Other Applications of the Theta Methods

In the same manner that the capital 0 method was applied above to solve problems involving specifications other than the total flow rates, the 0 method for single columns may be applied to solve problems involving specifications other than the total-flow rates. To demonstrate this application of the 0 method, it is applied to conventional distillation columns for which the reflux ratio L /D and the boilup ratio Vs/B are specified instead of the reflux rate Lj and the distillate rate D. The remaining specifications for the column are the same as those enumerated in Chap. 2 in the application of the 0 method of convergence to conventional distillation columns. 

The specification of Lt /D and VN/B gives rise to a 0 method which consists of seven variables and seven functions.8 The variables x are as follows 

The following calculational procedure may be used to solve problems of this type. 

Step 1. Assume a set of temperatures 7 and vapor rates Vj. Find the corresponding liquid rates Lj by use of total material balances. 

Step 2. Solve Eq. (2-18) for the vapor rates vji for each component i and compute the corresponding liquid rates /jf.  

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