A time dependent model of hydrogen hydrodynamic escape powered by solar EUV flux and solar wind and, accounting for oxygen frictional escape, has been implemented in primitive Venus conditions The model is. constrained by the present Ne-20/Ne-22 and Ar-36/Ar-38 ratios in Venus atmosphere. It suggests that the net total amount of water delivered to the planet during accretion (approximate to 10-100 Myr) is not in excess of the content of approximate to 5 Terrestrial Oceans (5 TO). In our preferred scenario, 60% of the oxygen (3 TO) is left behind the hydrogen during the first 100 Myr. From a comparison with Earth's case, we suggest that hydrodynamic escape has dried up Venus atmosphere early in its history (approximate to 70 Myr), triggering the crystallization of the magma ocean, and leaving no available water in the atmosphere to condense out and form an Earth-size water ocean On. the contrary, Earth, possibly endowed with more water, and subject to a weaker hydrodynamic escape, would have remained wet after the crystallization of its magma ocean. We suggest that the oxygen left behind the escaping hydrogen during the main hydrodynamic phase on Venus has been dissolved in the magma ocean, and lost through oxidation. In the proposed scenario, the dense Venus CO2 atmosphere doesn't result from an initial episode of runaway (or moist) greenhouse, but has been formed during the crystallization of the magma ocean, by progressive exsolution of carbon dioxide, at a time when the atmospheric partial pressure of water was of a few hundred bar. In the subsequent period, from approximate to 100 to approximate to 500 Myr, the hydrogen of the water delivered by comets may have been removed by continuing thermal escape, resulting at 500 Myr in a water global equivalent layer (GEL) of a few meters depth (or less), probably under the form of water vapor in the atmosphere, and a molecular oxygen atmosphere of approximate to 10 bar or so. At later times, pick-up ion escape may have removed most of the remaining water, and led to the present D/H atmospheric enhancement factor of 150. The approximate to 10 bar of oxygen may have been absorbed by crustal oxidation