The global phase diagram (GPD) of model binary mixtures of water and n-alkanols has been determined using the statistical associating fluid theory (SAFT) equation of state (EOS). Closed regions in the two-dimensional parameter space (the strength of the hydrogen bond of alkanol vs. the length of the alkanol molecule), where azeotropy and closed liquid-liquid immiscibility loops occur, have been found. When the diagram is transformed to the space of relative critical temperatures and volumes, no real aqueous mixture of alkanol lies in these regions; the disagreement is caused by the choice of parameters in this work,