Mineral precipitation associated with vertical fault zones: the interaction of solute advection,diffusion and chemical kinetics

This article is concerned with chemical reactions that occur between two interacting parallel fluid flows using mixing in vertical faults as an example. Mineral precipitation associated with fluid flow in permeable fault zones results in mineralization and chemical reaction (alteration) patterns, which in turn are strongly dependent on interactions between solute advection (controlled by fluid flow rates), solute diffusion/dispersion and chemical kinetics. These interactions can be understood by simultaneously considering two dimensionless numbers, the Damköhler number and the Z‐number. The Damköhler number expresses the interaction between solute advection (flow rate) and chemical kinetics, while the Z‐number expresses the interaction between solute diffusion/dispersion and chemical kinetics. Based on the Damköhler and Z‐numbers, two chemical equilibrium length‐scales are defined, dominated by either solute advection or by solute diffusion/dispersion. For a permeable vertical fault zone and for a given solute diffusion/dispersion coefficient, there exist three possible types of chemical reaction patterns, depending on both the flow rate and the chemical reaction rate. These three types are: (i) those dominated by solute diffusion and dispersion resulting in precipitation at the lower tip of a vertical fault and as a thin sliver within the fault, (ii) those dominated by solute advection resulting in precipitation at or above the upper tip of the fault, and (iii) those in which advection and diffusion/dispersion play similar roles resulting in wide mineralization within the fault. Theoretical analysis indicates that there exists both an optimal flow rate and an optimal chemical reaction rate, such that chemical equilibrium following focusing and mixing of two fluids may be attained within the fault zone (i.e. type 3). However, for rapid and parallel flows, such as those resulting from a lithostatic pressure gradient, it is difficult for a chemical reaction to reach equilibrium within the fault zone, if the two fluids are not well mixed before entering the fault zone. Numerical examples are given to illustrate the three possible types of chemical reaction patterns.