Carbon and others volatiles that are present in the Earth's mantle at ppm concentration levels, induce partial melting. CO2-H2O-rich melts are stable under the P-T-fO2 conditions of the Low Velocity Zone (LVZ). Recent experimental studies about the Earth mantle conductivity have shown the primordial importance of small amounts of hydrated CO2-rich melts in the geophysical signature of the LVZ. Nevertheless, the chemical composition of these melts is difficult to capture as it depends on T-P and redox state. Using Margules formalisms, we established 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. This parameterization is calibrated on crystal-liquid, redox, fluid-liquid and liquid-liquid equilibria obtained by experimental studies in the P-T range 1-10 GPa and 900-1800°C. We propose a calculation of the composition of melts produced in the oceanic LVZ as a function of age. At about 80 km depth, we show that the composition of the melts is >30 wt% SiO2 for ages <20 Ma, and comes closer to the carbonatitic terms for older lithosphere. Besides lateral chemical variations, our model calculates the melt composition along an oceanic ridge adiabat, predicting an abrupt compositional transition between a H2O-rich carbonatitic melt and a carbonated silicate melt, between 140 km and 160 km. With the distance to the ridge, this transition is shifted to lower depths between 70 and 90 km. We propose a chemical mapping of the melt composition (and of the degree of partial melting) as a function of the distance to the ridge and of the depth. The chemical variations between carbonated and silicated melts may be related to the geophysical observations.