A Batch Distillation Process

Chemical and environmental engineers must sometimes design batch processes for producing or purifying liquids and gases. Applications of such processes occur in food and medicine production, and in waste processing and water purification. An example of such a process is a system for heating a liquid benzene/toluene solution to distill a pure benzene vapor. A particular batch distillation unit is charged initially with 100 mol of a
60 percent mol benzene/40 percent mol toluene mixture. Let L (mol) be the amount of liquid remaining in the still, and let x (mol B/mol) be the benzene mole fraction in the remaining liquid. Conservation of mass for benzene and toluene can be applied to derive the following relation [Felder, 1986) Determine what mole fraction of benzene remains when L = 70. Note that it is difficult to solve this equation directly for x. Use a plot of x versus L to solve the problem

Solution

This equation involves both array multiplication and array exponentiation. Note that MATLAB enables us to use decimal exponents to evaluate L. It is clear that L must be in the range 0 ~ L ~ 100; however, we do not know the range of

Therefore, ‘we must make a few guesses for the range of x, using a session like the following. We find that L > 100 if x > 0.6, so we choose x = [0: 0.001: 0.6]. We use the ginput function to’ find the value of x corresponding to L = 70.

»x = [0:0.001:0.6];
»L = 100*(x/0.6) .”(0.625) .*( (1-x)/0.4) .”(-1.625);
»I1lot (L,x), grid,xlabel ( ‘ L(mol) ‘) ,ylabel (‘x (mol B/mol)’),
[L,x] = ginput(l)

The plot is shown in Figure 2.3–.5.The answer is x = 0.52 if L = 70. The plot shows that the remaining liquid becomes leaner in benzene as the liquid amount becomes smaller. Just before the still is empty (L = 0), the liquid is pure toluene.