Empirical Efficiency Prediction

Empirical Efficiency Prediction Two empirical correlations which have been the standard of the industry for distillation tray efficiency prediction are the Drickamer and Bradford, in Fig. 14-46 [Trans. Am. Inst. Chem. Eng. 39, 319 (1943)] and a modification of it by O Connell [Trans. Am. Inst. Chem. Eng. 42, 741 (1946)], in Fig. 14-47. The Drickamer-Bradford plot correlates efficiency as a function of liquid viscosity only, which makes it useful for petroleum cuts. O Connell added the relative volatility to the x axis. 

The combination of reasonable accuracy, good reliability, and simplicity, together with the weakness of theoretical tray efficiency correlations, rendered the O Connell distillation correlation (Fig. 7.5ar the standard of the industry. It has been recommended by most literature sources (4,10,18,33,126,131,151,152) as one of the best empirical methods available for tray efficiency prediction. The author has hed extensive favorable experience with the distillation correlation (Fig. 7.5a), and heard the same from many others in the industry. Frank (10) and the author believe that the O Connell plot is the best computational method for estimating distillation tray efficiency others (4,12,33), however, prefer theoretical methods. 

If the value of n = 2 is taken from the semi-empirical approach under the first paragraph of the above solution, both the wash liquid required and the washing time would increase proportionately. As the washing efficiency predicted by theory (see Figure 10.7) oi E = 76.9% is close to the experimental value given, the simple approach by Choudhury and Dahlstrom gives in this case a somewhat more pessimistic result than the full dispersion model. 

Rate of Mass Transfer in Bubble Plates. The Murphree vapor efficiency, much like the height of a transfer unit in packed absorbers, characterizes the rate of mass transfer in the equipment. The value of the efficiency depends on a large number of parameters not normally known, and its prediction is therefore difficult and involved. Correlations have led to widely used empirical relationships, which can be used for rough estimates (109,110). The most fundamental approach for tray efficiency estimation, however, summarizing intensive research on this topic, may be found in reference 111. 

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). 

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. 

The quantum efficiency of fluorescence of a molecule is decided by the relative rates of fluorescence, internal conversion and intersystem crossing to the triplet state. Up to the present time it has proved impossible to predict these relative rates. Thus, whilst it is now possible to calculate theoretically the wavelengths of maximum absorption and of maximum fluorescence of an organic molecule, it remains impossible to predict which molecular structures will be strong fluorescers. Design of new FBAs still relies on semi-empirical knowledge plus the instinct of the research chemist. 

Heat and mass balance equations are used in all aspects of process modelling however, what is key to this model is an understanding of the electrolytic process behind the cell. For example, the model must be able to predict current efficiency and k-factor if it is to predict electricity consumption. Most of these electrolytic parameters are calculated using empirical relationships derived from experimental data both from test cells and the full-scale plant. Considering k-factor, this is primarily a function of brine strength and temperature. Figure 20.5 illustrates the experimentally derived function used in the model. 

To what extent can theory predict the collision efficiency factor Two groups of researchers, Derjagin and Landau, and Verwey and Overbeek, independently of each other, have developed such a theory (the DLVO theory) (1948) by quantitatively evaluating the balance of repulsive and attractive forces that interact most effective tool in the interpretation of many empirical facts in colloid chemistry. 

In 1980, Katsuki and Sharpless described the first really efficient asymmetric epoxidation of allylic alcohols with very high enantioselectivities (ee 90-95%), employing a combination of Ti(OPr-/)4-diethyl tartrate (DET) as chiral catalyst and TBHP as oxidant Stoichiometric conditions were originally described for this system, however the addition of molecular sieves (which trap water traces) to the reaction allows the epoxidation to proceed under catalytic conditions. The stereochemical course of the reaction may be predicted by the empirical rule shown in equations 40 and 41. With (—)-DET, the oxidant approaches the allylic alcohol from the top side of the plane, whereas the bottom side is open for the (-l-)-DET based reagent, giving rise to the opposite optically active epoxide. Various aspects of this reaction including the mechanism, theoretical investigations and synthetic applications of the epoxy alcohol products have been reviewed and details may be found in the specific literature . 

The curves represent a plot of Log.(/V),(Reduced Plate height)against Log.(v), (Reduced Velocity). The lower the Log.(/7) curve versus the Log.(v) curve the better the column is packed. At low velocities the (B) term dominates and at high velocities the (C) term dominates as in the Van Deemter equation. The best column efficiency is achieved when the minimum is about 2 particle diameters and thus, Log (.ft) Is about 0.35. The minimum value for (H) as predicted by the Van Deemter equation has also been shown to be about two particle diameters. The optimum reduced velocity is in the range of 3 to 5 that is Log.(v ) takes values between 0.3 and 0.5. The Knox equation is a simple and effective method of examining the quality of a given column but, as stated before, is not nearly so useful In column design due to the empirical nature of the constants. 

Malkin s autocatalytic model is an extension of the first-order reaction to account for the rapid rise in reaction rate with conversion. Equation 1.3 does not obey any mechanistic model because it was derived by an empirical approach of fitting the calorimetric data to the rate equation such that the deviations between the experimental data and the predicted data are minimized. The model, however, both gives a good fit to the experimental data and yields a single pre-exponential factor (also called the front factor [64]), k, activation energy, U, and autocatalytic term, b. The value of the front factor k allows a comparison of the efficiency of various initiators in the initial polymerization of caprolactam [62]. On the other hand, the value of the autocatalytic term, b, describes the intensity of the self-acceleration effect during chain growth [62]. 

As might be expected, the vapour phase may offer the controlling resistance to mass transfer in high pressure distillations. Values for tray efficiencies at elevated pressure are scarce [23, 24]. The prediction of tray efficiency may be approached in several ways. One way is to utilize field performance data taken for the same system in very similar equipment. Unfortunately such data are seldom available. When they are available, and can be judged as accurate and representative, they should be used as a basis for efficiency specification [25], Another way is to utilize laboratory-or pilot-plant efficiency data. For example a small laboratory-Oldershaw tray-column can be used with the same system. Of course, the results must be corrected for vapour-and liquid mixing effects to obtain overall tray efficiencies for large-scale design [26], Another approach is the use of empirical or fundamental mass-transfer models [27-30],... 

Empirical Prediction Moore and Rukovena [Chemical Plants and Processing (European edition), p. 11, August 1987] proposed the empirical correlation in Fig. 14-64 for efficiency loss due to liquid maldistribution in packed towers containing Pall rings or Metal Intalox packing. This correlation was shown to work well for several case studies (Fig. 14-64), is simple to use, and is valuable, at least as a preliminary guide. 

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