Biogas upgrading processes by in-situ hydrogen (H-2) injection are still challenging and could benefit from a mathematical model to predict system performance. Therefore, a previous model on anaerobic digestion was updated and expanded to include the effect of H-2 injection into the liquid phase of a fermenter with the aim of modeling and simulating these processes. This was done by including hydrogenotrophic methanogen kinetics for H-2 consumption and inhibition effect on the acetogenic steps. Special attention was paid to gas to liquid transfer of H-2. The final model was successfully validated considering a set of Case Studies. Biogas composition and H-2 utilization were correctly predicted, with overall deviation below 10% compared to experimental measurements. Parameter sensitivity analysis revealed that the model is highly sensitive to the H-2 injection rate and mass transfer coefficient. The model developed is an effective tool for predicting process performance in scenarios with biogas upgrading.