Formulation of the Economic Objective Function

The economic objective function is formulated on the basis of (1) capital costs, (2) return on investment, and (3) operating costs. The objective function is formulated as an expression of the desire to minimize the total costs per mole of the most valuable product. The capital costs consist of the installed costs of the following items the pressure vessel or shell of the distillation column, the trays, the condenser, and the reboiler. 

After the column diameter had been estimated by use of the relationships recommended by Glitsch, Inc.,6 the cost of the shell was estimated by use of the data presented by Guthrie.7 Guthrie s data were also used to estimate the costs of the plates, the condenser, and the reboiler. Guthrie s data (originally presented in graphical form) were converted to the form of curve fits which are given below. 

A straight-line depreciation of the capital investment over a 10-year period was assumed, and the corresponding annual capital investment, C0, was computed. If R is used to denote the expected fractional return on investment, then the return on the investment per year is RCc, and the total cost associated with the capital investment is (1 + R)Cc. 

Operating costs, C0, consist of the costs of supplying the required condenser and reboiler duties for one year. A summary of the equations used to evaluate the objective function follow. 

To compute the costs of the empty column (or the shell), the diameter of the column is needed. Consider the case where the column is to be operated at 80 percent of vapor flood, and two-pass ballast trays with 24-inch tray spacings are to be used. The column diameter may be estimated by use of the following relationship given by Glitsch.6 

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