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 ∂ ρ = β ⁢ P ρ + Ω . The second departure point satisfies the equation α ⁡ ( ∂ P ∂ ρ - R ) + ( 1 - α ) ⁢ ( ∂ P ∂ ρ ) ⁢ | 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. When executed by the processor, the thermodynamic process simulation application invokes the thermodynamic equation of state application to determine a result based on the density root.