Grain-scale stable isotope disequilibrium during fluid-rock interaction .1. Series approximations for advective-dispersive transport and first-order kinetic mineral-fluid exchange

Stable isotope fronts provide lasting evidence of fluid-rock interaction. The processes involved in material transport and mineral-fluid exchange may be identified from an analysis of front geometries based on transport theory. For the interpretation of stable isotope fronts the distinction between equilibrium and disequilibrium scenarios is crucial. For fossil systems this distinction can be made only if two or more minerals are considered as stable isotope monitors simultaneously. We derive approximations that describe one-dimensional advective-dispersive transport and coupled first-order kinetic mineral-fluid exchange, where the various constituent minerals of the rock are allowed to have different exchange rates. The new formalism is an extension of transport theory that accounts for the polyphase nature of rocks and allows integration of isotopic information from several monitoring phases. Comparison of the geometries of stable isotope fronts monitored by different phases permits identification of departures from local equilibrium that occurred during fluid-rock interaction. Furthermore it permits distinction of the contributions of diffusion-dispersion and of kinetically controlled mineral-fluid exchange to the distension of an initially sharp front. If mineral-fluid exchange is kinetically controlled, this has an interesting implication for stable isotope thermometry in that the inter-mineral fractionations may vary as a function of space and time irrespective of the system temperature. The series approximations presented here provide a formal basis for the interpretation of such disequilibrium phenomena, In particular they facilitate extraction of quantitative relations among transport velocities, exchange rates, and the duration of fluid-rock interaction from front geometries.