Plate efficiency prediction

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. 

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. 

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

Van Winkle et al. (1972) have published an empirical correlation for the plate efficiency which can be used to predict plate efficiencies for binary systems. Their correlation uses dimensionless groups that include those system variables and plate parameters that are known to affect plate efficiency. They give two equations, the simplest, and that which they consider the most accurate, is given below. The data used to derive the correlation covered both bubble-cap and sieve plates. 

This method of predicting plate efficiency, published in 1958, was the result of a five-year study of bubble-cap plate efficiency directed by the Research Committee of the American Institute of Chemical Engineers. 

The AIChE method is the most detailed method for predicting plate efficiencies that is available in the open literature. It takes into account all the major factors that are known to affect plate efficiency this includes ... 

The AIChE method, and that of Van Winkle, predict the dry Murphree plate efficiency. In operation some liquid droplets will be entrained and carried up the column by the vapour flow, and this will reduce the actual, operating, efficiency. 

Prolonged and unnecessary enzymatic treatment, i.e., trypsinization of tumor cells, can also alter their survival and metastatic behavior in vivo. Moreover, viability tests (trypan blue exclusion) and even plating efficiency in vitro do not predict or correlate with the in vivo biological behavior of trypsinized cells. 

The required number of actual plates, Ap, is larger than the number of theoretical plates, App, because it would take an infinite contacting time at each stage to establish equilibrium. The ratio Aj Ap is called the overall column efficiency. This parameter is difficult to predict from theoretical considerations, however, or to correct for new systems and operating conditions. It is therefore customary to characterize the single plate by the so-called Alurphree vapor plate efficiency, Ey (98) ... 

In Sec. 13-1 the fundamental concepts of mass transfer are presented. In Sec. 13-2 these fundamentals are used in the development of predictive models for plate efficiencies. In the final section, 13-3, a treatment of packed columns is presented. 

First the equations for the modified Murphree plate efficiency are developed and then the corresponding equations for the Murphree plate efficiency are developed. Expressions for the vaporization efficiencies for each of these efficiencies are then presented. The section is concluded by the presentation of numerical examples for binary mixtures which demonstrate that essentially the same compositions of the vapor leaving a plate are predicted by vaporization efficiencies corresponding to the modified Murphree efficiency model as are predicted by the Murphree plate efficiencies. This result suggests that the correlations for the film coefficients developed by others4 for use with Murphree efficiencies may be used in the prediction of vaporization efficiencies for multi-component systems. 

Then, it follows from Eqs. (13-46) and (13-48) that one should be able to predict the modified Murphree plate efficiency on the basis of the total number of overall transfer units, namely,... 

After the interface point has been reached, the paths for the two models differ. In the case of the vaporization plate efficiency (based on the modified Murphree efficiency model), a projection is made from the point (xjf, yj,) to the point (xji, yji) with the slope Kjt that satisfies Eq. (13-40). In the case of the Murphree plate efficiency, a projection is made from the point (xjf, yj,) to the point (x i, yft) along the tangent line, yf = mjXj + blm Since the equilibrium curve is seldom straight, an appropriate value of mi lying between the values at (xf, y ) and (xjj, yft) is selected. The values of yjt predicted by use of vaporization efficiencies are calculated by use of Eqs. (13-40), (13-47), and (13-51). 

Table 13-5 Comparison of the experimental product distributions with those predicted by use of perfect plates and by the modified Murphree plate efficiency model...

NORMAL OPERATION OF SIEVE PLATE. A sieve plate is designed to bring a rising stream of vapor into intimate contact with a descending stream of liquid. The liquid flows across the plate and passes over a weir to a downcomer leading to the plate below. The flow pattern on each plate is therefore crossflow rather than countercurrent flow, but the column as a whole is still considered to have countercurrent flow of liquid and vapor. The fact that there is crossflow of liquid on the plate is important in analyzing the hydraulic behavior of the column and in predicting the plate efficiency. 

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