Number of Trays

The designer usually wants to specify stream flow rates or parameters in the process, but these may not be directly accessible. For example, the desired separation may be known for a distiUation tower, but the simulation program requires the specification of the number of trays. It is left up to the designer to choose the number of trays that lead to the desired separation. In the example of the purge stream/ reactor impurity, a controller module may be used to adjust the purge rate to achieve the desired reactor impurity. This further complicates the iteration process. 

Colburn relationship found that the optimum number of trays varies from 2 to 3 times the number at total reflux. Gilliland [Ind. Eng. Chem, . 32, 1220 (1940)] from the establishment of an empirical relationship between reflux ratio and theoretical trays based on a study of existing columns indicated that... 

After actual theoretical trays are determined (see Actual reflux and 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 composition. 

P = Pressure drop in inches of water SG = Specific gravity of the liquid on the tray at the appropriate temperature T = Number of trays T, = Tray spacing, in. 

Preliminary Process Flowsheet. This will show major equipment and lines, preliminary equipment details (vessel diameter, number of trays, pump flow and driver horsepower, etc.), major instrumentation, and, it is hoped, have a material balance at the bottom of each drawing with flows keyed to a numbering system on the diagram. The process flowsheets should cover both the process and utility sides of the plant. 

Trays versus packing for fractionation can be a standoff if large numbers of tray passes are allowed for large fractionation towers by the operating company. Often, company preferences will decide. The licensor may also have preferences based on field experience. 

The design of a distillation column is based on information derived from the VLE diagram describing the mixtures to be separated. The vapor-liquid equilibrium characteristics are indicated by the characteristic shapes of the equilibrium curves. This is what determines the number of stages, and hence the number of trays needed for a separation. Although column designs are often proprietary, the classical method of McCabe-Thiele for binary columns is instructive on the principles of design. 

The limiting condition occurs at minimum reflux ration, when an infinite number of trays will be required to effect separation. Most columns are designed to operate between 1.2 to 1.5 times the minimum reflux ratio because this is approximately the region of minimum operating costs (more reflux means higher reboiler duty). 

The actual number of trays needed for a particular separation duty depends on the efficiency of the plate, and the packings if they are used. Thus, any factors that cause a decrease in tray efficiency will also change the performance of the colunm. Tray efficiencies are affected by such factors as fouling, wear and tear and corrosion, and the rates at which these occur depends on the properties of the liquids being processed. Thus the proper materials of construction must be selected for tray construction. 

The temperature or number of trays can then be varied until the calculated outlet liquid composition equals the assumed composition, and the vapor pressure of the liquid is equal to or less than that assumed. If the vapor pressure of the liquid is too high, the bottoms temperature must be increased. 

The heat duty of amine reboilers varies with the system design. The higher the reboiler duty, the higher the overhead condenser duty, the higher the reflux ratio, and thus the lower the number of trays required. The lower the reboiler duty, the lower the reflux ratio will be and the more trays the tower must have. 

Figure 8-8. The number of trays can have a greater effect on dew-point depression than the circulotion rate.

The tower operates in the same manner as a condensate stabilizer with reflux. The inlet liquid stream is heated by exchange with the gas to approximately 30 F and is injected in the tower at about the point in the tower where the temperature is 30 F. By adjusting the pressure, number of trays, and the amount of reboiler duty, the composition of the bottoms liquid can be determined. 

The design of any of the distillation processes discussed requires choosing an operating pressure, bottoms temperature, reflux condenser temperature and number of trays. This is normally done using any one of several commercially available process simulation programs which can perform the iterative calculations discussed in Chapter 6. 

In Table 9-4 the actual number of trays are included. This is because complete equilibrium between vapor and liquid is normally not reached on each tray. For calculation purposes the number of theoretical flashes may be quite a bit less than the number of trays. For smaller diameter... 

