Erbar/Maddox method

For the separation specified in Example 11.5, evaluate the effect of changes in reflux ratio on the number of stages required. This is an example of the application of the Erbar-Maddox method. 

For binary systems or systems that approach binary, the Fenske-Underwood-Erbar/Maddox Method is recommended. For minimum stages, use the Fenske equation.12... 

Erbar-Maddox method (Fig. 3.9b). This method uses a plot of R/CR + 1) against NminfN, with R., J(R i + 1) as the parameter. When R = -ftmim x axis becomes zero. Therefore, the y axis of the diagram represents minimum reflux conditions. When N = N, both x andy coordinates become unity. 

The recommended method to use to determine the actual theoretical stages at an actual reflux ratio is the Erbar/Maddox relationship. In the graph, N is the theoretical stages and R is the actual reflux ratio L/D, where L/D is the molar ratio of reflux to distillate. N, is the minimum theoretical stages and R, is the minimum reflux ratio. 

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. 

A limitation of the Erbar-Maddox, and similar empirical methods, is that they do not give the feed-point location. An estimate can be made by using the Fenske equation to calculate the number of stages in the rectifying and stripping sections separately, but this requires an estimate of the feed-point temperature. An alternative approach is to use the empirical equation given by Kirkbride (1944) ... 

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. 

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). 

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. 

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.]... 

Unfortunately, the method of Underwood cannot be applied to nonideal mixtures and even to ideal ones, relative volatilities of the components that depend on the temperature. Therefore, tray by tray method was used for the calculation of minimum reflux mode for such ideal mixtures (Shiras, Hanson, Gibson, 1950 Erbar Maddox, 1962 McDonough Holland, 1962 Holland, 1963 Lee, 1974 Chien, 1978 Tavana Hanson, 1979) and others. 

Together with knowledge of feed condition and reflux ratio, the flow in the column profile can be calculated. Short-cut methods are available for preliminary investigations. The usual ones are the methods of Fenske, Underwood, Erbar-Maddox, and Smith-Brinkley. Two of the earliest rigorous methods were developed by Lewis-Matheson and Thiele-Geddes. 

There are several valuable references to developing and applying a multicomponent distillation program, including Holland [26, 27,169], Prausnitz [52, 53], Wang and Henke [76], Thurston [167], Boston and Sullivan [6], Maddox and Erbar [115], and the pseudo-K method of Maddox and Fling [116]. Convergence of the iterative trials to reach a criterion requires careful evaluation [114]. There are sever-... 

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. 

An alternate improved solution for Underwood s method is given by Erbar, Joyner, and Maddox [113] with an example, which is not repeated here. 

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. 

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. 

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. 

Cubic equations of state have become the main tool for high pressure VLE calculations. They combine simplicity with accuracy comparable to -or better than - that of other methods, including non-cubic EoS. For a comparison of the EoS approach with the Chao-Seader method, see Maddox and Erbar (1981). 

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