## Evaporator Calculations

Single-Effect Evaporators The heat requirements of a single-effect continuous evaporator can be calculated by the usual methods of stoichiometry. If enthalpy data or specific heat and heat-of-solution data are not available, the heat requirement can be estimated as the sum of the heat needed to raise the feed from feed to product temperature and the heat required to evaporate the water. The latent heat of water is taken at the vapor-head pressure instead of at the product temperature in order to compensate partially for any heat of solution. If sufficient vapor-pressure data are available for the solution, methods are available to calculate the true latent heat from the slope of the Duhring line [Othmer, Ind. Eng. Chem., 32, 841 (1940)].

The heat requirements in batch evaporation are the same as those in continuous evaporation except that the temperature (and sometimes pressure) of the vapor changes during the course of the cycle. Since the enthalpy of water vapor changes but little relative to temperature, the difference between continuous and batch heat requirements is almost always negligible. More important usually is the effect of variation of fluid properties, such as viscosity and boiling-point rise, on heat transfer. These can only be estimated by a step-by-step calculation.

In selecting the boiling temperature, consideration must be given to the effect of temperature on heat-transfer characteristics of the type of evaporator to be used. Some evaporators show a marked drop in coefficient at low temperatureâ€”more than enough to offset any gain in available temperature difference. The condenser cooling-water temperature and cost must also be considered.

Thermocompression Evaporators Thermocompression-evap-orator calculations [Pridgeon, Chem. Metall. Eng., 28, 1109 (1923); Peter, Chimia (Switzerland), 3,114 (1949); Petzold, Chem. Ing. Tech., 22, 147 (1950); and Weimer, Dolf, and Austin, Chem. Eng. Prog., 76(11), 78 (1980)] are much the same as single-effect calculations with the added complication that the heat supplied to the evaporator from compressed vapor and other sources must exactly balance the heat requirements. Some knowledge of compressor efficiency is also required. Large axial-flow machines on the order of 236-m3/s (500,000-ft3/min) capacity may have efficiencies of 80 to 85 percent. Efficiency drops to about 75 percent for a 14-m3/s (30,000-ft3/min) centrifugal compressor. Steam-jet compressors have thermodynamic efficiencies on the order of only 25 to 30 percent.

Flash Evaporators The calculation of a heat and material balance on a flash evaporator is relatively easy once it is understood that the temperature rise in each heater and temperature drop in each flasher must all be substantially equal. The steam economy E, kg evaporation/kg of 1055-kJ steam (lb/lb of 1000-Btu steam) may be approximated from

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