Theory of packed columns

Series coupling of columns containing the same stationary phase is used to enhance efficiency and with different stationary phases to fine tune selectivity [8]. Series coupling of packed columns became popular after it was demonstrated that the column pressure drop did not limit the total column efficiency to the extent that had been predicted (section 7.4.2). Serial coupling of 2 or 3 standard columns is practical for routine applications and provides a total plate count in excess of 50,000. There is no theory for selectivity optimization for coupled packed columns but suitable conditions often can be estimated from separations on the individual columns. Effective selectivity changes require that the coupled columns have different retention properties. A number of practical examples for the separation of polymer additives, polycyclic aromatic hydrocarbons, phytic acid impurities and enatiomers have been described [137,195,196]. Series coupling of open tubular columns with different stationary phases is less common, but changes in selectivity are predictable, at least when the pressure drop is low [197]. 

The performance of packed columns should be compared with that of packed column HPLC. As the diffusion coefficients are > 20 times greater, depending on the density, higher than in HPLC, SFC should in theory be more rapid and/or efficient than HPLC. The examples given here indicate... 

Attempts have been made to place the design of packed columns on a sound theoretical basis to avoid the large amount of empirical work with which it is frequently associated. The theory is often only approximate and cannot therefore be used as the sole guide for design purposes. It does however at least allow valuable qualitative or semi-quantitative predictions to be made, which reduces the development requirement. 

Billet, R., Theory and Practice of Packed Columns, Korea Institute of Energy and Resources, 1988, p. 70. 

In order to illustrate the use of packed columns in absorption operations, it is necessary to refer to mass transfer theory. The initial part of this chapter has been devoted to a review of the fundamental principles of mass transfer that need to be understood to design absorption and stripping columns. 

Eq.(79) is the second Pick s low. Its structure is the same as that of the differential equation of the convective h t transfer (in case of a st y state process Eq. (56)). This gives the possibility, as shown later, to calculate the heat transfer processes by means of experimental data or equations for mass transfer. The basic methods for these calculations are the similarily theory and the dimensional analysis. That is why before considering the theory of mass transfor processes, we present these important methods largely used in chemical engineering and in particular In the area of packed columns. 

Experimental Mass Transfer Coefficients. Hundreds of papers have been pubHshed reporting mass transfer coefficients in packed columns. For some simple systems which have been studied quite extensively, mass transfer data may be obtained directiy from the Hterature (6). The situation with respect to the prediction of mass transfer coefficients for new systems is stiU poor. Despite the wealth of experimental and theoretical studies, no comprehensive theory has been developed, and most generalizations are based on empirical or semiempitical equations. 

Other correlations based partially on theoretical considerations but made to fit existing data also exist (71—75). A number of researchers have also attempted to separate from a by measuring the latter, sometimes in terms of the wetted area (76—78). Finally, a number of correlations for the mass transfer coefficient itself exist. These ate based on a mote fundamental theory of mass transfer in packed columns (79—82). Although certain predictions were verified by experimental evidence, these models often cannot serve as design basis because the equations contain the interfacial area as an independent variable. 

Unfortunately, any equation that does provide a good fit to a series of experimentally determined data sets, and meets the requirement that all constants were positive and real, would still not uniquely identify the correct expression for peak dispersion. After a satisfactory fit of the experimental data to a particular equation is obtained, the constants, (A), (B), (C) etc. must then be replaced by the explicit expressions derived from the respective theory. These expressions will contain constants that define certain physical properties of the solute, solvent and stationary phase. Consequently, if the pertinent physical properties of solute, solvent and stationary phase are varied in a systematic manner to change the magnitude of the constants (A), (B), (C) etc., the changes as predicted by the equation under examination must then be compared with those obtained experimentally. The equation that satisfies both requirements can then be considered to be the true equation that describes band dispersion in a packed column. 

Hence, on the basis of the simple penetration theory, show that the rate of absorption in a packed column will be proportional to the square root of the diffusivity. 

There are surprisingly few studies of the retention mechanism for open tubular columns but the theory presented for packed columns should be equally applicable. For normal film thicknesses open tubular columns have a large surface area/volume ratio and the contribution of interfacial adsorption to retention should be significant for those solutes that exhibit adsorption tendencies. Interfacial adsorption has been shown to affect the reproducibility of retention for columns prepared with nonpolar phases of different film thicknesses [322-324]. The poor reproducibility of retention index values for columns prepared from polar phases was demonstrated to be c(ue to interfacial... 

You should be able to see that you have to be really careful in selecting those chaser, or pusher solvents mentioned. Sure, water (B.P. 100° C) is hot enough to chase ethyl alcohol (B.P. 78.3°C) from any column packing. Unfortunately, water and ethyl alcohol form an azeotrope and the technique won t work. (Please see Theory of Distillation, Chapter 28.)... 

In this chapter consideration is given to the theory of the process, methods of distillation and calculation of the number of stages required for both binary and multicomponent systems, and discussion on design methods is included for plate and packed columns incorporating a variety of column internals. 

This is a simple method of representation which has been widely used as a method of design. Despite this fact, there have been few developments in the theory. Murch 71 gives the following relationships for the HETP from an analysis of the results of a number of workers. Columns 50-750 mm diameter and packed over heights of 0.9-3.0 m with rings, saddles, and other packings have been considered. Most of the results were for conditions of total reflux, with a vapour rate of 0.18-2.5 kg/m2s which corresponded to 25-80 per cent of flooding. The relationship is ... 

In an attempt to test the surface renewal theory of gas absorption, Danckwerts and Kennedy measured the transient rate of absorption of carbon dioxide into various solutions by means of a rotating drum which carried a film of liquid through the gas. Results so obtained were compared with those for absorption in a packed column and it was shown that exposure times of at least one second were required to give a strict comparison this was longer than could be obtained with the rotating drum. Roberts and Danckwerts therefore used a wetted-wall column to extend the times of contact up to 1.3 s. The column was carefully designed to eliminate entry and exit effects and the formation of ripples. The experimental results and conclusions are reported by Danckwerts, Kennedy, and Roberts110 who showed that they could be used, on the basis of the penetration theory model, to predict the performance of a packed column to within about 10 per cent. 

As Sherwood and Pigford(3) point out, the use of spray towers, packed towers or mechanical columns enables continuous countercurrent extraction to be obtained in a similar manner to that in gas absorption or distillation. Applying the two-film theory of mass transfer, explained in detail in Volume 1, Chapter 10, the concentration gradients for transfer to a desired solute from a raffinate to an extract phase are as shown in Figure 13.19, which is similar to Figure 12.1 for gas absorption. 

CEC is a miniaturized separation technique that combines capabilities of both interactive chromatography and CE. In Chapter 17, the theory of CEC and the factors affecting separation, such as the stationary phase and mobile phase, are discussed. The chapter focuses on the preparation of various types of columns used in CEC and describes the progress made in the development of open-tubular, particle-packed, and monolithic columns. The detection techniques in CEC, such as traditional UV detection and improvements made by coupling with more sensitive detectors like mass spectrometry (MS), are also described. Furthermore, some of the applications of CEC in the analysis of pharmaceuticals and biotechnology products are provided. 

In the course of attempts to quantitatively and a priori describe separation of macromolecules by SEC, a theory was formulated, which considered the effect of porous structure of the column packing on the diffusion rate of separated macromolecules. The resulting theory of restricted diffusion by Ackers [56], however, rather contradicts the equilibrium conception of SEC. 

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