Unsteady Operation and Surface Inventories

The global design equations for packed beds, (e.g., Eqnations 10.1, 10.9, 10.39, and 10.40) all have the same limitation as does the axial dispersion model treated in Chapter 9. They all assume steady-state operation. Adding an accumulation term da jdt acconnts for the change in the gas phase inventory of component A bnt not for the snrface inventory of A in the adsorbed form. The adsorbed inventory can be a large mnltiple of the gas phase inventory. 

Estimate the surface inventory of component A for the catal54ic CSTR in Example 10.9. Assume that the surface reaction is rate-controlling and that A is the only adsorbed species. Suppose A is a moderately large molecule that occupies a site that is 1 nm x 1 nm. 

Solution If the surface reaction controls the overall rate, all the active sites will be occupied. Assume that the entire surface is active so that it will be covered with a monolayer of A molecules. The surface area is 101(400) = 40,400m (4ha or 10 U.S. acres ). 

Example 10.13 How long will it take the reactor in Example 10.9 to 

Solution The surface is estimated to contain 0.067mol of A in adsorbed form. The inlet gas contains 1.6 mol of A per cubic meter and is flowing at 150cm /s so that A is entering the reactor at a rate of 0.00024 mol/s. Five minutes are needed to supply the surface if all the incoming gas were adsorbed. Fifteen to thirty minutes would be a reasonable startup time. Recall that the reactor has a gas-phase residence time VjQout of only 1.5 s The residence time of the adsorbed species is 700 times larger than the average (nonadsorbed) molecule. 

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