Optimum Number of Evaporator Effects

A multiple-effect evaporator is to be used for evaporating 400,000 lb of water per day from a salt solution. The total initial cost for the first effect is 18,000, and each additional effect costs 15,000. The life period is estimated to be 10 years, and the salvage or scrap value at the end of the life period may be assumed to be zero. The straight-line depreciation method is used. Fixed charges minus depreciation are 15 percent yearly based on the first cost of the equipment. Steam costs 1.50 per 1000 lb. Annual maintenance charges are 5 percent of the initial equipment cost. All other costs are independent of the number of effects. The unit will operate 300 days per year. If the pounds of water evaporated per pound of steam equals 0.85 x number of effects, determine the optimum number of effects for minimum annual cost. 

Ramakrishna, P. Estimate optimum number of effects for multi-effect evaporation. Chem. Eng. 1987, 94, 82. 

Optimum number of effects. The cost of each effect of an evaporator per square meter or square foot of surface is a function of its total area and decreases with area, approaching an asymptote for very large installations. Thus the investment required for an iV-effect evaporator is about N times that for a single-effect evaporator of the same capacity. The optimum number of effects must be found from an economic balance between the savings in steam obtained by multiple-effect operation and the added investment required. 

Disregarding economics, there is a maximum number of effects in a multiple-effect system which is fixed by the boiling point elevation (BPE). The number depends on the over-all temperature range, the initial salt concentration, and the per cent yield. For the special case of a 35,000-p.p.m. NaCl feed, temperature range of 100° to 25° C., and 50% recovery, the maximum is about 107. Economics fixes a much smaller number and present indications are that the optimum number of effects will be somewhere between 10 and 20. This is for the case of boiling on the heat-transfer surface and not for flash evaporation, where the optimum number of stages is probably much greater. 

For a multiple-effect boiling evaporator the optimum number of effects would probably lie between 10 and 20. The absolute values naturally depend on the particular conditions and unit costs chosen, but the relative numbers for the two systems would probably not change very much. 

Installing Additional Effects When most existing evaporation systems were selected, one of the major design evaluations was determining the optimum number of effects. Much of the data may still be available, and these can be updated and used. The initial choice was probably based on economics and capital avail-ebility and in some cases, the physical size of the system also may have influenced the decision. The addition of effects sometimes can be used to increase production capacity as well as to reduce energy consumption, and thus there is a dual purpose for studying this option. 

The rate of Au(ffl) reduction should have a correlation with the cavitation efficiency at these frequencies. Therefore, the result of Fig. 5.8 suggests that maximum amounts of reductants are sonochemically formed at 213 kHz in the presence of 1-propanol. The existence of an optimum frequency in the sonochemical reduction efficiency would be explained as follows. As the frequency is increased, the number of cavitation bubbles can be expected to increase. This would result in an increase in the amount of primary and secondary radicals generated and an increase in the rate of Au(HI) reduction. On the other hand, at higher frequencies there may not be enough time for the accumulation of 1-propanol at the bubble/solution interface and for the evaporation of water and 1 -propanol molecules to occur during the expansion cycle of the bubble. This would result in a decrease in the amount of active radicals. Furthermore, the size of the bubbles also decreases with increasing frequency. These multiple effects would result in a very complex frequency effect. 

G. Materials of Construction. Evaporator materials of construction and their costs play a large role in determining the optimum compression ratio. Monel is a standard material of construction for brine evaporator bodies. Stabilized titanium (e.g.. Grade 12) is a frequent choice for heater tubing and Type 316 stainless steel for the circulating pumps. The evaporator normally will be of the forced-circulation type described in Section 9.3.3.2. It will either contain a number of effects or operate with vapor recompression. Salt-recovery centrifuges may be Monel or stainless steel. 

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