Marginal vapor flow

For nearly ideal mixtures, insights based on marginal vapor flows permit the development of a. simple. screening criterion computed using only relative volatilities and component feed flowrates to find the better column sequences from among the many possible. This criterion explains several of the traditional heuristics. 

The particular cost-related quantity we shall consider here is the marginal vapor flow rather than the actual annual cost. It is a quantity we can more readily estimate. In fact, for nearly ideal systems, we shall show a very easy way to approximate it. 

AV(i ,list) = Marginal vapor flow for column having i and j as light... 

Marginal vapor flow is the added vapor flow required in the column because the other species—i.e., those on the list—are present. The vapor flow in a column is an indicator of the cost of purchasing and operating the column. A difficult separation will have a large vapor flow because it will require a large reflux ratio. Also, refluxed material has to be vaporized and condensed, which directly affects the utility costs for operating the column. Therefore, it makes sen.se to try to minimize the total of the vapor flows for a system of columns. 

We should note that all sequences to separate a mixture will have the same set of binary splits. For example, each alternative sequence for the separation of ABCDE into five single-species pure products will have a split between A and B, another between B and C, etc. The difference among the alternative sequences is the presence or absence of other species when carrying out each of these binary splits. The total of the vapor flows for a sequence is the base set of vapor flows V(i/j), where / and j are A/B, B/C, C/D, and D/E, plus its marginal vapor flows. Thus, the difference in marginal vapor flows is the difference in total vapor flows among the sequences. The sequence with the minimum marginal vapor flows is the sequence with the minimum total vapor flows. 

How can we estimate a marginal vapor flow for a column One approach is to estimate the minimum reflux required using any method that is appropriate. If the separation is among species that are acting nearly ideally, we can use Underwood s method. 

Fig. 9. Relative size of numerators and denominators in term to estimate marginal vapor flow (a) terms relative to each other (b) ratios.

Using marginal vapor flows, we can also explain the following heuristic fairly straightforwardly, as the approximation for the added vapor flow for a species in any mixture in which it appears is proportional to its flow in the feed ... 

In other words, do the easy splits first. A split is easy if the relative volatility between the two key species is large. The (plausible) argument is that the hard splits should be done when no other species are present. Since the marginal vapor flow computation neither supports nor rejects this heuristic, we might draw the conclusion that this heuristic is not valid for the problem as we have posed it above. But there is some justification for this heuristic when we consider the energy integration of columns (e.g., using the heat expelled from the condenser of one column as the heat input into the reboiler of another). 

Applying Underwood s method gives us a minimum vapor flow of 72.5 kmol/h for a column accomplishing the separation of AB/CDE. Without species A, D, and E present, the minimum vapor flow is computed to be 44.5 kmol/h. The marginal vapor rate is therefore 38.0 kmol/h. 

The calculations were done using vapor pressure data available in Reid et al. (1987) for each of the species Table VI gives the results. The temperature selected for evaluating the vapor pressure is the bubble point at 1 atm for the feed mixture, i.e., at 434.21 K. Using the relative volatilities and feed flows shown in Table VI, we can estimate the marginal vapor rates shown in Table VII using the equation... 

A marginal but very important application of the drop calorimetric method is that it also allows enthalpies of vaporization or sublimation [162,169] to be determined with very small samples. The procedure is similar to that described for the calibration with iodine—which indeed is a sublimation experiment. Other methods to determine vaporization or sublimation enthalpies using heat flow calorimeters have been described [170-172], Although they may provide more accurate data, the drop method is often preferred due to the simplicity of the experimental procedure and to the inexpensive additional hardware required. The drop method can also be used to measure heat capacities of solids or liquids above ambient temperature [1,173],... 

NPSH. The net positive suction head is the most critical factor in a pumping system. A sufficient NPSH is essential, whether working with centrifugal, rotary, or reciprocating pumps. Marginal or inadequate NPSH will cause cavitation, which is the formation and rapid collapse of vapor bubbles in a fluid system. Collapsing bubbles place an extra load on pump parts and can remove a considerable amount of metal from impeller vanes. Cavitation often takes place before the symptoms become evident. Factors that indicate cavitation are increased noise, loss of discharge head, and reduced fluid flow. 

---