The purpose of this paper is to present a general model (COMAGMAT) for
the calculation of equilibrium temperatures and phase relations at a
given extent of crystallization or melting in natural magmatic systems
. This model is based on a set of empirical expressions that describe
mineral-melt equilibria for major and trace elements in terms of press
ure (up to 12 kbar), temperature, and liquid compositions for systems
ranging from primitive basalts to dacites. These expressions are in th
e form of empirically calibrated mineral-melt geothermometers for Oliv
ine, Augite, Pigeonite (Opx), Plagioclase, Ilmenite, and Magnetite use
d to develop the algorithm simulating multiply saturated magmatic melt
s. The results of the program are in the form of calculated liquid lin
es of descent, plus the equilibrium mineral proportions and compositio
ns. The phase equilibria calculations form the core of a model that al
lows the user to simulate processes ranging from simple isobaric cryst
allization to in situ differentiation processes resulted from crystal
settling, and polybaric fractionation.