Abstract Numerical model for heavy fuel oil and air mixtures combustion is presented to simulate the behavior of the fuel in an inert porous medium reactor for hydrogen production. Three-zone combustion of oil and petroleum cokes separated by temperature ranges starting from ambient temperature to 560 K, from 560 K to 673 K, and above 673 K, is presented. Hydrogen production is achieved using water gas shift equilibrium reaction on the combustion products at different temperatures. Results show a high enthalpy contribution due to coke combustion formed in the low temperature oxidation reaction, being the most important reaction in relation to its zone size. Simulations increasing filtration velocity (from 0.05 to 0.9 m/s) has a favorable effect on the maximum temperature and the combustion front velocity. The effect of the simplified combustion model lowers computational time, with acceptable results for temperature as well as hydrogen production in contrast to laboratory tests and other software simulation such as COMSOL Multiphysics.