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. 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 TMC-1-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 two-dimensional (2D) turbulent mixing. 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.