Number of effective plates

EFFECTIVE NUMBER OF PLATES. Desty et al. (31) introduced the term effective number of plates, N, to characterize open tubular columns. In this relationship adjusted retention volume, VR, in lieu of total retention volume Vp, is used to determine the number of plates. This equation is identical to Purnell s separation factor discussed below. 

This N value is useful for comparing a packed and an open tubular column when both are used for the same separation. Open tubular 

Similarly, the number of theoretical plates per unit time can be calculated  

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Equations 2.109 and 2.111 illustrate that the required number of plates will depend on the partition characteristics of the column and the relative volatility of the two components, that is on K and 3. Table 2.9 gives the values of the last term of Equation 2.109 for various values of k. These data point up a few interesting conclusions If k <5 the plate numbers are controlled mainly by column parameters if k >5 the plate numbers are controlled by relative volatility of components. The data also illustrate that k values greater than 20 cause theoretical number of plates, n, and effective number of plates, N, to be of the same order of magnitude, that is,... 

Estimates of efficiencies and resolution can be made by considering the chromatogram for 6.5% 2-methoxyethanol in carbon dioxide. The resolution between caffeine (k - 0.88) and theophylline (k = 1.24) is 2.17 and between theophylline (k s 1.24) and theobromine (k = 1.7) is 2.00, yielding an average effective number of plates (N) of 884 and an efflclency-per-unit-tlme parameter of 20 effective plates/s (theophylline). This is somewhat higher than expected for an LC system (Table I) and lower than the most efficient system. Compared to the values in Table I, the linear velocity is higher than optimum, the diffu-sivlty is different, and the analyte capacity factor (elution time) is lower. 

This A eff value is useful for comparing a packed and an open tubular column or two similar columns when both are used for the same separation. Open tubular columns generally have a larger number of theoretical plates. One can translate regular number of plates N to effective number of plates A eff hy the expression... 

The Rs value is set at the 6s level or 1.5. In terms of the required effective number of plates, Equation 3.11 would be... 

Feed Composition. Feed composition has a substantial effect on the economics of a distillation. Distillations tend to become uneconomical as the feed becomes dilute. There are two types of dilute feed cases, one in which the valuable recovered component is a low boiler and the second when it is a high boiler. When the recovered component is the low boiler, the absolute distillate rate is low but the reflux ratio and the number of plates is high. An example is the recovery of methanol from a dilute solution in water. When the valuable recovered component is a high boiler, the distillate rate, the reflux relative to the high boiler, and the number of plates all are high. An example for this case is the recovery of acetic acid from a dilute solution in water. For the general case of dilute feeds, alternative recovery methods are usually more economical than distillation. 

The number of plates, Np, and the height equivalent to a theoretical plate, HETP, are defined as measures of dispersion effects as ... 

In order to illustrate the critical process parameters of SMB process validation, we will consider the separation of the racemic drug as described in Process design. The study represents the effect of the influence of feed concentration, number of plates and retention factor on the second eluting enantiomer. The simulation of the process for different values of feed concentration is performed and the variations of the extract and raffinate purities are shown in Fig. 10.10. 

We first note the very large differences in column performance for the two methods. Effective plates per second represents the speed characteristics of a column (e.g., the number of plates that can be generated in a given time interval) (13). As can be seen, HPLC is 100 to 1000 times faster than classTcal LC. (We shall discuss the differences between PLB and PB in the next section.) This improved performance arises mainly from the use of significantly smaller particle sizes in HPLC. Moreover, in classical LC, the mobile phase is delivered to the column by gravity feed, hence, the very low mobile phase velocities. In HPLC, it is desireable to improve performance... 

There is no heat transfer across the end plates, so the number of effective plates will be the total number of plates less two. 

Number of plates = total heat transfer area / effective area of one plate = 72.92/0.75 = 97... 

Increase the number of plates in the column and study this effect on the separation obtained. 

Thus, an increase in R, at values near Rm, gives a marked reduction in the number of plates, although at higher values of R, further increases have little effect on the number of plates. Increasing the reflux ratio from Rm therefore affects the capital and operating costs of a column as follows ... 

Graphical representation of the effect of the absorption factor and the number of plates on the degree of absorption... 

The effective number of theoretical plates is the number of usable theoretical plates and is calculated after elimination of the void volume ... 

Theoretical Plate In a distillation column, it is a plate onto which perfect liquid-vapor contact occurs so that the two streams leaving are in equilibrium. It is used to measure and rate the efficiency of a column at separating compounds. The ratio of the number of theoretical plates to the actual number of plates required to perform a separation is used to rate the efficiency of a distillation column. Actual separation trays in refinery distillation units are usually less effective than theoretical plates. 

The HETP curve clearly shows, that for a packed column, the particle size has a profound effect on the minimum value of the HETP of a column and thus the maximum efficiency attainable. It would also appear that the highest efficiency column would be obtained from columns packed with the smallest particles. This will in due course be shown to be a fallacy, but what is true, is that the smaller the particle diameter the smaller will be the minimum HETP and thus, the larger the number of plates per unit length obtainable from the column. At this time it will suffice to point out that the total number of theoretical plates that can be obtained will depend on the length of the column which, in turn, must take into account the available inlet pressure... 

E. Extracolumn Band Broadening or Variance To maximize the effective number of theoretical plates, the contribution of the entire chromatographic system to band broadening (system variance, o-2ys) must be minimized. The system variance may be broken down into contributions from the column variance, a 01, as described above, and extracolumn diffusion and mixing processes, cr2x. As with the case of the column variance, extracolumn variance is an additive property and may be broken down into the major components ... 

The above discussion highlights some of the phenomena that contribute to higher separation efficiencies in CEC. The net effect of these is enhances mass transfer and more uniform flow distribution through the column, both of which contribute to obtaining higher number of plates when compared to HPLC. 

Using binary mixtures, Luyben (1971) studied the effects of holdup, number of plates, relative volatility, etc. on the capacity (total products/hr). For an arbitrarily assumed constant reflux ratio the author observed both positive and negative effects of tray holdup on the capacity for columns with larger number of plates, while only negative effects were observed for columns with smaller number of plates. It is apparent that these observations are related to the degree of difficulty of separation. 

From this point on the use of ZP no longer enables us to quantify the quality of the chromatogram, because it does not differentiate between chromatograms a and b. Moreover, above a certain threshold number of plates (around 10,000 in the example of figure 4.6) the ZP criterion becomes very insensitive to the number of plates and to changes in the relative peak positions, unless these changes have a significant effect on Rs values between about 0.6 and 1.5. 

Calculate the effective number of theoretical plates, N, and subsequently the value of H for each separation using the following formulae ... 

Resolution, like the separation factor, differs for each specific component pair and therefore fails as a global criterion of separation. For analytical separations, more universal criteria have evolved, such as plate height, number of plates, rate of generation of plates, and peak capacity (Chapter 5). While these indices differ somewhat from one component to another, they effectively establish a ballpark figure of merit for different systems and different conditions of operation. 

In the text it is stated that a molecular weight M of MO6 is necessary for effective operation in sedimentation FFF. We can examine this matter by further considering the system described in 9.6 above. If the two molecules (Af = 106, M = 107) are spherical globules, estimate the plate height and the number of plates in a channel 50.0 cm long. The flow velocity (u) is 1.25 cm/s. 

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