We study the complex phase transition behavior of CO2 in the porous medium using a robust multiphase poromechanics model. This model predicts pressure and saturation distributions under super- and sub-critical conditions during the injection process. We introduce a finite element implementation of the proposed model to analyze the behavior of a multiphase porous system. The proposed model can predict the phase transition of CO2 in the geologic reservoir, which causes a significant change in the density profile and decreases the migration mobility of CO2. The implementation of this model is provided.