Stage calculations stages—reflux relationships

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. 

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) ... 

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. 

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. 

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. 

---