Tray efficiency theory

Theoretical Efficiency Prediction Theoretical tray efficiency prediction is based on the two-film theory and the sequence of steps in Fig. 14-41. Almost all methods evolved from the AIChE model (AIChE Research Committee, Bubble Tray Design Manual, New York, 1958). This model was developed over 5 years in the late 1950s in three universities. Since then, several aspects of the AIChE model have been criticized, corrected, and modified. Reviews are given by Lockett (Distillation Tray Fundamentals, Cambridge University Press, Cambridge, England, 1986) and Chan and Fair [Ind. Eng. Chem. Proc. 

Ponchon-Savarit diagram. 26 Ponter underwetting theory, 516, 517 Porter rivulet model. 542 Porter and Jenkins packing HETP, 532-534 regime transition. 332 Poynting factor. 7 Prado and Fair tray efficiancy, 375 PRO/II. 169, 170,180... 

The second classification is the physical model. Examples are the rigorous modules found in chemical-process simulators. In sequential modular simulators, distillation and kinetic reactors are two important examples. Compared to relational models, physical models purport to represent the actual material, energy, equilibrium, and rate processes present in the unit. They rarely, however, include any equipment constraints as part of the model. Despite their complexity, adjustable parameters bearing some relation to theory (e.g., tray efficiency) are required such that the output is properly related to the input and specifications. These models provide more accurate predictions of output based on input and specifications. However, the interactions between the model parameters and database parameters compromise the relationships between input and output. The nonlinearities of equipment performance are not included and, consequently, significant extrapolations result in large errors. Despite their greater complexity, they should be considered to be approximate as well. 

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. 

To determine the required size of an absorption or stripping unit, it is necessaiy to know not only the equilibrium solubility of the solute in the solvent and the material balance around the column but also the rate at which solute is transferred from one phase to the other within the tower. This rate directly affects the volume of packing needed in a packed tower, the degree of dispersion required in a spray contactor, and (somewhat less directly) the number of trays required in a tray tower. The last effect occurs as a result of the influence of mass transfer rate on tray efficiency which is discussed in a later section. Because of its direct effect on packed tower design and the importance of this type of contactor in absorption, this discussion of mass transfer is aimed primarily at the packed tower case. A more detailed review of mass transfer theory is given in Chapter 2. 

Mass-transfer theory indicates that for trays of a given design the factors most hkely to inflnence E in absorption and stripping towers are the physical properties of the flnids and the dimensionless ratio Systems in which the mass transfer is gas-film-controlled may be expected to have plate efficiencies as high as 50 to 100 percent, whereas plate efficiencies as low as 1 percent have been reported for the absorption of gases of low sohibility (large m) into solvents of relatively high viscosity. 

The very first continuous distillation column was the patent still used to produce Scotch whiskey in the 1830s. It had 12 bubble-cap trays with weirs, downcomers, tray decks, and bubble caps with internal risers. Current trayed towers are quite similar. As most distillation towers have always been trayed rather than packed, one would have to conclude that trayed towers must have some sort of inherent advantage over packed towers. And this is indeed true, in a practical sense even though, in theory, a packed tower has greater capacity and superior separation efficiency than a trayed column. 

In spite of all the effort that has been expended on this topic, the prediction of mass transfer efficiency still is not on a satisfactory basis. The relatively elaborate method of the AIChE Bubble-Tray Manual (AIChE, New York, 1958) is based on the two-film theory but has not had a distinguished career. A number of simpler correlations have been proposed and have some value as general guidance. That literature has been surveyed recently by Vital, Grossel, and Olsen [Hyd. Proc., 55-56 (Oct. 1984) 147-153 (Nov. 1984) 75-78 (Dec. 1984)]. 

DISTILLATION PLATE EFFICIENCY. The two-film theory can be applied to mass transfer on a sieve tray to help correlate and extend data for tray effieiency. The bubbles formed at the holes are assumed to rise through a pool of liquid that is vertically mixed and has the local composition x. The bubbles change in composition as they rise, and there is assumed to be no mixing of the gas phase in the vertical direction. For a unit plate area with a superficial velocity the moles transferred in a thin slice dz are... 

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