Separation of dilute mixtures of acetic acid from water is an important separation problem, particularly in the food industry. The difficulty is not in designing a system that will do the separation. Instead, at low acetic acid concentrations, designing a system that covers its expenses is difficult. We want to process 400.0 \(\mathrm{kmol} / \mathrm{h}\) of a \(20^{\circ} \mathrm{C}\) feed that is \(1.0 \mathrm{~mol} \%\) acetic acid and \(99.0 \mathrm{~mol} \%\) water. We want a bottoms product that is \(95.0 \mathrm{~mol} \%\) acetic acid and a distillate product that is \(99.999 \mathrm{~mol} \%\) water. Operate at \(101.3 \mathrm{kPa}\), and at \(1.15 \times(\mathrm{L} / \mathrm{D})_{\min }\). Because CMO is not valid, a McCabe-Thiele diagram will not provide an accurate value of \((\mathrm{L} / \mathrm{D})_{\min }\). Determine the optimum value of \(\mathrm{N}_{\mathrm{F}}, \mathrm{N}\), column diameter, \(\mathrm{Q}_{\mathrm{C}}\), and \(\mathrm{Q}_{\mathrm{R}}\). UNIQUAC is a reasonable choice for VLE model. Since the calculated diameter is significantly larger in the stripping section than in the rectifying section, the methods in Section 10.4 will probably be useful.

Section 10.4

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Occasionally, calculated diameters at different column locations will vary by a large factor. For example, for distillation of a vapor feed of ethanol and water, calculated diameter at the top of the column was 3.7 times as large as the calculated diameter at the bottom of the column (Wankat, 2007a). For distillation of a liquid feed of acetic acid and water (water is more volatile), calculated diameter at the bottom was 1.7 times the calculated diameter at the top (Wankat, 2007b). Instead of building the entire column at the larger diameter, it may be possible to balance column diameters. Equation (10-14a) shows that column diameter is directly proportional to the square root of vapor velocity. If we can reduce V at the location with the largest calculated diameter and increase V elsewhere, we may be able to decrease column diameter significantly with very little effect on purity.