Formation and evolution of water in the Solar System and the origin of water on Earth constitute one of the most interesting questions in astronomy. The prevailing hypothesis for the origin of water on Earth is by delivery through water-rich small Solar system bodies. In this paper, the isotopic and chemical evolution of water during the early history of the solar nebula, before the onset of planetesimal formation, is studied. A gas-grain chemical model that includes multiply-deuterated species and nuclear spin-states is combined with a steady-state solar nebula model. To calculate initial abundances, we simulated 1 Myr of evolution of a cold and dark TMC1-like prestellar core. Two time-dependent chemical models of the solar nebula are calculated over 1 Myr: (1) a laminar model and (2) a model with 2D turbulent mixing. We find that the radial outward increase of the H2O D/H ratio is shallower in the chemo-dynamical nebular model compared to the laminar model. This is related to more efficient de-fractionation of HDO via rapid gas-phase processes, as the 2D mixing model allows the water ice to be transported either inward and thermally evaporated or upward and photodesorbed. The laminar model shows the Earth water D/H ratio at r ~<2.5 AU, while for the 2D chemo-dynamical model this zone is larger, r ~<9 AU. Similarly, the water D/H ratios representative of the Oort-family comets, ~2.5-10 x 10-4, are achieved within ~2-6 AU and ~2-20 AU in the laminar and the 2D model, respectively. We find that with regards to the water isotopic composition and the origin of the comets, the mixing model seems to be favored over the laminar model.
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