Sorel-Lewis method

The method proposed by Lewis and Matheson (1932) is essentially the application of the Lewis-Sorel method (Section 11.5.1) to the solution of multicomponent problems. Constant molar overflow is assumed and the material balance and equilibrium relationship equations are solved stage by stage starting at the top or bottom of the column, in the manner illustrated in Example 11.9. To define a problem for the Lewis-Matheson method the following variables must be specified, or determined from other specified variables ... 

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. 

Calculation of number of plates using the Lewis-Sorel method... 

Figure 11.14. Calculation of the number of plates by the Lewis-Sorel method for Example 11.7...

One of the most successful methods for calculating the number of plates necessary for a given separation is due to Lewis and Matheson(38). This is based on the Lewis-Sorel method, described previously for binary mixtures. If the composition of the liquid on any plate is known, then the composition of the vapour in equilibrium is calculated from a knowledge of the vapour pressures or relative volatilities of the individual components. The composition of the liquid on the plate above is then found by using an operating equation, as for binary mixtures, although in this case there will be a separate equation for each component. 

The trial-and-error calculations on every stage of the Sorel method are obviously slow and laborious. Lewis 119221 noted that in many cases the molar vapor and liquid flow rates in each section (a region between input and output ports) were constant. Thus in Figures 4-1 and 4-2. 

The Lewis method is obviously much faster and more convenient than the Sorel method. It is also easier to program on a conputer or in a spreadsheet, hi addition, it is easier to understand the physical reasons why separation occurs instead of becoming lost in the algebraic details. However, remember that the Lewis method is based on the assunption of CMO. If CMO is not valid, the answers will be incorrect. 

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... 

Sorel-Lewis Method. As an illustration of the Sorel-Lewis method, consider the rectification of a 50 mol per cent benzene and 50 mol per cent toluene mixture into a product containing 5 mol per cent toluene and a bottoms containing 5 mol per cent benzene. The feed will enter as a liquid sufficiently preheated so that its introduction into the column does not affect the total mols of vapor passing the feed plate f.e., such that Fn Fm. A reflux ratio 0 /Z), equal to 3, will be employed, and the column wilt dj Hte with a total condenser and indirect heat in the still. The y x equilibrium curve is given in Fig. 7-2. 

McCabe and Thiele Method (Ref. 11). By the Sorel-Lewis method, the relation between and Xn+i is a straight line, and the equation of this line may be plotted on the y,x diagram. Thus, for the example worked in the preceding section,... 

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