Calculation of External Concentration Differences

As mentioned earlier, in laboratory reactors the global rate is measured directly, and the question is whether these rates are influenced by extenlal physical processes. In this section we shall consider the method of solution for an isothermal case. Combined mass- and energy-transfer limitations are discussed in Sec. 10-4. 

Olson and Smith measured the rate of oxidation of sulfur dioxide with air in a differential fixed-bed reactor. The platinum catalyst was deposited on the outer surface of the cylindrical pellets. The composition and the rates of the bulk gas were known. The objective was to determine the significance of external diffusion resistance by calculating the magnitude of — C. If this difference is significant, then the values must be used in developing a rate equation for the chemical step. 

Example 10-1 Experimental, global rates are given in Table 10-2 for two levels of conversion of SOj to SO3. Evaluate the concentration difference for SO2 between bulk gas and pellet surface and comment on the significance of external diffusion. Neglect possible temperature differences. The reactor consists of a fixed bed of x -in. cylindrical pellets through which the gases passed at a superficial mass velocity of 147 lb/(hr)(ft ) and at a pressure of 790 mm Hg. The temperature of the catalyst pellets was 480°C, and the bulk mixture contained 6.42 mole % SOj and 93.58 mole % air. To simplify the calculations compute physical properties on the basis of the reaction mixture being air. The external area of the catalyst pellets is 5.12 ft /lb material. The platinum covers only the external surface and a very small section of the pores of the alumina carrier, so that internal diffusion need not be considered. 

Solution First the Reynolds number is evaluated. At 480°C the viscosity of air is about 0.09 lb/(hr)(ft). The particle diameter to employ is the diameter of the sphere with the same area as that of the cylindrical pellets. Hence %df will equal the sum of the areas of the lateral and end surfaces of the cylinder  

The numerical results are more meaningful if they are converted to partial pressures.-In atmospheres, the difference between bulk and surface pressures of sulfur dioxide is 

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