Advective transport in heterogeneous aquifers: Are proxy models predictive?

Abstract

Fiori et al. (2015) examine the predictive capabilities of (among others) two ''proxy'' non-Fickian transport models, MRMT (Multi-Rate Mass Transfer) and CTRW (Continuous-Time Random Walk). In particular, they compare proxy model predictions of mean breakthrough curves (BTCs) at a sequence of control planes with near-ergodic BTCs generated through two-and three-dimensional simulations of nonreactive, mean-uniform advective transport in single realizations of stationary, randomly heterogeneous porous media. The authors find fitted proxy model parameters to be nonunique and devoid of clear physical meaning. This notwithstanding, they conclude optimistically that ''i. Fitting the proxy models to match the BTC at [one control plane] automatically ensures prediction at downstream control planes [and thus] ii. . . . the measured BTC can be used directly for prediction, with no need to use models underlain by fitting.'' I show that (a) the authors' findings follow directly from (and thus confirm) theoretical considerations discussed earlier by Neuman and Tartakovsky (2009), which (b) additionally demonstrate that proxy models will lack similar predictive capabilities under more realistic, non-Markovian flow and transport conditions that prevail under flow through nonstationary (e.g., multiscale) media in the presence of boundaries and/or nonuniformly distributed sources, and/or when flow/transport are conditioned on measurements.

An Entrogram‐Based Approach to Describe Spatial Heterogeneity With Applications to Solute Transport in Porous Media

“…Following Jankovic et al () based on Fiori et al (), the accuracy of the numerical simulations is tested through comparisons between the mean advective velocity calculated from the results of the transport simulations and the mean of the component of the Eulerian velocity field parallel to the mean flow direction ( U mean ). In each simulation, the components of the Eulerian velocity field ( U = q / θ ) are calculated assuming homogeneous effective θ and by averaging the specific discharge ( q ) across the numerical grid block interfaces.…”

“…In hydrogeology, upscaling is the process by which the scale of measurement of a certain variable is mathematically adapted to the required scale of interest for a model-based analysis (e.g., de Marsily et al, 2005;Wen & Gómez-Hernández, 1996). A variety of upscaling methods have been presented for flow and solute transport processes, from surrogate and proxy models (Asher et al, 2015;Fiori et al, 2015;Neuman & Tartakovsky, 2009) to approaches explicitly describing the spatial heterogeneity of the hydraulic conductivity (K) fields (e.g., Fogg & Zhang, 2016;Sanchez-Vila & Fernàndez-Garcia, 2016). Two main approaches based on effective descriptions of the K field have been traditionally followed for solute transport upscaling.…”

“…Jankovic et al (2017) based onFiori et al (2015), the accuracy of the numerical simulations is tested through comparisons between the mean advective velocity U calculated from the results of the transport simulations and the mean of the component of the Eulerian velocity field parallel to the mean flow 10.1029/2018WR022827…”

Tracer travel and residence time distributions in highly heterogeneous aquifers: Coupled effect of flow variability and mass transfer

“…Interestingly, the quantity SK/CV does not depend on the control plane distance x. Skewness relative to the macro-dispersion (as quantified The same issue has been recently discussed in [23], and there are past examples where advective transport in highly heterogeneous formations has been modeled by a first order retention mechanism [e.g., 30]. In other words, the retention mechanism is often used as a proxy for fast and slow advection in heterogeneous formations of high σ 2 Y .…”

“…Higher order temporal moments can be derived from (23) and used for further exploring their dependency on heterogeneity and kinetics. Furthermore, alternative forms of g(t) (Appendix) and f (K) can be used for studying the impact on temporal moments of more complex mass transfer processes and distribution types for the hydraulic conductivity K.…”