Plasma reactors have the potential to enable CO₂ utilization technologies and so there is need to investigate their performance from a chemical or process engineering perspective. Multiphysics models are excellent tools to carry out this analysis; however, practical engineering models of plasma reactors are limited. Herein a two-step modelling approach for plasma reactors is presented. In the first step, a 2D plasma reactor model with a simple chemistry is used to characterize the discharge. The result of this step is used in the second step to develop a global (volume averaged) model of the reactor with the actual chemistry. The approach is applied in the case of CO₂ dissociation in a non-thermal surface wave microwave plasma reactor. Preliminary calculations reveal the need to include the vibrationally enhanced dissociation of CO₂ in the chemistry of the model. Reduced vibrational kinetics are employed for this purpose by introducing the fictitious species . The model predictions are compared to experimental results to validate the model and obtain insight into the performance of the reactor. In comparison to the experimental results the conversions obtained with the model are underestimated between 11% and 25%. The dominant dissociation paths in the plasma reactor are also identified. Further calculations are performed to show the importance of an approximate description of the power deposition. Limitations of the approach are discussed as well, especially those with major contribution to the discrepancies between experimental and modelling results.