Number of theoretical plates separating stages

The amount of the transition fraction between two concentrations of distillate. 

The last two criteria, in particular, are suitable for comparing separating efficiencies in the batch distillation of binary mixtures. The concept of the pole height was then 

It was not, however, until the concepts of the theoretical stage and the transfer unit had been introduced that it became possible to express in numerical terms the efficiency of a column and the difficulty involved in a separation. A theoretical (or ideal) plate (or stage) is defined to be such a section of a column that the vapour leaving it upwards (towards the next higher theoretical plate) and the liquid leaving it downwards (towards the next lower theoretical plate) are in thermodynamic-equilibrium (Fig. 24). 

Definition of pole height in batch distillation (after Bowmiin and Cichelli) 

A column with ideal plates and its behaviour as shown by the equilibrium curve 

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Figure 8-33. Variable reflux ratio at various theoreticeil plates to achieve a specified separation from x kettle to X3 distillate overhead. Note, all reflux ratios shown yield same separation, but with different numbers of theoretical plates/stages D = Distillate F = Kettle Conditions Xq, Vo at equilibrium. Used by permission, Ellerbee, R. W. Chem. Eng. May 28 (1973), p. 110.

It is important to notice at this stage that the result of a selectivity optimization procedure is often a separation that can be realized with a limited number of theoretical plates. For example, we have seen in chapter 4 that the complete resolution of 10 equally distributed peaks requires only 400 plates in the optimum situation at which the lowest analysis time can be achieved (see figure 4.11 and related discussion). Large numbers of theoretical plates are more appropriate for very complex samples, which contain large numbers of peaks, making selectivity optimization an unrealistic proposition. 

Annual cost for distillation column. The McCabe-Thiele simplifying assumptions apply for this case, and the number of theoretical plates can be determined by the standard graphical method shown in Fig. 11-8. The slope of the enriching operating line is 1.5 /(1.5 + 1) = 0.6. From Fig. 11-8, the total number of theoretical stages required for the given separation is 12.1. 

With the aid of a suitable computer software program, it is possible to investigate the effect of a number of reflux ratios on the number of stages that will be required to obtain the desired separation between ethylene and ethane. This approach is outlined on the computer software output which plots the effect of decreased reflux on the number of theoretical plates required for the separation. 

It is convenient to separate these contributions to the column HETP and to distinguish the number of mixing stages, Noisp, the number of mass transfer stages, Nm, and the apparent number of theoretical plates. Nap = L/H. These various contributions are described by the following equations... 

CEC is a hybrid separation technique that combines capillary HPLC (50-pm capillary diameter) with capillary zone electrophoresis, and its main advantage is the enormous number of theoretical plates that can be achieved. This is a result of the uniform, plug-like flow that electro-endoosmosis generates and the fact that this allows the use of very small particles (3 pm diameter). The technology is at an early stage of development (as there are problems inherent in packing columns of such small particle size f9J), but has already resulted in efficiency values of up to 387,000 theoretical plates per meter (10). 

NTU (Number of Transfer Units) The NTU required for a given separation is closely related to the number of theoretical stages or plates required to cariy out the same separation in a stagewise or plate-type apparatus. For equimolal counterdiffusion, such as in a binary distillatiou, the number of overall gas-phase transfer units Nqg required for changing the composition of the vapor stream from yi to yo is... 

Various authors [90] and researchers have published factors that influence the magnitude of HETP values. The lower the HETP value (i.e., number of feet (or inches) per theoretical plate/tray/stage) the more efficient is the packing (random or structured) for any particular separation system. Other influences include ... 

The NTU required for a given separation is closely related to the number of theoretical stages or plates required to carry out the same separation in a stage-wise or plate-type apparatus. 

The most useful measure of the separating power of packed towers is the HETP, the height equivalent to a theoretical plate or stage. It is evaluated simply as the ratio of packed height used for a certain degree of separation to the theoretical number of stages. Its relation to the fundamental quantity, HTU, or the height of a transfer unit, is... 

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