fluid_properties · eos
Wilson K-Value (Equilibrium Ratio)
Ki = (Pci/P) × exp[5.37(1+ωi)(1−Tci/T)]
click formula to derive ↑
Inputs
°F
psi
°F
psi
—
Description
Computes the vapor-liquid equilibrium ratio (K-value) for a single component using Wilson's (1968) correlation — a closed-form approximation derived from Raoult's and Dalton's laws plus a generalized vapor-pressure fit using the acentric factor. K-values are the building block of compositional flash and bubble/dew-point calculations: Ki = yi/xi, the ratio of a component's vapor-phase to liquid-phase mole fraction at equilibrium.
Variables
| Symbol | Unit | Description |
|---|---|---|
| Ki | — | Equilibrium Ratio (K-Value) |
| T | °F | Temperature at which the equilibrium ratio is evaluated. Converted internally to absolute temperature (Kelvin) — the correlation is only valid using an absolute temperature scale. |
| P | psi | System pressure at which the equilibrium ratio is evaluated. Wilson's correlation is a low/moderate-pressure, away-from-critical approximation — see limitations. |
| Tci | °F | Critical temperature of the component, from a physical-property table (e.g., Reid, Prausnitz & Poling). Default shown is ethane (Tc = 305.32 K = 32.17°C). |
| Pci | psi | Critical pressure of the component, from a physical-property table. Default shown is ethane (Pc = 4884 kPa = 708.3 psia). |
| ω | — | Pitzer's acentric factor for the component, from a physical-property table. Default shown is ethane (ω = 0.099). Most hydrocarbons of interest fall between 0 (methane) and ~0.6 (heavy paraffins). |
Assumptions
- Ideal solution and ideal gas behavior (Raoult-Dalton basis) — no real-mixture fugacity corrections
- Temperature and pressure inputs are converted to absolute scale (Kelvin) internally; the equation is not valid on a relative (°C/°F) scale
- Applies to a single, well-characterized pure component or defined pseudo-component with known Tc, Pc, and ω
Limitations
- Because Ki has no compositional dependence, it ignores real-mixture non-idealities (fugacity coefficients) — accuracy degrades away from ideal-solution behavior, e.g. for highly non-ideal or strongly interacting mixtures
- Intended for low-to-moderate pressure, away from the mixture's critical point; near-critical conditions (Tr close to 1, or high Pr) are explicitly outside its design range and are flagged by the calculator
- Widely used in industry as a fast initial K-value guess to seed a rigorous EOS flash iteration, not as a final answer for high-value compositional PVT work — see bubble_point_kvalue for how it is used as a starting point for a simple two-pseudo-component flash
Use Cases
- → Flash calculation initial guess: Seed a rigorous cubic-EOS flash calculation with Wilson K-values, which converge quickly to the correct root in most well-conditioned cases.
- → Quick-look bubble/dew point screening: Estimate whether a mixture composition is single-phase or two-phase at a given P/T without running a full compositional simulator — feeds directly into bubble_point_kvalue.
- → Component volatility ranking: Compare Ki across components at the same P/T to quickly rank relative volatility in a mixture (Ki > 1 favors the vapor phase, Ki < 1 favors the liquid phase).
Related Calculations
Region Notes
Global
Wilson K-values are a standard first guess across essentially every reservoir simulator and PVT package worldwide — there is no regional variation in the method itself, only in which components/pseudo-components a given fluid characterization uses.
References
Primary source
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