Thermodynamics — Equations of State

Cubic EoS (Peng-Robinson, SRK) for hydrocarbons/light gases and activity-coefficient models (NRTL, UNIQUAC, electrolyte-NRTL) for polar/non-ideal liquid mixtures — selected per `thermo_package` on the flowsheet schema.

thermodynamicseosnrtlpeng-robinson

Concept

Two families, picked per-flowsheet via thermo_package. Cubic EoS (Peng-Robinson, SRK) model the whole fluid — vapor and liquid — from one equation, good for hydrocarbons/light gases across pressure. Activity-coefficient models (NRTL, UNIQUAC) instead correct an ideal-vapor assumption with a liquid non-ideality factor γᵢ, tuned to real VLE data — the right tool for polar/hydrogen-bonding mixtures like ethanol-water.

The math

Show the governing equations

P = \frac{RT}{V-b} - \frac{a\,\alpha(T)}{V(V+b)+b(V-b)} \quad \text{(Peng-Robinson)}

\ln\gamma_i = \frac{\sum_j \tau_{ji}G_{ji}x_j}{\sum_k G_{ki}x_k} + \sum_j\frac{x_jG_{ij}}{\sum_k G_{kj}x_k}\left(\tau_{ij}-\frac{\sum_m x_m\tau_{mj}G_{mj}}{\sum_k G_{kj}x_k}\right)\ \text{(NRTL)}

K_i = \frac{\gamma_i P_i^{sat}}{P} \quad \text{(activity-coefficient K-value)}

Execution

Failure codes

SPEC_THERMODYNAMICALLY_IMPOSSIBLENRTL/UNIQUAC selected for a component pair with no pinned binary interaction parameters (only ethanol-water is pinned) — the server auto-coerces to Peng-Robinson and attaches a warning rather than crashing.

FLASH_NO_SOLUTIONRachford-Rice found no physically valid vapor fraction in [0,1] at the given T/P/composition.

Launch in MaximaLabs Workspace

Try it live

NRTL VLE curve

Live T-xy diagram — ethanol/water, NRTL, 1 atm

Computed on load by the same NRTL gamma-phi flash the solver runs — including the minimum-boiling ethanol-water azeotrope at ~x_ethanol ≈ 0.89.