Reflux-Stages Relationships

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. 

Simple analytical methods are available for determining minimum stages and minimum reflux ratio. Although developed for binary mixtures, they can often be applied to multicomponent mixtures if the two key components are used. These are the components between which the specification separation must be made frequendy the heavy key is the component with a maximum allowable composition in the distillate and the light key is the component with a maximum allowable specification in the bottoms. On this basis, minimum stages may be calculated by means of the Fenske relationship (34) ... 

The reason for this simple relationship is that the concept of minimum reflux implies an infinite number of stages and thus no change in composition from stage to stage for an infinite number of stages each way from the pinch point (the point where the McCabe-Thiele operating lines intersect at the vapor curve for a well-behaved system, this is the feed zone). The liquid refluxed to the feed tray from the tray above is thus the same composition as the flash liquid. 

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. 

Figure 8-1. In this graph of the Erbar-Maddox relationship of reflux versus stages, N is the theoretical stages and R is the reflux ratio L/D.7...

Having obtained the minimum number of stages from the Fenske Equation and minimum reflux ratio from the Underwood Equations, the empirical relationship of Gilliland10 can be used to determine the number of stages. The original correlation was presented in graphical form10. Two parameters (X and Y) were used to correlate the data ... 

In Chapter 9, a relationship was developed for total reflux conditions at any Stage n ... 

Figure 13.12. Gilliland relationship between actual reflux ratio R, minimum reflux ratio Rm, theoretical stages N and minimum theoretical...

Equation 7-117 shows the relationship for the feed, where q is the fraction of feed that is liquid at the feed tray temperature and pressure. For a bubble point feed, q = 1, and for a dew point feed, q = 0. The minimum reflux ratio is determined from Equation 7-117 by substituting into Equation 7-116. Coker [41] developed a numerical method for computing 6 and respectively. However, other methods should be tried, if R in gives a negative value. Also, it may be that the separation between the feed and the overhead can be accomplished in less than one equilibrium stage. 

The relationship between stages and reflux ratio was quantifled empirically by Gilliland and presented graphically in Figure 12.13a. Numerous authors have published mathematical fits to the Gilliland curve, a representative fit being that of Rusche ... 

FIGURE 12.13 (a) Gilliland relationship between actual reflux ratio R, minimum reflux ratio R, theoretical stages N, and minimum theoretical stages iV . (b) Optimum reflux ratio as a function of operating temperature level. (E. R. Gilliland, 1940. Ind. Eng. Chem. 32 1220.)... 

Calculate Required Stages or Transfer Units. After the model is selected, the number of theoretical stages or transfer units is compaled. This is an index of the difficulty of the. separation and is dependent on the amount of reflux that is used. It is in this step that the familiar stages/reflux relationship is developed, with the Anal combination of these two paramaters dependent on economics. 

Minimum surges may be determined analytically by means of tha Fensks relationship. For a bioury mixture of / (lighter component) and j. and with the recognition that at iota] reflux and at any stage n, xs = y jl and Jtj = y x., it can be shown that... 

For multicomponent systems, an approximate value of (he minimum number of stages (at total reflux) may be obtained from the Fanske relationship [Eq. (5.3-28)]. In the use of this relationship for multicomponent mixtures, die mole fractions and die relative volatility refer to die light and heavy keys only. However, values for the nonkey components may be inserted in the equation to determine (heir distribution after the numbet of minimum stages has been determined through the use of the key components. For a more rigorous approach to the determination of minimum stages, see die paper by Chien/... 

In this chapter, the fundamental principles and relationships involved in making multicomponent distillation calculations are developed from first principles. To enhance the visualization of the application of the fundamental principles to this separation process, a variety of special cases are considered which include the determination of bubble-point and dew-point temperatures, single-stage flash separations, multiple-stage separation of binary mixtures, and multiple-stage separation of multicomponent mixtures at the operating conditions of total reflux. 

The gap between the treatment of binary and multicomponent mixtures is closed in Chap. 1. This chapter is initiated by presenting the fundamental relationships and techniques needed for making bubble-point and dew-point calculations, and it is concluded by the presentation of techniques for solving a variety of special types of problems such as the separation of a multicomponent mixture by a single-stage flash process and the separation of a multicomponent mixture by use of multiple stages at the operating condition of total reflux. 

Equal-molal overflow could be assumed, but if the calculations are done by computer, an enthalpy balance would probably be made and the change in pressure from stage to stage would also be allowed for. The calculations are continued in this fashion, alternating the use of equilibrium and material-balance relationships, until the composition is close to that of the feed. Similar calculations are carried out for the lower section of the column starting with an estimated reboiler or bottoms composition. The next step is to match the Compositions at the feed stage for the two sets of calculations. Based on the differences for individual components, the product compositions are adjusted and the calculations repeated until all errors fall below a specified value. In some procedures, the number of plates and the feed plate are fixed beforehand, and the calculations are repeated for different reflux ratios until the desired match is obtained at the designated feed plate. 

---