Critical evaluation of coupling particle size distribution with the shrinking core model

Abstract

The shrinking core model (SCM) is widely used to model fluid–solid reactions such as the leaching of metals from minerals. In most cases, however, the particle size distribution (PSD) of the solid material was disregarded. In this paper the erroneous shift in the control regime when neglecting PSD was quantified and the dependence of the shift on the coefficients of variation (CV) and the type of PSD was analysed. By coupling the SCM with a Gamma PSD, it was found that neglecting the PSD would shift the control regime from chemical reaction to inert/ash layer diffusion, when the CV was between 0.7 and 1.2. For a system controlled by liquid film diffusion, neglect of the PSD, would shift the control regime to chemical reaction when CV is between 0.3 and 0.7 or to inert/ash layer diffusion when CV is greater (0.9–1.5). It was therefore postulated that some researchers had unknowingly made invalid conclusions about the control regime due to the neglect of PSD. However, an inert/ash layer diffusion-controlled process was insensitive to the neglect of PSD. When CV<0.3, neglect of the PSD would not cause any erroneous shifts, irrespective of the control regime. Experimental data confirmed the observation. For a given CV, the deviation in the fraction reacted from the mono-PSD increases with CV and decreases with time. The maximum deviation, which occurs at the beginning, is about 10% with a gamma PSD of CV=0.3. The percent deviation is dependent of the type of PSDs. Gamma PSD gives the lowest deviation while Gaudin–Schuhmann results in the largest deviation (maxi. ∼19%, with CV=0.3) in the first half of dissolution process. Log-normal distribution gives a larger deviation than gamma but quickly approaches the latter with time. The deviation for Rosin–Rammler is between log-normal and Gaudin–Schuhmann. For systems with CV less than 0.3, the SCM can be fairly used without considering PSD. When CV is greater than 0.3, particularly in the early stage of a dissolution process with a PSD other than gamma, PSD should be included to avoid substantial errors.