A procedure for the solution of multicomponent reactive transport problems

Abstract

[1] Modeling transport of reactive solutes is a challenging problem, necessary for understanding the fate of pollutants and geochemical processes occurring in aquifers, rivers, estuaries, and oceans. Geochemical processes involving multiple reactive species are generally analyzed using advanced numerical codes. The resulting complexity has inhibited the development of analytical solutions for multicomponent heterogeneous reactions such as precipitation/dissolution. We present a procedure to solve groundwater reactive transport in the case of homogeneous and classical heterogeneous equilibrium reactions induced by mixing different waters. The methodology consists of four steps: (1) defining conservative components to decouple the solution of chemical equilibrium equations from species mass balances, (2) solving the transport equations for the conservative components, (3) performing speciation calculations to obtain concentrations of aqueous species, and (4) substituting the latter into the transport equations to evaluate reaction rates. We then obtain the space-time distribution of concentrations and reaction rates. The key result is that when the equilibrium constant does not vary in space or time, the reaction rate is proportional to the rate of mixing, r T u D ru, where u is the vector of conservative components concentrations and D is the dispersion tensor. The methodology can be used to test numerical codes by setting benchmark problems but also to derive closed-form analytical solutions whenever steps 2 and 3 are simple, as illustrated by the application to a binary system. This application clearly elucidates that in a three-dimensional problem both chemical and transport parameters are equally important in controlling the process.Citation: De Simoni, M., J. Carrera, X. Sánchez-Vila, and A. Guadagnini (2005), A procedure for the solution of multicomponent reactive transport problems, Water Resour. Res., 41, W11410,

HYTEC results of the MoMas reactive transport benchmark

“…The major objective of the benchmark is to provide more efficient numerical methods and mathematical resolution schemes in order to improve reactive transport models, in particular for applications in the domain of deep underground radioactive waste disposal. Contrary to the approach suggested by [5], the benchmark exercise does not focus on an existing analytical solution, but rather on problems with strong coupling and stiffness. The lack of reference solution will cause some problems when the accuracy of the results will be discussed.…”

“…Several possiblities are open to test the precision and accuracy of the codes. Analytical solutions are the ideal tool, when available [5,15,21,13]; however, they are not easy to devise and are limited to simplified systems: specific hydrodynamic, simplistic chemistry, weak feedbacks. It is also possible to use laboratory or field experiments [6,12].…”

Toward efficiency in heterogeneous multispecies reactive transport modeling: A particle‐tracking solution for first‐order network reactions

“…For instance, first-order degradation reactions of a single species can be included into PTMs by assigning to every particle a variable mass, which develops in time according to first-order kinetics [Kinzelbach, 1987;Wen and Gomez-Hernandez, 1996]. When all species share the same transport operator, certain reactions in chemical equilibrium can be easily simulated with particle tracking by using conservative components [Molins et al, 2004;Kr€ autle and Knabner, 2005;De Simoni et al, 2005;FernandezGarcia et al, 2008;Fernandez-Garcia and Sanchez-Vila, 2011], i.e., a linear combination of the species concentrations that can be used to decouple the system of equations into simpler problems. Fast kinetic reactions have been properly simulated by applying simple proximity relationships between nearby particles [Edery et al, 2009[Edery et al, , 2010.…”

Conditional Probability Density Functions of Concentrations for Mixing-Controlled Reactive Transport in Heterogeneous Aquifers

“…The former requirements are met by systems either in local chemical equilibrium or instantaneous, complete, irreversible reactions (Ham et al 2004;Liedl et al 2005) and can also be used for specific cases of kinetic reactions (Molins et al 2004;Cirpka and Valocchi 2007). A methodology to compute directly homogeneous and heterogeneous reaction rates under instantaneous equilibrium has been presented recently by De Simoni et al (2005. Their general expressions illustrate that mixing processes control equilibrium reaction rates, and includes Phillips's model (1991) as a particular case.…”