The current work is a computational simulation, with the geometry of the Parr reactor series 4581, of a multiphase system with two fluids (hydrocarbon and hydrogen) and two domains (tank and impeller) for the kinetics of residue catalytic hydrocracking. The fluid dynamics modeling is based on the SPH process and the fundamental equations of mass balance and momentum quantities in an isothermal system. The turbulence phenomena are considered through the k-? model for the hydrocarbon and ``disperse phase zero equation" for the hydrogen. The chemical reactions are modeled by the means of a reactional net based on the pseudo components concept, with their loads and products separated according to the commercial cuts, schematized with six parallel reactions, three thermal and three catalytic, with pseudo-first order reaction rates. The domains are composed of hydrocarbon as a general fluid (a mixture of pseudo components + catalyst = ``slurry phase") and the hydrogen as an ideal gas.