Feed-plate matching

If one continued calculations from the pinches found in Examples 11-2 and 11-3 to the feed plate by introducing appropriate amounts of components 1 and 4 as described previously, a match in compositions would be obtained at the feed plate because the solution sets of [Pg.374]

Equal-molal overflow could be assumed, but if the calculations are done by computer, an enthalpy balance would probably be made and the change in pressure from stage to stage would also be allowed for. The calculations are continued in this fashion, alternating the use of equilibrium and material-balance relationships, until the composition is close to that of the feed. Similar calculations are carried out for the lower section of the column starting with an estimated reboiler or bottoms composition. The next step is to match the Compositions at the feed stage for the two sets of calculations. Based on the differences for individual components, the product compositions are adjusted and the calculations repeated until all errors fall below a specified value. In some procedures, the number of plates and the feed plate are fixed beforehand, and the calculations are repeated for different reflux ratios until the desired match is obtained at the designated feed plate. 

Actually there is no sharp line of demarcation between these five sections, but this division serves as a useful picture for considering the case of the minimum reflux ratio. The feed to the fractionating column would be introduced on some plate in intermediate section 3, and the true criterion for the minimum reflux ratio should be based on matching the ratio of the concentrations of the key components above and below the feed plate under conditions such that a pinched-in section occurs both above and below the feed plate. For mixtures of normal volatility, a pinched-in region in only one section does not necessarily mean that an infinite number of plates would be required to perform the desired separation at the reflux ratio under consideration, since by relocating the feed plate, such as to shift the ratio of the concentrations of the key components at this plate, the section that was not limited could be made to do more separation and thereby relieve the load on the pinched-in section. In other words, for mixtures of normal volatilities the condition of the minimum reflux ratio is not determined by either the fractionation above or below the feed plate alone, but is determined such that the separation is limited both above and below the feed. The conditions in the intermediate feed section lead to... 

These equations can be used to calculate the concentrations of the key components for evaluating the minimum reflux ratios for Cases I and II, which would involve matching the ratio of the concentrations of the key components above the feed plate with the same ratio below the feed plate This leads to a quadratic solution for the minimum reflux ratio. Thus for Case I the ratio of the key components above and below the feed plate are equated, and allowance is made for all components at their asymptotic values in both sections. 

Matching the optimum feed-plate ratio, with the pinched-in region,... 

This matching is complicated by the fact that the values of light components obtained for the top section of the tower in the first calculations will be reduced somewhat by the introduction of the heavy components into this section, and it is therefore a matter of successive approximations to obtain an exact match. The quantity of the components to be added on a given plate to obtain a desired value requires trial and error but can be simplified by the fact that for a light component below the feed plate the operating line is essentially Vri yn, = siucc the value of Wxw is negligible. This can be... 

By such rematching procedure, it is possible to obtain exact agreement at the feed plate for all the light components and all the heavy components because they are arbitrarily chosen in one portion of the tower. However, it may be impossible to obtain an exact match of the key components because an even number of theoretical plates will not be consistent with the design chosen. In this case, it is possible to bracket the required number of plates within a difference of one, plate. While this rematching operation gives a more consistent set of... 

In many cases, the use of these equations is complicated by the fact that a trial-and-error procedure is involved. If the terminal compositions are known, the trial-and-error operation involves matching at the feed plate. Usually the terminal conditions are not completely known, and additional trial and error may be required. In most cases a three-component problem can be solved just as rapidly by the usual stepwise procedure, and variations in the relative volatility can be included. 

Continuation of the calculations gives an approximate match of ratio of keys in feed to those on plate 10. Then feed tray is number 10 from bottom and this is also number 11 from top. 

But the composition of the non-key components on the plate does not match the feed composition. 

The two principal tray-by-tray procedures that were performed manually are the Lewis and Matheson and Thiele and Geddes. The former started with estimates of the terminal compositions and worked plate-by-plate towards the feed tray until a match in compositions was obtained. Invariably adjustments of the amounts of the components that appeared in trace or small amounts in the end compositions had to be made until they appeared in the significant amounts of the feed zone. The method of Thiele and Geddes fixed the number of trays above and below the feed, the reflux ratio, and temperature and liquid flow rates at each tray. If the calculated terminal compositions are not satisfactory, further trials with revised conditions are performed. The twisting of temperature and flow profiles is the feature that requires most judgement. The Thiele-Geddes method in some modification or other is the basis of most current computer methods. These two forerunners of current methods of calculating multicomponent phase separations are discussed briefly with calculation flowsketches by Hines and Maddox (1985). 

For continuous cascade operation, the friction plate is lowered in the bowl so that a volume of material always remains inside while excess overflows. The residual volume can be either measured experimentally or calculated, assuming that the cross-section of the rope may be approximated by a fourth of a circle (quarter torus). To obtain a particular spheronization effect, an overall residence time must be maintained. The processing time in each machine can be calculated as the ratio of residual volume divided by the volumetric feed rate (= volumetric throughput). Since bowl diameters are predetermined and fixed by the design, the position of the friction plate in the bowl is the only variable which can be modified to match a certain feed rate or system capacity to the desired or necessary residence time. 

Since bowl diameters are fixed by the manufacturer, the plate height is the only variable that is changed to match a certain feed rate to the required residence time. 

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