A vapor recompression evaporator is to concentrate a very dilute aqueous solution. The feed rate is to be 30,000 lb/h; the evaporation rate will be 20,000 lb/h. The orator will operate at atmospheric pressure, with the vapor mechanically compressed as shown in Fig. 16.10 except that a natural-circulation calandria will be used. If steam costs $8 per 1,000 lb, electricity costs 3 cents per kilowatthour, and heat-transfer surface in the heater costs $70 per square foot, calculate the optimum pressure to which the vapor should be compressed. The overall compressor efficiency is 72 percent. Assume all other costs are independent of the pressure of the compressed vapor. To how many effects will this evaporator be equivalent?

Fig. 16.10

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Compressor Motor or turbine Makeup steam Condensate HO Heater Circulating pump 111 - Body Thick liquor discharge Feed FIGURE 16.10 Mechanical recompression applied to forced-circulation evaporator.