involve additional feeds and/or sidestreams, add (C + 3) degrees of freedom for each additional feed (C + 2 to define the feed and 1 to designate the feed stage) and 2 degrees of freedom for each side-stream (1 for the sidestream flow rate and 1 to designate the side-stream-stage location). Any number of elements or units can be combined to form complex processes. No new rules beyond those developed earlier are necessary for their analysis. When applied to the thermally coupled distillation process of Fig. 13-6b, the result is N= 2(N + M) + C + 18. Further examples are given in Henley and Seader (op. cit.). An alternative method for determining the degrees of freedom for equipment and processes is given by Pham [Chem. Eng. Sci., 49, 2507 (1994)].

TABLE 13-6 Design Variables N" for Separation Units


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