Equilibrium Models in Hydro- and Geochemistry
In the last decades, a large variety of models and computer programs has been developed for applications in hydro- and geochemistry. From a thermodynamic point of view they solve the following task:
|Given:||temperature T, pressure P, and total concentrations of elements1|
|Find:||concentrations ci (or molar amounts ni) of chemical species in aqueous and other phases in equilibrium state|
In all calculations partial/local equilibrium is assumed, therefore they are also termed “thermodynamic equilibrium models” (in contrast to kinetic models).
Despite the huge diversity we encounter in hydro/geochemistry models and software today, all these approaches fall into two major categories:
- models based on LMA – Law of Mass Action
- models based on GEM – Gibbs Energy Minimization
LMA. The LMA approach is common, and available in many computer programs, such as PhreeqC, Minteq2, Wateq4f3, EQ3/64, Chess/JChess5, The Geochemist’s Workbench6 and others. The program aqion, that relies on the numerical solver of PhreeqC, belongs to the LMA category as well.
The mathematical treatment of the equilibrium speciation problem yields nonlinear equation systems that can only be solved iteratively (such as root finding with Newton-Raphson method and other techniques). Thus, the application of numerical computer programs is a natural consequence.
Remarks & References
They are called ‘master species’. ↩
Allison, J.D., D.S. Brown, K.J. Novo-Gradac: MINTEQA2/ProdefA2, A Geochemical Assessment Model for Environmental Systems, Version 3.0, User’s Manual, EPA/600/3-91/021, March 1991 ↩
Ball J.W. and D.K. Nordstrom: WATEQ4F – User’s manual with revised thermodynamic data base and test cases for calculating speciation of major, trace and redox elements in natural waters, USGS Open-File Report 90-129, 185 p, 1991. ↩
Wolery, T.J., S.A. Daveler: EQ6, A Computer Program for Reaction Path Modeling of Aqueous Geochemical Systems: Theoretical Manual, User’s Guide, and Related Documentation (Version 7.0), Lawrence Livermore National Laboratory UCRL-MA-110662 PT IV, Oct 1992 ↩
Jan van der Lee, L. DeWindt: CHESS Tutorial and Cookbook, User’s Manual, Ecole Nationale Superieure des Mines de Paris Report LHM/RD/02/13, Centre d’Informatique Geologique, Apr 2002 ↩
Bethke, C.M., S. Yeakel: The Geochemist’s Workbench User’s Guides, Version 10.0. Aqueous Solutions LLC, Champaign, 2014 ↩
Eriksson. G, Chem. Scr., 8, p 100-103, 1975 ↩
Eriksson, G., K. Hack: CHEMSAGE – A computer program for the calculation of complex chemical equilibria. Metallurgical Transactions B b21, 1013-1023, 1990 ↩
Bale, C.W., P. Chartrand, S.A. Degterov, G. Eriksson, K. Hack, R. Ben Mahfoud, J. Melançon, A.D. Pelton, S. Petersen: FactSage Thermochemical Software and Databases, published by Elsevier Science Ltd, Calphad, Vol.26, No.2, pp. 189-228, 2002 ↩
Karpov I.K., K.V. Chudnenko, D.A. Kulik, O.V. Avchenko, V.A. Bychinskii: Minimization of Gibbs free energy in geochemical systems by convex programming, Geochem. International, 39, 1108-1119 2001 ↩
Kulik, D., U. Berner, E. Curti: Modeling chemical equilibrium partitioning with the GEMS-PSI code. PSI Scientific Report 2003 / Volume IV, Nuclear Energy and Safety. Villigen, Paul Scherrer Institut: 109-122, 2004 ↩