Relating Reactive Transport to Hierarchical Sedimentary Architecture. Part 2. Lagrangian-Based Transport Models

Abstract:

We present new Lagrangian-based transport models for both the time-dependent effective retardation factor and the particle displacement variance of reactive solutes undergoing linear equilibrium sorption. The models represent the influence of hierarchical and multi-scale sedimentary architecture. The formulations are based on hierarchical expressions of the spatial covariance of log-permeability, Y=ln(k), log sorption distribution coefficient, Ξ=ln(K_d), and their spatial cross-covariance. 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 hierarchical sedimentary architecture including univariate statistics for Y, Ξ, and proportions and facies lengths. The models allow the study of the contribution of each scale of stratal architecture to the time-dependent effective retardation factor and the composite particle displacement variance, and thus the study of how hierarchical stratal architecture controls reactive plume spreading. The well-documented perchloroethene (PCE) tracer test at the Borden research site is used to illustrate the models. The models give a viable explanation for the observed PCE plume behavior. The results show that linear equilibrium sorption and heterogeneity in hydraulic and reactive attributes can explain both the PCE plume deceleration and the dispersion that was observed. The models give the contribution of each scale of stratal architecture to these processes.