Or = reflux from condenser before solvent is added at top Xds, Xrs = mol fraction of solvent in distillate and total liquid added to the top of tower, including reflux and solvent Fs = solvent added with feed a, a! — relative volatilities for solvent concentrations above and below feed, respectively If the feed is binary mixture, the terms involving Xdi and xwh are dropped. For certain special cases, simpler equations can be employed. For example, if solvent is added with the feed such that its concentration is the same above and below the feed plate, the minimum vapor required can be calculated on a solvent-free basis by the regular minimum reflux equations, and then this vapor requirement is increased to allow for the solvent in the vapor. In case the solvent is so high boiling that its concentration in the vapor is negligible, no correction to the solvent-free calculation is necessary. In making the calculation for the solvent-free conditions, the relative volatilities employed are those for the pinched-in region with the solvent present. By equating Eqs. (10-7) and (10-8) it is possible to calculate the amount of solvent that must be added with the feed to obtain equal concentrations above and below the feed plate. For simplification, the last terms in the numerator can be neglected because they are usually small.

where Sf = mols of solvent added with feed

A = Om - 0 n — Sf = increase in overflow due to feed to tower The value of xSn can be obtained from Eq. (10-7), and On can be obtained from a balance on the upper portion of the tower. For the case in which the solvent rate is maintained proportional to the reflux rate,

Feed-plate Location. In case solvent is added with the feed to maintain the same concentration in the upper and lower sections, the optimum key ratio can be calculated by the same method as for a regular distillation. If the solvent concentration is not the same in the two sections, there are usually two main factors tending to modify the optimum ratio. If the solvent concentration is lower below the feed plate than above, then (1) the relative volatility for the key components may be less favorable in the lower section and (2) the mol fraction of the solvent in the vapor is greater in the upper section. The first factor would make it desirable to use a low key component ratio for the feed plate to take advantage of the better relative volatility. Owing tc the higher solvent vapor concentration above the feed plate, it would be desirable to use a higher key ratio than normal. The safest method is to calculate the feed-plate ratio for a regular distillation, and in the plate-to-plate analysis test several plates in the region to determine the optimum condition.

Concentration of Nitric Acid by Extractive Distillation. The concentration of nitric acid by the use of sulfuric acid will be used as an example of extractive distillation employing a nonvolatile agent. A typical flow sheet of a commercial unit is shown in Fig. 10-4. By the oxidation of ammonia and the absorption of the nitrogen oxides a 62 weight per cent nitric acid is made. A portion of this feed acid is mixed with 92 weight per cent sulfuric acid and added to the top of the tower. The remainder of the feed is vaporized and introduced into the middle region of the column. Direct steam is added at the

Fig. 10-4. Concentration of nitric acid

bottom. The overhead vapors are 99 weight per cent HN03, and an over-all recovery of nitric of 99 per cent is obtained. The sulfuric acid removed from the bottom is 65.0 weight per cent. The addition of the feed to the top of the tower is unusual and, in general, is not good distillation practice, but in this case the strong sulfuric acid would cause decomposition of concentrated nitric acid and is therefore diluted by the feed. The feed to the middle region is vapor so that there will be less dilution of the sulfuric acid. 1.2 lb of 92 per cent sulfuric is used per pound of 62 per cent nitric concentrated. The mixed acid added at the top is colder than the tower temperature, and the condensate produced in the column to heat it serves as reflux.

The operation of this nitric acid system will be analyzed to determine the number of theoretical plates involved. An analysis of the enthalpy values indicates that the usual simplifying assumptions will not be satisfied, but the deviations are not large and the assumptions will be used to simplify the calculations. The problem can be solved more exactly on an enthalpy-composition diagram. In general such a diagram is not suitable for a three-component mixture, but due to the negligible volatility of the sulfuric acid, a modified form of the diagram can be used. Equilibrium data (Refs. 2, 4) are given in Fig. 10-5.

Relative Volatility Diagram
Fig. 10-5. Vapor-liquid equilibrium system, nitric acid-water-sulfuric acid.

These equilibrium data illustrate the effect of the added agent on the relative volatility. With no sulfuric acid present, nitric acid and water form a maximum boiling azeotrope containing 38 mol per cent acid. The 62 weight per cent feed available is 31.8 mol per cent nitric acid. It is therefore impossible to make 99 weight per cent nitric acid from this feed unless some method of passing the azeotrope is available. The addition of sulfuric increases the volatility of nitric acid relative to water, and the equilibrium curves for liquid phases containing various mol fractions of sulfuric acid are given in Fig. 10-5. The units of the ordinates are expressed on a sulfuric acid-free basis. When the liquid phase contains 10 mol per cent sulfuric acid, the volatility of nitric acid is increased and the azeotrope composition becomes 12 mol per cent nitric acid. This sulfuric acid strength could be employed in a two-tower system to give the desired separation. The 31.8 mol per cent acid could be treated to extractive distillation with 10 mol per cent H2SO4 in the liquid to give the desired concentrated product and a bottoms containing about 15 mol per cent nitric acid. These bottoms would be fractionated without sulfuric acid being present to give water overhead and 31.8 per cent HNO3 as bottoms which would be recycled. Instead of this two-tower arrangement, it is found more practical to use more sulfuric acid and make the complete separation in one step. In order to obtain a satisfactory relative volatility of nitric acid to water at the low end of the curve requires 20 to 25 mol per cent sulfuric acid in the liquid phase. The actual acid consumption for 25 mol per cent sulfuric acid is approximately the same as for 20 mol per cent, because the lower relative volatility for the latter requires more stripping steam which increases the acid requirement.

Solution. Basis: 100 mols of 62 weight per cent nitric acid.

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