Transport Upscaling in Highly Heterogeneous Aquifers and the Prediction of Tracer Dispersion at the MADE Site

Abstract

We present an upscaled Lagrangian approach to predict the plume evolution in highly heterogeneous aquifers. The model is parameterized by transport-independent characteristics such as the statistics of hydraulic conductivity and the Eulerian flow speed. It can be conditioned on the tracer properties and flow data at the injection region. Thus, the model is transferable to different solutes and hydraulic conditions. It captures the large-scale non-Gaussian features for the evolution of the longitudinal mass distribution observed for the bromide and tritium tracer plumes at the Macrodispersion Experiment (MADE) site (Columbus, Mississippi, USA), which are characterized by a slow moving peak and pronounced forward tailing. These large-scale features are explained by advective tracer propagation due to a broad distribution of spatially persistent Eulerian flow speeds as a result of spatial variability in hydraulic conductivity. Plain Language Summary The prediction of solute transport in highly heterogeneous porous media has been a long-standing question. We propose an approach that predicts and explains observed tracer distributions in terms of medium and flow heterogeneity. The model is parameterized by the statistical characteristics of hydraulic conductivity, distribution of flow speeds, porosity, and retardation coefficient, that is, transport-independent parameters. This study gives new insight for the understanding and prediction of large-scale tracer dispersion in heterogeneous aquifers.

A Comparison of Six Transport Models of the MADE-1 Experiment implemented with Different Types of Hydraulic Data

“…The present study takes advantage of these possibilities and compares predictions of plume transport by six previously developed models that use different information to characterize the spatial variability of hydraulic conductivity. Thus, the FOA (Fiori et al, 2017), the MIM and self-consistent approximation (MIMSCA) (Fiori et al, 2013), and the TDRW (Dentz et al, 2020) models utilize extensive hydraulic profiling data (Bohling et al, 2016), for inferring geostatistical parameters. In contrast, the binary inclusions model (Zech et al, 2021) uses pumping tests and a few flowmeter data whereas the Binary Facies model relies on granulometric data.…”

“…We examine the ability of six transport models of different aquifer conceptualization to predict the observed relative mass distribution without calibration of transport parameters: (a) the first order approximation (FOA) (Fiori et al, 2017); (b) the multi-indicator model and self-consistent approximation (MIMSCA) (Fiori et al, 2013); (c) the time-domain random walk (TDRW) of Dentz et al (2020); (d) the Binary Inclusions model (Zech et al, 2021); (e) a Binary Facies model, and (f) the flow reactors model (see Section 3 for details). We further examine the predictive power of the models by extending the time (t = 1,000 days) beyond MADE observations (t max = 503 days).…”

A Comparison of Six Transport Models of the MADE‐1 Experiment Implemented With Different Types of Hydraulic Data

“…The basic idea is to quantify particle motion in spatially variable flow fields through a Markov process for equidistant particle velocities, whose steady state distribution is given by the flux-weighted distribution of flow velocities. While details can be found in Dentz et al (2020), we describe here the main features of the model. This modeling approach has been used and verified for the prediction of the evolution of particle velocity statistics, particle distributions, dispersion and breakthrough curves in pore, and Darcy-scale heterogeneous porous media (Comolli et al, 2019;Hakoun et al, 2019).…”

“…Background: TDRW and CTRWapproaches have been used extensively over the past two decades for the modeling of transport in heterogeneous porous media (Noetinger et al, 2016). Within this framework and based on the stochastic TDRW method of Comolli et al (2019), Dentz et al (2020) derived a predictive upscaled model that avoids calibration against transport observations. The basic idea is to quantify particle motion in spatially variable flow fields through a Markov process for equidistant particle velocities, whose steady state distribution is given by the flux-weighted distribution of flow velocities.…”

“…While details can be found in Dentz et al. (2020), we describe here the main features of the model. This modeling approach has been used and verified for the prediction of the evolution of particle velocity statistics, particle distributions, dispersion and breakthrough curves in pore, and Darcy‐scale heterogeneous porous media (Comolli et al., 2019; Hakoun et al., 2019).…”