ by facies type. The duration of the time-dependent change in R approximate to eff(t) is a function of the effective ranges of the cross-transition probability structures (i.e., the ranges of indicator correlation structures) for each scale of stratal architecture. The plume velocity and the effective retardation stabilize at a large-time limit after the plume centroid has traveled a distance that encompasses the effective ranges of these cross-transition probability structures. The well-documented perchloroethene (PCE) tracer test at the Borden research site is used to illustrate the model. The model gives a viable explanation for the observed PCE plume deceleration, and thus the observed R approximate to(t) can be explained by the process of linear equilibrium sorption and the heterogeneity in k and K-d. In part 2 [Soltanian et al., ], reactive plume dispersion, as quantified by the particle displacement variance is linked to stratal architecture using a Lagrangian-based transport model.