Dynamic treatment of invariant and univariant reactions in metamorphic systems

Abstract

A simple model is presented that incorporates the essential dynamics of metamorphic processes leading to reactions along univariant curves and up to and beyond the invariant point. The model includes both heat flow by conduction and convection as well as fluid flow in and out of a representative volume. Overall mineral reactions can then take place within this rock volume in response to internal and external factors. The paper derives a simple "back-of-the-envelope" expression for the steady state reached by the system. The steady state composition of the fluid and the steady state temperature are then compared with the composition and temperature predicted by the assumption of thermodynamic equilibrium. Expressions for the amount of fluid passing through the system based on the kinetic model are compared with previous calculations of the mass of fluid added to the system using the equilibrium assumptions. The approach to this steady state is also analyzed and an analytical solution is obtained for the time evolution up to the steady state. Both the steady state and the time evolution solution are then applied to an understanding of the dynamics involved in obtaining T-X-t paths in nature. The results of the kinetic approach lead to major revisions in many of the previously held concepts used in petrologic fluid flow models. These include the expected reaction pathway, the role of metastable reactions, the calculation of fluid flux, the role of the invariant point, and the interpretation of mineral textures and modal abundances of minerals.