A general kinetic-based model for precipitation has been identified and validated. The model is first order in mineral state and nth order in supersaturation. The model is tolerant to a fast kinetic coefficient, but not a slow coefficient. The kinetic effect of temperature can be corrected with Arrhenius-relationships. This base model can be applied to multiple simultaneous precipitation reactions.
73(a) an assumption that precipitation reactions are occurring at sufficiently rapid rates to be 74 effectively at equilibrium Hanhoun et al., 2011; Loewenthal et al., 1995; 75 et al., 1998;Scott et al., 1991;Wrigley et al., 1992) The CCM experiments used a crystallizer (See schematic in Supporting Information) which 148 was a 1.0 L (working volume = 900 mL) Pyrex glass vessel with a glass heating/cooling 149 jacket and a sealed lid with crimp-sealed ports for sensors to minimize atmospheric gas- GA) and is given in Table 1. Seed crystal morphology was examined with scanning electron 207 microscopy (JEOL 2100, JEOL Ltd, Tokyo, Japan) and was found to resemble the typical 208 morphology of calcite with reasonably uniform particle size.
210The major elements (Ca, Na) in the synthetic aqueous solution were analysed with ICP-OES The species and components were also used to determine precipitation or dissolution, by Nordstrom et al., 1990;Plummer and Busenberg, 1982). For a given aqueous 289 phase, three conditions exist:
290• 0, the aqueous phase is undersaturated and a mineral solid phase can dissolve 291 into the aqueous phase;
292• 0, the aqueous phase is saturated or at equilibrium; or any time t (a dynamic state variable) (similar to the approach of (Wiechers et al., 1975)) and
308 is the order of the precipitation reaction with respect to supersaturation, , calculated as 309 follows (Nielsen, 1984):
311A non-zero initial condition of of 1×10 -6 M (which is 0.1 mg.L -1 ) was used to model 312 the dynamic titration experiment that had no seed crystals added (self-nucleating).
314The gaseous species carbon dioxide (CO 2 ) is not considered in this model (only dissolved The only adjustable parameter in the baseline model (Eq. (7) where k cryst,25 is the reference value of k cryst at 25°C (298K), R is the ideal gas constant The objective function J (residual sum of squares) is presented in Fig. 2 and shows that the minutes (never at equilibrium). These results suggest that the precipitation was still