On the narrowing of particle‐size distributions in staged vessels with classified product removal

Abstract

A well-known, but quite inefficient, representation of dead time in a continuous process is that of a series of staged vessels with equal time constants. Buckley (1) compares such a series approximation for dead time, TD, with other methods of dead time representation. The transfer function for this approximation (equivalent to k wellmixed stages in series) is given as The transfer function given by Equation ( 1) , applied to the problem of residence-time distributions of particles residing in a system of k serially-staged well-mixed vessels, indicates that as the number of tanks in series increases, a uniformity of residence time within the total system occurs.As k -+ 00 the residence-time distribution of plug-flow (pure dead time) is predicted.Robinson and Roberts ( 2 ) attacked the problem of predicting crystal size distribution in a staged crystallizer by calculating the residence-time distribution of particles in the system, assuming they grew at the same linear rate in each of the vessels. It was further necessary to assume that all particles entered (were formed) at zero size in the first stage. These authors did not dwell on the narrowing of crystal size distribution expected in such a system. Randolph and Larson (3) considered the same problem of crystal size distribution in staged systems, but allowed for particle formation (nucleation) in each of the stages. The resultant population distribution leaving the kth stage was calculated to be (2) L rT rV where x = -= -LQ is a dimensionless particle size.Again, it was necessary to assume that the product of linear growth rate and mean retention time was equal in each stage. Cumulative weight distribution was obtained from population distribution as Alan D. Randolph ib at the University of Arizona, Tucson, Arizona. Chand Deepak is with the American 0 1 1 Co., Whiting, Indiana.The occurrence of nucleation in each stage results in a wider distribution of residence times, and hence wider crystal size distribution, but the above cited reference did not comment on this aspect.In the general problem of predicting crystal size distribution from a serially-staged crystallization process, one must take into account nucleation-growth rate kinetics as well as a mass balance, which latter constrains the growth rates obtainable. A sufficient set of equations to describe crystal size distribution produced from a general staged crystallization process with segregated particle withdrawal is as follows. The solution of these equations for a particular system would yield complete information about the system, including concentrations, production rates, and crystal size distribution in each stage. Such calculations can only be meaningful when a large amount of information concerning kinetics of nucleation and growth, as well as particle draw-down rates, Q(L), is available on a particular system.It is the purpose of this paper to generalize on the form, but not the magnitude, of crystal size distribution obtainable from such serially staged processes. Particle drawdown rates, Q ...

The Role of Residence Time Distribution in the Continuous Steady-State Mixed Suspension Mixed Product Removal Crystallization of Glycine

“…Rapid intermittent withdrawal is considered a form of continuous operation since changes in steady-state conditions are negligible when slurry slug size withdrawn is less than 10% of the crystallizer volume. , Specifically, we study the impact of process parameters including MSMPR temperature and mean residence time on the steady-state product CSD, mean crystal size, and yield. To address the backmixed nature of the MSMPR, different configurations have been employed with the chief aim of obtaining better CSD quality alongside process yield. − Attempts to control product CSD using multistage MSMPR crystallizers have been reported in the literature, , and these studies have suggested that the single-stage MSMPR crystallizer is inefficient, because it produces a product with a broader CSD than the multistage MSMPR crystallizer. Also, in terms of process operability, the single-stage MSMPR crystallizer has limited temperature controllability because of its small heat transfer area .…”

“…To address the backmixed nature of the MSMPR, different configurations have been employed with the chief aim of obtaining better CSD quality alongside process yield. 25−28 Attempts to control product CSD using multistage MSMPR crystallizers have been reported in the literature, 29,30 and these studies have suggested that the single-stage MSMPR crystallizer is inefficient, because it produces a product with a broader CSD than the multistage MSMPR crystallizer. Also, in terms of process operability, the single-stage MSMPR crystallizer has limited temperature controllability because of its small heat transfer area.…”

Operating Strategy for Continuous Multistage Mixed Suspension and Mixed Product Removal (MSMPR) Crystallization Processes Depending on Crystallization Kinetic Parameters

“…Another advantage of the MSMPR system is its easy conversion from batch processes to continuous processes through the use of simple technologies . Using the mathematical model for MSMPR developed by Randolph and Larson, effective design and configuration of the MSMPR crystallizer to improve product quality has been extensively researched. ,− Several researchers have reported that the single-stage MSMSR crystallizer is inefficient, because it produces a product with a broader CSD than the multistage MSMPR crystallizer. , In addition, from the view of process operability, the single-stage MSMPR crystallizer is unfavorable, since the temperature controllability is limited, because of its small cooling surface area . This results in a higher operating cost than for the multistage MSMPR crystallizer.…”

“…1,11−15 Several researchers have reported that the single-stage MSMSR crystallizer is inefficient, because it produces a product with a broader CSD than the multistage MSMPR crystallizer. 15,16 In addition, from the view of process operability, the single-stage MSMPR crystallizer is unfavorable, since the temperature controllability is limited, because of its small cooling surface area. 17 This results in a higher operating cost than for the multistage MSMPR crystallizer.…”