Evaporation multiple-effect calculations

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. 

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 ... 

Storrow, J. A. Ind. Chemist 27 (1951) 298. Design calculations for multiple-effect evaporators — Part 3. 

A thermodynamic analysis of the energy requirements of desalting processes is presented, to clarify the conditions under which such calculations are valid. The effects of departure from isothermal operation, finite product recovery, differential as opposed to single-stage operation, and salt concentration in the feed are examined. A comparison shows that there is essentially no difference between the energy requirements for a distillation and a freezing process. The minimum heat consumption and maximum number of efFects for a multiple-effect evaporation plant are calculated. The above analysis leads to the conclusion that efficiencies in the range 10 to 20% will be very difficult to achieve. 

If a multiple-effect evaporator system produces 10 pounds of fresh water per pound of saturated steam at 35 p.s.i.a. (t = 259° F.) and t0 = 70° F., the work equivalent per 1000 gallons of fresh water is 60 kw.-hr. and the energy efficiency using the differential process with 50% recovery as the standard, is 6.9%. This calculation assumes that the available heat is simply the latent heat of condensation at the constant temperature of 259° F. 

Multiple-effect evaporators are most often used in glycerine recovery plants of medium to large size, with the typical plant having a two-effect evaporator. The user must calculate and compare the savings in steam use for operating additional effects against the additional equipment and maintenance costs as well as space and operational complexity for additional effects. 

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. 

In doing calculations for a multiple-effect evaporator system, the values to be obtained are usually the area of the heating surface in each effect, the kg of steam per hour to be supplied, and the amount of vapor leaving each effect, especially the last effect. The given or known values are usually as follows (1) steam pressure to first effect, (2) final pressure in vapor space of the last effect, (3) feed conditions and flow to first effect, (4) the final concentration in the liquid leaving the last effect, (5) physical properties such as enthalpies and/or heat capacities of the liquid and vapors, and (6) the overall heat-transfer coefficients in each effect. Usually, the areas of each effect are assumed equal. 

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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