Binary McCabe-Thiele Method

The McCabe-Thiele method is a graphical approach that shows very nicely in pictorial form the effects of vapor-liquid equilibrium (VLE), reflux ratio, and number of trays. It is limited to binary systems, but the effects of parameters can be extended to multicomponent systems. The basic effects can be smnmarized 

The easier the separation, the fewer trays required and the lower the required reflux ratio (lower energy consumption). 

The higher the desired product pmities, the more trays required. But the required reflux ratio does not increase significantly as product pmities increase. 

There is an engineering trade-off between the number of trays and the reflux ratio. An infinite number of columns can be designed that produce exactly the same products, but have different heights, different diameters, and different energy consumptions. Selecting the optimum column involves issues of both steady-state economics and dynamic controllability. 

There are minimum values of the number trays (A min) and the reflux ratio (RRmin) that are required for a given separation. 

---

Hengstebeck [137] presents a simplified procedure for reducing a multicomponent system to an equivalent binary using the key components. From this the number of stages or theoretical plates and reflux can be determined using conventional binary procedures and involving the McCabe-Thiele method. 

The McCabe-Thiele Method is restricted in its application because it only applies to binary systems and involves the simplifying assumption of constant molar overflow. However, it is an important method to understand as it gives important conceptual insights into distillation that cannot be obtained in any other way. 

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. 

EXAMPLE 17.2 BATCH DISTILLATION OF A BINARY SYSTEM BASED ON THE MCCABE-THIELE METHOD... 

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. 

Figures 5.5-10 and 5.5-11 are intended to be illustrative aud are useful for approximations and Tor binary systems. Further information on the use of the McCabe-Thiele method in this connection may be found in the early work of. Bogan16 and in several other sources.

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."... 

Calculate, by modified McCabe-Thiele methods, residue composition and distillation time for binary batch rectification with constant reflux for a given number of ideal stages, boil-up rate, and specified average distillate composition. 

McCabe-Thiele Method - This MathCAD document creates a McCabe-Thiele Diagram for a binary distillation. Data are from Example 6-5. 

McCabe-Thiele diagrams for adsorption, 320 for binary distillation, 326, 329, 330, 332, 334 for countercurrent multistage separator, 309 for extraction, 317 for ion exchange, 322 for rectifying column, 314 McCabe-Thiele method for distillation, 310-315, 322-340... 

According to the McCabe-Thiele method, the system for separation is considered on a quasi-binary basis. In this approach, it must be possible to neglect the influence of the solvent, which is acceptable if the phase boundary lines (solubilities) do not change much with concentration during separation. In this case, the number of theoretical stages, the minimal reflux (ratio), the minimum number of theoretical stages, and their mutual dependence can be determined. 

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. 

What is often called the McCabe-Thiele method " for binary distillation calculations deploys a y-x (or y-x) diagram, say, for the more-volatile component, here designated the more-permeable component i. This furnishes substantiation that a separation can indeed be attained by the use of recycle or reflux in a multistage or cascade operation. 

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... 

---