Membrane Column Profile

The conditions of Case 1 compel all the entries of Xa = to be positive, that is. to lie within the bounds of the MET. Case 2, on the other hand, allows Xa to exist anywhere in the xi X2 space, both inside and outside the MET For this reason, we will select an Xa within the MET, thereby covering columns profiles for both cases concurrently. 

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This is different from the distillation profiles generated earlier in this book, where the CMO assumption was employed those profiles had only x associated with every point. The reflux was held constant, and did not change down the length of the CS. In this scenario, however, both compositions and flows change down the length of the MGS. Hence, both x and change along a membrane column profile. 

Arbitrarily chosen values for x and are used in order to demonstrate a membrane column profile for Cases 1 and 2. However, any positive flowrate, R, is feasible, as is any point within the MET a possible top retentate composition. Figure 9.9a displays column profiles for a fixed x = [0.3, 0.2], varying as indicated. Figure 9.9b, on the other hand, shows a range of column profiles for select x s at a constant r = 6. 

Thus far, only binary mixtures have been separated in the total membrane column. Results of this work have been discussed elsewhere (28,29). A sample shell-side composition profile from a total column experiment with a CO2-O2 mixture is shown in Figure 2. Table I summarizes the total column data obtained to date. 

The curves shown in Figures 3 and 4 are simulated composition profiles based on experimental data. The calculated trends fit the experimental compositions quite well, and in each case the experimental methane peak is well described. This demonstrates that the basic model for the membrane column can be applied to multicomponent systems as well as to binary mixtures. 

Usually in an enricher or the enriching section of the membrane column, the more permeable component is steadily concentrated from the feed inlet to the compressor. However, some of the results show that the shell-side and even the tube-side composition profiles can pass through a minimum. Note the experimental data in Figures 7 and 8. In these cases the feed flow is relatively slow and reflux action, rather than bulk flow, is predominant. Figure 8 Illustrates that a composition minimum can also occur dinring operation of the total column when the residue flow rate from the enriching section is too slow. 

The set of Equations 32 -r 37 has to be solved numerically. For the special case of total reflux, however, an analytical solution for the concentration profile along the membrane column can be derived if the pressure losses are neglected. In the case of total reflux, for every section of the column (Figure 6.21) ... 

Figure 6.23 Calculated concentration profile of a membrane column, total reflux.

APPLICATION OF COLUMN PROFILE MAPS TO ALTERNATIVE SEPARATION PROCESSES MEMBRANE PERMEATION... 

For demonstration purposes, a simple constant relative permeability flux model is employed to determine the continually changing retentate flow. Various possible operating conditions of a CS are explored. Using the difference point equation, column profiles for each condition can be plotted. The behavior of the profiles is discussed both mathematically and graphically. This innovative way of investigating membrane processes provides a unique way of synthesizing and designing them. 

In seeking the most efficient process possible, a designer will wish to explore a wide range of feasible designs. To make this possible, an efficient method for the synthesis and assessment of any hybrid separation process has been developed. Since both processes have been analyzed using similar mathematical backgrounds, it is possible to use residue curve maps and column profile maps for both distillation and membranes to design hybrid systems of the two. 

Using membrane profiles in conjunction with column profile maps allows one to graphically interpret hybrids in an efficient manner. Furthermore, by focusing on the membrane in isolation, one is not limited to a single hybrid configuration,... 

Figure 2. Elution profile from columns (100 x 1.0 cm) of controlled pore glass beads of l,4-/ -linked products formed in vitro by pea membranes in 30 min. Products were dissolved in hot paraformaldehyde DMSO and eluted with DMSO in 1 ml fractions. Open circles, 1 mM UDP-[14C]glucose alone closed circles, 1 mM UDP-[14C]glucose plus 50 /iM UDP-xylose. Size markers show the molecular weight of peak elution volumes of standard dextrans, 264 = 264000 D 70 = 70000 D. (Taken with permission from Ref. 18. 1988 J. Wiley k, Sons.)...

Fig. 4 Elution profiles for (A) propranolol (a), promethazine (b), and chlorprom-azine (c) applied separately on a 5-mm ILC column containing cytoskeleton-depleted red blood cell membrane vesicles entrapped in dextran-grafted agarose gel beads (1.4 /amol phospholipid, 0.5 mL/min) and (B), from left to right, acetylsalicylic acid, salicylic acid, warfarin, and pindolol on a capillary continuous bed containing liposomes immobilized by use of C4 ligands (1.0 /xmol phospholipid, 10 /xl./min). The elution volumes in the absence of lipid are shown (a0, b0, and c0, and the arrow, respectively). (Part A is reprinted with permission, with slight modification, from Ref. 26. Copyright 1999 Elsevier Science. Part B is reprinted with permission from Ref. 23. Copyright 1996 Elsevier Science.)...

Figure 19.6. Gas permeation equipment and performance, (a) Cutaway of a Monsanto Prism hollow fiber module for gas separation by permeation, (b) Flowsketch of a continuous column membrane gas separator, (c) Composition profiles of a mixture of C02 and Oz in a column 5 m long operated at total reflux [Thorman and Hwang in ( Turbak, Ed.), Synthetic Membranes II, American Chemical Society, Washington DC, 1981, pp. 259-279],...

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