The phase equilibrium behavior of a basic statistical mechanical model of a binary mixture of water and a simple fluid are investigated. For water we use a primitive model which incorporates no attractive forces other than hydrogen bonds within a hard-sphere core, and the simple fluid is modeled by a fluid of hard spheres with an attractive mean-field term. The qualitative behavior of the phase equilibria and P-T critical lines of this model are calculated using an accurate theoretical equation of state for primitive water obtained in analytical form using the Wertheim thermodynamic perturbation : theory, for a range of values,of the mixture’s two underlying parameters, the hard-sphere size ratio and the mean field strength. The model exhibits type IIId and type IV* phase behavior of three qualitatively different types, characterized by the existence of either one or two three-phase lines. The model exhibits a range of phenomena, including tricritical points and double critical end points. The implications of the model results for corresponding real fluid mixtures are also discussed.