Separation factor optima

St = Theoretical trays/stages at actual reflux, L/D, including reboiler and total condenser Sopt = Optimum stripping factor (SR)i = Separation factor... 

Having chosen the test mixture and mobile diase composition, the chromatogram is run, usually at a fairly fast chart speed to reduce errors associated with the measurement of peak widths, etc.. Figure 4.10. The parameters calculated from the chromatogram are the retention volume and capacity factor of each component, the plate count for the unretained peak and at least one of the retained peaks, the peak asymmetry factor for each component, and the separation factor for at least one pair of solutes. The pressure drop for the column at the optimum test flow rate should also be noted. This data is then used to determine two types of performance criteria. These are kinetic parameters, which indicate how well the column is physically packed, and thermodynamic parameters, which indicate whether the column packing material meets the manufacturer s specifications. Examples of such thermodynamic parameters are whether the percentage oi bonded... 

Table Vtll. Simultaneous bensity and Temperature Optimization via an Interpretive (Window Diagram) Approach Criterion threshold separation factor (CRF-4, equation 9) Optimum conditions density, 0.19 g/mL temperature, 104 °C Chromatogram Figure 10 ...

Figure 4.11 Calculated characteristics for optimum chromatograms (r = 1) containing 10 equally resolved peaks as a function of the separation factor S. Plotted on a logarithmic scale are the capacity factor of last peak (1 +k eqn.4.46), the required number of plates (Afne eqn.4.47), the required analysis time under conditions of constant flow rate and particle diameter (rne f>(ji eqn.4.48), and required analysis time under conditions of constant pressure drop fne p eqn.4.49). For explanation see text.

A rough estimation nicely highlights the contribution and importance of a well-developed separation factor. Whereas changes in k from 3 to 5 only improve the peak resolution by 10.7% and a doubhng of N by 41.4%, the increase of selectivity from 1.2 to 2.2 will result in an improvement of 83.3%. Since in most cases the technical parameters hke particle size and pressure are given and used under optimum conditions, the search for high selectivity cannot be overemphasized. 

From a practical point of view, it is likely to be sufficient to estimate the column saturation capacity using the retention time method from several single-component overloaded elution profiles. Part of the purpose of the screening tests is also to determine the impact of the column saturation capacity of the product for different mobile-phase systems, temperatures and packing media. Since the optimum amount loaded is a stronger function of the separation factor than the column saturation capacity, estimation of the column saturation factor over an exact measurement may be sufficient. It is likely to be sufficient to use only the product species saturation capacity as measures of the... 

In summary, as the separation factor increases, the optimum flow rate decreases, thus the required plate count. A lower plate count is acceptable to achieve similar yields because the separation is easier. The optimum amount loaded per gram increases, the production rate increases and. thus the total cost decreases. 

Dimethylnaphthalene concentrate contains significant amounts of 2,6-dimethylnaphthalene bound in a binary eutectic with 2,7-dimethylnaphthalene. This eutectic cannot be broken by distillation or solvent crystallization. A practical method for separating this eutectic mixture of 2,7-dimethylnaphthalene and 2,6-dimethylnaphthalene has been achieved. Selective adsorption of 2,7-dimethylnaphthalene from a dimethylnaphthalene concentrate is obtained with sodium type Y molecular sieves. 2,6-Dimethylnaphthalene then can be crystallized from the unadsorbed raffinate fraction. Separation factors of 6 to 8 are obtained, indicating the high selectivity of these particular molecular sieves for this adsorption. Previous work in this area achieved a separation factor of 2.7. A continuous method has been developed for adsorption and desorption of 2,7-dimethylnaphthalene. Toluene has been selected as the optimum desorbent. This process makes 2,7-dimethylnaphthalene potentially available. 

One method which can be used to establish the optimum conditions for the separation of a complex mixture (i.e., not only a pair) of compounds consists in searching for the maximum of a function denoted the chromatogram quality criterion. The evaluation of separation selectivity can be conducted with the aid of different criteria of chromatogram quality such as the sum of resolution, E 7 [6], the sum of separation factors, E 5 [2], and other sums and products of elementary criteria, selected examples of which are the resolution product, n Rs [7],... 

