A key step in phase equilibrium calculations is determining if, in fac
t, multiple phases are present. Reliably solving the phase stability a
nd, ultimately the phase equilibrium problem, is a significant challen
ge for high pressure vapor/liquid, liquid/liquid and vapor/liquid/liqu
id equilibrium. We present the first general-purpose computational met
hod, applicable to any arbitrary equation of state or activity coeffic
ient model, that can mathematically guarantee a correct solution to th
e phase stability problem. In this paper, we demonstrate the use of th
is new method, which uses techniques from interval mathematics, for th
e van der Waals equation of state to determine liquid/liquid and liqui
d/vapor phase stability for a variety of representative systems. Speci
fically, we describe and test interval methods for phase stability com
putations for binary mixtures that exhibit Type I and Type II behavior
, as well as for a relatively simple ternary mixture. This shows that
interval techniques can find with absolute certainty all stationary po
ints, and thus solve the phase stability problem with complete reliabi
lity.