Rate-Based Analysis

Tray Hydraulics, Rate-Based Analysis, and Tray Efficiency 

The tray hydraulics model may be extended to include mass and heat transfer rates for calculating the liquid and vapor flow rates and compositions in trayed columns on the basis of a rate-based model. The objective is to more realistically represent the actual performance of the column by providing a basis for estimating a tray. For this approach to be practical, methods should be available for reliably predicting the mass and heat transfer rates. General rate-based models are also discussed in Chapter 15 for solving packed columns. 

FIGURE 14.7 Tray rate-based analysis schematic. 

The liquid phase on the tray being well mixed, its temperature is uniform, is equal to the temperature of the liquid leaving the tray, Tf-. The vapor enters tray j at temperature and leaves at. An energy balance and heat transfer equation for tray j is written as 

The froth on the tray is where mass transfer takes place between the phases, assumed to exist at equilibrium at the vapor-liquid interface. The well mixed liquid phase is at its bubble point temperature at equilibrium with the vapor interfacial composition Y. The vapor leaving tray j with composition Fy, is at temperature Ty, determined by heat transfer rates according to Equations 14.17 and 14.18. This temperature may be above the dew point. 

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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. 

This rate-based analysis of trayed columns gives an estimate of the number of overall gas phase mass transfer units corresponding to a given tray. The practical application of this analysis is to provide a means for estimating the tray Murphree vapor efficiency discussed in Section 14.3. 

The rate-based analysis introduced in Section 14.2 can be developed as outlined below to define a general, rigorous, multi-component rate-based stage model. It takes into account mass and energy transfer between the phases within a stage, and can be connected to other stages to form multistage columns. 

Describe equilibrium- and rate-based analysis of separation processes. 

Equation 18.12 is the basis for the derivative approach to rate-based analysis, which involves directly measuring the reaction rate at a specific time or times and relating this to [A]fl. Equation 18.11 is the basis for the two different integral approaches to kinetic analysis. In one case, the amount of A reacted during a fixed time is measured and is directly proportional to [A]o ( fixed-time method) in the other case, the time required for a fixed amount of A to react is measured and is also proportional to [A]o variable-time method). Details of these methods will be discussed in Section... 

This appendix shows how the Aspen Plus simulator can be used to do detailed rate-based analysis of distillation using the Maxwell-Stefan approach outlined in Sections 15.7 and 16.8. Lab 10 should be done before this lab. NOTE If you have convergence problems, reinitialize and try running again. 

Mueller I., C. Pech, D. Bhatia, and E. Y. Kenig, Rate-based analysis of reactive distillation sequences with different degrees of integration, Chem. Eng. Sci., 62, 7327-7335 (2007). 

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