Perturbation chromatography in chemically reactive systems

Abstract

A one-dimensional column is considered i n which a number of chemical reactions with arbitrary kinetics may take place among an arbitrary number of components. initially, the column is i n complete chemical and physical equilibrium. A localized small p e r t u r b t i o n is introduced i n the column a t time t = 0. It i s shown that, i n general, this initial perturbation separates into a definite number of peaks which move with different velocities. Each peak broadens according t o an asymptotic relation, depending on a characteristic dispersion coefficient. I f n is the number of components, m the number of independent reactions, and u the number of equations of state t o be considered, there are n-m-u peaks. These peaks do not correspond t o single substances as in classical chromatography, but each peak has an eigencomposition. The velocities of the peaks are derived as functions of stoichiometry and equilibrium data. The dispersion coefficients depend, i n addition, on the kinetics of the chemical reactions and on the rate of mass transfer. Thus, perturbation chromatography offers a means of determining both equilibrium and rate data. The theory is illustrated by means of two examples.The term perturbation chromatography used in the title of this paper covers a broader class of phenomena than is normally associated with chromatography. A definition will now be given which, at the same time, delimits the scope of this work. Consider the steady flow of a multicomponent fluid over a uniformly distributed fixed adsorbent-catalyst phase. In the initial steady state condition, fluid composition is independent of position and time and determines the concentrations in the fixed phase through various physical and chemical equilibrium relations. At some time zero, the system is perturbed over a small portion of its length by a small change in composition of one of the phases. Perturbation chromatography is the behavior of the system after time zero. The description and use of the set of disturbances which propagates downstream is considered here.Earlier work in this area is summarized by Collins and Deans ( 2 ) , who discussed the number and velocity of peaks to be expected under ideal, local equilibrium conditions. In the present work, the equilibrium theory is generalized, and chemical and mass transport kinetics are taken into consideration. The behavior of the set of disturbances resulting from the initial perturbation will be related to the equilibrium composition of both phases, the stoichiometry of the reactions taking place, the chemical and physical equilibrium functions, and the interphase transfer and intraphase chemical reaction rates. These relations can be put to practical use in obtaining unknown equilibrium and rate information from observation of pulse behavior.The information to be gained is quite general. In particular, no limitation as to number of components or reactions is necessary; the restriction of infinite dilution Gemot Klauser is with the

Determination of multicomponent sorption equilibria using perturbation gas chromatography

“…The column residence time for each peak (measured to the center of mass for the peak) in general will depend upon both phase equilibrium and m a s transfer resistance. Under the experimental condition of sufficiently low mobile phase flow rate, however, the effect of the mass transfer rate on peak retention times can be eliminated (Deans et al, 1970) and this condition is an assumption of perturbation chromatography theories, including that presented here.…”

“…Theoretical approaches designed for these specific circumstances have appeared in the literature but are not readily adaptable to more general systems. Generalized theories for systems of multiple interfering species have been outlined by Stalkup,and Deans (1963), Helfferich and Klein (1970), and by Deans et al (1970), but the variety of end-use equations that have been determined for specific experimental situations is very limited.…”

“…Peterson and Helfferich (1965) also point out the importance of including sorption effects and discuss a number of finite concentration situations. A more recent paper by Deans et al (1970) explains a very general linearized analysis for multicomponent systems that includes any number of components at finite concentration and allows for chemical and mass transfer reactions as well as axial dispersion. This treatment is so very general, however, that its application to desired experimental situations is quite cumbersome.…”

“…Sorption is assumed to be non-stoichiometric (there is no constraint on the amount of sorption of any of the components individually, other than equilibrium, or on the total amount), local equilibrium is assumed to hold everywhere in the column, and axial dispersive effects (from diffusion in both phases along with flow dispersion in the mobile phase) are neglected on the grounds that they result in peak broadening but do not alter the peak propaga-tion velocity (Peterson and Helfferich, 1965;Deans et al, 1970). Additionally, the column pressure, temperature, and vapor-phase total concentration (moles/volume) are assumed constant, flow is assumed to be one-dimensional, and the column packing is assumed to be uniformly distributed.…”

Multicomponent equilibrium theory for ion‐exchange columns involving reactions

“…Fixed-bed sorption processes involving reactions in the bulk phases have been studied for 20 years (Magee, 1963;KoEiiik, 1967;Collins and Deans, 1968;Deans et al, 1970;Bunge and Radke, 1975;Schweich et a]., 1978Schweich et a]., , 1980. However, discussions of multicomponent systems are still quite limited.…”