1. Thermodynamic Vapor-Liquid Equilibrium (VLE)
For a multicomponent mixture at temperature \(T\) and pressure \(P\), phase equilibrium is governed by the equality of chemical fugacities \(\hat{f}_i\) for every component in vapor and liquid phases:
\[ \hat{f}_i^V(T, P, y) = \hat{f}_i^L(T, P, x) \quad \implies \quad y_i \phi_i^V(T, P, y) = x_i \phi_i^L(T, P, x) \]
The equilibrium ratio (K-value) is defined as:
\[ K_i = \frac{y_i}{x_i} = \frac{\phi_i^L(T, P, x)}{\phi_i^V(T, P, y)} \]
Fugacity coefficients \(\phi_i^V\) and \(\phi_i^L\) are computed from the cubic Peng-Robinson Equation of State (PR-EOS).
2. The Retrograde Condensation Phenomenon
Unlike pure substances whose vapor and liquid curves coincide into a single vapor pressure line terminating at the critical point, multicomponent mixtures form a broad two-phase region bounded by bubble and dew point curves. In the retrograde region—between the mixture critical temperature (\(T_c\)) and the cricondentherm (\(T_{cct}\))—an isothermal reduction in pressure induces condensation rather than vaporization. This counter-intuitive behavior is responsible for heavy liquid dropout when high-pressure reservoir gas expands through wellhead chokes or long-distance pipelines.
3. Key Phase Envelope Boundary Coordinates
- Critical Point (\(T_c, P_c\)): The unique state where vapor and liquid properties become completely indistinguishable (\(K_i = 1\) for all components).
- Cricondenbar (\(P_{ccb}\)): The maximum pressure above which no liquid can form at any temperature, regardless of cooling.
- Cricondentherm (\(T_{cct}\)): The maximum temperature above which no liquid phase can exist at any pressure, representing the absolute hydrocarbon dew point limit of the gas.