A FORMALISM FOR GEOCHEMICAL REACTION MODELING USING COMBINED MASS-BALANCE, REACTION-PATH, AND STOCHASTIC METHODS: APPLICATION TO THE OZARK AQUIFER SYSTEM

The traditional method of constructing geochemical reaction models of hydrologic systems has no established formalism for integrating mass-balance and reaction-path calculations in a robust manner. The lack of formalism makes it difficult to quantify the sensitivity of a reaction-path model to the effects of varying mass-transfer and/or thermodynamic quantities, and to evaluate if a reaction path based on mass-balance calculations is an accurate model of observed chemical relationships within a hydrologic system.

A more robust approach to constructing reaction models is to combine mass-balance and reaction-path calculations with statistical methods and stochastic simulation. This approach is applied in the construction of a reaction model of the evolution of ground water in the Ozark Plateaus aquifer system. Sets of mass-transfer coefficients are calculated, and statistically summarized, that account for the chemical composition of a sample population of water analyses representative of each aquifer unit. The error distribution of each mass-transfer calculation is then simulated and tested for thermodynamic validity in reaction-path calculations using Monte Carlo methods. The sensitivity of each reaction-path simulation to changes in mass-transfer of phases, associated errors, and/or changes in errors of speciation-solubility constants are acquired through test statistics on probability distribution functions of input errors and output parameters of interest. Bootstrapping techniques are used to estimate the accuracy of each reaction model at predicting observed elemental concentrations.

The reaction model of the Ozark aquifer system developed by the combined mass-balance, reaction-path, and stochastic methods describes the linked processes of dissolution of carbonates, oxidation of sulfides, ion exchange with clays, and mixing between aquifers. The sensitivity of each of these modeled processes to changes in reaction components and variance of parameters is summarized with model statistics. The model accurately describes over 90% of the 400 water samples from the Ozark aquifer system. In cases where the model fails, model statistics can be used to estimate what components and/or input parameters could change to account for discrepancies.