The equations to calculate the capital cost of all the equipment and the energy cost of the energy are given in the Matlab program shown in Table 4.2. The numerical example is for the 32-stage column studied in Chapter 3.

Table 4.3 gives results for a range of values for the total number of stages. The 32-stage case is shown in the second column. The capital cost of the column shell, which is 5.91 m in diameter and 1.2(0.61)(30) = 22 m in length, is $1,400,000. The capital cost of the two large heat exchangers at $1,790,000 is more than the vessel. The total annual cost is $5,090,000 per year. Note that most of this is energy ($4,030,000 per year).

The other columns in Table 4.3 give results for columns with other total stages. If the number of stages is reduced to 24, which gives a shorter column, reboiler heat input increases. This increases column diameter and heat exchanger areas. This results in an increase in both capital and energy costs.

If the number of stages is increased, the column becomes taller, but its diameter becomes smaller because reboiler heat input decreases. This decreases heat exchanger costs and energy costs. However, the cost of the vessel increases because it is longer.

So the effect of increasing the number of stages is to increase the capital cost of the shell and to decrease the capital cost of the heat exchangers and energy costs. As more and more

TABLE 4.2 Matlab Program to Evaluate Economics

% economics for distillation column Example 1 (depropanizer) % Given Qr, Qc and number of trays, calculate TAC % for standard column % using SI units (m, K, MW) % Cost of energy=$4.7 per kJ


% 3 2 stage column nt=3 0;d=5.91;qr=27.17;qc=22.68;


.7457/(dtc*uc); hx=72 9 6*(ar^0.65 +ac^0.65); energy=qr*costenergy*3 60 0*24*3 65/10 00; capital=shell+hx; tac=energy+capital/3;


TABLE 4.3 Rigorous Optimization Results


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