Ind. Eng. C h e m . Res. 1990,29, 1076-1084
1076
Heat Effects in Adsorption Column Dynamics. 1. Comparison of Oneand Two-Dimensional Models Shamsuzzaman Farooq and Douglas M. Ruthven* Department of Chemical Engineering, University of New Brunswick, P.O. Box 4400, Fredericton, New Brunswick, Canada E3B 5A3
A two-dimensional model that includes radial thermal conduction has been developed to investigate the dispersive effect of heat, including the effect of a radial temperature gradient, on adsorption column dynamics. Such effects can be much greater than axial dispersion. The form of the breakthrough curves can be well represented by the isothermal dispersed plug flow model using an appropriately modified dispersion coefficient. When the natural velocity of the temperature wave is lower than that of the concentration wave, leading to a combined wave front, a simple one-dimensional model with heat transfer to the column wall provides a good prediction of the dynamic behavior. However, when the thermal front leads the concentration wave (pure thermal wave formation), the one-dimensional model overpredicts the dispersion. To obtain an accurate prediction of the dynamic behavior under these conditions requires the use of the two-dimensional model. The effect of the heat of adsorption on the dynamic performance of an adsorption column has been studied by several investigators. Adiabatic sorption has been considered by Leavitt (1962), Carter (1966, 1968a,b), Carter and Barrett (19731, Pan and Basmadjian (1967, 19701, Marcussen (1982), Yoshida and Ruthven (1983), and Raghavan and Ruthven (1984),among others. Although the behavior of large-diameter industrial columns can be adequately simulated by using adiabatic models, a more realistic model including a finite rate of heat loss at the wall is needed to understand the behavior of smaller units. One-dimensional models for such systems have been presented by Ruthven et al. (1975),Sircar et al. (1983),and Kaguei et al. (1985). In these models, the radial temperature gradient is neglected and all resistance to heat transfer is lumped into an overall effective coefficient of wall heat transfer. However, under conditions of finite heat loss at the wall, there must be a significant radial temperature gradient that will, in general, affect the characteristic velocity of the concentration front, thus increasing the dispersion of the mass-transfer zone. Inclusion of radial conduction in the differential heat balance equation can therefore be expected to provide an improved representation of the dispersive effect of heat on the adsorption column dynamics. However, such a two-dimensional model is obviously more complex than the standard one-dimensional dispersion model, and it is therefore pertinent to inquire whether and under what conditions the simpler model can provide an adequate representation of the dynamic behavior. This may be established either by comparing the theoretical response c w e s from the oneand two-dimensional models or by comparison between theory and experiment. The advantage of the former approach, which is followed in this paper, is that the range of process conditions may be more easily varied over a wide range to cover different regimes. The results of such a comparison suggest that under most practical conditions the one-dimensional model provides an adequate approximation. This conclusion is confirmed experimentally in part 2. To investigate the dispersive effect of the radial temperature gradient, a two-dimensional model that includes the effect of radial heat conduction has been developed.
* Author to whom correspondence
should be addressed.
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In order to isolate the dispersive effect of the thermal gradient, we consider a plug flow system with negligible mass-transfer resistance and a linear adsorption equilibrium isotherm. For such a system, the breakthrough response under isothermal conditions is simply a delayed shock. The theoretical breakthrough curves derived from this model are compared with the curves for an isothermal dispersed plug flow system in order to compare the form of the response and to determine the equivalent Peclet number arising from the dispersive effect of the temperature gradient.
Theoretical Model The system considered is an adsorption column packed with porous spherical adsorbent particles through which an inert carrier flows at a steady rate. At time zero, a steady concentration of an adsorbable component is introduced at the column inlet. After the breakthrough is complete, the adsorbable component is withdrawn from the feed, and the equilibrated bed is regenerated by desorption. The following assumptions are made. (1)The concentration of adsorbable component is small. (2) Frictional pressure drop through the bed is negligible. (3)The adsorption equilibrium isotherm is linear, and the equilibrium constant (Henry’s constant) shows the normal exponential temperature dependence. (4) Adsorption/desorption equilibrium is established instantaneously (negligible mass-transfer resistance). (5) The flow pattern is described by the plug flow model. Axial and radial dispersion of mass is neglected. (6) Local thermal equilibrium is assumed between fluid and adsorbent particles. (7) Bulk flow of heat and conduction in the radial direction are considered in the heat balance equation. Axial conduction of heat has been neglected. (8) The temperature of the column wall is maintained at the feed temperature. (9) Film resistance to heat transfer inside the column wall is neglected. (10) The temperature dependence of gas and solid properties is assumed negligible. Assumptions 1 and 2 imply a constant linear velocity through the adsorbent bed. We have chosen a linear isotherm because the effect of temperature on the adsorption equilibrium is greatest in the linear range. Assumptions 0 1990 American Chemical
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