It may be noted that, for a fixed degree of enrichment from the feed to the top product, the number of trays required increases rapidly as the difficulty of separation increases, that is as the relative volatility approaches unity. There is no simple relation between Rm and the optimum value, although practical values are generally 1.1-1.5 times the minimum, with much higher values being employed, particularly in the case of vacuum distillation. The final total is shown by curve C which has a minimum value corresponding to the economic reflux ratio. The total charges may be obtained by adding the fixed and operating charges as shown in Figure 11.19, where curve A shows the steam costs and B the fixed costs.
The associated condenser and reboiler will also be larger and hence more expensive. (c) The capital cost rises at high values of R, since there is then only a very small reduction in the number of plates, although the diameter, and hence the area, continually increases because the vapour load becomes greater. (b) The capital cost initially falls since the number of plates falls off rapidly at this stage. (a) The operating costs rise and are approximately proportional to (R + 1). Increasing the reflux ratio from Rm therefore affects the capital and operating costs of a column as follows: Thus, an increase in R, at values near Rm, gives a marked reduction in the number of plates, although at higher values of R, further increases have little effect on the number of plates. The minimum reflux ratio for this case is 0.81. For a column separating a benzene-toluene mixture, for example, where xf = 0.79, xd = 0.99 and xw = 0.01, the numbers of theoretical plates as given by the McCabe-Thiele method for various values of R are given as follows. The reduction in the required number of plates as R is increased beyond Rm will tend to reduce the cost of the column.
The relationship between the number of plates n and the reflux ratio R, as derived by Gilliland(30), is discussed in Section 11.7.7. This will be a minimum when R equals Rm, and will steadily rise as R is increased. From a material balance over the top portion of the column, Vn = D(R + 1), and hence the steam required per mole of product is proportional to (R + 1).
The steam required will be proportional to Vm, which may be taken as Vn where the feed is liquid at its boiling point. The depreciation charges may be taken as a percentage of the capital cost, and the two together taken as the overall charges. The cost of a distillation unit includes the capital cost of the column, determined largely by the number and diameter of the plates, and the operating costs, determined by the steam and cooling water requirements.
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