Phase Envelope

Overview

A phase envelope (or pressure-temperature diagram) maps the boundary between single-phase and two-phase regions for a given composition. It consists of the bubble point curve and the dew point curve, which meet at the critical point.

The phase envelope is essential for:

Fluid classification — oil, gas condensate, volatile oil, dry gas
Process design — separator conditions, pipeline operating envelope
Reservoir management — understanding phase changes during depletion
Flow assurance — avoiding two-phase flow in unexpected locations

Anatomy of a Phase Envelope

                    ▲ Pressure
                    │
                    │           Cricondenbar
                    │          ●━━━━━━━━━━━●
                    │        ╱               ╲
                    │      ╱   Single Phase    ╲
                    │     ╱      Liquid          ╲
                    │    ╱                        ╲  Dew Point
                    │   ╱ Bubble Point              ╲  Curve
                    │  ╱    Curve            ●       ╲
                    │ ╱               Critical Point    ╲
                    │╱                                    ╲
                    │         Two-Phase Region              ╲
                    │         (Vapor + Liquid)                ╲
                    │                                          ╲
                    │                            Single Phase    ╲
                    │                              Vapor          ●
                    │                                    Cricondentherm
                    └──────────────────────────────────────────────▶ Temperature

Key Points

Feature	Definition	Significance
Critical point	Where bubble and dew curves meet	Liquid and vapor become identical
Cricondenbar	Maximum pressure on the envelope	Above this pressure, always single phase
Cricondentherm	Maximum temperature on the envelope	Above this temperature, always single phase
Quality lines	Constant vapor fraction inside envelope	Show how much vapor exists at given P, T

Fluid Classification

The shape of the phase envelope and the location of reservoir conditions relative to the critical point determine the fluid type:

Fluid Type	Reservoir Conditions	Critical Point Position
Black oil	$T_{res} \ll T_c$ , far left of critical	Low GOR, shrinkage oil
Volatile oil	$T_{res}$ near $T_c$ , just left	High GOR, significant shrinkage
Gas condensate	$T_{res}$ just right of $T_c$	Retrograde condensation occurs
Wet gas	$T_{res} > T_{ct}$ at reservoir, but separator in two-phase	Surface liquid recovery
Dry gas	$T_{res} > T_{ct}$ , separator also single phase	No liquid at any condition

Retrograde Condensation

For gas condensates ( $T_c < T_{res} < T_{ct}$ ), pressure reduction causes liquid to form — the opposite of normal vaporization behavior. This "retrograde" phenomenon occurs because:

At reservoir temperature, the fluid is above the critical point (single-phase gas)
As pressure drops during depletion, the mixture enters the two-phase region from the dew point side
Liquid drops out in the reservoir, reducing gas productivity

Construction Methods

Saturation Point Continuation

The phase envelope is traced by solving a series of connected saturation point problems. Starting from a known point (e.g., a bubble point at low pressure), the algorithm:

Takes a step along the envelope (incrementing pressure or temperature)
Solves for the other variable (temperature or pressure) at the saturation condition
Records the point and continues

Mathematical Formulation

At any saturation point, the following system must be satisfied simultaneously:

For bubble points ( $V = 0$ ): $\sum_{i=1}^{N} K_i z_i - 1 = 0$

For dew points ( $V = 1$ ): $\sum_{i=1}^{N} \frac{z_i}{K_i} - 1 = 0$

Combined with the EoS equations for K-values: $\ln K_i = \ln \hat{\phi}_i^L - \ln \hat{\phi}_i^V$

Compositional Effects

Effect of C7+ Fraction

Heavier compositions shift the envelope:

Higher cricondenbar (larger two-phase region)
Higher critical temperature
Wider envelope overall

Effect of Non-Hydrocarbons

Component	Effect on Envelope
CO2	Shrinks envelope, lowers cricondenbar
N2	Shifts envelope to lower temperatures
H2S	Complex — can expand or contract depending on concentration

Practical Applications

Separator Optimization

The phase envelope shows which P-T conditions produce two phases. Optimal separator conditions lie within the two-phase region where maximum liquid recovery occurs.

Pipeline Design

Operating conditions must be known relative to the phase envelope to:

Predict liquid holdup in gas pipelines
Size slug catchers
Design hydrate prevention strategies

Reservoir Depletion Path

Plotting the depletion path (pressure decline at reservoir temperature) on the phase envelope shows when the fluid will enter the two-phase region.

Limitations

Limitation	Description
Two-phase only	Standard envelope does not show three-phase (VLLE) regions
Composition-specific	Any change in composition requires a new envelope
Near-critical accuracy	Convergence can be difficult near the critical point
C7+ sensitivity	Results are highly dependent on C7+ characterization

EoS Overview — Choosing PR vs. SRK for phase behavior
Flash Calculations — Computing phase splits within the envelope
Peng-Robinson EoS — The underlying equation for envelope construction
C7+ Characterization — Impact of heavy fractions on the envelope

References

Whitson, C.H. and Brule, M.R. (2000). Phase Behavior. SPE Monograph Vol. 20.
Michelsen, M.L. (1980). "Calculation of Phase Envelopes and Critical Points for Multicomponent Mixtures." Fluid Phase Equilibria, 4(1-2), 1-10.
Pedersen, K.S. and Christensen, P.L. (2007). Phase Behavior of Petroleum Reservoir Fluids. CRC Press.
Ahmed, T. (2016). Equations of State and PVT Analysis, 2nd Edition. Gulf Professional Publishing.
Danesh, A. (1998). PVT and Phase Behaviour of Petroleum Reservoir Fluids. Elsevier.