Optimum number of stages

As mentioned earlier, because the number of stages has a significant effect in determining the velocity ratio, consider the effect the gas conditions have in determining tlie optimum number of stages. To make this determination, the following parameters should be considered ... 

The optimum number of stages is n. For a constant performance ratio the total cost of the evaporator is... 

The results in terms of optimum number of stages, vapour load, reflux ratio, cut time, etc. are summarised in Table 1 for both columns. The results also show the operating cost per batch, annualised capital cost, profit per batch and per year. For MultiVBD column the total number of stages required is 40% more than that required for the conventional column CBD). However, the vapour load for the MultiVBD column is about 25% lower compared to CBD and the operating cost (a measure of energy cost) is 30% lower. Finally, the overall profit realised by MultiVBD column is about 3% more that that by CBD column. The product demand and qualities (purities) of each main-cut and off-cut are achieved to the given specifications. Figure 4 shows the product quality at the end of the batch ior MultiVBD column in each vessel. 

The optimum number of stages and feed locations can be determined graphically... 

Disregarding economics, there is a maximum number of effects in a multiple-effect system which is fixed by the boiling point elevation (BPE). The number depends on the over-all temperature range, the initial salt concentration, and the per cent yield. For the special case of a 35,000-p.p.m. NaCl feed, temperature range of 100° to 25° C., and 50% recovery, the maximum is about 107. Economics fixes a much smaller number and present indications are that the optimum number of effects will be somewhere between 10 and 20. This is for the case of boiling on the heat-transfer surface and not for flash evaporation, where the optimum number of stages is probably much greater. 

If the cost of energy is reduced, the optimum number of stages becomes smaller. Using an energy cost of half that assumed above, the optimum number of stages is 42 instead of 44, and the TAC drops to 2,980,000 per year from 4,823,000. It is clear that energy costs dominate the design of distillation columns. 

Stainless steel is used in the cost estimates given in Table 4.1. If the materials of construction were more exotic, the optimum number of stages would decrease. 

The next issue is to find the economic optimum number of stages in each column. The locations of the feeds were scaled up or down directly with the total number of stages using the results for the 32-stage columns. Note that the distillate of the recovery column (D3) is fed to the top of the azeotropic column in aU cases. 

Then the number of stages in the recovery column is varied with the number of stages in the azeotropic column fixed at 62. Table 17.5 shows that the optimum number of stages (12 is selected as the minimum practical number) is much smaller than recommended in the Ryan-Doherty design. 

Remember that these results are for an 85 mol% ethanol beer stiU distillate. Combining all three columns is considered in the next section. We assume that the optimum numbers of stages in the azeotropic and recovery columns do not change significantly as the beer still distillate composition varies over the range of 75-85 mol% ethanol. 

The beer still distillate flow rate decreases slightly as distillate composition is increased but less organic reflux (R2) is required. This reduces reboiler duty in the azeotropic column (QR2). However, the reboiler duty in the beer still (QRl) increases as distillate composition is increased, as does the optimum number of stages in the beer still (NTl). So, beer still capital and energy costs increase while those costs in the azeotropic column decrease. 

For the multistage evaporating plant schematically shown in Figure 2.11, the optimum number of stages with regard to the minimization of the manufacturing costs shall be determined. 

For the current conditions and feed plate location, there are more than the optimum number of stages in the rectifying (top) section. This suggests that the unit may have been designed to process a lower concentration of feed material or to produce a higher-concentration distillate stream than is required currently. 

The optimization problem considered indicates that the best way to operate a crosscurrent cascade is by equal subdivision of solvent or adsorbent. The reader should be aware, however, that the complete optimization of a plant must also consider the cost of the stages, the cost of solvent recovery, and the value of the extracted solute itself. Thus, in addition to optimmn solvent use, we also need to determine the optimum number of stages, and this... 

Clearly the reduction in the amount of adsorbent is achieved at the expense of more processing stages. Conversely, a better purification could be achieved with a given amount of adsorbent M if it were divided equally among a number of stages. The optimum number of stages needs to be obtained from an economic evaluation. 

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