To reduce carbon emissions, renewable energy sources are gradually becoming more and more common and new ways to exploit them are constantly researched. Among the different technologies, the concept of Power to Fuel allows the production of a fuel that is easy to use and to store, using only green electricity. In this work a Simulink model of a fed-batch ex-situ bio-methanation reactor is created, with the goal of assessing the impact that different variables have on the methane production and predict the results that can be obtained with a specific system. Before the construction of the model, a laboratory scale reactor was studied, and data were collected to then verify the correct working of the model.