Equations used to calculate the capital cost of all the equipment and the energy cost of the heat added to the reboiler are needed to perform economic optimization calculations. The major pieces of equipment in a distillation column are the column vessel (of length L and diameter D, both with units of meters) and the two heat exchangers (reboiler and condenser with heat transfer areas AR and AC, respectively, with units of m2). Smaller items such as pumps, valves, and the reflux drum are seldom significant at the conceptual design stage. The cost of the trays themselves is usually small compared to the costs of the vessel and heat exchangers unless expensive internals are used such as structured packing. Table 4.1 gives the economic parameter values and the sizing relationships and parameters used.
The sizing of the column vessel has been discussed in Chapter 3. The condenser and reboiler heat duties are determined in the simulation, but we need to have an overall heat transfer coefficient and a differential temperature driving force in each heat exchanger to be able to calculate the required area. The values of these parameters given in Table 4.1 are typical of condensing and boiling hydrocarbon systems. Note that the overall heat transfer coefficient of the condenser is larger than that of the reboiler. Reboilers have a greater tendency to foul because of the higher temperature (more coking or polymerization) and because any heavy material in the feed drops to the bottom of the column.
Various objective functions are used for economic optimization. Some are quite elegant and incorporate the concept of the "time value of money." Examples are "net present value" and "discounted cash flow." These methods are preferred by business majors, accountants, and economists because they are more accurate measures of profitability over an extended time period. However, many assumptions must be made in applying these methods, and the accuracy of these assumptions is usually quite limited. The prediction of future sales, prices of raw materials and products, and construction schedule is usually a guessing game made by marketing and business managers whose track record for predicting the future is almost as poor as that of the weather forecaster (meteorologist).
Therefore, the use of some simple economic objective function usually serves the purpose of optimizing a distillation column design. We will use the total annual cost (TAC). As shown in Table 4.1, this measure incorporates both energy cost and the annual cost of capital. The units of TAC are $/year. The units of capital investment are U.S. dollars ($). The units of annual cost of capital are $/year, and it is obtained by dividing the cost of capital by a suitable payback period.
TABLE 4.1 Basis of Economics
Heat transfer coefficient Differential temperature Capital cost Reboilers
Heat transfer coefficient Differential temperature Capital cost Column vessel capital cost
7296 (area in m2)0 65
7296 (area in m2)0.65
17,640 [diameter (D) in meters]1066
TAC =--h energy cost payback period
The cost of energy varies quite a bit from plant to plant. In some locations energy sources are plentiful and inexpensive. For example, in Saudi Arabia gas coming from an oil well is sometimes simply flared (burned). In other locations, fuel is quite expensive because it must be transported long distances. For example, in Japan some of the natural gas is shipped in from Indonesia on liquefied natural gas tankers (LNG), which are very expensive. Therefore energy costs depend on location. A value of $4.7 per kilojoule is used in the results presented below.
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