Evaluation of the heat requirements in batch distillation operations

Abstract

A rigorous method is presented for the evaluation of the heat requirements in binary batch fractionations which involve negligible column hold up. The method, in which the additional variables of the discontinuous process are taken into account, is a modification of the methods of Ponchon and Savarit for continuous operation. Two examples, one for a fractionation in which the composition of the product is constant and the other in which the reflux ratio is constant, are given as illustrations of the method.The application of the method permits more accurate evaluation of reboiler and condenser heat loads and, in turn, better design.The methods (1, 6) which are available for the solution of batch fractionation problems are often modifications of the McCabe-Thiele ($9) solution for continuous-rectification problems. Consequently, the heat loads at the reboiler and condenser cannot be evaluated rigorously but can be only approximated. The degree of accuracy of the approximation depends upon the validity of the assumptions made in the McCabe-Thiele development: (1) molal latent heat independent of composition, (2) negligible heat of solution, and (3) negligible sensible heat effects. However, since the errors introduced by these individual assumptions may often tend to be compensating, better criteria for the applicability of the McCabe-Thiele method are that the saturated liquid and vapor lines on an enthalpy concentration are straight and, further, that the molal latent heat of vaporization is independent of composition. Either the chemical molecular weight or a fictitious molecular weight may be used as a basis for the determination of the molal latent heat.Furthermore, when a modified McCabeThiele solution is applied to batchfractionation problems, the condenser and reboiler loads become identical. For reasons cited above, it appears worth while to develop a method whereby the heat effects in batch distillation operations can be determined rigorously.The methods of Ponchon (4) and Savarit (5) offer a rigorous means of solving two-component distillation problems in which the composition on a given plate is independent of time, i.e., steady state-operation. To apply this method to batch-fractionation problems, one must allow for the fact that the liquid and vapor compositions are functions of time as well as of plate number. Also one must take into account the fact that a batch fractionation may be carried out under conditions in which the product composition is constant and the reflux ratio varied or in which the reflux ratio is constant and the product composition allowed to change. PROPOSED METHODThe batch fractional-distillation system is shown diagrammatically in Figure 1. An over-all differential material balance is(1) and an over-all differential-component material balance isIf Equation (4) is rearranged, an equation similar to the Rayleigh equation is obtained:In a batch distillation in which the composition of the overhead production is held constant by variation of the reflux ratio, the preceding equation...