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Nigerian crude oil type Okoro 2012 was applied in this study owing to its low API value 23.54 and high residual percentage value of 42.16% from conventional modular refinery operations in Nigeria. The residue acted as a precursor or feedstock to the hydrocracker reactor of the modified modular refinery operation, which is an hydrogenation catalytic process at operating conditions of 380˚C and 183 bar respectively and the hydrogen gas applied is produced via steam-methane reforming since the operational feedstocks are available as methane is the first gaseous product from the modified modular refinery process. Thus, more valuable products such as liquefied petroleum gas, naphtha and diesel were produced from modified modular refinery thereby resolving the residue or bottom product issue associated with conventional modular refinery operation in Nigeria. Models were developed from the first principle through the application of the principle of conservation of mass to predict the performance of the hydrocracker reactor and the developed models were sets of ordinary differential equations, which were solved using Mat-Lab ODE45 solver and validated using simulation data of Aspen Hysys software for the hydrocracker reactor. The results gave a minimum percentage absolute error (deviation) between model predictions and Aspen Hysys results of 4.45%, 5.0% and 2.02% for liquefied petroleum gas, naphtha and diesel products respectively. Hence, the model developed predicted the output performance of the hydrocracker reactor very closely and was applied in studying or simulation of the effects of catalyst effectiveness factor on the overall performance of the hydrocracker reactor.