Catalyst Regeneration Using a Shrinking Core Model
The shrinking core model describes the behavior of a solid particle that shrinks by dissolution or reaction. This model has applications ranging from catalyst regeneration to coal particle burning and pills disolving in the stomach. Coking is a type of catalyst deactivation where carbon will build up in the catalyst and completely obstruct the catalyst's pores. Consider a gas-phase reactant (e.g. oxygen) reacting with a species (e.g. carbon) contained in an inert solid matrix (e.g. a catalyst). Carbon is removed from the outer edge of the pellet and then from the core of the deactivated catalyst particle. The dimensionless concentration of oxygen is given by:[more]
where is the radial position of the carbon/gas interface and is the radius of the catalyst pellet; is a function of the dimensionless time, , where is a characteristic time. One can derive the following relationship between and . See  for the definition and derivation of all parameters in the expression for : .
This Demonstration plots the dimensionless oxygen concentration versus the dimensionless radial position, , for user-set values of the dimensionless time, . It also shows a spherical catalyst pellet where the regenerated region is indicated in gray and the still deactivated region, in green. Finally, the actual value of the radial position of the oxygen-carbon interface is shown in green.[less]
 H. S. Fogler, Elements of Chemical Reaction Engineering, 3rd ed., Upper Saddle River, NJ: Prentice Hall, 1999.