The purpose of this study is to develop a detailed dynamic model of a typical FCC unit that consists of the reactor: regenerator, and catalyst transfer lines. A distributed parameter model is presented for the reactor riser to predict the distributions of the catalyst and gas-phase velocities, the molar concentrations of 4-lump species, and the temperatures. The regenerator is also modeled in such detail that the two-regime, two-phase behavior of typical fluidized beds can be accounted for. An efficient model solver was constructed on the basis of a modular approach in which the model equations are grouped into 12 modules each corresponding to a specific part of the unit and type of equations. The dynamic model is implemented in Part II of this paper for extensive simulation study on FCC processes.