Generalized shrinking particle model of leaching: Effect of the order of surface chemical reaction, liquid-to-solid ratio and non-ideal behaviour of the liquid phase

A generalized non-porous shrinking particle model (G NSPM) of leaching has been verified and used for numerical simulations. Unlike the commonly used “simple” non-porous shrinking particle model (S NSPM), the G NSPM assumes n−th order chemical reaction, the influence of the L/S ratio and non-ideal behaviour of the leach solution. The leaching of dead-burned magnesite with hydrochloric acid has been chosen to verify the proposed mathematical model, as the (apparent) reaction order for HCl, n, may be both positive and negative, depending on the HCl concentration. Comparison of the simulations with experiments revealed that the S NSPM does not reflect the qualitatively different leaching behaviour at positive and negative n, especially at near-to-stoichiometric HCl/MgO ratio. The G NSPM reflects the effect of n not only qualitatively, but also with acceptable accuracy. At the stoichiometric HCl/MgO ratio, the mean squared error of the predictions obtained using the S NSPM was 100–130 rel. % as compared to those provided by the G NSPM. The common effect of the reaction order, n, L/S ratio (represented by the reduced HCl/MgO molar ratio, ϕ) and non-ideal behaviour of the acid were studied in detail by means of numerical simulations. The values of parameters n and ϕ can alter the leaching behaviour qualitatively. In contrast, the activity coefficient of HCl only slightly modifies the shape of the kinetic curves, but does not change the overall picture. The error of the time for complete conversion of MgO calculated using the S NSPM can reach more than 100 rel. % for n = − 0.5 and even up to several hundred rel. % for n = 1, because the conversion vs. time curves predicted by the G NSPM are markedly skewed towards longer leaching times.