Erbar-Maddox correlation

Empirical methods, which are based on the performance of operating columns, or the results of rigorous designs. Typical examples of these methods are Gilliland s correlation, which is given in Volume 2, Chapter 11, and the Erbar-Maddox correlation given in Section 11.7.3. 

Figure 11.11. Erbar-Maddox correlation (Erbar and Maddox, 1961)...

Agw 3a Continued) Reflux-stages correlations. b) the Erbar-Maddox correlation. (Part a freon C. Robinson and E. K. Gilliland. Copyright by McGraw-Hill. Inc. Reprinted by permission. Part b from J. H. Erbar and R. N. Madden, Pet. Pc/., vol. 10, no. 6, p. 183,1661. Reprinted courtesy of Hydrocarbon Process... 

In the Erbar-Maddox correlation, minimum stages are calculated by the Winn method (Sec. 3.2.1) and minimum reflux by the Underwood method (Sec. 3.2.2), but the Fenske minimum stages method (Sec. 3,2.1) can also be used (11,26). 

For an operating reflux ratio of 1.722 (1.25 times the minimum), the Erbar-Maddox correlation is used to find the stage requirement. With reference to Fig. 5.3-15. 

Figure 11.7-3. Erbar-Maddox correlation between reflux ratio and number of stages R based on Underwood method.) [From J. H. Erbar, R. N. Maddox, Petrol. Refiner. 40 (5), 183 (1961). With permission.]... 

FIGURE 5.3-15 Erbar-Maddox correlation for theoretical stages as a function of reflux ratio (Ref. 18). 

The most popular reflux-stages relationships are by Gilliland (45) and Erbar and Maddox (46). Many designers (9,11,29,47) recommend both, some (10,23,28,30,32,33,48) prefer Gilliland s, while others (13,49) prefer Erbar and Maddox s. The Erbar and Maddox correlation is considered more accurate (22,26,29,33,49), especially at low reflux ratios (49) however, the accuracy of Gilliland s equation for shortcut calculations is usually satisfactory. The single curve in Gilliland s correlation is easier to computerize. 

A second type of empirical correlation is Erbar Maddox (see Fig. 11.7-3 in Geankoplis) ... 

FI. What variables does the Gilliland correlation not include How might some of these be included Check the Erbar-Maddox (1961) method (or see King, 1980, or Hines and Maddox, 1985) to see one approach that has been used. 

Erfoar-Maddox correlation An empirical method used for the design of distillation columns that relates the number of ideal stages for a given separation and reflux ratio to the minimum number at total reflux and the minimum reflux ratio. The minimum reflux ratio corresponds to an infinite number of stages to bring about separation. It is named after American chemical engineers John H. Erbar and Robert N. Maddox. 

The two most frequently used empirical methods for estimating the stage requirements for multicomponent distillations are the correlations published by Gilliland (1940) and by Erbar and Maddox (1961). These relate the number of ideal stages required for a given separation, at a given reflux ratio, to the number at total reflux (minimum possible) and the minimum reflux ratio (infinite number of stages). 

A short-cut design method for distillation is another subroutine. This method is based upon the minimum reflux of Underwood (17, 18, 19, 20), the minimum stages of Fenske (21) and Winn (22), and the reflux vs stages correlation of Erbar and Maddox (23) and Gray (24). In SHORT, which uses polynomial K and H values, the required number of equilibrium stages may be found for a specified multiple of minimum reflux, or alternatively, the reflux ratio may be found for a given multiple of minimum stages. 

It is important to use a consistent set of minimum reflux/minimum stages/reflux-stages correlation (27). Both the Gilliland and the Erbar and Maddox methods are consistent with the popular Fenske (Sec. 3,2.1) and Underwood (Sec, 3,2.2) methods. 

NUMBER OF IDEAL PLATES AT OPERATING REFLUX. Although the precise calculation of the number of plates in multicomponent distillation is best accomplished by computer, a simple empirical method due to Gilliland is much used for preliminary estimates. The correlation requires knowledge only of the minimum number of plates at total reflux and the minimum reflux ratio. The correlation is given in Fig. 19,5 and is self-explanatory. An alternate method devised by Erbar and Maddox is especially useful when the feed temperature is between the bubble point and dew point. 

The importance of accurate thermodynamic property correlations to design of operable and economic equipment cannot be overemphasized. For example, Gully showed for a deethanizer that reboiler vapor rate varied by approximately 20% depending upon which of four enthalpy correlations was used. Stocking, Erbar, and Maddox found even more serious differences for a hypothetical depropanizer. Using six K-value and seven enthalpy correlations, they found that reboiler duties varied from 657 to 1111 MJ/hr (623,000 to 1,054,000 Btu/hr) and condenser duties varied from 479 to 653 MJ/hr (454,000 to 619,000 Btu/hr). 

For most situations Eq. f7-42b) is appropriate. The fit to the data is shown in Figure 7-3. Naturally, the equations are useful for computer calculations. Erbar and Maddox n9611 (see King. 1980. or Hines and Maddox. 19851 developed a somewhat more accurate correlation that uses more than one curve. 

An alternative to the GilHIand method has been provided by Erbar and Maddox and is shown in Fig. 5.3-15. This correlation is based on more extensive stagewise calculations, using rigorous computer solutions, and should give slightly better results than the method of Gilliland. 

Compute (a) The minimtim reflux ratio and (h) the minimum number of trays. At a reflux ratio 2.0, estimate (c) the product analyses and (d) the number of theoretical trays by the correlations of Gilliland (17], Erbar and Maddox [12], Brown and Martin [5], and Strangio and Trcybal [59]. 

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