Applicability of Single Parameter ModelsConditions under which simplified, single parameter models may be used to predict breakthrough curves in linear, packed bed adsorbers and thermal regenerators are examined with reference, in particular, to earlier conditions proposed by Handley and Heggs and by Babcock and co-workers. I t is found that for high values of heat capacity ratio the Schumann model provides a satisfactory description of packed bed dynamics where fluids axial dispersion and solids conduction effects are lumped into a single parameter the curve spread parameter u*.For low values of heat capocity ratio, the equivalent conductivity model of Babcock and co-workers should provide a more accurate description. The value of the Biot number Bi was found to provide the sole criterion for estimating the relative importance of the internal solids conduction. Empirical correlations are presented which allow rapid estimates of breakthrough curves to be mode from the curve spread parameter and which facilitate analysis of experimental data from breakthrough curve experiments.The prediction of breakthrough curves in linear, packedbed adsorbers and thermal regenerators has been the subject of many theoretical and experimental investigations since Schumann's work (19) in 1929. This interest arises fundamentally because of the economic importance of fixed bed-fluid transfer processes and because of the resultant need to rapidly and accurately design related equipment.Design procedures for well insulated thermal regenerators or adsorbers in which particle internal conductivities may be regarded as infinite have been well developed and were summarized by McAdams (21 ) . Such procedures depend on the Schumann model which makes the assumption amongst others that axial conduction or dispersion in the fluid phase is of negligible importance. The addition of a term for fluid phase axial dispersion (5, 7 ) to the Schumann equation greatly complicates the mathematical solution of the equations and raises the question of whether it is necessary to devise a completely new set of design procedures.In this paper the conditions under which the Schumann solution may be extended to cover the cases of finite particle conductivity and axial fluids dispersion are considered. It has also been necessary to examine critically the conditions proposed earlier by Handley and Heggs (9) and by Babcock and co-workers (2, 3 ) .It is shown that for most cases of practical importance the well-established design procedures referred to above may continue to be used, subject to the satisfaction of a number of simple criteria. At the same time, one of the objects of this paper is to make the task of the design engineer easier by presenting empirical correlations of points on a breakthrough curve against nondimensional groups commonly used in chemical engineering. The use of these groups simplifies the tasks of design and analysis and facilitates translation of the results from heat to mass transfer.The application of complex mathematical "models" to...

parallel lines are observed in Figure 9 for the values of Hf" of the hydrates of MgC1:; and FeC13. We assume, therefore, that the same relation also holds for the values of Gf" of the hydrates of MgCl2 and FeC13. Since Gf" for FeC13 is known, we are now able to calculate Gf" for the hydrates of FeC13. If data for Hf" and Gf" of other metal chlorides (e.g. BaC12, CaC12, and NiC12) and their hydrates are used as a basis of the analogy, the same results are obtained quantitatively. A plot of the values of Gf" (FeClYnHz) vs.[H20]/[FeC13] is a straight line. It appears therefore, that for all equilibria between the hydrates of FeC13, K = 1.On the basis of the data mentioned above, we calculated the fraction active catalyst, [FeC13-H20]/[FeC13] as a function of the degree of hydration, [H20]/[FeC13]. The results are given in Table IV. NomenclatureB = benzene cp = specific heat, J kg-' "C-' D = diffusivity of Clz dissolved in B, m2 s-l DCB = dichlorobenzene E , = activation energy, J kmol-I "C-I H = heat capacity of the flow reactor, J "C-' a d i l = heat of dilution, J kmol-I a h = heat of hydration, J kmol-' AHr = enthalpy change over a reaction, J kmol-I 121 = first-order reaction rate constant, s-l 122 = second-order reaction rate constant, s-l kmol-I m3 123 = third-order reaction rate constant, s-l kmold2 m6 k2* = r/[Clz][FeC13], i3-l kmol-l m3 k3* = r/[Cl2] [FeC13] [€3], s-l kmol-2 m6 MCB = monochlorobenzene Q = heat loss factor, . I OC-l s-l r = rate of reaction per unit volume, first chlorination step, r' = rate of reaction per unit volume, second chlorination step, T = temperature, "C or K kmol m-3 s-l kmol m-3 s-l T -To' = temperature difference measured over the flow t = time, s V , V' = volume, m3 [ ] = concentration, kmol m-3 0', O = mean residence time, s p = density of liquid, kg-3

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