Binary separations, graphical

If the value of mv is known for each stage in a binary separation (or is taken at a single known constant value for the whole sequence of stages), it may be readily used in the McCabe-Thiele graphical construction. Chapter 4, on distillation, has a section which illustrates this approach. 

The distillation of binary mixtures is covered thoroughly in Volume 2, Chapter 11, and the discussion in this section is limited to a brief review of the most useful design methods. Though binary systems are usually considered separately, the design methods developed for multicomponent systems (Section 11.6) can obviously also be used for binary systems. With binary mixtures fixing the composition of one component fixes the composition of the other, and iterative procedures are not usually needed to determine the stage and reflux requirements simple graphical methods are normally used. 

Three typical binary mixtures were considered. The mixtures were 1. Benzene-Toluene, 2. Cyclohexane-Toluene and 3. Butane-Pentane. Some of the results were presented graphically to show the role of holdup in terms of the degree of difficulty of separation and minimum time operation. 

FIG U RE 10.4 Separation by forming two binary azeotropes, (a) amount of entrainer by graphical material balances, (b) liquid composition isotherms, and (c) typical separation flowsheet. 

In Chapters 7 through 11, the performance of multistage separation processes was analyzed qualitatively on the basis of fundamental principles developed in Chapters 3 through 6. The objective was to gain an understanding of the different types of separation processes and columns and the factors that affect their performance. Chapters 5 and 6 employed graphical and semi-quantitative methods to represent a limited set of separation processes, namely binary distillation. Chapters 10 and 11 also used combinations of graphical and analytical methods applied to binary or ternary systems to represent speciflc classes of nonideal separations. 

The graphical-based shortcut methods for binary batch distillation may be applied to multicomponent distillation only when the separation is between two key components to produce one distillate product and the residue. In this case the calculations may be approximated by lumping the other components with either of the key components and treating the system as a pseudo-binary. 

The separation of a binary mixture by distillation may be represented in two-dimensional space while n-dimensional space is required to represent the separation of a multicomponent mixture (i > 2). The graphical method proposed by McCabe and Thiele9 for the solution of problems involving binary mixtures is presented in a subsequent section. The McCabe-Thiele method makes use of an equilibrium curve which may be obtained from the boiling-point diagram."... 

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... 

For the case where the total flow rates Vj and Lj vary throughout each section of the column, these flow rates may be determined by solving the enthalpy balances simultaneously with the above set of equations. For binary mixtures, the desired solution may be found by use of either graphical methods (Refs. 10, 13) or the numerical methods proposed in subsequent chapters for the solution of problems involving the separation of multicomponent mixtures. 

Operating Line and "Equilibrium" Curve. Both terms are of importance for the graphical solution of a separation problem, i.e., for the graphical determination of the number of stages of a cascade. This method has been developed for the design of distillation columns by MacCabe and Thiele and should be well known. For all cases, the operating line represents the mass and material balances. In distillation, the equilibrium curve represents the thermodynamical va-por/liquid equilibrium. For an ideal binary system, the equilibrium curve can be calculated from Raoult s law and the saturation-pressure curves of the pure components of the mixture. In all other cases, however, for example, for all membrane processes, the equilibrium curve does not represent a thermodynamical equilibrium at all but will represent the separation characteristics of the module or that of the stage. 

The phase behavior of mixtures forms the basis of industrial separations. What makes such separation possible is the fact that when a mixture is brought into a region of multiple coexisting phases, each phase has its own composition. Understanding the phase behavior of multicomponent systems is very important in the calculation of separation processes. In this chapter we review graphical representations of the phase behavior of binary and ternary systems. Since we are dealing with several independent variables, pressure, temperature, and composition, special conventions are used in order to represent information in two-dimensional graphs. 

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