A new method for modeling phase changes in multistream heat exchangers (MHEXs) is presented. In many industrially relevant applications, streams in MHEXs will undergo phase changes between their inlet and outlet. In this model, nonsmooth equations are formulated which properly account for the existence or nonexistence of phases in heat integration, flash and physical property calculations in a MHEX. These new equations are used in conjunction with a recently developed nonsmooth model for MHEXs to create a compact equation system which can be used for the simulation and design of complex processes. Notably, this formulation does not involve the solution of a difficult optimization problem, since it avoids the use of either disjunctive or complementarity constraints. The robustness and functionality of the new formulation is illustrated through several simulations of the well-known Poly Refrigerant Integrated Cycle Operations (PRICO) process for liquefied natural gas production.