Heat Transfer Parameters in Packed Beds

Heat Transfer Parameters in Packed Beds 8.3.1. Effective thermal conductivities, kt 

As shown by Eqs. (8-17) and (8-18), the effective thermal conductivities in the radial and axial directions are considered to be composed of the effective thermal conductivity with stagnant fluid, kea, and the contribution of fluid flow. 

Kunii and Smith (I960) presented theoretical equations for estimating kes. In most adsorption operations, temperature ranges suggest that contribution of radiant heat transfer is negligible, so kea can be calculated when thermal conductivity of the particle, ki, is given. 

Several examples of calculated from this equation are given in Table 8 1 

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Dixon, A. G. and Cresswell, D. L., Theoretical prediction of effective heat transfer parameters in packed beds, AIChE /., 25, 663-676 (1979). 

In spite of much research (1-7), identification of the relevant heat transfer parameters in packed beds and their subsequent estimation continue to provide challenging problems,especially so for beds having a small tube to particle diameter ratio, where so few experimental data are reported. 

Heat generation also affects measurement of adsorption rate by batch techniques such as the gravimetric method. First, the effect of heat transfer rate on measurement of adsorption rate by a batch method is shown using a simple model as an example of nonisothermal effect. Then fundamental equations for heat transfer in packed beds are shown and simplified models presented. Estimation mehtods for heat transfer rate parameters in packed beds are introduced followed by a discussion of heat transfer in an adsorbent bed in adsorption equilibrium to show the coupling effect of heat and mass dispersion. Finally, the effect of heat transfer on adsorption dynamics in a column is illustrated using simple models. 

De Wasch and Froment (1971) and Hoiberg et. al. (1971) published the first two-dimensional packed bed reactor models that distinguished between conditions in the fluid and on the solid. The basic emphasis of the work by De Wasch and Froment (1971) was the comparison of simple homogeneous and heterogeneous models and the relationships between lumped heat transfer parameters (wall heat transfer coefficient and thermal conductivity) and the effective parameters in the gas and solid phases. Hoiberg et al. (1971)... 

Such a comparison is given in Fig. 7 where the two heat transfer parameters X, and aw plus the external catalyst surface ap, the bed void fraction e and the pressure drop Ap are given for a selection of different random and regular catalyst packings in a tube of 50 mm internal diameter and a mass flow velocity of G. = 1 kg/(m2 s). 

The heat transfer parameters have been derived for an annular packed bed in the range 200 < Re < 800 and... 

Parametric Sensitivity. One last feature of packed-bed reactors that is perhaps worth mentioning is the so-called "parametric sensitivity" problem. For exothermic gas-solid reactions occurring in non-adiabatic packed-bed reactors, the temperature profile in some cases exhibits extreme sensitivity to the operational conditions. For example, a relatively small increase in the feed temperature, reactant concentration in the feed, or the coolant temperature can cause the hot-spot temperature to increase enormously (cf. 54). This sensitivity is a type of instability, which is important to understand for reactor design and operation. The problem was first studied by Bilous and Amundson (55). Various authors (cf. 57) have attempted to provide estimates of the heat of reaction and heat transfer parameters defining the parametrically sensitive region for the plug-flow pseudohomogeneous model, critical values of these parameters can now be obtained for any reaction order rather easily (58). 

Here the numerical constants employed are consistent with in BTU/h —°R, T is in °R, h is the solid-gas heat transfer coelScient [c.f. equation (7-83)], Kg the thermal conductivity of the solid phase, Npe the mass Peclet number, G the mass velocity, Cp the heat capacity, dp the particle diameter, and e is the bed porosity. The second term in brackets represents the radiative heat transfer contribution to the apparent thermal conductivity this is normally negligible for operation at less than 300-350 °C. The quantity / is a surface emissivity factor that normally can be estimated as 0 < / <0.1 (see Argo and Smith). Keep in mind that equation (7-153) is for gas flow in packed beds with Npe < 40. Other situations are discussed by both Beck, and Argo and Smith. Note also that, with the possible exception of /, there are no adjustable parameters in equation (7-153). Since the radiative contribution is normally quite small except at very elevated temperatures, a typical working form of equation (7-153) is... 

Sagara, M., Schneider, R, and Smith, J.M., The determination of heat transfer parameters for flow in packed beds using pulse testing and chromatography theory, Chem. Eng. J., (1) 47, 1970. 

Since there is no easily defined heat-transfer area in direct-contact equipment, active volume is used as a measure of its size (Section 9.1.3.1). In the case of a packed bed, for example, the volume of the bed and not the full volume of the vessel is the parameter of interest. A volumetric heat-transfer coefficient measures the efficiency of the process. At a differential section of the exchanger, we have as a variation on Eq. (1)... 

Reactions carried out in three-phase fixed-bed reactors such as hydrogenation, oxidation, and hydrodesulfurization can be highly exothermic. Such situations require incorporation of an efficient heat removal system in order to avoid hot spots or catalyst deactivation as much as possible [13, 92]. A good knowledge of the packed-bed heat transfer parameters is necessary for the design of the reactor and heat removal system. 

The balances for packed beds contain several other parameters. In the review of Kulkarni and Doraiswamy [22], several expressions are presented for the estimation of the heat transfer parameters (X, U,...) some parameter values are summarized in Table 5.7. 

To measure e.g. heat transfer parameters under reacting and non-reacting conditions, the operating conditions of the reactor were selected so that in the first zone of the 1200 mm long packed bed, chemical reaction was dominant, whereas in the second zone pure heat transfer took place. The experimental data shown in Fig. 9 relate to the oxidation of CO with air using 5 mm particles of silica supported CuO-catalyst. The radial temperature and concentration profiles in the different measurement planes are depicted in Figure 10. 

H. Hofmann Industrial process kinetics and parameter estimation, Adv.Chem.Ser. 109(1972)519-534 /2/ P. Trambouze, H. van Landeghem and J.P. Wauquier Les reac-teurs chimiques. Edition Technip, Paris 1984 /3/ H. Hofmann, G. Emig and W. Rdder The use of an integral reactor with sidestream-analysis for the investigation of complex reactions, EFCE Publ.Ser. 37(1984)4 19-426 /4/ S. Yagi and D. Kunii Studies on the effective thermal conductivities in packed beds, AIChE J. (1957)373-381 /5/ D. Kunii and J.M. Smith Heat transfer characteristics of porous rocks, AIChE J. (1960)71-78 /6/ N. Wakao and J.M. Smith Diffusion in catalyst pellets, Chem.Eng.Sci. 17(1962)825-834... 

Figure 4.9 Overall heat transfer coefficient (a) and heat transfer parameters (b) of a highly conductive structured catalyst in methanol synthesis as a function of the syngas stoichiometric number in the fresh feed stream (Mp). (Squares) Commercial Lurgi multitubular packed-bed reactor (PB) (circles) copper honeycomb monoliths (HM) (triangles) open-cell foams (OF). In Figure 4.9b, the radial effective thermal conductivity is plotted with solid symbols and the wall heat transfer coefficient, h, with empty ones. Reprinted from Montebelli etal. [162], with permission from Elsevier.

Figure 4a, Heat transfer in packed beds of spheres with different void fraction Nu as a function of Re with Pr parameter according Gnielinski (S), The authors of the experimental data are given in the legend.

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