Product particle size distribution prediction

Tailoring of the particle size of the crystals from industrial crystallizers is of significant importance for both product quality and downstream processing performance. The scientific design and operation of industrial crystallizers depends on a combination of thermodynamics - which determines whether crystals will form, particle formation kinetics - which determines how fast particle size distributions develop, and residence time distribution, which determines the capacity of the equipment used. Each of these aspects has been presented in Chapters 2, 3, 5 and 6. This chapter will show how they can be combined for application to the design and performance prediction of both batch and continuous crystallization. 

Perhaps the greatest difficulty in predicting fluidization performance via the Geldart (1973) classification is deciding on a single diameter to represent the complete material, especially if the product possesses a wide particle size distribution. This is supported to some extent by the more recent bulk density approach proposed by Geldart et al. (1984). 

Model simulations of particle volume concentrations in the summer as functions of the particle production flux in the epilimnion of Lake Zurich, adapted from Weilenmann, O Melia and Stumm (1989). Predictions are made for the epilimnion (A) and the hypolimnion (B). Simulations are made for input particle size distributions ranging from 0.3 to 30 pm described by a power law with an exponent of p. For p = 3, the particle size distribution of inputs peaks at the largest size, i.e., 30 pm. For p = 4, an equal mass or volume input of particles is in every logaritmic size interval. Two particle or aggregate densities (pp) are considered, and a colloidal stability factor (a) of 0.1 us used. The broken line in (A) denotes predicted particle concentrations in the epilimnion when particles are removed from the lake only in the river outflow. Shaded areas show input fluxes based on the collections of total suspendet solids in sediment traps and the composition of the collected solids. 

A continuous crystallizer producing 25,000 lb/h (11,340 kg/h) of cubic solids is continuously seeded with 5000 lb/h (2270 kg/h) of crystals having a crystal size distribution as listed in Table 10.2. Predict the product crystal size distribution if nucleation is ignored. If the residence time of solids in the crystallizer is 2 h, calculate the average particle-diameter growth rate G. 

The presence of nucleation can be determined by product screening If particles of size less than the seeds can be found, then nucleation is present. In such a case, prediction of product crystal size distribution requires a knowledge of nucleation kinetics see Randolph and Larson [3] for the basic mathematics. 

When a process is continuous, nucleation frequently occurs in the presence of a seeded solution by the combined effects of mechanical stimulus and nucleation caused by supersaturation (heterogeneous nucleation). If such a system is completely and uniformly mixed (i.e., the product stream represents the typical magma circulated within the system) and if the system is operating at steady state, the particle-size distribution has definite hmits which can be predicted mathematically with a high degree of accuracy, as will be shown later in this section. 

Vanadium molecular size distributions in residual oils are measured by size exclusion chromatography with an inductively coupled plasma detector (SEC-ICP). These distributions are then used as input for a reactor model which incorporates reaction and diffusion in cylindrical particles to calculate catalyst activity, product vanadium size distributions, and catalyst deactivation. Both catalytic and non-catalytic reactions are needed to explain the product size distribution of the vanadium-containing molecules. Metal distribution parameters calculated from the model compare well with experimental values determined by electron microprobe analysis, Modelling with feed molecular size distributions instead of an average molecular size results in predictions of shorter catalyst life at high conversion and longer catalyst life at low conversions. 

These models require information about mean velocity and the turbulence field within the stirred vessels. Computational flow models can be developed to provide such fluid dynamic information required by the reactor models. Although in principle, it is possible to solve the population balance model equations within the CFM framework, a simplified compartment-mixing model may be adequate to simulate an industrial reactor. In this approach, a CFD model is developed to establish the relationship between reactor hardware and the resulting fluid dynamics. This information is used by a relatively simple, compartment-mixing model coupled with a population balance model (Vivaldo-Lima et al., 1998). The approach is shown schematically in Fig. 9.2. Detailed polymerization kinetics can be included. Vivaldo-Lima et a/. (1998) have successfully used such an approach to predict particle size distribution (PSD) of the product polymer. Their two-compartment model was able to capture the bi-modal behavior observed in the experimental PSD data. After adequate validation, such a computational model can be used to optimize reactor configuration and operation to enhance reactor performance. 

Addition of an antisoivent is potentially the best method to achieve controlled and scalable particle size distribution (PSD). The addition can be either semibatch—antisoivent added to product solution or product solution added to antisoivent (reverse addition)—or continuous using an in-line mixer or stirred vessel. Of these, the in-line mixer offers in some cases the highest potential for predictable results, as wUl be discussed below. 

This chapter has presented a theoretical derivation of continuous particle size distributions for a coagulating and settling hydrosol. The assumptions required in the analysis are not overly severe and appear to hold true in oceanic waters with low biological productivity and in digested sewage sludge. Further support of this approach is the prediction of increased particle concentration at oceanic thermoclines, as has been observed. This analysis has possible applications to particle dynamics in more complex systems namely, estuaries and water and waste-water treatment processes. Experimental verification of the predicted size distribution is required, and the dimensionless coeflBcients must be evaluated before the theory can be applied quantitatively. 

An abbreviated version of the test procedure, incorporating an additional safety factor is used for routine product quality control and for the screening of development products. With this test, a reliable prediction of the enzyme s column performance can be made from a small sample in about an hour. It is important to realise that the hydraulic properties of the enzyme bed are related to the enzyme particle size distribution and rigidity. These properties in turn can be influenced by environmental factors, e.g. pH, ionic concentration, temperature and these effects have been studied extensively. 

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