An empirically derived kinetic model for albitization of detrital plagioclase

Abstract

We propose an empirically derived model that estimates the extent of reaction for albitization of plagioclase as a function of time, grain surface area, and temperature from 0 to 200°C. We use a kinetic formulation independent of pressure, and consistent with the Rate Law, which quantifies the dependence of the reaction rate on the initial concentration of the reacting material, and the Arrhenius equation. The formulation is described by the function: \[{-}\frac{d{[}An{]}}{dt}{=}S_{m}k{[}An_{o}{]}^{2}(1{-}{\bar{{\Omega}}})\] where d[An]/dt is the rate change of the anorthite mole fraction with time, Sm the mineral surface area (cm2), k the rate constant 1/cm2 s, [Ano] is a constant representing the initial anorthite mole fraction, and Ω a constant weighed average saturation index. We derive the apparent activation energy (Ea) and frequency factor (A), both present in the rate constant k, by fitting them to the extent of albitization measured in 11 samples from the San Joaquin Basin. Subsequently, we test the model against two independent albitization trends, one from the Texas Gulf Coast basin and one from the Denver Basin of Colorado. Our results indicate that albitization in all three basins can be fit by an Ea of 68 ± 4 kJ/mole and A of (6.5 ± 0.5) × 103 1/cm2 Ma. The rate dependence on temperature is consistent with experimental values for albite crystal growth and with empirically derived precipitation rates of other diagenetic silicates such as illite and quartz. The parameters and fit suggest that albitization can be modeled as a surface controlled reaction, primarily dependent on temperature.