TABLE OF CONTENTS 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...
