The link between volatiles and mantle melting has so far been illuminated by experiments revealing punctually, at a given P-T condition and under a specific chemical system, properties such as solubility laws, redox equilibria, and phase equilibria. Our aim is to establish a multi-component model describing the Gibbs free energy of melt produced by mantle melting in presence of CO2-H2O: that are carbonatite-carbonated melt-nephilinite-basanite and basalt with increasing degree of partial melting. Near solidus melts are dominated by carbonate-rich compositions, evolving towards basaltic compositions at higher temperatures. However, this carbonate-silicate transition is complex, abrupt, and dependent on temperature, pressure and the chemical composition of the system. In order to simulate partial melting in a variety of mantle conditions, we established a parameterization of the mixing properties allowing the complex activity-composition relationships for multi-component hydrated carbonated melts to be accounted for. Using the Margules formalism, this parameterization is calibrated on crystal-liquid, graphite-liquid, fluid-liquid and liquid-liquid equilibria obtained by experimental studies in the P-T range 1-10 GPa and 900-1800°C. We so far adjusted the activity of the SiO2 and CO2 melt components, which constitutes the main part of the silicated and carbonated frameworks. The SiO2-CO2 interaction reveals a strong non-ideality requiring a strongly asymetric Margules formulation. We also determined the standard thermodynamic properties for the CO2 melt component and we have refined the standard volume properties for liquid SiO2.