Abstract: A system for thermodynamic modeling is provided. The system comprises a computer having a processor, a thermodynamic process simulation application, and a thermodynamic equation of state application. When executed by the processor, the thermodynamic equation of state application determines a density root based on a first and second point of departure from an equation of state and based on a first and a second extrapolation equation. The first departure point satisfies the equation ? P ? ? = ? ? P ? + ? . The second departure point satisfies the equation ? ? ( ? P ? ? - R ) + ( 1 - ? ) ? ( ? P ? ? ) ? | dp ? ? 1 = 0. The density root is determined as a pseudo-density in a phase two when the specified pressure is greater than the second departure point pressure and in a phase one when the specified pressure is less than the first departure point pressure.