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. This article is protected by copyright. All rights reserved.