Multiple effect evaporation heat balance

Multiple-Effect Evaporators A number of approximate methods have been published for estimating performance and heating-surface requirements of a multiple-effect evaporator [Coates and Pressburg, Chem. Eng., 67(6), 157 (1960) Coates, Chem. Eng. Prog., 45, 25 (1949) and Ray and Carnahan, Trans. Am. Inst. Chem. Eng., 41, 253 (1945)]. However, because of the wide variety of methods of feeding and the added complication of feed heaters and condensate flash systems, the only certain way of determining performance is by detailed heat and material balances. Algebraic soluflons may be used, but if more than a few effects are involved, trial-and-error methods are usually quicker. These frequently involve trial-and-error within trial-and-error solutions. Usually, if condensate flash systems or feed heaters are involved, it is best to start at the first effect. The basic steps in the calculation are then as follows ... 

Several comprehensive examples of heat balances and surface requirements of multiple effect evaporation are worked out by Kern (1950). 

MULTIPLE-EFFECT CALCULATIONS. In designing a multiple-effect evaporator the results usually desired are the amount of steam consumed, the area of the heating surface required, the approximate temperatures in the various effects, and the amount of vapor leaving the last effect. As in a single-effect evaporator, these quantities are found from material balances, enthalpy balances, and the capacity equation (16.1). In a multiple-effect evaporator, however, a trial-and-error method is used in place of a direct algebraic solution. 

In multiple effect evaporation nnits the steam consumption ) and the liquid flow rates between the various effects can be calculated by means of energy and material balances of the first effect or any other effect. The steam consumption b (here only the heat of condensation r is utihzed) of a forward-feed operation unit according to Fig. 7.2-2 is given by... 

The economic advantages of a multiple-effect evaporation resulting from better steam utilization are reduced to a certain extent by additional costs due to (a) pressure gradient over the series of evaporators, which is necessary to maintain the reasonable temperature difference between steam and boiling solution in a sequence of evaporators, and (b) larger heat transfer surface area necessary to maintain a technically justified evaporation rate. Therefore, the design of a particular evaporation system should be based on economic-balance calculations. 

Because each effect of an evaporator produces almost as much vapor as the amount it condenses, the total evaporation accompHshed per unit of prime steam, or steam economy, iacreases ia almost direct proportioa to the number of effects used. The total heat load is also spHt up betweea the effects so that each effect has a much lower heat duty than a single effect for the same total evaporation load. However, the total available AT is also spHt up similarly so that each effect of a multiple effect requites about as much heating surface as a single effect operating over the same total temperature difference. Thus ia selecting the number of effects to use ia any iastallatioa, steam cost savings and capital cost of effects have to be balanced. Even before... 

One important component of any evaporator installation is the equipment for condensing the vapour leaving the last effect of a multiple-effect unit, achieved either by direct contact with a jet of water, or in a normal tubular exchanger. If M is the mass of cooling water used per unit mass of vapour in a jet condenser, and H is the enthalpy per unit mass of vapour, then a heat balance gives ... 

In evaporator calculations, three relations must be satisfied material balance required rates of heat transfer and heat balance. These relations must be applied to each effect in a multiple-effect system as well as to the total system. The equations describing evaporator systems can be solved algebraically but the process is tedious and time consuming. Trial-and-error procedures are generally used as follows ... 

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