Chromatography constant pattern

A very detailed study of the combined effects of axial dispersion and mass-transfer resistance under a constant pattern behavior has been conducted by Rhee and Amundson [10]. They used the shock-layer theory. The shock layer is defined as a zone of a breakthrough curve where a specific concentration change occurs (i.e., a concentration change from 10% to 90%). The study of the shock-layer thickness is a new approach to the study of column performance in nonlinear chromatography. The optimum velocity for minimum shock-layer thickness (SLT) can be quite different from the optimum velocity for the height equivalent to a theoretical plate (HETP) [9]. 

The same approaches that were successful in linear chromatography—the use of either one of several possible liunped kinetic models or of the general rate model — have been applied to the study of nonlinear chromatography. The basic difference results from the replacement of a linear isotherm by a nonlinear one and from the coupling this isotiienn provides between the mass balance equations of the different components of the mixture. This complicates considerably the mathematical problem. Analytical solutions are possible only in a few simple cases. These cases are limited to the band profile of a pure component in frontal analysis and elution, in the case of the reaction-kinetic model (Section 14.2), and to the frontal analysis of a pure component or a binary mixture, if one can assume constant pattern. In all other cases, the use of numerical solutions is necessary. Furthermore, in most studies found in the literature, the diffusion coefficient and the rate constant or coefficient of mass transfer are assumed to be constant and independent of the concentration. Actually, these parameters are often concentration dependent and coupled, which makes the solution of the problem as well as the discussion of experimental results still more complicated. 

When Req is very small or tends toward 0 (note that in the case of irreversible adsorption, Req = 0), the number of transfer units required to achieve constant pattern becomes very small, and the corresponding column length is very short. By contrast, in linear chromatography, Req becomes very close to 1 and Niiu, tends toward infinity. Thus, we cannot reach constant pattern imder linear conditions. Knowing the value of Req = 1/(1 -b bCo) permits the derivation of an estimate for Num, hence (see Eqs. 14.8e and 14.8f) of an estimate of the column length at which constant pattern wUl be practically achieved. 

Equation 14.45 applies in linear chromatography. The correct HETP equation in frontal analysis imder constant pattern behavior, and with the same solid film linear driving force model is Eq. 14.36b. Comparison of these two equations shows that an error is made when the latter is used to replace the former, in the equilibrium-dispersive model. We should replace in Eq. 14.44 and 14.45 Atq by k — FAq)/AC. In the case of the Langmuir isotherm, this would give k = fc )/(l + bCo) = X. 

In Chapter 14, we discussed the case of a single-component band. In practice, there are almost always several components present simultaneously, and they have different mass transfer properties. As seen in Chapter 4, the equilibrium isotherms of the different components of a mixture depend on the concentrations of all the components. Thus, as seen in Chapters 11 to 13, the mass balances of the different components are coupled, which makes more complex the solution of the multicomponent kinetic models. Because of the complexity of these models, approximate analytical solutions can be obtained only under the assumption of constant pattern conditions. In all other cases, only numerical solutions are possible. The problem is further complicated because the diffusion coefficients and the rate constants depend on the concentrations of the corresponding components and of all the other feed components. However, there are still relatively few papers that discuss this second form of coupling between component band profiles in great detail. In most cases, the investigations of mass transfer kinetics and the use of the kinetic models of chromatography in the literature assume that the rate constants and the diffusion coefficients are concentration independent. This seems to be an acceptable first-order approximation in many cases, albeit separation problems in which more sophisticated theoretical approaches are needed begin to appear as the accuracy of measru ments improve and more interest is paid to complex... 

Constant pattern The asymptotic solution in frontal analysis or displacement chromatography. Each point of the concentration profile moves at the same velocity, so the profile migrates but its shape remains constant. 

In Section 16 of this general chemical engineering handbook, T. Ver-meulen, M. D. LeVan, N. K. Hiester and G. Klein provide an overview of adsorption and ion exchange. Subject matter includes sorbent materials and sorbent-process analysis, fluid-sorbent equilibrium, equilibrium-limited transitions, rate-limited constant pattern transitions, linear equilibrium and other rate limited transitions, regeneration, chromatography, multivariant systems, multiple transitions, batch and continuous processes. The authors comprehensive yet concise approach is essentially analytical in nature and descriptions of processes and equipment are not included. 

Ion chromatography (see Section 7.4). Conductivity cells can be coupled to ion chromatographic systems to provide a sensitive method for measuring ionic concentrations in the eluate. To achieve this end, special micro-conductivity cells have been developed of a flow-through pattern and placed in a thermostatted enclosure a typical cell may contain a volume of about 1.5 /iL and have a cell constant of approximately 15 cm-1. It is claimed15 that sensitivity is improved by use of a bipolar square-wave pulsed current which reduces polarisation and capacitance effects, and the changes in conductivity caused by the heating effect of the current (see Refs 16, 17). 

There are simple algebraic solutions for the linear ideal model of chromatography for the two main coimter-current continuous separation processes. Simulated Moving Bed (SMB) and True Moving Bed (TMB) chromatography. Exphcit algebraic expressions are obtained for the concentration profiles of the raffinate and the extract in the columns and for their concentration histories in the two system effluents. The transition of the SMB process toward steady state can be studied in detail with these equations. A constant concentration pattern can be reached very early for both components in colimm III. In contrast, a periodic steady state can be reached only in an asymptotic sense in colunms II and IV and in the effluents. The algebraic solution allows the exact calculation of these limits. This result can be used to estimate a measure of the distance from steady state rmder nonideal conditions. 

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