Kinetic rate laws invariant to scaling the mineral formula unit

Abstract

A modified form of the kinetic rate law for mineral dissolution and precipitation is proposed that is invariant to a scale transformation of the mineral formula unit. The scale factor appears in both the affinity factor determining the extent of disequilibrium and in the prefactor term, which multiplies the affinity factor. The form of the rate law is obtained by imposing invariance of the reactive transport equations on scaling the mineral formula unit, a basic requirement of all kinetic rate laws describing mineral reactions. This requirement is shown to be consistent with the Horiuti-Temkin formulation of the overall reaction rate for stationary-state conditions. The overall rate law is derived by summing a network of elementary reaction steps each weighted by a stoichiometric number giving the rate of the ith intermediate step relative to the overall reaction rate. However, it is noted that current formulations of mineral kinetic rate laws are more empirically based and do not always satisfy the requirement that the elementary reaction steps defining a reaction mechanism sum to form the overall reaction. In addition, there appears to be confusion in the literature between the Temkin average stoichiometric number and the scale factor related to the mineral formula unit, which are shown to be two distinct quantities. Finally, it is noted that in recent numerical simulations modeling sequestration of supercritical CO₂ in deep geologic formations, different chemical formulas for oligoclase have been used related by a scale factor of five without taking into account the scale factor in the kinetic rate law. This oversight could result in potentially significantly larger oligoclase dissolution rates, and exaggerated CO₂ mineralization through precipitation of dawsonite.