Phase separation in polymers is important for many technical applications but is difficult to predict theoretically. Recently, extensive experimental studies on the miscibility of polyolefins revealed that these systems display a wider variety of mixing behavior than their chemical similarity suggests. In order to predict phase diagrams of polyolefin blends from pure component properties, we have developed a method in which small scale simulations of local interactions are combined with an analytical model for the thermodynamics, the Born-Green-Yvon lattice model. In this work, we present results for a variety of polyolefin blends and show that the new approach yields qualitatively correct results for phase separation in these blends, including the effects of varying pressure and molar mass of the components on phase separation temperatures.