McCabe-Thiele method

Although Smoker and Rose presented the calculation method independent of time, the time can be introduced through the vapor boilup rate V of the reboiler. The resulting equation for determining total batch time is given by  

This operation policy is the easiest one and is commonly used. The following example illustrates this policy. 

Example 4.2 Consider the same mixture presented in Example 4.1 but use batch distillation column with five theoretical plates and reflux ratio equal to 5.630. 

Solution The distillation operation requires 40 percent of the mixture to be distilled, which corresponds to 60 percent of the original feed F remaining in the reboiler, i.e., B = 0.6F. The problem is that of determining the distillate and still 

For various values of the operating lines are drawn and the bottom composition is calculated using the procedure shown in Pignre 4.5. Prom trial and error, we discover that the initial value of xd corresponding to the still composition of xp = 0.4 is 0.9471. The rest of the xd are chosen below this composition, and 

Equations 11.21 and 11.22 and the equilibrium relationship are conveniently solved by the graphical method developed by McCabe and Thiele (1925). The method is discussed fully in Volume 2. A simple procedure for the construction of the diagram is given below and illustrated in Example 11.2. 

Plot the vapour-liquid equilibrium curve from data available at the column operating pressure. In terms of relative volatility  

It is usually more convenient, and less confusing, to use equal scales for the x and y axes. 

Make a material balance over the column to determine the top and bottom compositions, xd and xb, from the data given. 

The top and bottom operating lines intersect the diagonal at xd and xb respectively mark these points on the diagram. 

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The McCabe-Thiele method employs the simplifying assumption that the molal overflows in the stripping and the rectification sections are constant. This assumption reduces the rectifying and stripping operating line equations to ... 

Operating Lines The McCabe-Thiele method is based upon representation of the material-balance equations as operating lines on the y-x diagram. The lines are made straight (and the need for the energy balance obviated) by the assumption of constant molar overflow. The liqmd-phase flow rate is assumed to be constant from tray to tray in each sec tiou of the column between addition (feed) and withdrawal (produc t) points. If the liquid rate is constant, the vapor rate must also be constant. 

These differential equations are readily solved, as shown by Luyben (op. cit.), by simple Euler numerical integration, starling from an initial steady state, as determined, e.g., by the McCabe-Thiele method, followed by some prescribed disturbance such as a step change in feed composition. Typical results for the initial steady-state conditions, fixed conditions, controller and hydraulic parameters, and disturbance given in Table 13-32 are listed in Table 13-33. 

One way of calculating the number of equilibrium stages (or number of theoretical plates, NTP) for a mass exchanger is the graphical McCabe-Thiele method. To illustrate this procedure, let us assume that over the operating range of compositions, the equilibrium relation governing the transfer of the pollutant from the... 

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 can be used for the design of columns with side streams and multiple feeds. The liquid and vapour flows in the sections between the feed and take-off points are calculated and operating lines drawn for each section. 

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. 

In this particular example, all these lines are closely spaced and the relevant section is enlarged in the inset of Figure 11a. By stepping off the theoretical plates as in the McCabe-Thiele method, it is seen that 18 theoretical plates are represented by the column. 

The equilibrium data are plotted in Figure 1 lh. As the compositions are given as mass per cent, these must first be converted to mole fractions before the McCabe-Thiele method may be used. 

A fractionating column is required to distill a liquid containing 25 per cent benzene and 75 per cent toluene by mass, to give a product of 90 per cent benzene. A reflux ratio of 3.5 is to be used, and the feed will enter at its boiling point. If the plates used are 100 per cent efficient, calculate by the Lewis-Sorel method the composition of liquid on the third plate, and estimate the number of plates required using the McCabe-Thiele method. 

This example is solved by a simple application of the McCabe-Thiele method and is illustrated in Figure lln, where it is seen that 10 theoretical plates are required. The... 

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... 

Figure 11.15. Determination of number of plates by the McCabe-Thiele method (Example 11.8)...

The reduction in the required number of plates as R is increased beyond Rm will tend to reduce the cost of the column. For a column separating a benzene-toluene mixture, for example, where Xf = 0.79, xd = 0.99 and xw = 0.01, the numbers of theoretical plates as given by the McCabe-Thiele method for various values of R are given as follows. The minimum reflux ratio for this case is 0.81. 

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. 

Instead of an energy balance, the McCabe-Thiele method assumes... 

Step by Step the McCabe-Thiele Method Introduction to the McCabe-Thiele method for countercurrent multistage distillation, from your About.com Guide, Dr. Bernhard Spang. http //Chemeneineer. about comllibrarvlweeklylaa 11 1599.h. 

Equilibrium diagram for benzene-toluene mixtures at total pressure of 760 mm Hg (McCabe-Thiele method for determining number of theoretical plates). 

Apply the McCabe-Thiele method of column design, based on an xy diagram... 

As an alternative to the McCabe-Thiele method, design the column by using the Fenske-... 

Variations of the basic McCabe-Thiele method, such as incorporating tray efficiencies, nonconstant molal overflow, side streams, or a partial condenser, are often outlined in standard texts. These modifications usually are not justified modern computer programs can calculate complex column arrangements and nonideal systems considerably faster and more accurately than use of any hand-drawn diagram can. 

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