Catalytic 1-dimensional reactor models were developed using the Gibbs energy minimization approach in order to describe gas composition, molar fractions, and conversions of both water gas shift and carbon monoxide methanation at low partial pressure ratios of CO/H2. The extent of reaction in terms of CO amount in the system was used as an additional constraint on the chemical system while solving the local thermodynamic equilibrium. The validity of the model was checked against experimental data gathered from the literature. The known theory about heterogeneous catalysis was incorporated in the Gibbsian multiphase analysis by means of the advancements of a diffusional limited water gas shift reaction and the catalyzed methanation of CO using virtual phases in the conservation matrix. The advantages of the use of this technique to describe a 1D catalyzed reaction, namely qualitative data regarding the chemical system and reduced ordinary differential equations (ODE) input, among others, are outlined in this report.