Removal of carbon dioxide to upgrading biogas is possible by cryogenics and frost formation. In this work, it is targeted removing carbon dioxide by frost deposition (physical transition from gas to solid state) at low pressure and temperature from biogas, as well as assessing the impact of mass flow rate, temperature and the initial CO2 content in biogas on the carbon dioxide removal process. The Solid-Gas phase equilibrium between CH4 and CO2 is presented. It is followed by a sensitivity study of CO2 deposition on a flat plate and the assessment of different geometries of the heat exchanger generating frost. The global process including CO2 removal and biomethane liquefaction is simulated in AspenTech tools that are linked to a specific module modelling frost formation phenomenon. This module is coded in Dymola (Modelica language). Different operating modes of the heat exchanger are compared: thermal inertia or by direct cooling by nitrogen gas obtained after liquefaction of the biomethane. The temperature of the heat exchanger increases as CO2 deposits. Results show that cryogenic CO2 frost formation can be used for simultaneous liquefaction and upgrading of methane at 97% vol. minimum of purity and a reduction of cooling cycles on site by cold recovery from frost. This implies a reduction of energy intensity to remove carbon dioxide compared to conventional cryogenic technologies.