Binary mixtures McCabe-Thiele diagram

The design of a distillation column is based on information derived from the VLE diagram describing the mixtures to be separated. The vapor-liquid equilibrium characteristics are indicated by the characteristic shapes of the equilibrium curves. This is what determines the number of stages, and hence the number of trays needed for a separation. Although column designs are often proprietary, the classical method of McCabe-Thiele for binary columns is instructive on the principles of design. 

If the presence of the other components does not significantly affect the volatility of the key components, the keys can be treated as a pseudo-binary pair. The number of stages can then be calculated using a McCabe-Thiele diagram, or the other methods developed for binary systems. This simplification can often be made when the amount of the non-key components is small, or where the components form near-ideal mixtures. 

Phase equilibrium data have been measured for many binary mixtures with a special apparatus and are available in compiled form. These McCabe Thiele diagrams show the mole fraction of volatiles in the liquid phase in relation to the mole fraction of volatiles in the vapour phase in equilibrium at constant pressure [21, 22]. 

Calculations for the policy of constant distillate composition can also be made with the McCabe-Thiele diagram for binary mixtures. An overall material balance for the light-key component at any time, t, is given by rearrangement of equation (6-108) at constant xD for W as a function of... 

The calculation of the minimum reflux and reboil ratios of nonpreferred separations is based on the fact that, in ideal mixtures, the states of constant reflux ratio = const, constitute a straight line in the triangular concentration space of Fig. 5.2-30. Their endpoints on the side lines of the triangle can easily be determined from the McCabe-Thiele diagram showing the equilibrium curves of the binary mixtures a-b and a-c. From a first estimation of the reflux ratio the operating line is drawn. Its points of intersection with the equilibrium lines dehver the endpoints... 

Fig. 1-56. Scliematic of a rectification column for the separation of an ideal binary mixture, and the corresponding McCabe-Thiele diagram.

Fig. 2-56. McCabe-Thiele-diagram for calculating the number of theoretical stages for the batch distillation of a binary mixture.

For the reversible distillation, the operation fine should coincide with the equilibrium line for the binary mixture in the McCabe-Thiele diagram. 

Fig. 2.5 McCabe-Thiele diagram for the binary Oj/Ar-mixture of the crude argon column.

In practice, the systems tend to be more complex than the simple binary example used here, and the computations are done using appropriate computer packages. Today, these packages are quite powerful and are able to handle mixtures of many components without recourse to the simplifying assumption of equimolal overflow and vaporization. The McCabe-Thiele diagram nevertheless remains a valuable tool for visualizing the principal features of the fractionation process and for providing the student an entry into the treatment of more complex systems. 

Figure 10.1.5. (a) Distillation column with a reboiler and a total condenser for a binary mixture separation, (b) Separation of a binary mixture into two pure compounds by binary distillation McCabe-Thiele diagram. (After Humphrey and Keller (1997).)... 

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."... 

McCabe-Thiele method. This method is used to assess qualitatively the impact of changing a design variable (Lee et al., 2000c). For the RD case, two main features are tracked to sketch the diagram for a binary mixture of reactants imdergoing an isomerization reaction and under CMO assumption,... 

The development of the McCabe and Thiele diagram (McCabe Thiele, 1925) that allowed minimum reflux number and minimum number of theoretic plates for binary mixtures was of decisive significance for the creation of distillation theory for such mixtures. For many years, this diagram was the basis for investigation of... 

The McCabe-Thiele approach for a binary mixture can be described as follows. First, we take the vapor-liquid equilibrium diagram y/x plot). Then we draw the operating lines based on the mass balance for the liquid and the vapor phase. There is one operating line for the stripping section and one for the top (rectification or enriching) section. The assumption of (in each case) constant molar flows of liquid and vapor ensures strictly straight operating lines. 

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