ABSTRACT-The study presents a mathematical model to analyze the dynamic evolution of molar concentrations of toluene (C 7 H 8 ) , water vapor (H 2 O) carbon monoxide (CO), hydrogen (H 2 ) , methane (CH 4 ) and carbon dioxide (CO 2 ) in a catalytic reactor of fixed bed. The mathematical model was discretized using the method of lines (MDLs) to transform the system of partial differential equations (PDEs) in a system of ordinary differential equations (ODEs). The system of ODEs has been solved by the implementation of the method of Runge-Kutta Gill to estimate the chemical species C 7 H 8, H 2, CO, H 2, CH 4 and CO 2 .The estimation allows the quantification of individual forecasts of the variables presented in this study. However, valuable information can be obtained from the estimated behaviors in catalytic fixed bed reactor. The model has allowed the validation of chemical species (H 2, CO and CO 2 ) by comparing the optimized values. Additionally, the concentrations for chemical species C 7 H 8, H 2, CO, H 2, CH 4 and CO 2 was studied.