Actual theoretical stages

The recommended method to use to determine the actual theoretical stages at an actual reflux ratio is the Erbar/Maddox relationship. In the graph, N is the theoretical stages and R is the actual reflux ratio L/D, where L/D is the molar ratio of reflux to distillate. N, is the minimum theoretical stages and R, is the minimum reflux ratio. 

B = parameter in correlating equation In = natural logarithm log = logarithm to the base 10 N = actual theoretical stages required for a given separation... 

After actual theoretical trays are determined (see Actual Reflux and Actual Theoretical stages) one needs to estimate the actual physical number of trays required in the distillation column. This is usually done by dividing the actual theoretical trays by the overall average fractional tray efficiency. Then a few extra trays are normally added for offload conditions, such as a change in feed... 

The overall stage efficiency of a staged extraction system is simply the number of theoretical stages divided by the number of actual stages times 100 [Eq. (15-28)]. 

Gilliland" tells how his famous correlation was developed for relating actual and minimum reflux to actual and minimum theoretical stages for a fractionating column. Numerous plate-to-plate calculations were made and the results plotted using his well-known correlating parameters. The best curve was then drawn through points. 

The number of actual equilibrium stages determines the number of flashes that will occur. The more stages, the more complete the split, but the taller and more costly the tower. Most condensate stabilizers will normally contain approximately five theoretical stages. In a refluxed tower, the section above the feed is known as the rectification section, while the section below the feed is known as the stripping section. The rectification section normally contains about two equilibrium stages above the feed, and the stripping section normally contains three equilibrium stages. 

The component with the lowest equilibrium constant is called the key component in the stripping process, because it yields the largest value of Vnjm- This largest value is the true minimum air flowrate, whereas the actual air flowrate should be selected at 1.20 to 2.0 times the minimum. This becomes a balance between fewer theoretical stages at actual air flowrate, yet requires a larger diameter column to carry out the operation. 

The actual stage can be a mixing vessel, as in a mixer-settler used for solvent extraction applications, or a plate of a distillation or gas absorption column. In order to allow for non-ideal conditions in which the compositions of the two exit streams do not achieve full equilibrium, an actual number of stages can be related to the number of theoretical stages, via the use of a stage-efficiency factor. 

The number of theoretical stages required to effect a required separation, and the corresponding rates for the liquid and vapour phases, may be determined by the procedures described previously. In order to translate these quantities into an actual design the following factors should be considered ... 

The relaxation method is certainly slower than the other methods of calculation. However, because of its simple nature, any process can be calculated and the complexities of the process cease to be a major concern. If future attention were directed toward performing an exact calculation of the individual stage, these more exact calculations could replace the flash calculations of the theoretical stages, and the calculated process would then fit much more closely the actual process operation. 

Actual number of theoretical stages calculated for input actual reflux ratio of 2.0 = 9.60 (add two more stages for condenser and reboiler, or 12 theoretical total)... 

What does ETF do ETF simply tells you how many actual trays make up one theoretical stage of a fractionation column. This is an agonizing question I have heard repeated many times. I personally have gained much income by resolving this question as a consultant. (In my case, the IRS has also gained considerable income ) The quest continues even now for a good and reliable answer. My answer is ETF. 

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