Simultaneous Calculation of Chemical and Isotope Equilibria Using the GEOCHEQ_Isotope Software: Carbon Isotopes

Abstract— The program package GEOCHEQ_Isotope was developed for the simultaneous calculation of chemical and isotope equilibria in hydrothermal and hydrochemical systems by the method of Gibbs free energy minimization. It utilizes the formalism of the β-factor and is a modification of the GEOCHEQ software, which was designed to calculate chemical equilibria. An algorithm was proposed for the calculation of the Gibbs free energy of formation of a rare isotopologue, G*(P, T), from the Gibbs free energy of formation of the main isotopologue, the β-factor of this substance, and the mass ratio of the rare and main isotopes of the element. The ideal mixing of isotopes was assumed. The temperature dependence of the β-factor was unified as a polynomial in reciprocal absolute temperature. The implementation of the software and an appropriate database was illustrated by the example of carbon isotopes. The available information on carbon isotope equilibria involving geochemically important compounds was critically analyzed, and temperature dependences of their β-factors were correspondingly optimized. The thermodynamic database was updated by adding information on the temperature dependence of β-factors specified by eight polynomial coefficients for each substance. The use of the GEOCHEQ_Isotope was exemplified calculating the equilibrium compositions of phases and carbon isotope fractionations in carbonate hydrothermal systems with and without iron at pH ranging from 4 to 11.