Non-porous shrinking particle model of leaching at low liquid-to-solid ratio

Abstract

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.