Stochastic approach for the prediction of PSD in nonisothermal antisolvent crystallization processes

Abstract

A stochastic formulation for the description of cooling-antisolvent mediated crystal growth processes based on the Fok- ker-Planck equation is discussed. Previous results are further extended to include not only the additional degree of free- dom (temperature) in the approach, but also to formulate the model parameters dependencies with the input manipulated variables (antisolvent flow rate and temperature) toward a global model to be used within all possible operating regimes. The obtained global models are used to define, for the first time, an operating map of the crystalliza- tion process, where asymptotic isomean and isovariance curves are reported in an antisolvent flow-rate-temperature plane. Input multiplicities are identified and validated both numerically and experimentally for the NaCl-water-ethanol nonisothermal antisolvent crystallization system

A generalized stochastic modelling approach for crystal size distribution in antisolvent crystallization operations

“…To use the model over the whole operating range, linear piece‐wise interpolation approaches have been first exploited . Later, Cogoni et al extended these results by eliminating the linear piece‐wise interpolation and defining analytical expression for the parameters dependencies on the operating conditions. In the following we will extend these ideas in terms of the new formulation proposed in previous sections and propose an explicit dependence of the stochastic model parameters on input variables, , where represents the antisolvent flow rate and the bulk temperature.…”

“…From the inspection of the experimental behavior, it is possible to hypothesize that the model parameters can have a nonlinear or weak nonlinear dependence on inputs. From the above considerations, the proposed input‐parameter models are required to satisfy the following conditions: (1) simple linear or quadratic dependences have been preferred to describe the input‐parameter relationships and (2) the cross term dependence on and should be avoided . In spite of these simplifications, there are however many possible models to be implemented; indeed each parameter may depend on several combinations of and and thus, there are many alternative models to be considered.…”

“…To detect the most suited model among the possible alternatives, which depends on the functionality of and , the Akaike information criterion (AIC) measure has been used . The AIC definition is reported in Eq.…”

“…Recently, an alternative approach to the PB was proposed by Grosso et al, where the crystal length was assumed to be a random variable and the Fokker‐Planck equation (FPE) was solved to describe the CSD time evolution. The model developed by Grosso et al was improved by assessing the most appropriate stochastic component, and describing the dependence of model parameters from input variables . All previous results were obtained by applying a variable transformation to obtain a constant diffusion term in the FPE, which made easier its numerical integration.…”

On‐line control of crystal properties in nonisothermal antisolvent crystallization

“…The recent development of a stochastic approach to model the nonisothermal antisolvent crystallization process of sodium chloride, allowed an accurate analysis on the controllability property of such system. Different control strategies to track the system toward the desired CSD were compared by simulation using the nonlinear global stochastic model .…”