Distillation has been known and practiced since antiquity, and it remains by far the most widely used separation process in the chemical and allied industries. In this dissertation, a comprehensive self-contained geometric theory of multicomponent distillation is developed. The theory is applicable to all mixtures (constant relative volatility, ideal, nonideal and azeotropic), and provides a rich, yet surprisingly compact, framework within which the behavior of the column composition profile, for any multicomponent mixture, can be readily and systematically constructed from its phase equilibrium behavior. As a result, many longstanding unsolved problems in distillation are shown to be tractable. The geometric theory also satisfactorily explains the more complex behavior of multicomponent mixtures, in contrast to binary and ternary systems. Although the theory is developed formally for homogeneous mixtures, methodologies for extending the analysis to include heterogeneous systems, reactive distillation, complex column configurations, and hybrid distillation columns are also described. An essential ingredient of any systematic synthesis and design procedures for multicomponent distillation is a simple and accurate method for designing (i.e., computing the minimum flow rates and the number of theoretical stages) each individual column. Utilizing geometric concepts, a simple, robust algebraic method for calculating minimum flows in multicomponent distillation columns is developed. This procedure does not require a priori knowledge of the exact product distribution, and applies to ideal, nonideal, and azeotropic systems. Moreover, in the special case of constant relative volatility mixtures, our method and Underwood's method are shown to be identical. A simple noniterative computer-aided design procedure for multicomponent distillations columns is also developed. The procedure is geometric in nature, and applies to all homogeneous mixtures, including those that exhibit azeotropes and distillation boundaries. The design technique provides an accurate and efficient method for determining the number of theoretical stages in the column, the feed stage location, and the product distribution, without the use of lengthy iterative schemes involving column simulations, as is the current practice. This procedure is easily extended to include certain retrofit design of distillation columns.
