Nontrace Systems

In the preceding analysis the term cdv/dz was dropped from the differential fluid phase mass balance [Eq. (8.1)]. This is justified provided- that the concentration of the adsorbable species is sufficiently small, that is, for a trace component in an inert carrier. However, if this condition is not fulfilled a more detailed analysis is required since the variation in fluid velocity over the mass transfer zone must be accounted for. For generality we first consider a two-component (i thermal) system in which both components are adsorbable. For such, a 8yistenl we lean write two differential fluid phase mass balance equations, one fcji each component  

The equation fori comporient 2 is similar. These two equations are not 

Measurement of the retention time for a system with ai mixed carrier stream of known composition containing both an inert and adprbable component yields immediately dq jdc as a function of c,. The uilibrium isotherm f(c,) may be found directly by integration.  

The variation of fluid velocity through the columh is feiven by 

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Nontrace systems have been considered [Sircar and Kumar, Jnd. Eng. Chem. Proc. Des. Dev., 22, 271 (1983)]. 

This is clearly an increasing function of T. Thus, for a nontrace system, the sorption effect (variation in fluid velocity due to sorption of the adsorbable species) leads to an increase in the propagation velocity with increasing concentration. The effect is thus qualitatively similar to the effect of curvature of the equilibrium isotherm and leads to the chromatographic response having a sharp front and a broadening tail as sketched in Figure 8.7. 

Kluge. G., et al.. Estimation of component loadings in fixed-bed adsorption from breakthrough curves of binary gas mixtures in nontrace systems, Chem. Eng. Sci.. 46(1), 368-371 (1991). 

Note that if the species adsorbed is in trace amounts, the change in along z due to adsorption would be negligible. Thus, for nontrace systems, using these two relations, relation (7.1.26) can be simplified to... 

Nontrace isothermal systems give the adsorption effect (i.e., significant change in fluid velocity because of loss or gain of solute). Criteria for the existence of simple waves, contact discontinmties, and shocks are changed somewhat [Peterson and Helfferich, J. Phy.s. Chem., 69, 1283 (1965) LeVan et al., AIChE J., 34, 996 (1988) Frey, AJChE J., 38, 1649(1992)]. 

The effect of concentration on in a nontrace gaseous system is, then, similar to that observed with a favorable isotherm (see Figure 7.1.4). A spread out profile along the column is compressed to a front sharper than would have been possible otherwise. 

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