Catalyst Deactivation in Reactors

deactivation order n

temperature T (K)

Damköhler number Da₀

deactivation constant k_d0 (h⁻¹)

moving-bed catalyst time t_s (h)

time on stream t (h)

packed bed CSTR moving bed

time axis maximum (h)

Directions

A first-order, irreversible, liquid-phase reaction A → B takes place on a catalyst that loses activity with time on stream. The same mass of catalyst is used in three reactors: a packed-bed reactor (PBR) and a CSTR, in which the catalyst stays in the reactor and deactivates uniformly, and a moving-bed reactor, in which fresh catalyst is fed continuously and spent catalyst is removed.

Select the deactivation order (0, 1, or 2) and use the sliders to set the Damköhler number and the deactivation rate constant at the reference temperature (500 K), the reactor temperature, and the residence time of the catalyst in the moving bed.

The left plot shows catalyst activity versus time; the dashed segment is the average activity of the catalyst in the moving bed. The right plot shows conversion versus time on stream. The moving-bed reactor operates at steady state, so its conversion does not change with time.

Drag on either plot (or use the time-on-stream slider) to move the vertical line; values at that time, and conversions averaged from 0 to that time, are listed below the plots. Use the checkboxes to hide or show reactors and the menu to change the time axis.

Details

The catalyst activity is the ratio of the reaction rate on used catalyst to the rate on fresh catalyst:

The activity decays by an th-order, concentration-independent (separable) deactivation law:

which integrates to

The rate constants depend on temperature through the Arrhenius equation, relative to the reference temperature K:

with kJ/mol and kJ/mol. Because , raising the temperature increases the initial rate but makes the catalyst deactivate faster. The Damköhler number for fresh catalyst is

where is the catalyst mass and is the volumetric flow rate.

Packed bed and CSTR (catalyst stays in the reactor). Deactivation is slow compared with the fluid residence time, so the reactor is at pseudo-steady state at each time on stream and the whole bed has the same activity :

Moving-bed reactor. Fresh catalyst enters with the feed and moves through the bed in plug flow with residence time , where is the catalyst feed rate (kg/h). Catalyst at position has been in the bed for , so its activity is . Integrating the mole balance:

The moving bed operates at steady state, so its conversion does not change with time on stream; a shorter catalyst residence time (faster catalyst feed rate) gives higher activity and conversion, but requires more catalyst regeneration.

Time-averaged conversion. For the PBR and the CSTR, the average conversion from the start of operation to time is

which is proportional to the total amount of product made up to time .

Definitions

	catalyst activity (dimensionless)
	average activity of the catalyst in the moving bed
	concentration of reactant A (mol/L)
	Damköhler number for fresh catalyst at temperature
	Damköhler number for fresh catalyst at
	activation energy of the reaction (J/mol)
	activation energy of deactivation (J/mol)
	reaction rate constant per mass of catalyst (L/(kg h))
	deactivation rate constant at temperature (h⁻¹)
	deactivation rate constant at (h⁻¹)
	deactivation order
	ideal gas constant, 8.314 J/(mol K)
	rate of consumption of A per mass of catalyst (mol/(kg h))
	reactor temperature (K)
	reference temperature, 500 K
	time on stream (h)
	integration variable for time (h)
	residence time of the catalyst in the moving bed (h)
	catalyst feed rate to the moving bed (kg/h)
	volumetric flow rate (L/h)
	catalyst mass in the reactor (kg)
	catalyst mass from the moving-bed entrance to a given position (kg)
	conversion of A
	time-averaged conversion from 0 to

About

This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by John L. Falconer using Claude AI. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988). Address any questions or comments to LearnChemE@gmail.com.