Phase relation for mantle?
Perple_X (http://www.perplex.ethz.ch/) is software designed to do exactly that.

It has thermodynamic and mineral property databases for phases in interest. This is pretty much automation of method 3 given by the other answer.

In short, the way it works: you input your bulk composition, pressure, and temperature, and it spits out the phase relations.

A bit of warning: this software is very poorly documented with many tutorials and guides referring to older version that don't work exactly like the new one. I recommend going on their discussion forum which is very active, and the developer himself is commonly there. He is usually very responsive and can fix bugs pretty much on the spot (time-zone constraints permitting).