Plate Efficiencies

The situation for any plate n, with liquid composition x corresponding to an equilibrium vapour composition y , but with actual vapour composition y , is represented on a small section of the McCabe-Thiele diagram in Fig. 3.62. 

Additional equations, as above, can thus be used to correct the values of y , obtained from the equilibrium data to give actual plate values, y . 

Murphree plate efficiency (Murphree, 1925), defined in terms of the vapor compositions by 

Point efficiency (Murphree point efficiency). If the vapor and liquid compositions are taken at a point on the plate, equation 11.64 gives the local or point efficiency, 

Overall column efficiency. This is sometimes confusingly referred to as the overall plate efficiency. 

An estimate of the overall column efficiency will be needed when the design method used gives an estimate of the number of ideal stages required for the separation. 

In some methods, the Murphree plate efficiencies can be incorporated into the procedure for calculating the number of stages and the number of real stages determined directly. 

The use of a plate efficiency correction enables the simulation of columns with a real number of plates to be simulated. This may be important in the study of real columns, when incorporating an allowance for plate hydrodynamic behaviour. 

Actual change of composition Maximum possible change of composition 

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In the case of a plate column the performance of a real plate is related to the performance of a theoretical one by the plate efficiency. In the case of a packed column the height equivalent to a theoretical plate HETP) gives a measure of the contacting efficiency of the packing. 

This is the one case where the overall column efficiency can be related analytically to the Murphree plate efficiency, so that the actual number of plates is calculable by dividing the number of theoretical plates through equation 86 ... 

Nonisothermal Gas Absorption. The computation of nonisothermal gas absorption processes is difficult because of all the interactions involved as described for packed columns. A computer is normally required for the enormous number of plate calculations necessary to estabUsh the correct concentration and temperature profiles through the tower. Suitable algorithms have been developed (46,105) and nonisothermal gas absorption in plate columns has been studied experimentally and the measured profiles compared to the calculated results (47,106). Figure 27 shows a typical Hquid temperature profile observed in an adiabatic bubble plate absorber (107). The close agreement between the calculated and observed profiles was obtained without adjusting parameters. The plate efficiencies required for the calculations were measured independendy on a single exact copy of the bubble cap plates installed in the five-tray absorber. 

Murphree vapor plate efficiency, see equation 82 poiat value of plate efficiency... 

In air conditioning (qv) of closed spaces, a wider latitude in design features can be exercised (23,24). Blowers are used to pass room or cabin air through arrays of granules or plates. Efficiencies usuaHy are 95% or better. The primary limiting factor is the decreased rate of absorption of carbon dioxide. However, an auxHiary smaH CO2 sorption canister can be used. Control of moisture entering the KO2 canister extends the life of the chemical and helps maintain the RQ at 0.82. 

At other refineries, only two continuous stills in series are used, but these ate of 80—100 plate efficiency and yield pure grades of phenol and o-cresol and a base mixture of cresols, xylenols, and higher boiling tar acids. The latter are fractionated batchwise to various saleable grades of cresyHc acids. 

A moie useful plate efficiency for tlieoietical prediction is the Murphiee plate efficiency (55) ... 

EmpiricalEfficieny Prediction Methods. Numerous empirical methods for predicting plate efficiency have been proposed. Probably the most widely used method correlates overall column efficiency as a function of feed viscosity and relative volatiHty (64). A statistical correlation of efficiency and system variables has been developed from numerous plate efficiency data (65). 

Most distillation systems ia commercial columns have Murphree plate efficiencies of 70% or higher. Lower efficiencies are found under system conditions of a high slope of the equiHbrium curve (Fig. lb), of high Hquid viscosity, and of large molecules having characteristically low diffusion coefficients. FiaaHy, most experimental efficiencies have been for biaary systems where by definition the efficiency of one component is equal to that of the other component. For multicomponent systems it is possible for each component to have a different efficiency. Practice has been to use a pseudo-biaary approach involving the two key components. However, a theory for multicomponent efficiency prediction has been developed (66,67) and is amenable to computational analysis. 

An alternative to determining packed height is through the use of an empirical term, height equivalent to a theoretical plate (HETP). This term can be measured in a fashion similar to that used for the overall plate efficiency of a column (eq. 44) ... 

Research. Much of the research on commercial-size distiUation equipment is being done by Fractionation Research, Inc. (FRI), a nonprofit, industry-sponsored, research corporation. The industrial sponsors are fabricators, designers, and constmctors, or users of distiUation equipment. PubHcations include Hquid mixing on sieve plates (91), bubble cap plate efficiency (92), and sieve plate efficiency (93,94). A motion picture of downcomer performance is also avaUable (95). References 96 and 97 cover the Hterature from 1967 to 1990. 

Tray Efficiencies in Plate Absorbers and Strippers Compn-tations of the nnmber of theoretical plates N assnme that the hqnia on each plate is completely mixed and that the vapor leaving the plate is in eqnihbrinm with the liqnid. In actnal practice a condition of complete eqnihbrinm cannot exist since interphase mass transfer reqnires a finite driving-force difference. This leads to the definition of an overall plate efficiency... 

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 best procedure for making plate-efficiency corrections (which obviously can be quite large) is to use experimental-test data from a prototype system that is large enough to be representative of an acliial commercial tower. 

Entrainment Entrainment in a plate column is that liquid which is carried with the vapor from a plate to the plate above. It is detrimental in that the effective plate efficiency is lowered because hquid from a plate of lower volatility is carried to a plate of higher volatility, thereby diluting distillation or absorption effects. Entrainment is also detrimental when nonvolatile impurities are carried upward to contaminate the overhead product from the column. 

If design shows a condition above the appropriate curve of Fig. 14-27, weeping will not be deleterious to plate periormance as measured by a drop in plate efficiency (as in Fig. 14-24 for the sieve plate). 

Plate Efficiency The efficiency of a plate for mass transfer depends upon three sets of design parameters ... 

Methods for predicting plate efficiency are of three general types ... 

The method for estimating point efficiency, outhned here, is not the only approach available for sieve plates, and more mechanistic methods are under development. For example, Prado and Fair [Ind. Eng. Chem. Re.s., 29, 1031 (1990)] have proposed a method whereby bubbling and jetting are taken into account however the method has not been vahdated tor nonaqueous systems. Chen and Chuang [Ind. Eng. Chem. Re.s., 32, 701 (1993)] have proposed a more mechanistic model for predicting point efficiency, but it needs evaluation against a commercial scale distillation data bank. One can expect more development in this area of plate efficiency prediction. 

Example 12 Estimation of Plate Efficiency For the conditions of Examples 9 and 11, estimate the point efficiency of the tray. Additional property data ... 

Ejfects of Gas and Liquid Mixing As noted previously, it is necessary in most instances to convert point efficiency E g to Murphree plate efficiency E, ,. This is true because of incomplete mixing only in small laboratoiy or pilot-plant columns, under special conditions, is the assumption E g = E, , likely to be valid. For a crossflow plate with no hquid mixing there is plug flow of hquid. For this condition of liquid flow, Lewis [Ind. Eng. Chem., 28, 399 (1936)] analyzed effects of gas mixing on efficiency. He considered three cases ... 

FIG. 14-41 plate efficiencies, ethanol-water. To convert (feet per second) (pounds per ciihic foot) " to (meters per second) (kilograms per ciihic meter) " , multiply hy 1.2199. (Kiischhaum, Destilher-Rektifiziertechnik, 4th ed., Sptinger-Verlag, Berlin and Heidelherg, 1969.)... 

Additional plate-efficiency data are hsted in Table 14-6. 

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