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The kinetics of the leaching of natural magnesite with hydrochloric or nitric acid has been studied. Relatively high values of the apparent activation energy (from 46.5 to 70.0 kJ mol−1), but especially the low values of the apparent reaction order for H+ cations, $n$ n , have shown that the whole process is controlled by the surface chemical reaction. The value of $n$ n decreases continuously with increasing activity of H+ cations in the range of pH 5 to −1.4. At ${\rm{pH}}\,\lt 2.6$ pH < 2.6 there is a transition from the kinetic regime characterized by $n \cong $ n ≅ 0.5 to another one with $n$ n close to zero. [ABSTRACT FROM AUTHOR]

Leaching kinetics of natural magnesite with nitric acid was investigated, and the results of a detailed critical analysis are presented. The reaction system MgCO3-HNO3-H2O has been studied with special regard to the production of pure magnesium salts. The generalised non-porous shrinking particle model considering the n-th order liquid-solid reaction was fitted to the measured kinetic data and the values of apparent activation energy, EA, and reaction order, n, were calculated. Relatively high values of EA (43.7 and 58.5 kJ mol-1) obtained for both "low" (0.01-0.1 M) and "high" (1-6 M) concentrations of HNO3, respectively, lay within the range of values presented by other authors and indicate that the overall process is controlled by the chemical reaction in the whole range of reaction conditions considered (temperature from 70 to 100°C and concentration of HNO3 from 0.01 to 6M). This hypothesis has been confirmed by the calculated values of n, which considerably differ from 1. Until now, it has been assumed in the literature that n=1 and no attention has been paid to the actual mechanism of the intrinsic chemical reaction. In this work, the value of n=0.22 was calculated for the solutions with "low" HNO3 concentration, and n=0.05 was obtained for the concentrated HNO3 solutions. These values of n are considerably lower than the value of n=0.5, predicted by the theory. It is hypothesised that the decrease in n with increased acid concentration might be related to the formation of CO2 and its transfer from the liquid to the gaseous phase. [ABSTRACT FROM AUTHOR]

All alternatives of the non-porous shrinking particle model (NSPM) referred to in the literature were reviewed and critically compared – they differ especially in their ability to reflect the role of three crucial model parameters: the order of reaction, liquid/solid ratio and activity coefficient of the leaching reagent. A procedure to calculate an experimental error related to the methodology of laboratory leaching tests (including the effect of different ore-particle size) has been proposed. Error propagation in the process of determination of the apparent order of reaction and activation energy from experimental data was analysed in detail, to estimate the systematic error of the simulation model developed. The simulation models tested were validated using the experimental data for the reaction system MgO-HCl-H 2 O. Based on the results obtained, some recommendations for an effective practical use of the NSPM have been suggested. • Methodology of kinetic leaching tests was analysed in detail. • Reaction mechanism for the system MgO-HCl-H 2 O has been proposed. • Experimental error for the system MgO-HCl-H 2 O was estimated. • Error propagation in determining the kinetic parameters of leaching was analysed. • Practical recommendations for the non-porous shrinking particle model were proposed based on the performed simulations. [ABSTRACT FROM AUTHOR]

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 q ualitatively 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. • G eneralized non-porous shrinking particle model (SPM) of leaching was verified. • Verified model reflects reality significantly better than the commonly used SPM. • Simulation model reveals the influence of the reaction order and L/S ratio. • The model shows the effect of non-ideal behaviour of the leach solution. [ABSTRACT FROM AUTHOR]

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 < 0. The simplified NSPM (which does not take into account the L/S ratio) describes the leaching process with sufficient accuracy when ϕ ≥ 10, but at ϕ < 10 the error grows exponentially with decreasing ϕ and can reach up to 11–17% rel. under the stoichiometric conditions (i.e., at ϕ = 1), in dependence on the value of n. It is assumed that the proposed generalized NSPM model provides a useful tool for planning kinetic experiments, identifying the kinetic model parameters and simulation of the leaching process even under stoichiometric conditions. • Reflects reality better than the commonly used simplified form, especially at low L/S ratio. • Makes determination of control mechanism more reliable. • Can be used for planning kinetic experiments, identifying model parameters and simulation. [ABSTRACT FROM AUTHOR]