Columns Having a Common Condenser and Reboiler

To illustrate this type of energy exchange, suppose that it is desired to use the condenser of column 2 of Fig. 7-1 as the reboiler for column 1. In order for such an operation to be feasible, it is of course necessary for the dew-point temperature T2 2 of the overhead V2,2 from column 2 to be greater than the bubble-point temperature Tv-1, i of the liquid Ls i, i entering the reboiler of column 1. Obviously, many pairs of operating pressures P2 Pi exist for which 

There follows a description of the use of the capital 0 method in the determination of a solution for the system of columns shown in Fig. 7-1 such that the reboiler duty of column 1 is equal to the condenser duty of column 2, that is, such that QRl = QC2. For the system of columns shown in Fig. 7-1, suppose that column 1 has a partial condenser and that the flow rate, composition, and thermal condition of the feed are fixed as well as the pressure, the number of stages, and the feed-plate location. Likewise, suppose that the number of plates, the feed-plate location, and the pressure of column 2 are fixed. Two additional specifications may be made on each column. Since the precise choice of these additional specifications determines the form of the calculational procedures for each column as well as the system, only these additional specifications are listed in the problems considered. In each instance it is supposed, however, that the usual specifications of the type listed above have been made. 

To demonstrate the use of the capital 0 method in the solution of problems involving such a system, suppose that the following set of additional specifications are made. 

The last subscript refers to tjhe number of the column. The boilup ratio (VNl /By)n of column 1 is to be adjusted from one system trial to the next until a solution has been found such that Qcl = QRi. 

On the basis of an assumed value for VNl/B, denoted by (Vni/B, one complete trial is made on column 1. The results so obtained are used to make one complete trial on column 2. Then the capital 0 method of convergence is applied in order to find a new value (Vsi/Bl)n+ x such that all of the energy and material balances enclosing the terminal streams as well as the equilibrium relationships for these streams are satisfied at the condition QRi = QC2 The value so obtained for VNi/B is used to make the next column trial on column 1. 

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