A mathematical formulation for reactive transport that eliminates mineral concentrations

Abstract

Abstract. We present a concise and general mathematical formulation for reactive transport in groundwater for general applications. By means of linear algebraic manipulations of the stoichiometric coefficients of the chemical reactions we are able to reduce the number of unknowns of the equations to be solved to the number of degrees of freedom according to thermodynamic rules. We present six formulations that differ from each other by number and type of unknowns and discuss their advantages and disadvantages with respect to the two most important numerical solution methods, the Sequential Iteration Approach (SIA) and the Direct Substitution Approach (DSA). Our conclusion is that the proposed reduction of the number of variables is of special interest for the DSA. We have applied one of these formulations to an example of the flushing of saline water by fresh water.

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

“…A common method to estimate spatial distributions of chemical species concentrations and associated reaction rates is to employ numerical modeling. A series of mathematical formulations are available in the literature, which are included in a variety of codes (Rubin 1990;Yeh and Tripathi 1991;Friedly and Rubin 1992;Lichtner 1996;Steefel and MacQuarrie 1996;Tebes-Stevens et al 1998;Clement et al 1998;Saaltink et al 1998;Parkhurst and Appelo 1999;Robinson et al 2000;Molins et al 2004). All these methodologies are based on the idea that reactive transport problems can be reformulated mathematically in terms of chemical components, defined as linear combinations of reactive species concentrations.…”

Reactive transport modelling of ore mineral zoning and the paragenesis of copper sulfides in sediment-hosted stratiform ore deposits, the Katanga Copperbelt (DRC)

“…The reactive transport modelling has been carried out with the geochemical simulator Retraso (Saaltink et al, 1998), which couples multi-element transport in solution with chemical reactions from 0 to 300 °C. The fluids compositions obtained with Phreeqc were used as starting solutions for the reactive transport models.…”

Numerical Models of Groundwater Flow and Transport

“…Such a transformation is always possible, but not unique. It can be described by the multiplication of the system (6) with another matrix U from the left (Saaltink et al, 1998), which is equivalent to the transition from species concentrations to total concentrations, also called components.…”

“…In general for a set of species, the coupled problem for reactive transport is given by: (Saaltink et al, 1998), where the vector c contains all species concentrations. The vectors r eq and r kin denote the reaction rates of equilibrium and kinetic reactions, and the matrices S eq and S kin relate reactions (in rows) and species (in columns) for equilibrium and kinetic reactions.…”