Thermal reaction experiments of vacuum residuum were conducted in a micro-batch reactor at 410-480 degrees C. The product yield variation with time indicated that the secondary cracking reaction mainly occurs in the heavy fraction of the liquid product. A narrow fraction model for low-severity thermal cracking of heavy oil, with the secondary reaction taken into account, was developed. To simplify the reaction network, a pseudo-lump was introduced, which was defined as the fraction generated from the secondary cracking reaction of the heavy fraction (420-540 degrees C). Furthermore, a sequential method to estimate rate constants in complex models was employed, and the kinetic parameters were estimated by Arrhenius' law. The model-predicted lump yields agreed well with the experimental values. The ratio of secondary cracking/primary cracking was calculated. The result indicated that, even at the initial stage of the reaction, the ratio in the heavy distillate reaches up to 15-36%; therefore, the secondary cracking reaction cannot be ignored even in low-severity thermal cracking.