When the equilibrium curve is always concave downward, the minimum reflux ratio can be calculated algebraically. The required relationship can be developed by solving simultaneously equations (6-18), (6-31), and the equilibrium relationship \(y^{*}=f(x)\). The three unknowns are the coordinates of the point of intersection of the enriching operating line and the \(q\)-line \(\left(x_{i n t}, y_{i n t}\right)\) and \(R_{\min }\).

Write a Mathcad program to calculate the minimum reflux ratio under these conditions and test it with the data of Example 6.4. In this case, the equilibriumdistribution relationship is a table of VLE values; therefore, an algebraic relationship of the form \(y^{*}=f(x)\) must be developed by cubic spline interpolation.

Data From Example 6.4:-

A trayed tower operating at 1 atm is to be designed to continuously distill 200 kmol/h (55.6 mol/s) of a binary mixture of 60 mol% benzene, 40 mol% toluene. A liquid distillate and a liquid bottoms product of 95 mol% and 5 mol% benzene, respectively, are to be produced. Before entering the column, the feed—originally at 298 K—is flash-vaporized at 1 atm to produce an equimolal vapor–liquid mixture (VF/F = LF/F = 0.5). A reflux ratio 30% above the minimum is specified. Calculate:

(a) quantity of the products;

(b) minimum number of theoretical stages, Nmin;

(c) minimum reflux ratio;

(d) number of equilibrium stages and the optimal location of the feed stage for the reflux ratio specified; and

(e) thermal load of the condenser, reboiler, and feed preheater.

Equation 6-18 and 6-31:-

Transcribed Image Text:

R 1 y=- -x+. R+1 -xD R+1 (6-18)