Binary mixtures McCabe-Thiele method

For these conditions there are two basic methods for determining the number of plates required. The first is due to Sorel(25) and later modified by Lewis126 , and the second is due to McCabe and Thiele(27). The Lewis method is used here for binary systems, and also in Section 11.7.4 for calculations involving multicomponent mixtures. This method is also the basis of modem computerised methods. The McCabe-Thiele method is particularly... 

For a binary mixture under constant pressure conditions the vapour-liquid equilibrium curve for either component is unique so that, if the concentration of either component is known in the liquid phase, the compositions of the liquid and of the vapour are fixed. It is on the basis of this single equilibrium curve that the McCabe-Thiele method was developed for the rapid determination of the number of theoretical plates required for a given separation. With a ternary system the conditions of equilibrium are more complex, for at constant pressure the mole fraction of two of the components in the liquid phase must be given before the composition of the vapour in equilibrium can be determined, even for an ideal system. Thus, the mole fraction yA in the vapour depends not only on X/ in the liquid, but also on the relative proportions of the other two components. 

Whereas Example 17.2 was solved based on the McCabe-Thiele method, the way this example is defined favors the shortcut, Fenske-Underwood-Gilliland approach. This method may be used for multicomponent mixtures, but it is not a method selection criterion in this example, which is a binary system. 

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."... 

We now have all the material available for the graphical calculation of distillation conditions by the McCabe-Thiele method. This is one of the most used and simplest methods for the calculation of batch and continuous distillations of binary mixtures. It involves the simplifying assumptions that the molar heats of evaporation of the components and their mixtures are identical, and there are no heat losses from the column the consequence ist that the vapour and liquid flow rates, in moles per unit time, are constant throughout any section of the column, provided there is no addition or withdrawal of material. 

An alternative graphical method for handling binary mixtures is that of Ponchon and Savatit, and while mote cumbersome to use flian McCabe-Thiele, it dlows for variations in the molar latem heat of vaporization and thus removes the principal assumption of the McCabe-Thiele method. As basic information it requires not only a y -x equilibrium relatkm ip but also data on enthalpy of vaporization as a function of composition, and, except for a few mixtures, such data are not readily available. 

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,... 

Introduction. In Section 11.4B the McCabe-Thiele method was used to calculate the number of theoretical steps or trays needed for a given separation of a binary mixture of A and B by rectification or fractional distillation. The main assumptions in the method are that the latent heats are equal, sensible heat differences are negligible, and constant molal overflow occurs in each section of the distillation tower. In this section we shall consider fractional distillation using enthalpy-concentration data where the molal overflow rates are not necessarily constant. The analysis will be made using enthalpy as well as material balances. 

The use of a y-x curve in the McCabe-Thiele method for binary distillation calculations brings up the matter of a flash-vaporization representation, in case the feedstream mixture is at saturation. An inspection of the y-x curve relative to a given feed composition shows that the equilibrium mixture varies along the curve over a range from the bubble point (where the liquid phase composition x is equal to that of the feed mixture x ) to the dew point (where the vapor composition y is equal to that of the feed mixture Xj.). Between the two is the region of flash vaporization, where the equilibrium compositions (y, x) respectively of phases V and L must satisfy the flash material balance relation F = V + L, where... 

A useful method for a binary mixture employs an analysis based on the McCabe-Thiele graphical method. In addition to the usual assumptions of adiabatic column and equimolal overflow on the trays, the following procedure assumes neghgible holdup of hquid on the trays, in the column, and in the condenser. 

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. 

Calculation Methods. An often satisfactory approximation is to take the mixture in the presence of the solvent to be a pseudobinary of the keys on a solvent-free basis, and to employ the McCabe-Thiele or other binary distillation method to find tray and reflux demands. Since the relative volatility varies with concentration of the solvent, different equilibrium curves are used for above and below the feed based on average loads in those zones. Figure 13.25 is of such a construction. 

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... 

Owing to the availability of high-speed computers, short cut methods for designing distillation processes (e.g. McCabe-Thiele and Ponchon-Savarit for binary systems or the equations of Fenske, Underwood and Gilliland for multicomponent mixtures, see Gmehling and Brehm, 1996 and Satder, 2001 for details) are no longer required. 

Introduction and assumptions. A mathematical-graphical method for determining the number of theoretical trays or stages needed for a given separation of a binary mixture of A and B has been developed by McCabe and Thiele. The method uses material balances around certain parts of the tower, which give operating lines somewhat similar to Eq. (10.3-13), and the xy equilibrium curve for the system. 

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