Surface reaction versus diffusion control of mineral dissolution and growth rates in geochemical processes

The kinetics of chemical reactions at mineral surfaces and the rates of diffusion of species in an aqueous phase are coupled in many geochemical systems. Analytical solutions to equations describing coupled mineral dissolution/growth and solute transport in both transient and steady-state systems are used to delimit regimes of pure reaction control, pure transport control and mixed kinetic control of mass-transfer rates. The relative significance of the two processes depends on the magnitudes of the diffusion coefficients and rate constants as functions of temperature, and the degree of disequilibrium in the system. In addition, the system geometry, the ratio of mineral surface area to diffusion cross-section, and the porosity and tortuosity of the medium through which aqueous species diffuse affect reaction vs. diffusion control. In general, diffusion control increases with increasing temperature and increasing distance over which diffusion occurs. Calculations for the mixed kinetic regime in transient systems demonstrate that the relative significance of diffusion and surface reaction varies with reaction progress, and approaches a limiting value as equilibrium is approached. This limiting value may be appropriate to natural water-rock interactions that occur at conditions that are close to equilibrium. This result permits extension of simple models for irreversible mass transfer in homogeneous systems to systems in which mass-transfer kinetics are controlled by coupled surface reactions and mass transport. Criteria are established for time and length scales and fluid velocity limits on the validity of the continuum hypothesis and the local equilibrium assumption in mass-transport modeling.