Mass transfer analysis stage efficiency

In packed columns, it is conceptually incorrect to use the staged model even though it works if the correct height equivalent to a theoretical plate (HETP) is used. In this chapter we will develop a physically more realistic model for packed columns that is based on mass transfer between the phases. After developing the model for distillation, we will discuss mass transfer correlations that allow us to predict the required coefficients for common packings. Next, we will repeat the analysis for both dilute and concentrated absorbers and strippers and analyze cocurrent absorbers. A simple model for mass transfer on a stage will be developed for distillation, and the estimation of stage efficiency will be considered. After a mass transfer analysis of mixer-setder extractors. Section 16.8 and the appendix to Chapter 16 will develop the rate model for distillation. 

Because extraction mixer-setders typically operate at stage efficiencies above 80% and often in the range from 95% to 100%, the equilibrium stage analysis in Section 13.14 is often used with an assumed value for the stage efficiency. However, a more accurate design will result if a mass-transfer analysis is used to estimate the stage efficiency. The purpose of the analysis will be to estimate the value of the dispersed-phase Murphree stage efficiency, Ej. ... 

Thus adsorption asks a different kind of question than the questions asked in absorption, distillation, or extraction. In absorption or differential distillation, the basic question is how tall a tower is needed. This question is answered with a mass transfer analysis, including an operating line and an equilibrium line. The mass transfer analysis includes overall and individual coefficients summarized by dimensionless correlations. In staged distillation or extraction, the basic question is how many stages are needed. This question is resolved largely with operating and equilibrium lines, with the mass transfer aspects conveniently compressed into an efficiency. In absorption, distillation, and extraction, the analysis is sufficiently reliable to answer the questions without experiment. 

A major assumption made in the column models of Chapters 3 through 13 was the equilibrium stage. Tray hydraulics provides additional information essential for applying mass transfer theories to evaluate the column performance with a rate-based approach. This analysis provides a basis for calculating the tray efficiency associated with an equilibrium stage. The topics of rate-based analysis and tray efficiency are also discussed in this chapter. 

Except for the short introductory Section 1.3. to this point the entire analysis of separation processes has been equilibrium based. Effects of nonequilibrium operation have been lunped into either a stage efficiency f Sections 4.11.10.2.12.5. and 13.51 or to the height equivalent of a theoretical plate (HETP Sections 10.9 and 10.111. We must move beyond an equilibrium analysis if we want to be able to predict values of the stage efficiency and the HETP fChapter 161. to study membrane separators fChapter 171. or to study sorption separations fChapter 181. For all of these situations, we must look at the mass transfer occurring in the separator. This chapter presents the fundamentals of diffusion and mass transfer in sufficient detail so that the analysis in the remaining chapters is understandable. Additional information on mass transfer is presented as needed in Chapters 16 to 18. If you have already studied mass transfer and diffusion, most, but probably not all, of this chapter will be a review, and you will not have to spend much time studying the material. 

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