Compositional controls on melting and dissolving a salt into a ternary melt

We explore theoretically the controls on dissolution of salt A, in an under-saturated brine of salts A and B. We show that, as the concentration of B increases, the disso- lution rate of A decreases, for brine of given temperature. We also show that there is a sharper decrease in dissolution rate with increasing concentration, for concen- trations of B above a critical value, where B limits the equilibrium concentration. We explore the implications of the predictions for dissolution of KCl or NaCl, by a mixed brine of NaCl and KCl, a common reaction that may arise in dissolution of evaporites. We predict that, with mixed-composition brine, KCl crystals dissolve more rapidly than NaCl crystals, unless the (far-field) brine is nearly saturated in KCl. We also predict that the dissolution rate of these salts is largely independent of fluid temperature, and is controlled by compositional diffusion. There are natural and industrial processes, including salt dissolution during water flooding of porous rocks, melting caused by hot magma intrusion into the shallow crust of the Earth, and solution mining of minerals, in which a soluble solid dissolves into a multi-component liquid solution. In particular, in the context of evaporite formation and extraction, there is interest in the dissolution of one salt by an aqueous solution containing two or more solutes. The purpose of this paper is to quantify the dissolution rate, as a function of the temperature and the concentration of each salt in the melt. We restrict attention to the situation in which diffusion is the dominant mechanism for heat and mass transport, building from the classical Stefan problem approach for equilibrium phase change (cf. Carslaw & Jaegar, 1986; Woods, 1992). Although in many natural situations, fluid convection may develop, there are regimes in which diffusion provides the dominant mass transport process. For example, as evaporites are formed, there are periods in which relatively fresh fluid may enter a lagoon (cf. Sonnenfeld, 1985). This may then lead to dissolution of salt from the bed of the lagoon, and formation of a stable stratification. Also, in the context of sea ice/ocean interaction, relatively warm, saline ocean water may impinge on the underside of sea ice. The ice may then melt into the ocean water, again forming a stable stratification (cf. van Andel, 1994). In these cases, the phase change will be diffusion-controlled. Even where there is a driving force for convection, our analysis provides a reference, with which to compare the effects of convection on the phase change. In section 3 we build on the self-similar solutions for dissolution of a single species in a brine