Catalyst Bed Energy Balance

We now develop the solid phase catalyst bed thermal energy equation. Since the catalyst bed is stationary, the general energy balance becomes 

We normalize the equation with respect to the last term. This gives the dimensionless coefficients, 

The final scaled catalyst thermal energy balance is 

We can now compare the relative time scales for the gas phase and catalyst phase balances. To do this, we normalize the gas phase balance by the heat transfer term so that both catalyst and gas equations are normalized by the same term. This gives 

Comparing the leading coefficient of the two accumulation terms shows that the ratio of the fluid dynamics to the catalyst dynamics is 

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