Effective thermal conductivity catalyst

Effective Thermal Conductivities of Porous Catalysts. The effective thermal conductivity of a porous catalyst plays a key role in determining whether or not appreciable temperature gradients will exist within a given catalyst pellet. By the term effective thermal conductivity , we imply that it is a parameter characteristic of the porous solid structure that is based on the gross geometric area of the pellet perpendicular to the direction of heat transfer. For example, if one considers the radial heat flux in a spherical pellet one can say that... 

The effective thermal conductivities of common commercial porous catalysts are quite low and fall within a surprisingly narrow range. 

The physical properties of the catalyst (specific surface area, porosity, effective thermal conductivity, effective diffusivity, pellet density, etc.). 

ILLUSTRATION 12.7 DETERMINATION OF THE EFFECTIVE THERMAL CONDUCTIVITY OF A PACKED BED OF CATALYST PELLETS... 

The overall heat transfer coefficient for thermal energy exchange between the tube wall and the reacting fluid may be taken as 1.0 x 10 3 cal/cm2-sec-°K. The effective thermal conductivity of the catalyst pellets may be taken as equal to 6.5 x 1CT4 cal/(sec-cm-°C). 

Recently, such a temperature oscillation was also observed by Zhang et al (27,28) with nickel foils. Furthermore, Basile et al (29) used IR thermography to monitor the surface temperature of the nickel foil during the methane partial oxidation reaction by following its changes with the residence time and reactant concentration. Their results demonstrate that the surface temperature profile was strongly dependent on the catalyst composition and the tendency of nickel to be oxidized. Simulations of the kinetics (30) indicated that the effective thermal conductivity of the catalyst bed influences the hot-spot temperature. 

The equations describing the concentration and temperature within the catalyst particles and the reactor are usually non-linear coupled ordinary differential equations and have to be solved numerically. However, it is unusual for experimental data to be of sufficient precision and extent to justify the application of such sophisticated reactor models. Uncertainties in the knowledge of effective thermal conductivities and heat transfer between gas and solid make the calculation of temperature distribution in the catalyst bed susceptible to inaccuracies, particularly in view of the pronounced effect of temperature on reaction rate. A useful approach to the preliminary design of a non-isothermal fixed bed catalytic reactor is to assume that all the resistance to heat transfer is in a thin layer of gas near the tube wall. This is a fair approximation because radial temperature profiles in packed beds are parabolic with most of the resistance to heat transfer near the tube wall. With this assumption, a one-dimensional model, which becomes quite accurate for small diameter tubes, is satisfactory for the preliminary design of reactors. Provided the ratio of the catlayst particle radius to tube length is small, dispersion of mass in the longitudinal direction may also be neglected. Finally, if heat transfer between solid cmd gas phases is accounted for implicitly by the catalyst effectiveness factor, the mass and heat conservation equations for the reactor reduce to [eqn. (62)]... 

Thiele(I4>, who predicted how in-pore diffusion would influence chemical reaction rates, employed a geometric model with isotropic properties. Both the effective diffusivity and the effective thermal conductivity are independent of position for such a model. Although idealised geometric shapes are used to depict the situation within a particle such models, as we shall see later, are quite good approximations to practical catalyst pellets. 

When a fast reaction is highly exothermic or endothermic and, additionally, the effective thermal conductivity of the catalyst is poor, then significant temperature gradients across the pellet are likely to occur. In this case the mass balance (eq 32) and the enthalpy balance (eq 33) must be simultaneously solved using the corresponding boundary conditions (eqs 34-37), to obtain the concentration profile of the reactant and the temperature profile inside the catalyst pellet. The exponential dependence of the reaction rate on the temperature thereby imposes a nonlinear character on the differential equations which rules out an exact analytical treatment. Approximate analytical solutions [83, 99] as well as numerical solutions [13, 100, 110] of eqs 32-37 have been reported by various authors. 

To use the various criteria given in the previous section, some experimental data on the reacting system are necessary. These are the effective diffusivity of the key species in the pores of the catalyst, the heat and mass transfer coefficients at the fluid-solid interface, and the effective thermal conductivity of the catalyst. The accuracy of some of these parameters, which are usually obtained from known correlations, may sometimes be subject to question. For example, under labo-... 

Example 9.2 Maximum temperature difference in the hydrogenation of benzene Consider the hydrogenation of benzene, which is exothermic with a heat of reaction 50 kcal/mol. For the catalyst pellet containing 58% Ni on Kieselguhr Harshaw (Ni-0104P), the effective thermal conductivity and diffusivity are 3.6 X 10 4cal/(cmsK) and 0.052 cm2/s, respectively. For a benzene surface concentration of 4.718 X 10-6 mol/cm3, and a surface temperature of 340 K, fromEqs. (9.18) and (9.19),... 

Measurements of A, are scarce. The available data are reviewed by Satterfield [2], The effective thermal conductivity of a porous catalyst can be estimated from the correlation of Russell [30] ... 

There is even more uncertainty in estimating the heat-transfer coefficient at the wall of the tube than in estimating the effective thermal conductivity in the bed of catalyst. The measurement is essentially a difficult one, depending either on an extrapolation of a temperature profile to the wall or on determining the resistance at the wall as the difference between a measured over-all resistance and a calculated resistance within the packed bed. The proper exponent to use on the flow rate to get the variation of the coefficient has been reported as 0.33 (C4), 0.47 (C2), 0.5 and 0.77 (HI), 0.75 (A2), and 1.00 (Ql). 

It is evident from the foregoing discussion that the effective diffusivity cannot be predicted accurately for use under reaction conditions unless surface diffusion is negligible and a valid model for the pore structure is available. The prediction of an effective thermal conductivity is even more difficult. Hence sizable errors are frequent in predicting the global rate from the rate equation for the chemical step on the interior catalyst surface. This is not to imply that for certain special cases accuracy is not possible (see Sec. 11-10). It does mean that heavy reliance must be placed on experimental measurements for effective diffusivities and thermal conductivities. Note also from some of the examples and data mentioned later that intrapellet resistances can greatly affect the rate. Hence the problem is significant. 

The effective thermal conductivities of catalyst pellets are surprisingly low. Therefore significant intrapellet temperature gradients can exist, and the global rate may be influenced by thermal effects. The effective conductivity is the energy transferred per unit of total area of pellet (perpendicular to the direction of heat transfer). The defining equation, analogous to Eq. (11-18) for mass transfer, may be written... 

Fig. 11-3 Effective thermal conductivity of alumina [boehmite) catalyst pellets at 10 to 25 microns Hg pressure...

Heat transfer within catalyst particles occurs by conduction and an effective thermal conductivity /.g for the pellet is used with Fourier s law, to describe the intraparticle heat conduction. 

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