Based on the flow pattern of perfect mixing and the age probability density exponential function of equilibrium catalyst in commercial FCC unit

a model equation was established by derivation of catalyst deactivation kinetics

in which equilibrium catalyst activity or micro-reactor activity was related to carbon and metal contents on catalyst

replacement rate of catalyst

temperature and steam partial pressure in regenerator. The mathematical model with high calculation precision for equilibrium catalysts activity or micro-reactor activity was developed through the simulation for operation data of commercial FCC unit and model parameter estimation. The comparison of model parameters indicated that the effect of V contaminate on catalyst activity is the biggest and the effect of Na is the smallest

while the effect of Ni and Fe is in the middle. The results predicted by the model showed that the activity or micro-reactor activity of equilibrium catalyst increases with the decrease of metal and carbon contents on catalyst and the increase of catalyst consumption. It would be advantageous to the activity or micro-reactor activity of equilibrium catalyst to reduce properly the catalyst hold-up or the temperature in regenerator.