Defined total reflux ratio

Porter and Momoh have suggested an approximate but simple method of calculating the total vapor rate for a sequence of simple columns. Start by rewriting Eq. (5.3) with the reflux ratio R defined as a proportion relative to the minimum reflux ratio iimin (typically R/ min = 1-D- Defining Rp to be the ratio Eq. (5.3) becomes... 

In the formulation of this problem it is supposed that the variables listed as usual specifications are fixed. Of the four remaining variables required to completely define the column, three are fixed, the purity specifications bjdi, bh/dh and the reflux ratio L1/D. Thus, one additional variable remains to be fixed in order to determine the column. Consequently, the problem to be solved consists of finding the feed plate location kx which minimizes the total number of plates k2 (see Fig. 9-1) required to achieve the purity specification at the specified value of the reflux ratio. A concise statement of the problem follows ... 

Notation used in this chapter To avoid confusion with the various symbols, some of the notation used in this chapter may not conform to that used in the rest of the book. Most notably, since R is used to denote retentate flow, then reflux ratio will be defined noncapitalized as Ta. Also, the symbol tt will be used for total pressure (unlike the usual symbol of F). This has been done since P (and many of its derivatives) has been or will be used for other parameters. 

The design of a distillation column involves many parameters product compositions, product flow rates, operating pressure, total number of trays, feed-tray location, reflux ratio, reboiler heat input, condenser heat removal, column diameter, and column height. Not all of these variables are independent, so a degrees of freedom analysis is useful in pinning down exactly how many independent variables can (and must) be specified to completely define the system. 

The first of these two equations is true at any reflux ratio, but the latter is true only at total reflux. However, new variables may be defined such that... 

The basic assumption of the Fenske-Underwood relation is that the ratio of the equilibrium constants or the relative volatility, as defined by Eq. (6.19), in a binary mixture or the two key components present in a multicomponent mixture remain constant over the temperatures encountered in the distillation column. If this can be assumed without the introduction of excessive error, the minimum number of plates at total reflux can be determined from... 

Now, the separation factor of any separating unit is defined by the ratio of the product and waste abundance ratios according to Eq. (3). In the case of. V < 1 considered here, a = Xp/Xw, so that Eq. (68) is the separation factor at total reflux ... 

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