Geochemical algorithms

The most common approach used by geochemical modeling codes to describe the water-gas-rock-interaction in aquatic systems is the ion dissociation theory outlined briefly in chapter 1.1.2.6.1. However, reliable results can only be expected up to ionic strengths between 0.5 and 1 mol/L. If the ionic strength is exceeding this level, the ion interaction theory (e.g. PITZER equations, chapter 1.1.2.6.2) may solve the problem and computer codes have to be based on this theory. The species distribution can be calculated from thermodynamic data sets using two different approaches (chapter 2.1.4)  

Both processes presuppose the establishment of chemical equilibrium and mass balance. Being in equilibrium, the interrelation between the equilibrium constant K and the free energy is defined as (see also chapter 1.1.2.2)  

If the solubility constant for a certain reaction is not explicitly given in a data set, but the solubility constants of partial reactions are known, the solubility constant of the total reaction can be calculated from the solubility constants of the partial reactions (see Table 19). 

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As proton sources, organic acids have an important influence on a variety of pH dependent reactions, especially between 80 and 120 C. Using the geochemical algorithm PHREEQE... 

Albarede, F. Provost, A. (1977). Petrological and geochemical mass balance an algorithm for least-squares fitting and general error analysis. Comp. Sci., 3, 309-26. 

Karpov, I. K., Chudnenko, K. V. Kulik, D. A. 1997. Modeling chemical mass transfer in geochemical processes Thermodynamic relations, conditions of equilibria, and numerical algorithms. American Journal of Science, 297, 767-806. 

Grzyb, K.R. (1995) NOAEM (natural organic anion equilibrium model) a data analysis algorithm for estimating functional properties of dissolved organic matter in aqueous environments Part I. Ionic component speciation and metal association. Org. Geochem., 23, 379-390. 

Surfaces generated by the MIDW algorithm are reclassified by means of the concentration-area fractal method (C—A) developed by Cheng et al. (1994a) for geochemical anomaly separation. 

Two types of algorithm are used in speciation-solubility models those that use equilibrium constants and those that use free energy minimization. Most geochemical models we described in the text belong to the first type. Interested readers are referred to Anderson and Crerar (1993) for a more detailed discussion. 

Computational Errors. Errors in computation can be attributed to two specific circumstances convergence criteria and improper selection of parametric equations. Most geochemical codes require that mass balance and mass action equations be solved to obtain an acceptable mathematical model of the aqueous solution. Minimal error can be attributed to the mathematical formulation of the equation solvers, because such narrow convergence criteria are used in the matrix inversion or iterative solution algorithms. Numerical dispersion or out of bounds computations generally do not occur unless phase boundaries are exceeded. 

We observed in Chapter 3 that a chemical system is at thermodynamic equilibrium when the Gibbs free energy of the system is at a minimum. For a given pressure, temperature, and bulk composition, at equilibrium there will be one or more phases in which the concentrations of all species are fixed. Many different methods have been developed to compute the equilibrium state, as outlined by Van Zeggeren and Storey (1970) and Smith and Missen (1982). As an illustration, we will summarize an algorithm derived by Harvie et al. (1987), which has been applied with great success to geochemical systems. 

Apart from the problem of lack of data, especially kinetic data, this situation probably constitutes the most serious problem in the application of thermodynamics to geochemical problems involving hydrothermal solutions. The development of an algorithm which is more accurate than the B-dot method as presently used, but which could still be used for any species at any T and P would be a significant advance in geochemical modeling practice. 

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