Figure 18.4 Optimum operating parameters as functions of the separation factor, the crude cost, and the inlet pressure, a, b, c, d Effects of the separation factor e, f, g, h Effects of the crude costs i, j, k, 1 Effects of the inlet pressure, a, e, i Variations of the flow rate and the column efficiency b, f, j loading/g packing and recovery 5neld c, g, k Column length and cycle time d, h, 1 cost per grams produced and production rate. Reproduced with permission front A. Katti, in Handbook of Analytical Separations, Vol. 1, "Separation Methods in Drug Synthesis and Purification," K. Valko, Ed., Elsevier, Amsterdam, The Netherlands, 2000, p. 213 (Figs. 7.8, 7.14, and 7.18).

Finally, the dependence of the production rate on the separation factor is complex since No, 7, x, and X depend on a, [21]. x varies rapidly with a when the relative concentration of the second component is large, and the displacement effect is dominant [2], Nevertheless, it can be shown that at constant pressure AP, the maximum production rate obtained with an optimized column is approximately proportional to [(a — l)/a] [28]. For a given i.e., nonoptimized) column, the production rate is proportional to [(a - T)/ ]y, with y between 2 and 3, depending on the importance of the difference between the given and the optimum columns [28]. 

Figure 18.13 Plot of the optimum value of the ratio d /L in elution versus the retention factor of the first component of a 1 3 mixture. Separation factor curve 1 1.1 curve 2,1.2 curve 3,1.5 curve 4,1.8. Reproduced from permission from A. Felinger and G. Guiochon, f. Chromatogr., 591 (1992) 31 (Fig. 17).

Table 18.3 Optimum Conditions for Maximum Production Rate of the Components of a Binary Mixtiue, Influence of the Separation Factor ...

In the former case [32], the production rate of 99% pme enantiomers from the racemic mixture of R- and S-2-phenylbutyric acid was maximized as a function of the sample size and the mobile phase composition. The calculations were based on the column performance and the equilibrium isotherms of the two components (bi-Langmuir isotherms. Chapter 3). The separation was performed on immobilized bovine serum albumin, a chiral stationary phase, using water-methanol solution as the mobile phase. The retention times decrease with increasing methanol content, but so does the separation factor. For this reason, the optimum retention factor is around 3. Calculated production rates agree well with those measured (Table 18.4). The recovery yield is lower than predicted. 

The optimum gradient steepness is different for the less and the more retained component. It varies with the separation factor. For the less retained component, the production rate usually reaches a plateau without a maximum and, in most cases, there is no production rate gain above G = 0.4-0.6. Although the cycle time should decrease when the gradient steepness is increased, the optimum column efficiency increases with increasing gradient steepness and these two effects compensate each other, resulting in a nearly constant cycle time. 

Figure 18.29 Plot of the maximum production rate of the two components versus the retention factor of the first eluted one. Separation factor, a. = 1.5. All symbols correspond to the production rate of the optimum column, operated at the optimum velocity and sample size. Curve 1, first component, elution. Curve 2, second component, elution. Curve 3, first component, displacement. Curve 4, second component, displacement, (a) Feed composition 3 1. (b) Feed composition 1 3. Reproduced with permission ofWiley-Liss Inc., a subsidiary of John Wiley Sons, Inc. from A. Felinger and G. Guiochon, Biotechnol. Bioeng., 41 (1993) 134 (Fig. 4). (g)1993, John Wiley Sons.

N characterizes the column efficiency. The number of theoretical plates increases as a function of better packing, longer column length and optimum mobile phase flow rate conditions. A column with a high number of plates can also separate mixtures in which the components have similar separation factors, a. If a is small, then the required degree of resolution can only be achieved by incorporating more plates, as shown in Table 2.1. 

By selecting optimum impeller speed during emulsification, surfactant concentration, volume ratio of surfactant solution, carrier concentration, and a suitable feed phase composition, uniformly distributed stable emulsion could be obtained to provide a high separation factor and higher mass transfer rate. 

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