Availability of large digital computers has made possible rigorous solutions of equilibrium-stage models for multicomponent, multistage distillation-type columns to an exactness limited only by the accuracy of the phase equilibrium and enthalpy data utilized. Time and cost requirements for obtaining such solutions are very low compared with the cost of manual solutions. Methods are available that can accurately solve almost any type of distillation-type problem quickly and efficiently. The material presented here covers, in some detail, some of the more widely used computer algorithms as well as the classical Thiele-Geddes manual method. All are rating methods, in that the number of equilibrium stages and feed and withdrawal stages are specified. However, a successive-approximation design method that utilizes a rating method is given by Ricker and Grens [Am. Inst. Chem. Eng. J., 20, 238 (1974).] Those desiring further details are referred to the textbooks by Henley and Seader, King, and Holland cited under "General References" at the beginning of this section. These books, in turn, cite a myriad of references in chemical engineering journals. The mathematics involved is that of dealing with sets of nonlinear algebraic equations. The general nature of the main mathematical problems is presented lucidly by Friday and Smith ["An Analysis of the Equilibrium Stage Separation Problem— Formulation and Convergence," Am. Inst. Chem. Eng. J., 10, 698 (1964)].
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