Consider the system shown in Fig. 6-11 and suppose that two of the specifications consist of the rates Bt and B2. Since 0.94 B2 is recycled back to column 1 from column 2, and 0.06 B2 is withdrawn from the system, the flow rates of all terminal streams may be computed where it is, of course, understood that the feed rates Fu F2, F3, and their compositions have been specified. Let the positive multipliers 0, and 02 be defined as follows where the subscript ca denotes the most recently calculated value of the variable, and bit t /d, 1? and bit 2 /dit 2 denote the corrected values which are to be found by the capital 0 method of convergence. The values of the 0's are to be determined such that the corrected component-flow rates satisfy the component-material balances

ca ca

and are in agreement with the specified values of B, and B2. Equations (6-18) through (6-21) may be solved simultaneously for ditl and d{ 2. However, in

order to avoid possible numerical problems, it is better to solve for the ratios Pi ! and pL 2 which are defined by

To facilitate the solving for these ratios, let Eqs. (6-18) and (6-19) be restated as follows

Elimination of , and bi% 2 from Eqs. (6-20) and (6-21) by use of Eqs. (6-24) and (6-25) followed by the restatement of the resulting equations in matrix notation yields

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