Parametric Pumping and Cycling Zone Adsorption
SIR: Although as Harris suggests, the cause of the separation in parametric pumping is the ability to drive solute to and from the solid by changing the system temperature, the novel contribution of the inventors is the use of recycle in a periodic operation. Baker (1969) showed that when a singlecolumn parametric pump is operated without returning any effluent to the column-Le., no recycle-the maximum separation, even in a column having a n infinite number of theoretical plates (operating under the local equilibrium condition) will be cy
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The method and nomenclature are t h s s a m e as those of Pigford et al. (1969). On the other hand, by using recycle in a batch system, Wilhelm et al. (1968) have demonstrated numerically and experimentally that much larger separations are possible. The recycle is not constant as in a steady-state process but timed to coincide with other variations; hence the use of the slightly complex explanations to which Harris refers. Furthermore, in a continuous version of the parametric pump with recycle which has been discussed by Horn and Lin (19691, extremely large separations were predicted. Here a cyclic steady state is reached in which, after a line-out period, the concentration a t any point in the column is a periodic function of time. The use of the term "time staging," which applies only to the batch version, refers to the fact that rather than having smoothly continuously changing conditions as in a batch multistage distillation column until limiting conditions are reached, there are finite step changes after each synchronous temperature and flow switch. Since these switches are imposed on the system and the period between them is by design, i t is not unreasonable to term the procedure time staging. The utility of the local equilibrium assumption is well precedented in adsorption and chromatographic theory. il more refined theory including dispersive effects was developed by Wilhelm et al. (1968) even before our simple theory. However,
SIR: I would like to comment on the remarks of Harris (1970) regarding the equilibrium theory of parametric pumping and cycling zone adsorption. Harris says, in effect, that dispersion reduces (hence limits) separation and that all real systems have dispersion. I agree completely. However, these ideas do not diminish the value of the equilibrium theory discussed by Pigford et al. (1969), Aris (19691, and Gregory and Sweed (1970). The equilibrium theory is not intended for accurate design of separation systems any more than one would design a distillation column based solely on a n equilibrium stage model. Equilibrium models are idealizations of real systems; they must be viewed and used with this in mind. The ideal model of parametric pumping assumes that there are no dispersive forces acting in the system-Le., no molecular diffusion, no interparticle mixing, and instantaneous mass transfer rates. This does not mean they do not exist in a real 686 Ind. Eng. Chem. Fundam., Vol. 9, No. 4, 1970
its complexity is such that it is hard to understand the more fundamental aspects of the process-the usefulriess of recycle and the effect of t'he phase relationship between the flow and temperature forcing. The equilibrium theory isolates these effects and, additionally, provides a n estimate of the maximum possible separation which agrees closely with the experimental case. As Lin and Horn (1969) show, the theory can be extended to the continuous case. They develop the analogy with the equivalent countercurrent version known as the dual temperat,ure process, in which the solid is also circulated, and discuss the equivalent assumptions resulting in perfect separations in both cases. Just as in distillation when the operation lineequilibrium line pinch is located a t one end of the column, it is possible, if one has a column with an infinite number of equivalent theoretical stages, to have perfect separation in continuous operation without having an infinite recycle ratio. I disagree with Harris' comment that the equilibrium theory is not valid when no dispersive effects exist. This is by definition when it is valid. Since the column in this case contains a n infinite number of theoretical stages, the fact that it is of finite length is not important. As soon as any dispersion is allowed, the length of the column does, however, play a role in determining the effect of the dispersion. For commercial designs, the more refined theory will be necessary, since economics mill dictate a reasonable flow rate and a limit t'o the size of the column. literature Cited
Baker, B., Ph.D. dissertation, University of California, Berkeley, 1969.
Horn, F. J. AI., Lin, L. H., Ber. Bunsenges. Phys. Chenz. 73, 575 (19691.
Pigford,'R. L., Baker, B., Blum, D. E., I N DE. N GCHEM. . FCNDAX. 8,848 (1969).
Wilbelm, R . H., Rice, A. W., Rolke, R. R., Sweed, N . H., IKD.ENG.CHEY.F V N D . ~7,M337 . (1968).
Burke Baker I I I Shell Oil Co. Deer Park, Tex. 77536
system; they certainly do. But we know that dispersion cannot' improve separation. I t always acts to reduce concentration gradients and hence separation. I t follow, therefore, that the equilibrium theory gives us the best possible separation in a parametric pump. I t is also important that we can calculate these ideal separations very easily, without resorting to a computer. If an idealized separation process looks promising for a part'icular application, we still must determine the effect of dispersion before we design the real system. However, if the ideal separation looks marginal or unpromising-even though we have given ourselves every possible benefit in the idealization-we can be certain that the real process will be unsatisfactory. The ability to screen processes rapidly is a major advantage of the equilibrium theory. I do not agree with Harris that "equilibrium stage concepts , , . , are fundamental idealizations of all separation
