The possible specifications for DCOL and probably all multicomponent staged separation routines can be misleading. It is very easy to make specifications that are impossible to satisfy due to (1) material imbalance or (2) insufficient number of stages for the separation requested. The best way to avoid these problems is to specify reflux ratio (RR) and the bottom (or top) to total feed ratio when both a condenser and reboiler are present. The routine should be able to converge for nearly any set of values for those specs. The rare cases that fail are probably due to the method of initialization for an unusual case or an improper feed location.
Survey the possibilities using case studies
The stream 5 in the PPP default archive contains ethane, propane, isobutane, n-butane, and hexane. Suppose we eventually want isobutane. We could strip out the light compounds first, but let's model a separation of the isobutane and lighter from the n-butane and hexane. We desire a high recovery of isobutane and a low concentration of n-butane in the overhead product. Instead of setting those specifications, I set up a case study of 6 RR and 6 bottom/feed ratios. The results below are with 20 stages.
20 stage results
The two plots show the isobutene recovery (left) and the n-butane concentration (right) for the distillate overhead product. The plot on the left shows that high RR and low btm/feed results in high isobutane recovery (> 90% in red area). The plot on the right indicates that n-butane concentration below 1% (purple area) requires high btm/feed ratio. The red area on the left and the purple area on the right have no overlap in btm/feed specifications. It doesn't appear that increasing RR will help. Thus, the number of stages needs to be increased.
50 stage results
Without expanding the RR and btm/feed ranges, the increased number of stages has expanded the suitable IC4 recovery area and the low concentration n-C4 area. It appears that a btm/feed ratio of 0.54 and a RR > 3 will produce the desired separation. We also can see that results do not change greatly when RR > 3. Higher RR will just increase the cost of utilities and possibly increase column diameter to accommodate additional vapor traffic.
At this point, you could run a case with the RR and btm/feed pair selected above and see what recovery and purity were obtained. Or, you can run a case with the RR selected and IC4 recovery specified. Before you do the latter, you may want to get a better idea of the possible IC4 recoveries by looking at the result matrix, as shown below. Also, I recommend that you specify only one spec involving a component, even if you have made the survey. Making two component specs greatly increases the probability that you have given DCOL a problem with no solution.
For our "optimum", we select the second RR (RR=3) and the third BF (BF=0.54) values from the plot. In the recovery matrix, it looks like a recovery of 0.9 is possible. The amount of nbutane in this product should be < 1%.
The purpose of this example was to demonstrate the case study method. The separation shown probably would not be conducted for the stream. I hope to show more realistic separations using this stream in future posts.
Case Study execution and plotting is fast
The Mathcad contour plots were easily created using the GUI windows: no code was required to make the plots. This case method is better than trial and error because it should be faster and you also end up with more information, such as the lack of change for RR > 3. It took about 1 day to develop and debug the program. The 36 cases above take about 30 seconds to run. The second set of cases was made by changing just one variable, the number of stages. Feed location was set as a fraction of the total number of stages. I will explore the effect of feed location in a later post.
If you have a full process simulation program, try to take advantage of its case study capability for problems like this. It might help you to quickly arrive at optimal design conditions. Also, contour plots are a great way to display case study results: use them if you can easily get your case study results into that format.
The CSTR design model is another example of the use of case studies to explore feasible operating conditions.