It is essential to realistically establish the condensing conditions of the distillation overhead vapors, and any limitations on bottoms temperature at an estimated pressure drop through the system. Preliminary calculations for the number of trays or amoimt of packing must be performed to develop a fairly reasonable system pressure drop. With this accomplished, the top and bottom column conditions can be established, and more detailed calculations performed. For trays this can be 0.1 psi/actu-al tray to be installed [149] whether atmospheric or above, and use 0.05 psi/tray equivalent for low vacuum (not low absolute pressure). 

The condition of the feed as it enters the column has an effect on the number of trays, reflux requirements and heat duties for a given separation. Figure 8-15 illustrates the possible situations, i.e., sub-cooled liquid feed, feed at the boiling point of the column feed tray, part vapor and part liquid, all vapor but not superheated, and superheated vapor. The thermal condition is designated as q, and... 

The conditions of total liquid reflux in a column also represent the minimum number of plates required for a given separation. Under such conditions the column has zero production of product, and infinite heat requirements, and Lj/Vs = 1.0 as shown in Figure 8-15. This is the limiting condition for the number of trays and is a convenient measure of the complexity or difficulty of separation. 

Because the feed tray is essentially non-effective it is suggested that an additional theoretical tray be added to allow for this. This can be conveniently solved by the nomographs [21] of Figures 8-16 and 17. If the minimum number of trays in the rectifying section are needed, the)t can be calculated by the Fenske equation substituting the limits of xpi for x jj and x i, and the stripping section can be calculated by difference. 

Example 8-4 Determine Minimum Number of Trays by Winn s Method (used by permission [99])... 

The minimum number of trays necessary to debutanize the effluent from an alkylation reactor will be calculated. The feed, products, and vapor-liquid equilibrium costants of the key components at conditions of temperature and pressure corresponding to the top tray and reboiler are shown in Table 8-1. 

For values of a near 1.0, extreme care must be used in establishing data, as a small change in the value of Oavg-may double the number of trays. 

Actually, any point on one of the curves represents a condition of reflux and number of trays that will perform the required separation. 

Assume xi values of bottoms compositions of light key for approximate equal increments from final bottoms to initial feed charge. Calculate L/V values corresponding to the assmned xi values by inserting the various xi values in the Fenske equation for minimum reflux ratio of l-(d). The xi values replace the x b of this relation as the various assumptions are calculated. The actual (L/D) are calculated as in l-(d) keeping the minimmn number of trays constant. Complete the table values. 

This is not unusual to select an operating reflux ratio ten, or even fifty times such a low minimum. Selecting a higher reflux can reduce the number of trays required, and this becomes a balance of the reduction in trays versus operating and capital expense in handling the increased liquid both external to the column and internally. 

At minimum reflux, the regions in which the number of trays approaches infinity (called the pinch zones and region of constant compositions) are ... 

Note that Nmin is the number of trays in the column and does not include the reboiler. When a varies considerably through the column, the results will not be accurate using... 

The minimum reflux ratio (L/D)min been determined to be 1.017. Using the Brown and Martin graph [9], evaluate the theoretical number of trays at an operating reflux of 1.5 times the minimum. The minimum number of stages was determined to be 22.1 including the reboiler. See Figure 8-49. 

The actual number of trays in the rectifying section (Nact)r be determined by ... 

N = number of trays (theoretical) or transfer units for a packed tower... 

UK. = Light key component in volatile mixture L/V = Internal reflux ratio L/D = Actual external reflux ratio (L/D) ,in = Minimum external reflux ratio M = Molecular weight of compound Mg = Total mols steam required m = Number of sidestreams above feed, n N = Number of theoretical trays in distillation tower (not including reboiler) at operating finite reflux. For partial condenser system N includes condenser or number theoretical trays or transfer units for a packed tower (VOC calculations) Nb = Number of trays from tray, m, to bottom tray, but not including still or reboiler Nrain = Minimum number of theoretical trays in distillation tower (not including reboiler) at total or infinite reflux. For partial condenser system,... 

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