Search

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.

A generalized non-porous shrinking particle model (NSPM) of leaching is proposed, which - unlike commonly used “simplified” mathematical models - takes into account the influence of the L/S ratio (by means of the so-called reduced A/B molar ratio, ϕ, which indicates how many times the leaching agent (A)-to-valuable substance (B) molar ratio actually used exceeds its stoichiometric value) and non-ideal behaviour of concentrated lixiviants. Moreover, n-th order chemical reaction with power-law kinetics is considered, which makes determination of the rate-determining step of the overall process more reliable. Correlation between the proposed model and experiment was tested using the hydrochloric acid leaching of dead-burned magnesite, which provides the opportunity to experimentally verify how the mathematical model fits the leaching data for both the positive and negative reaction order. Calculated values of the reaction order for HCl, n, different from unity (n = 0.28 and n = −0.23 obtained for low (0.20–1.03 M) and high HCl concentrations (2.06–3.83 M), respectively), together with relatively high values of the activation energy (57.5 J mol−1 and 56.6 J mol−1) indicate that the leaching rate is controlled by the intrinsic chemical reaction under the conditions considered in the present work. Simulations made using the calculated values of the parameters have shown that the proposed generalized NSPM model clearly reflects two most important experimental facts: (a) L/S ratio affects the leaching process; and (b) qualitatively different leaching behaviour has been observed for the positive and negative reaction order. Unlike the simplified NSPM model, the generalized model describes the leaching process quantitatively in the whole range of the parameter ϕ, for both n > 0 and n

The overall process for producing pure magnesium compounds from serpentinite usually starts with acid leaching. However, if serpentinite is calcined prior to leaching, not only faster magnesium dissolution is achieved, but use of thermally activated serpentine also significantly reduces the problems relating to corrosion of the leaching equipment, because less aggressive leaching agents can be used and/or lower leaching temperatures and pressures can be applied. This paper compares how calcination influences the dissolution behaviour of magnesium in solutions of hydrochloric acid, acetic acid and ammonium chloride. Fine-grained serpentinite, characterized by the extent of serpentine decomposition between 85 and 95%, displayed the highest reactivity. The initial magnesium dissolution rate of calcined serpentinite was up to 30-, 125- and 165-times higher as compared to that of uncalcined serpentinite in solutions of hydrochloric acid, acetic acid and ammonium chloride, respectively, under identical reaction conditions.

The kinetics of the reaction between particulate stibnite and mixed Na2S + NaOH solutions were studied. The effects of the concentration of the Na2S and NaOH (from 0.5% to 2.0%), temperature (from 292 K to 327 K) and particle size (from 40 μm to 500 μm) were investigated. The results are presented in terms of the shrinking (non-reacted) core model and the shrinking porous-particle model. The apparent activation energy was approximately 44 kJ mol− 1, and the apparent reaction order for Na2S varied from 1.4 to 1.7. The calculated values of the kinetic parameters indicate that the leaching process is controlled by both the intrinsic chemical reaction between Sb2S3 and Na2S at the liquid/solid interface and pore diffusion.

Kinetics of the reaction between dead-burned magnesite and hydrochloric acid were investigated with special regard to the rate of chemical dissolution of MgO. The effect of process parameters viz. temperature, activity of H + ions, and particle size and composition of the solid was investigated. The dissolution of MgO was strongly affected by temperature (from 45 to 75 °C) and particle size (from 63 to 355 μm), while the effect of composition of the solid was weak. The results are presented in terms of the shrinking particle model. The dissolution of MgO is controlled by the chemical reaction of MgO with H + ions at the liquid–solid interface. The apparent activation energy was 58–64 kJ mol −1 . Acid concentration (from 1.0 to 5.3 M) was surprisingly found to have a decelerating effect on the dissolution rate of MgO, resulting in negative values of reaction order for H + ions (from −0.1 to −0.2). We conclude that the leaching behaviour studied here corresponds to the regime referred to in the literature as the “initial stage of dissolution of MgO”. This regime, during which the dissolution rate increases rapidly despite a decrease in H + concentration, is characterised by far from mass-transfer control conditions, which was exactly the situation analysed in the present work.

The leaching of calcined magnesite using ammonium chloride has been tested in a pH-stat to ascertain the effect of process parameters viz. temperature, concentration of NH 4 Cl, pH, and particle size and reactivity of the solid. The main purpose of the approach adopted was to keep the lixiviant composition constant during individual measurements. A simple mathematical model has been used to describe the dissolution of magnesium during leaching and to analyse the kinetic data. The apparent activation energy of leaching was found to depend on the particle size of the solid — the values 57.8 and 48.5 kJ mol −1 were obtained for the leaching of particles of −100+90 and −180+160 μm, respectively. It was concluded that the leaching process is controlled by the chemical reaction of MgO with H + ions at the liquid–solid interface and by pore diffusion.