دانلود رایگان مقاله مدل سازی ریاضی و طراحی بهینه چند مرحله تبلور جریان اسلاگ

Abstract

Inspired from experimental progress in continuous crystallizer designs based on air/liquid slug flow that generate crystals of target sizes at high production rates and low capital costs (e.g., Eder et al., 2010; 2011; Jiang et al., 2014; 2015; and citations therein), a mathematical model and procedure are derived for the design of slug-flow crystallizers with spatially varying temperature profiles. The method of moments is applied to a population balance model for the crystals, to track the spatial variation of characteristics of the crystal size distribution along the crystallizer length. Design variables for the cooling slug-flow crystallizer such as tubing lengths and types and numbers of heat exchangers are analyzed and optimized for product crystal quality (e.g., minimized secondary nucleation and impurity incorporation) and experimental equipment costs, while ensuring high yield. This study provides guidance to engineers in the design of slug-flow crystallizers including their associated heat exchanger systems.

5. Conclusions

Mathematical models and design procedures are proposed for two continuous slug-flow crystallization systems. By combining constant-temperature cooling baths in series, the temperature of the slugs is stepped down gradually to maintain low supersaturation, to promote growth over nucleation, while allowing high yield. The advantage of simplicity is offset by relatively high spikes in supersaturation at the inlet to each bath. An alternative system is investigated that uses multiple counterflow double-pipe heat exchangers in series to reduce the temperature more gradually. The double-pipe heat exchange system provides similar high yield, while reducing the maximum supersaturation by a factor of three in a case study using realistic experimental values for the parameters. In the case study, it was observed that increasing the number of heat exchangers beyond three had only a small effect on the optimal design objective and tradeoff curve (Fig. 7). For either heat exchanger design, an extra length of tubing can be used to ensure that the desired yield is achieved for a specified uncertainty in growth kinetics (Fig. 6).