Heat pore diffusion

Treatment of thermal conductivity inside the catalyst can be done similarly to that for pore diffusion. The major difference is that while diffusion can occur in the pore volume only, heat can be conducted in both the fluid and solid phases. For strongly exothermic reactions and catalysts with poor heat conductivity, the internal overheating of the catalyst is a possibility. This can result in an effectiveness factor larger than unity. 

The activity calculated from (7) comprises both film and pore diffusion resistance, but also the positive effect of increased temperature of the catalyst particle due to the exothermic reaction. From the observed reaction rates and mass- and heat transfer coefficients, it is found that the effect of external transport restrictions on the reaction rate is less than 5% in both laboratory and industrial plants. Thus, Table 2 shows that smaller catalyst particles are more active due to less diffusion restriction in the porous particle. For the dilute S02 gas, this effect can be analyzed by an approximate model assuming 1st order reversible and isothermal reaction. In this case, the surface effectiveness factor is calculated from... 

Regarding mass transfer, the slowest step is normally pore diffusion rather than external mass transfer, whilst for heat transfer the slowest step is the interphase heat transfer between the particle and the fluid phase rather than the internal heat transfer in the solid particle. 

Film and Pore Diffusion Together with Interphase Heat Transfer... 

A special type of fluid-solid catalyzed reaction is obtained when either the reaction rate is so fast that the reactants become completely exhausted at the external catalyst surface (i.e. at very high reaction temperatures) or when the catalyst is nonporous. Then, pore diffusion and effective heat conduction inside the pellet need not be considered. Thus, the problem is reduced to a treatment of the coupled interphase heat and mass transport. 

Pore diffusion and heat conduction (combined effect) 5 < 65... 

The pore diffusivity used in this analysis was determined by the Renkin equation4, the axial dispersion coefficient calculated by assuming a constant Peclet number of 0.2, and the mass transfer coefficient from the bulk to the particle surface calculated by the correlation of Wakao and Kaguei. The product of the heat capacity and density of the solid phase was taken to be the same as that used by Raghavan and Ruthven17. The density of the fluid phase was assumed to be that of pure C02 and was calculated from data provided by the Dionix Corporation in their AI-450 SFC software. Constant pressure heat capacities for the mobile phase were also assumed to be that of pure C02 and were taken from Brunner3. 

For the reaction conditions chosen it is shown, that pore diffusion limitations must occur, and that the heat conductivity of the silver containing particles is high enough, so that the particles can be considered to be isothermal. Further it is shown that there must be quite a difference in temperature between the catalyst particles and the flowing gas, so that a particle runaway study must be made. 

The evaporation rate for pore diffusion and pore heat transfer gives a size dependent evaporation rate given by... 

Thus the surface temperature is fixed at 65.6°C with pore diffusion the rate determining step. At all other surface temperatures, pore diffusion gives the largest t value for the mass transfer steps, and boimdary layer heat transfer gives the largest t value for the heat transfer steps. 

After freezing, the time to sublimate the solvent is given by the drying expressions in Tables 8.3 and 8.4, where the enthalpy of vaporization for drying is replaced by the enthalpy of sublimation. The enthalpy of sublimation is often equal to the sum of the heats of fusion and vaporization [16]. The enthalpy of sublimatian is also substituted for the enthalpy of vaporization in the Clausius Clapeyron equation (8.9) required for the calculation of the solvent partial pressure. The same rate determining steps of boundaiy layer mass transfer and heat transfer as well as pore diffusion and porous heat conduction are applicable in sublimation. 

Using these equations for heat conduction in the porous network emd the pseudo-steady state emalysis described for pore diffusion, the time to dry a spherical green body with pore heat conduction as the rate determining step is given by... 

These expressions are good for rate limiting steps of only pore diffusion and pore heat conduction corresponding to the decreasing rate period. Combined with the equations in Table 14.1, all the possible rate controlling steps are established allowing the prediction of the total time, Tjot, to dry a green body ... 

This same reaction sequence can be used to describe the thermal decomposition of polymers under reducing conditions. In this case, the value of n is equal to 0 and h is usually set equal to 1.0 in the generalized reaction. Under these conditions, the mass transfer is limited to the removal of the volatiles from the porous green body. This mass transfer can be limited by the pore diffusion or the boundary layer. We still must consider that the surface reaction or the steps of heat transfer in the boundary layer or heat conduction in the porous body could also be rate controlling in this case of the thermal decomposition of polymers under reducing conditions. 

Experimental Measurements of Reaction Kinetics. The reaction expressions discussed in the following model the intrinsic reaction on the catalyst surface, free of mass-transfer restrictions. Experimental measurements, usually made with very fine particles, are described by theoretically deduced formulas, the validity of which is tested experimentally by their possibility for extrapolation to other reaction conditions. Commonly the isothermal integral reactor is used with catalyst crushed to a size of 0.5-1.5 mm to avoid pore diffusion restriction and heat-transfer resistance in the catalyst particles. To exclude maldistribution effects and back mixing, a high ratio of... 

For pore diffusion resistances in reactions having moderate heat evolution, the following phenomena characteristically hold true in industrial ammonia synthesis [212] in the temperature range in which transport limitation is operative, the apparent energy of activation falls to about half its value at low temperatures the apparent activation energy and reaction order, as well as the ammonia production per unit volume of catalyst, decrease with increasing catalyst particle size [211], [213]-[215]. For example at the gas inlet to a TVA converter, the effective rate of formation of ammonia on 5.7-mm particles is only about a quarter of the rate measured on very much smaller grains (Fig. 13) [157]. 

Similarly, impervious yttria-stabilized zirconia membranes doped with titania have been prepared by the electrochemical vapor deposition method [Hazbun, 1988]. Zirconium, yttrium and titanium chlorides in vapor form react with oxygen on the heated surface of a porous support tube in a reaction chamber at 1,100 to 1,300 C under controlled conditions. Membranes with a thickness of 2 to 60 pm have been made this way. The dopant, titania, is added to increase electron How of the resultant membrane and can be tailored to achieve the desired balance between ionic and electronic conductivity. Brinkman and Burggraaf [1995] also used electrochemical vapor deposition to grow thin, dense layers of zirconia/yttria/terbia membranes on porous ceramic supports. Depending on the deposition temperature, the growth of the membrane layer is limited by the bulk electrochemical transport or pore diffusion. 

Operative. For the non isothermal case, effectiveness factors greater than unity are possible. Weisz and Hicks have considered this problem in some detail and constructed a number of graphs for various heats of reaction and activation energies. When a reaction is limited by pore diffusion, the reaction rate is proportional to yjky. If the temperature effects can be expressed as a simple Arrhenius relationship = A txp —E/RT), then the measured activation energy E will be about half the true activation energy. Very low values of the activation energy, i.e, 1-2 kcal. mole are only observed when mass transfer to the external catalyst surface is limiting the rate. 

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