Retrograde Condensation

Directions

This simulation shows the pressure–temperature (P–T) phase envelope of a fixed-composition binary mixture (70 mol % methane, 30 mol % n-heptane), computed with the Peng–Robinson equation of state. In the pink area in the pressure–temperature plot, retrograde condensation occurs — that is, when the pressure is lowered at constant temperature, liquid condenses.

Drag the vertical dashed line left or right (or use the Temperature slider) to choose an isotherm.
Drag the filled circle up or down along that line (or use the Pressure slider) to change the pressure at fixed temperature.
The panel on the right reports the phase state, the liquid fraction, and (when two phases are present) the methane mole fraction in each phase. The small cylinder sketches the liquid (blue, bottom) and vapor (top) volumes in a constant-composition PVT cell.
The small plot shows liquid volume fraction versus pressure along the current isotherm — watch how its shape changes as you move the temperature slider through the shaded band.
Choose a temperature inside the shaded pink band (between the critical point and the cricondentherm) and press Animate depressurization. Starting from single-phase vapor at high pressure, watch liquid appear as pressure falls, pass through a maximum, and then disappear again — all without ever crossing a bubble-point curve. This is retrograde condensation.
For comparison, move the temperature below the critical point: the same isothermal depressurization now shows the ordinary behavior — a single dew point, followed by a liquid fraction that decreases monotonically to zero.

Details

Retrograde condensation For a mixture of two or more components, the dew-point curve on a P–T diagram extends to temperatures above the mixture's critical temperature, out to the cricondentherm — the highest temperature at which two phases can coexist. At any temperature between the critical temperature and the cricondentherm, a vertical (constant-T) line crosses the dew curve twice: once at high pressure and once at low pressure. Between those two dew points the mixture is two-phase.

Consider an isothermal depressurization starting as a single-phase vapor above the upper dew point. As pressure falls, the mixture crosses the upper (retrograde) dew point and liquid begins to condense — even though the pressure is decreasing, which is the opposite of ordinary intuition. The liquid volume fraction rises, reaches a maximum, and then falls back to zero at the lower dew point, after which the system is single-phase vapor again. This behavior, unique to multicomponent mixtures, is called isothermal retrograde condensation.

Key points on the envelope

Cricondentherm — highest temperature at which liquid and vapor can coexist (on the dew curve).
Cricondenbar — highest pressure at which liquid and vapor can coexist.
Critical point (T_c, P_c) — bubble and dew curves meet; liquid and vapor become identical.

Peng–Robinson equation of state

\[ P = \frac{RT}{V-b} - \frac{a\alpha}{V(V+b) + b(V-b)} \] \[ a_i = 0.45724\,\frac{R^2 T_{c,i}^2}{P_{c,i}}, \qquad b_i = 0.07780\,\frac{R T_{c,i}}{P_{c,i}} \] \[ \alpha_i(T) = \Big[1 + \kappa_i\big(1-\sqrt{T/T_{c,i}}\big)\Big]^2, \qquad \kappa_i = 0.37464 + 1.54226\,\omega_i - 0.26992\,\omega_i^2 \]

Mixing rules and fugacity coefficient (van der Waals one-fluid, k_ij = 0):

\[ a_{mix} = \sum_i \sum_j x_i x_j \sqrt{a_i \alpha_i \, a_j \alpha_j}\,(1-k_{ij}), \qquad b_{mix} = \sum_i x_i b_i \]

\[ \ln \hat\phi_i = \frac{b_i}{b_{mix}}(Z-1) - \ln(Z-B) - \frac{A}{2\sqrt{2}\,B}\left(\frac{2\sum_j x_j\sqrt{a_i\alpha_i\,a_j\alpha_j}(1-k_{ij})}{a_{mix}} - \frac{b_i}{b_{mix}}\right) \ln\!\left(\frac{Z+(1+\sqrt2)B}{Z+(1-\sqrt2)B}\right) \]

\[ A = \frac{a_{mix}P}{R^2T^2}, \qquad B = \frac{b_{mix}P}{RT}, \qquad K_i = \frac{\hat\phi_i^{\,L}(x)}{\hat\phi_i^{\,V}(y)} \]

Isothermal–isobaric flash (Rachford–Rice), binary case For a binary feed with overall mole fractions $z_1,z_2$, vapor fraction $V$ satisfies $\sum_i z_i(K_i-1)/[1+V(K_i-1)] = 0$, which for two components reduces to a closed-form expression:

\[ V = \frac{-\big[z_1(K_1-1) + z_2(K_2-1)\big]}{(K_1-1)(K_2-1)}, \qquad x_i = \frac{z_i}{1+V(K_i-1)}, \qquad y_i = K_i x_i \]

The simulation iterates this flash (updating $K_i$ from the Peng–Robinson fugacity coefficients each pass) at whatever temperature and pressure you select, so every liquid fraction and phase composition shown is computed directly from the equation of state — not read from a stored table.

Component constants used

Methane: T_c = 190.6 K, P_c = 46.0 bar, ω = 0.011
n-Heptane: T_c = 540.2 K, P_c = 27.4 bar, ω = 0.351

Computed for this mixture (z₁ = 0.70): critical point, cricondentherm, and cricondenbar values are shown once the diagram loads.

About

This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by John L. Falconer using Claude AI. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988). Address any questions or comments to LearnChemE@gmail.com.