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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