Modeling and Measurement of the Dissolution Rate of Solid Particles in Aqueous Suspensions – Part I: Modeling

Abstract

The dissolution/crystallization rate of suspended particles is a substantial parameter in particle/fluid systems. Frequently, the mass transfer is accompanied by chemical reactions, which affect the mass transfer in the boundary layer surrounding the particles. Additionally, in particular in liquids, the physical interactions between the species dissolved in the suspension have to be considered.In the modeling of such systems one has to differentiate between fast chemical reactions, which instantaneously attain chemical equilibrium, and reactions, which are slow with respect to mass transfer. An important example for the influence of fast and slow reactions on the mass-transfer rate is the dissolution of limestone in aqueous electrolyte solutions, where solid limestone (CaCO 3 ) particles dissolves under formation of calcium (Ca 2 + ), carbonate (CO 3 2± ) and hydrogencarbonate ions (HCO 3 ± ):(1)While the reactions (1) and (2) are instantaneous, the hydrolysis of the dissolved CO 2 ,is slow. Moreover, the limestone dissolution rate is affected by other dissolved species, e.g. soluble salts (physical effect), as well as by reactions, which change the pH (chemical effect). Since also gaseous CO 2 affects the dissolution rate of limestone, for the calculation of the dissolution process a three-phase system consisting of the gas phase, the liquid and the suspended solid particles has to be modeled which, in addition to the dissolution/crystallization of the particles, also considers the absorption/desorption processes between the gas and the liquid phase.The general model for the limestone dissolution is developed in three steps. First, under consideration of the mass transfer, the reaction kinetics and the thermodynamic equilibrium a reaction diffusion model for single limestone particles is set up. In the second step, an universal dynamic mass-transfer model for the three-phase system gas/liquid/ solid is developed. Subsequently, the single-particle model is combined with the population balance and integrated into the dynamic model. After adjustment and validation the model enables the simulation of instationary dissolution and crystallization processes with polydisperse solids. A Reaction-Diffusion Model of the Limestone Dissolution RateThe flux of the calcium ions, which corresponds to the dissolution rate of the limestone particles, can be expressed by

Dissolution rate of limestone for wet flue gas desulfurization in the presence of sulfite

“…(5) at a given utilization, the area of limestone particles from each size fraction can be determined by Eqs. (4) and (6), then the dissolution flux of the limestone sample can be calculated by Eq. (3).…”

“…Toprac and Rochelle [1] found that there is no effect of limestone type and particle size distribution is the most important influence factor of limestone dissolution. Chan and Rochelle [2], Wallin and Bjerle [3] and Allers et al [4,5] studied the dissolution rate of limestone in a pH-stat apparatus under various conditions and reported that the dissolution process can be successfully simulated by mass transfer model combined with the effects of several equilibrium acid/base reactions and the finite reaction of CO 2 and H 2 O in the boundary layer. Other researchers found that surface reaction may also affect the dissolution process of limestone.…”

Modeling and Measurement of the Dissolution Rate of Solid Particles in Aqueous Suspensions – Part II: Experimental Results and Validation

“…The decrease of the particle volume V p is essentially determined by the mole fractions of the calcium ions at the particle surface, x L Ca 2+ can be computed for each particle size from the set of equations of the reaction-diffusion model presented in [2]. Introducing the initial particle volume V 0 , Eq.…”

“…Under the assumption that each particle size distribution is adequately represented by its mean particle size, the monodisperse model presented in [2] was adjusted to these data in the following way.…”

“…The adjusted single particle model was combined with the population balance and the three-phase model presented in [2] to a general simulation model for the dissolution of polydisperse solids. Extensive calculations and measurements have been performed to verify the model [1].…”