In this work, we used a mathematical model to quantify components concentration profiles in the methane reforming process with carbon dioxide, taken into account, reaction mechanism of three elementary reactions, including the decomposition of methane, shift and reverse Boudouard reactions. The model was obtained on the basis of differential mass balance, including a reaction rate for methane according to the Langmuir-Hinshelwood model. Considering that the solid phase is composed by small spherical particles, an average process in the radial coordinate of the particle transport equation to eliminate the radial dependence of these equations. This average process is based on the technique of Coupled Integral Equations Approach (CIEA). Then, we employed the Generalized Integral Transform Technique (GITT) in the resulting PDEs, obtaining a new system of Ordinary Differential Equations (ODEs) in time. The reduced model was solved numerically using the routine IVPAG of IMSL Library.