A random walk solution for modeling solute transport with network reactions and multi-rate mass transfer in heterogeneous systems: Impact of biofilms

We address modern topics of stochastic hydrogeology from their potential relevance to real modeling efforts at the field scale. While the topics of stochastic hydrogeology and numerical modeling have become routine in hydrogeological studies, nondeterministic models have not yet permeated into practitioners. We point out a number of limitations of stochastic modeling when applied to real applications and comment on the reasons why stochastic models fail to become an attractive alternative for practitioners. We specifically separate issues corresponding to flow, conservative transport, and reactive transport. The different topics addressed are emphasis on process modeling, need for upscaling parameters and governing equations, relevance of properly accounting for detailed geological architecture in hydrogeological modeling, and specific challenges of reactive transport. We end up by concluding that the main responsible for nondeterministic models having not yet permeated in industry can be fully attributed to researchers in stochastic hydrogeology.

Section: Discussion: Do Stochastic Models Represent Somehow Reality? mentioning

confidence: 99%

Debates—Stochastic subsurface hydrology from theory to practice: Why stochastic modeling has not yet permeated into practitioners?

Sánchez-Vila

Fernàndez-García

2016

“…The solute transport problem was solved using the code RW3D that solves advection, dispersion and multirate mass transfer using the RWPT approach (Fernàndez‐Garcia et al, ; Henri & Fernàndez‐Garcia, ; Henri & Fernàndez‐Garcia, ; Salamon et al, ). The governing equation for advective‐dispersive transport is given by the following:

italicθR \frac{\partial c}{\partial t} = \nabla \cdot ((), θ boldD \nabla c) - \nabla \cdot ((), boldq c)

where q (L/T) is the groundwater flux, D (L 2 /T) is the dispersion tensor, θ (dimensionless) is the porosity, c (M/L 3 ) is the aqueous concentration, and R (dimensionless) is the retardation factor.…”

Section: Methodsmentioning

confidence: 99%

“…The solute transport problem was solved using the code RW3D that solves advection, dispersion and multirate mass transfer using the RWPT approach Henri & Fernàndez-Garcia, 2014;Henri & Fernàndez-Garcia, 2015;Salamon et al, 2006). The governing equation for advectivedispersive transport is given by the following:…”

Section: Solute Transport Modelmentioning

confidence: 99%

Upscaling of Regional Scale Transport Under Transient Conditions: Evaluation of the Multirate Mass Transfer Model

Guo

Fogg

Henri

2019

Self Cite

Regional scale transport models are needed to support the long‐term evaluation of groundwater quality and to develop management strategies aiming to prevent serious groundwater degradation. The purpose of this study is to evaluate the capacity of a previously developed upscaling approach to adequately describe the main solute transport processes, including the capture of late‐time tails under changing boundary conditions. Potential factors that impact the performance of upscaling methods, including temporal variations in mass transfer rates and mass distributions, were investigated. Advective‐dispersive contaminant transport in a 3‐D heterogeneous domain was simulated and used as a reference solution. The equivalent transport under homogeneous flow conditions was then evaluated by applying the multirate mass transfer (MRMT) model. The random walk particle tracking method was used to solve the solute transport for heterogeneous and homogeneous MRMT scenarios under steady state and transient conditions. The results indicate that the MRMT model can capture the tails satisfactorily for plumes transported with ambient steady state flow fields at all studied scales using the same parameters. However, when the boundary conditions change in either local, plume, or regional scale, the mass transfer model calibrated for transport under steady state conditions cannot accurately reproduce the tailings observed for the heterogeneous scenario. The deteriorating impacts of transient boundary conditions on the upscaled model are more significant for regions where the flow fields are dramatically affected, which highlights the poor applicability of the MRMT approach for complex field settings. This finding also has implications for the suitability of other potential upscaling approaches.

“…Solute transport was modeled using the code RW3D that solves advection, dispersion, and MRMT using the random walk particle tracking approach (Fernàndez-Garcia et al, 2005;Henri & Fernàndez-Garcia, 2014;Henri & Fernàndez-Garcia, 2015;Salamon et al, 2006). Longitudinal, transverse, and vertical dispersivities representing grid-scale dispersion were set to 1.0, 0.1, and 0.01 m, respectively.…”

Section: Groundwater Flow and Solute Transport Modelsmentioning

confidence: 99%

Adaptive Multirate Mass Transfer (aMMT) Model: A New Approach to Upscale Regional‐Scale Transport Under Transient Flow Conditions

Guo

Henri

Fogg

et al. 2020

Self Cite

The long‐term evaluation of regional‐scale groundwater quality needs efficient upscaling methods for transient flow. Upscaling techniques, such as the Multirate Mass Transfer (MRMT) method with constant upscaling parameters, have been used for transport with steady‐state flow, yet the upscaling parameters (i.e., rate coefficients) may be time dependent. This study proposed and validated an adaptive MRMT (aMMT) method by allowing the mass transfer coefficients in MRMT to change with the flow field. Advective‐dispersive contaminant transport simulated in a 3‐D heterogeneous medium was used as a reference solution. Equivalent transport under homogeneous flow conditions was evaluated by applying the MRMT and aMMT models for upscaling. The relationship between mass transfer coefficients and flow rates was fitted under steady‐state flow driven by various hydraulic gradients. A power law relationship was obtained, which was then used to update the mass transfer coefficients in each stress period under transient flow conditions in the aMMT method. Results indicated that for advection‐dominated transport, both the MRMT and aMMT methods can upscale the anomalous transport dynamics affected by subgrid heterogeneity under transient flow conditions. Whereas for diffusion‐dominated systems, the MRMT model failed to capture the tails of tracer breakthrough curves after the boundary condition changed, but the results from the aMMT model were significantly improved. However, if the overall flow direction changed, both MRMT and aMMT failed to represent the breakthrough curve tail generated by the heterogeneous system. The results point toward a promising path for upscaling transport in complex aquifers with transient flow.