### Cumulative Relative Reactivity: A Tool for Catchment-Scale Reactive Transport

*Matthias Loschko*

^{1}, Thomas Wöhling

^{2}, David Rudolph

^{3}, Olaf Cirpka

^{1}Zentrum für Angewandte Geowissenschaften, Universität Tübingen

^{2}Institut für Hydrologie und Meteorologie, Technische Universität Dresden

^{3}Department of Earth and Environmental Sciences, University of Waterloo

O 13.1

*in*Reactive transport modeling

14.04.2016, 14:15-14:30, Audimax A, Geb. 30.95

Quantitative understanding of pollutant fluxes from diffuse input and turnover of pollutants at catchment scale requires process-based numerical models that can explain observed time series of heads, fluxes, and concentrations under current conditions and predict future states under changing conditions. The uncertainty of forcing, parameters, and conceptual assumptions as well as the unresolved subscale variability calls for a probabilistic framework, predicting probabilities of reactive-species concentrations rather than single values. Due to the high computational effort, such evaluations cannot be done with a fully coupled, multi-dimensional, spatially explicit reactive-transport model. Conceptual simplifications are needed, keeping spatially explicit calculations whenever required and computationally manageable, but simplifying reactive-transport computations without sacrificing mechanistic understanding.

These simplifications can be achieved with travel- and exposure-time based approaches, where reactive transport is calculated along pathlines, and spatial coordinates are replaced by groundwater travel time. The one-dimensional transport is further simplified by introducing a concentration-independent relative reactivity, which parameterizes the supply of electron donors from the rock matrix. Materials with strong reduction potential, such as peat lenses, exhibit a large relative reactivity, materials clean quartz sand would have a relative reactivity of zero.

With the concept of relative reactivity, the concentrations at a given location and time can be computed from (1) the origin and travel-time of the water parcel, determining the initial concentrations of the compounds when the water parcel was introduced, and (2) the cumulative relative reactivity that the water parcel has experienced while passing through the aquifer. Origin, travel-time, and cumulative relative reactivity are evaluated by particle tracking. For the reactions, ordinary differential equations (ODEs) are solved, in which time is replaced by cumulative relative reactivity. Thus, with a finite set of initial-concentration values, one ODE solution per initial condition, and the information from particle tracking, concentrations of the electron acceptors can be computed at all times and locations, reducing the computational effort by orders of magnitude. The computational effort is strikingly decreased, and Monte Carlo simulations become possible to account for all uncertainties encountered.

The concept of relative reactivity was tested on a synthetic test case with a single reactive zone. The reactive system involves aerobic respiration and denitrification in the saturated zone. The model runs show that the proposed approach enables an efficient way to create a stochastic framework for catchment-scale reactive transport.

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