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In this study, the preferential CO oxidation (CO-PROX) reaction is simulated under advection–diffusion conditions in a CuO/CeO2 catalyst-supported monolith built by 3D-printing. The simulation incorporates the mass balances in the bulk of the fluid, the momentum balance, and the heterogeneous chemical reactions. In the monolith constricted channels, the fluid velocity is 80% larger than in the wider channels. Three reactive regimes are identified: the CO oxidation-dominated regime governing up to 85 °C and the early and late transition regimes where the H2 oxidation eventually increases. Up to 175 °C, a H2 oxidation-dominated reactive regime was not identified. The simulation accurately predicts experimental results of CO conversion and selectivity in the range from 25 to 175 °C. A sensitivity analysis demonstrates that the composition of gas mixture fed significantly affects the ratio of reaction rates and, consequently, the CO conversion and CO selectivity; meanwhile, the rate of gas injection yields moderate changes in reactivity.