Basis for Computer Evaluation of Multicomponent Separations

The integrals are defined as numbers of transfer units for absorption or stripping, 

HTUs vary with the type and size of packing, the flow rates, the distribution of flow across the cross section, and sometimes with the packing height and column diameter. They are necessarily experimental data. Some of these data are discussed at the end of this chapter. 

The way in which interfacial concentrations y are related to the bulk concentrations y required for evaluation of the integrand of Eq. (13.184) is explained in Example 13.13, which finds trays and transfer units for an absorption problem. 

Until the advent of computers, multicomponent distillation problems were solved manually by making tray-by-tray calculations of heat and material balances and vapor-liquid equilibria. Even a partially complete solution of such a problem required a week or more of steady work with a mechanical desk calculator. The alternatives were approximate methods such as those mentioned in Sections 13.7 and 13.8 and pseudobinary analysis. Approximate methods still are used to provide feed data to iterative computer procedures or to provide results for exploratory studies. 

The two principal tray-by-tray procedures that were performed manually are the Lewis and Matheson and Thiele and Geddes. The former started with estimates of the terminal compositions and worked plate-by-plate towards the feed tray until a match in compositions was obtained. Invariably adjustments of the amounts of the components that appeared in trace or small amounts in the end compositions had to be made until they appeared in the significant amounts of the feed zone. The method of Thiele and Geddes fixed the number of trays above and below the feed, the reflux ratio, and temperature and liquid flow rates at each tray. If the calculated terminal compositions are not satisfactory, further trials with revised conditions are performed. The twisting of temperature and flow profiles is the feature that requires most judgement. The Thiele-Geddes method in some modification or other is the basis of most current computer methods. These two forerunners of current methods of calculating multicomponent phase separations are discussed briefly with calculation flows-ketches by Hines and Maddox (1985). 

A Naphthali-Sandholm program appears in Fredenslund, Gmehling, and Rasmussen (Vapor-Liquid Equilibria Using UNIFAC, Elsevier, New York, 1977). 

A Newton-Raphson SC (simultaneous correction) program of Newman is reproduced by King (Separation Processes, McGraw-Hill, New York, Appendix E). 

Abundant descriptions of the theoretical basis and procedures for computer methods appear in recent literature and are summarized in books by Holland (1981), King (1980, Chap. 10), 

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When all of the coefficients are known, this can be solved for the concentrations of component i in every stage. A straightforward method for solving a tridiagonal matrix is known as the Thomas algorithm to which references are made in Sec. 13.10, Basis for Computer Evaluation of Multicomponent Separations Specifications. ... 

BASIS FOR COMPUTER EVALUATION OF MULTICOMPONENT SEPARATIONS 433 Start... 

BASIS FOR COMPUTER EVALUATION OF MULTICOMPONENT SEPARATIONS 407 4. H equation—energy balance (one for each stage) ... 

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