Multiple-Stage Separation of Binary Mixtures

Although all of the separation problems involving binary mixtures may be solved by use of the general methods presented in subsequent chapters for multi-component mixtures, it is, nevertheless, rewarding to consider the special case of the separation of binary mixtures because this separation may be represented graphically in two-dimensional space. Many of the concepts of distillation may be illustrated by the graphical method of design proposed by McCabe and Thiele.9 

In the description of this process, the following symbols are used in addition to those explained above. The mole fraction of the most volatile component in the feed is represented by X, in the distillate by XD, and in the bottoms by xB. The subscript j is used as the counting integer for the number of the stages. Since the distillate is withdrawn from the accumulator (j = 1) and the bottoms is withdrawn from the reboiler (j = N the mole fractions in the distillate and bottoms have double representation that is, X Di = xu (for a column having a total condenser) and xBi = xNi. For the case where the column has a partial condenser (D is withdrawn as a vapor), X , = yu. 

The rectifying section consists of the partial or total condenser and all plates down to the feed plate. The stripping section consists of the feed plate and all plates below it including the reboiler. When the total molar flow rates do not vary from plate to plate within each section of the column, they are denoted by Vr (vapor) and Lr (liquid), in the rectifying section and by Vs and Ls in the stripping section. The feed rate F, distillate rate D, bottoms rate B, and reflux rate Lj are all expressed on a molar basis. 

The design method of McCabe and Thiele9 is best described by solving the following numerical example. 

Example 1-6 It is desired to find the minimum number of perfect plates required to separate an equal molar mixture of benzene and toluene into a distillate product containing 96 percent benzene (XD= 0.96) and a bottom product containing no more than 5 percent benzene (xB = 0.05) at the following operating conditions (1) the column pressure is 1 atm, and a total condenser is to be used (D is a liquid), (2) the thermal condition of the feed is such that the rate Ls at which liquid leaves the feed plate is given by Ls = Lr- 0.6F, and (3) a reflux ratio L1/D = 2.2 is to be employed. The equilibrium sets x, yA of benzene used to construct the equilibrium curve shown in Fig. 1-9 were found by solving Prob. 1-1. 

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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. 

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