Generic Issues of Batch Dissolution Exemplified by Gypsum Rock

Abstract

Recent work has emphasized that the empirical rate equation for batch dissolution of a solid consists of a forward term involving the surface area minus a back reaction term involving surface area and concentration of dissolved solid. Integrated forms exist for use at extremes of high under-saturation and of very heavy solid loadings which lead to saturation. A middle condition allows for significant decrease in solid supply and simultaneous arrival at saturation. This study tests the three approaches simultaneously to the batch dissolution of gypsum, thereby demonstrating a consistent applicability of the aforementioned rate equation. Previously, some mineral dissolutions have displayed so-called nonlinear kinetics and hence have not appeared to conform to this rate equation. This paper provides a template for future investigation of those situations; dissolution experiments are not easy to perform, and instances of the so-called nonlinear kinetics may represent experimental artefact. The relationship between this empirical approach and that of Transition State Theory used in mineral dissolution is discussed, and a new, linear proof for the applicability of the 'middle ground' equations is demonstrated. Stirring experiments highlight the difference between the conditions in fluidized bed and laminar flow reactors. Gypsum dissolution is found to be transport limited at all but very vigorous laboratory stirring conditions, although the relationship between the rate of shrinkage of gypsum particles and stirring seems to be relatively simple. A stirring factor is applied to the rate equation overall to allow for differences in reactor design, and it is suggested that this should also be applicable to laminar flow reactors. The link between batch and chemo-stat dissolutions is stressed, together with a need to contour dissolution data on a new graph of particle size versus stirring rate.

Rate Equations and an Ion-pair Mechanism for Batch Dissolution of Gypsum: Repositioning the Shrinking Object Model at the Core of Hydrodynamic Modelling

“…An improved ion-pair model had to be designed to cope with the calcium and sulphate concentrations at ratios other than 1:1, which occur when calcium and sulphate are added as common ions. While this study completes the validation of the shrinking object model with gypsum, it also completes the larger programme involving salts, sucrose, silica gel, and the gypsum (Truesdale 2007(Truesdale , 2008(Truesdale , 2009(Truesdale , 2010a. Accordingly, it is timely to place the shrinking object dissolution model in a much wider context of reaction mechanisms as well as hydrodynamics.…”

“…The shrinking object model (Truesdale 2009(Truesdale , 2010aKamatani et al 1980) originates from the O'Connor and Greenberg (1958) rate equation:…”

“…The equation can be fitted to real data either non-linearly (Truesdale 2007) or linearly (Truesdale 2010a), and a given run yields a value of a Ka , which consequently has been named as the shrinking object rate parameter by Truesdale 2010a). Taking account of the N 1/3 term in the right-hand side of Eq.…”

“…Using gypsum, Truesdale (2010a) validated the shrinking object model for batch dissolution in a turbulent, fluidised-bed reactor. Two of three markedly different sets of conditions (Truesdale 2007(Truesdale , 2008(Truesdale , 2009(Truesdale , 2010a were validated: highly under-saturated dissolutions that terminate because the supply of solid runs out; and highly loaded dissolutions that go to saturation.…”

“…Two of three markedly different sets of conditions (Truesdale 2007(Truesdale , 2008(Truesdale , 2009(Truesdale , 2010a were validated: highly under-saturated dissolutions that terminate because the supply of solid runs out; and highly loaded dissolutions that go to saturation. Because of the deficiencies in the calibration procedure needed for the conductimetry (Truesdale 2010a), middle-ground dissolutions that terminate either side of saturation but where the surface area of the solid decreases significantly during dissolution were not studied. Meanwhile, the study did show that stirring rate is important in gypsum dissolution but easily accommodated by the shrinking object model as an exponentially increasing function.…”