Point Efficiency Fundamentals

Lockett, M. J., Distillation Tray Fundamentals, Cambridge University Press, Cambridge, England, 1986. Lockett, M. J. and Ahmed, I. S., Tray and Point Efficiencies from a 0.6 Metre Diameter Distillation... 

The point efficiency is a fundamental criterion of mass transfer, whereas the overall tray efficiency is the value that can be measured, especially for larger distillation columns. Large-column... 

A third type of tray efficiency, the Murphree point efficiency, is used sometimes in attempts to correlate efficiency with fundamental mechanisms occurring on the iray, The point efficiency . is defined as follows ... 

Point efficiency Eqq is calculated from fundamental laws of mass transfer. Adjnst-ing these laws to tray columns yields... 

If data are not available, a detailed calculation of the efficiency can be made on the basis of fundamental mass and heat transfer calculations. With this method, you first calculate point efficiencies from heat and mass transfer calculations and then determine Murphree and overall efficiencies from flow patterns on the tray. Unfortunately, the results are often not extremely accurate. A sinple application of this method is developed in Chapter 16. 

This is the loced iciency or point efficiency, and because a liquid concentration gradient is not involved, it cannot have a value greater than 1.0. Thus, it is a more fundamental concqM, but it suffers in application since concentration profiles of operating trays are difficult to predict. As in the case of the Mur ree tray efficiency, it is possible to use a liquid-phase point efficiency. 

Plate Efficiency Definitions and Relations. Over-all Column Eficiency, The relation between the performance of actual and theoretical plates is expressed as plate efficiencies. A number of different plate efficiencies have been proposed, but the two most commonly used are the over-all column efficiencywhich was proposed by Lewis (Ref. 20) and plate or point efficiencies suggested by Murphree (Ref. 24). The over-all column efficiency, is the number of theoretical plates necessary for a given separation divided by the number of actual plates required to perform the same separation i.e., it is the factor by which the number of theoretical plates is divided to give the actual number of plates. This efficiency has no fundamental mass-transfer basis, but it serves as an easily applied and valuable design factor and is therefore widely used. 

The value of S , and E y are the most commonly used design factors for plate efficiencies. The over-all tower plate efficiency is simpler to apply than the Murphree efficiencies because only terminal conditions are required whereas in the calculation of the Murphree plate efficiency, plate-to-plate compositions are required, and for the Murphree point efficiency, complete liquid- and vapor-composition traverses are required on each plate. However, the Murphree efficiencies are probably on a more fundamental basis than the over-all efficiencies. 

The plate to plate type calculation is a fundamental procedure wherein the tower is assumed to be composed of theoretical equilibrium plates. The actual plates required are determined from the number of theoretical plates using a predicted overall tower efficiency. The starting point for a tower calculation is usually a specified feed composition, feed temperature, and tower operating pressure. The procedure involves defining the compositions and temperamres on each plate in the tower and subsequently the resultant compositions and temperatures of the product streams. The actual computations, which involve trial... 

The Hawthorne and Davis approach thus aids considerably our understanding of a/s plant performance. The main point brought out by their graphical construction is that the maximum efficiency for the simple [CHT]i cycle occurs at high pressure ratio (above that for maximum specific work) whereas the maximum efficiency for the recuperative cycle [CHTX]i occurs at low pressure ratio (below that for maximum specific work). This is a fundamental point in gas turbine design. 

The fundamental mechanisms of free radical reactions were considered in Chapter 11 of Part A. Several mechanistic issues are crucial in development of free radical reactions for synthetic applications.285 Free radical reactions are usually chain processes, and the lifetimes of the intermediate radicals are very short. To meet the synthetic requirements of high selectivity and efficiency, all steps in a desired sequence must be fast in comparison with competing reactions. Owing to the requirement that all the steps be fast, only steps that are exothermic or very slightly endothermic can participate in chain processes. Comparison between addition of a radical to a carbon-carbon double bond and addition to a carbonyl group can illustrate this point. 

It is important to point out at this point that the rate constant k and the quantum yield for a photochemical reaction are not fundamentally related. Since the quantum yield depends upon relative rates, the reactivity may be very high (large kr), but if other processes are competing with larger rates, the quantum yield efficiency of the reaction will be very small. That there is no direct correlation between the quantum yield and the rate is clearly seen from the data in Table 1.2 for the photoreduction of some substituted aromatic ketones in isopropanol ... 

We consider that the practical electrode s efficiency at operation under high current density conditions and during service life is determined by the state of the particles of conductive additive s surface. With reference to this, we can point out two main factors effecting fundamentally reliable operation of the NiOx electrode. 

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