Cumulative relative reactivity: A concept for modeling aquifer-scale reactive transport

Abstract

We simulate aquifer‐scale reactive transport using an approach based on travel times and relative reactivity. The latter quantifies the intensity of the chemical reaction relative to a reference reaction rate with identical concentrations and can be interpreted as the strength of electron‐donor (or electron‐acceptor) release by the matrix, scaled by a reference release. In general, the relative reactivity is a spatially variable property reflecting the geology of the formation. In the proposed approach, we track the path of individual water parcels through the aquifer and evaluate the age of the water parcels and the relative reactivity integrated along their trajectories. By switching from spatial discretization to cumulative relative reactivity, advective‐reactive transport can be simulated by solving a single system of ordinary differential equations for each combination of concentrations in the inflow. We test the validity of the approach in a two‐dimensional test case of steady state groundwater flow and reactive transport involving aerobic respiration and denitrification. Here we compare steady state concentration distributions of the spatially explicit virtual truth, accounting for dispersive mixing, with the approximation based on cumulative relative reactivity and show that the errors introduced by neglecting dispersive mixing are minor if the target quantities are the mass fluxes crossing a control plane or being collected by a well. We further demonstrate the efficiency of the approach in a synthetic three‐dimensional case study. The proposed approach is computationally so efficient that ensemble runs to assess statistical distributions of concentration time series of reactive solutes become feasible, which is not practical with a spatially explicit model.

An Electron‐Balance Based Approach to Predict the Decreasing Denitrification Potential of an Aquifer

“…The biogeochemical conditions of an aquifer commonly vary in space and time within an aquifer. Loschko et al () extended the exposure‐time based modeling framework by implementing the so‐called “relative reactivity.” The dimensionless relative reactivity parameterizes the intensity of a specific reaction at every location in the domain. Loschko et al () expanded the latter approach to account for the decreasing reaction potential of the aquifer matrix along streamlines without returning to a fully spatially explicit description.…”

“…In preceding studies, we have intensively analyzed under which conditions dispersive mixing can be neglected in reactive transport calculations, which is a prerequisite for transport formulations using travel times, exposure times, or the cumulative relative reactivity (Sanz‐Prat et al , ; Loschko et al , ). From these preceding studies we conclude that restricting physical transport to advection is permissible if the dissolved reactants are introduced over large areas and long times and if they react with components of the aquifer matrix.…”

“…The biogeochemical conditions of an aquifer commonly vary in space and time within an aquifer. Loschko et al (2016) extended the exposure-time based modeling framework by implementing the so-called "relative reactivity." The dimensionless relative reactivity parameterizes the intensity of a specific reaction at every location in the domain.…”

Can Convolution and Deconvolution Be Used as Tools for Modeling Multicomponent, Mixing‐Limited Reaction Networks?

“…Transfer functions have seen widespread use across the diverse spectrum of hydrogeologic applications ranging from simulating solute dispersion (e.g., Dagan, 1984;Jury, 1982;Simmons, 1982) to upscaling aquifer reactivity (Cvetkovic & Dagan, 1994;Loschko et al, 2016;Seeboonruang & Ginn, 2006) and flow (Jiménez-Martínez et al, 2013;Pedretti et al, 2016), among numerous other applications. The mathematics of transfer functions is reviewed in section 2, but the basic concept is that a response function is used to filter an input signal and the resulting output models breakthrough curves, head fluctuations, or any number of other generic responses.…”

Accounting for the Decreasing Reaction Potential of Heterogeneous Aquifers in a Stochastic Framework of Aquifer‐Scale Reactive Transport

“…The classical exposure‐time concept may not address the heterogeneity to the extent necessary, as the reactivity in biogeochemically favorable zones may vary on a continuous scale. In a preceding study, we addressed such variability by introducing a relative reactivity, which quantifies the reaction rate for given solute concentrations scaled by the reaction rate under reference conditions (Loschko et al, ). We further introduced the cumulative relative reactivity, which is the relative reactivity experienced by a water parcel integrated over travel time, and used this as master variable for reactive‐transport simulations.…”