K-values (Equilibrium Ratios)

PVT Analysis of Reservoir Fluids › 11. K-values (Equilibrium Ratios)

Reviewed by Coretest reservoir-fluids engineers · Updated 21 June 2026

Purpose↑ Contents

The K-value test quantifies, component by component, how a gas condensate fluid partitions between the coexisting vapor and liquid phases at a defined pressure and temperature. The equilibrium ratio \( K_i \) (also called the equilibrium constant, distribution coefficient, or split factor) is the single most important closure data set for vapor-liquid equilibrium (VLE) calculations in compositional reservoir and surface-process modeling. It answers concrete production questions: at a given separator stage, what fraction of each component (especially the intermediates C3 to C6+ and the heavy C7+ fraction that constitute condensate value) ends up in the sales gas versus the liquid drop-out; how much retrograde condensate forms in the near-wellbore region as reservoir pressure declines below the dew point; what the optimum separator pressure/temperature train is to maximize stock-tank liquid recovery; and how the C7+ characterization and binary interaction parameters of an equation of state (EOS) must be tuned so the simulator reproduces measured phase splits. Measured K-values are the primary regression target when calibrating a Peng-Robinson (PR) or Soave-Redlich-Kwong (SRK) EOS for a compositional simulation of a gas-condensate reservoir.

Physical principle↑ Contents

At thermodynamic equilibrium the vapor and liquid phases of a multicomponent mixture coexist with no net mass transfer of any component between them. The rigorous equilibrium criterion is equality of component fugacities in each phase:

$$f_i^v = f_i^l \quad \text{for every component } i$$

where \( f_i^v \) and \( f_i^l \) are the fugacities (units of pressure, e.g. bar or psia) of component \( i \) in the vapor and liquid phases respectively. Expressing fugacity through fugacity coefficients, \( f_i^v = y_i\,\phi_i^v\,p \) and \( f_i^l = x_i\,\phi_i^l\,p \), where \( y_i \) and \( x_i \) are the vapor and liquid mole fractions, \( \phi_i^v \) and \( \phi_i^l \) are the dimensionless fugacity coefficients computed from the EOS, and \( p \) is the system pressure. Substituting into the equality of fugacities gives the thermodynamic definition of the equilibrium ratio:

$$K_i = \frac{y_i}{x_i} = \frac{\phi_i^l}{\phi_i^v}$$

So \( K_i \) is the experimentally accessible ratio of mole fractions, while \( \phi_i^l / \phi_i^v \) is the EOS-predicted counterpart that regression drives toward the measured value. \( K_i \) is dimensionless. \( K_i > 1 \) means component \( i \) favors the vapor phase (light components such as N2, C1, C2); \( K_i < 1 \) means it favors the liquid (heavy components C7+); \( K_i = 1 \) defines the component that does not preferentially partition. At the convergence pressure all \( K_i \) approach unity.

The overall mass-balance closure that ties \( K_i \) to the feed (the Rachford-Rice equation) is:

$$\sum_i \frac{z_i\,(K_i - 1)}{1 + \beta\,(K_i - 1)} = 0$$

where \( z_i \) is the overall (feed) mole fraction of component \( i \), and \( \beta = n_v / n \) is the vapor mole fraction of the total system (moles of vapor divided by total moles, also written \( V/F \)). Solving this for \( \beta \) with the measured or EOS \( K_i \) yields the phase split; phase compositions then follow from \( x_i = z_i / (1 + \beta(K_i - 1)) \) and \( y_i = K_i\,x_i \), with the constraints \( \sum x_i = 1 \) and \( \sum y_i = 1 \).

Useful low-pressure idealization: for an ideal system \( K_i = p_i^{sat}(T) / p \), where \( p_i^{sat} \) is the pure-component vapor pressure. This holds only at low pressure and large component separation; near the critical/convergence region the rigorous fugacity-based definition is mandatory because pressure and composition strongly couple. K-values are commonly correlated against pressure at fixed \( T \) using the Wilson approximation \( K_i = \frac{p_{ci}}{p}\,\exp\!\left[5.37\,(1 + \omega_i)\,\left(1 - \frac{T_{ci}}{T}\right)\right] \) as a starting estimate, where \( p_{ci} \), \( T_{ci} \) are the critical pressure and temperature and \( \omega_i \) the acentric factor of component \( i \); this is only an initial guess and is replaced by measured values.

Apparatus & conditions↑ Contents

A windowed (visual) high-pressure, high-temperature PVT cell is used, typically a mercury-free piston-type or motorized variable-volume cell rated to the reservoir pressure and temperature (commonly to about 1000 to 1400 bar and up to roughly 200 C, depending on the rig). The cell is housed in an air bath or oil jacket held isothermal at reservoir temperature within +/-0.1 C. The cell is equipped with a magnetic stirrer or a rocking/rotating mechanism for rapid mass-transfer-driven equilibration, calibrated quartz pressure transducers, and dedicated vapor (top) and liquid (bottom) sampling ports so each equilibrated phase can be withdrawn without cross-contamination. Phase compositions are determined offline by gas chromatography (GC): an extended-analysis GC with FID (and a TCD channel for N2/CO2/H2S where present) carried to C36+ or beyond, or a combination of GC plus a low-pressure flash/blowdown train so the heavy liquid can be quantitatively analyzed.

The test is run on a recombined gas-condensate fluid prepared to the reservoir GOR from validated separator gas and separator liquid samples. The controlled variables are pressure and temperature; the held constant is normally temperature (reservoir \( T \)), while pressure is set to one or more target levels of interest (for example a sequence of pressures spanning from above the dew point down through the retrograde region). At each \( (p, T) \) state the cell volume is whatever the closed system adopts at equilibrium; the system overall composition \( z_i \) is fixed by the recombination.

Procedure↑ Contents

1. Charge the PVT cell with the validated recombined gas-condensate fluid at a pressure above the dew point and bring the cell to reservoir temperature; confirm the charge mass and overall composition \( z_i \).
2. Set the target pressure \( p \) and temperature \( T \) for the first equilibrium state, adjusting cell volume (piston position) to reach the desired pressure.
3. Agitate the contents (stir or rock the cell) vigorously to promote interphase mass transfer and accelerate approach to equilibrium.
4. Stop agitation and allow the phases to settle and separate by gravity until a sharp, stable vapor-liquid interface is visible through the window and the cell pressure is constant with time; record the equilibration period (typically hours, longer near the dew point and for heavy fluids).
5. Confirm equilibrium by checking that pressure is stable at fixed volume and, where instrumented, that phase volumes/levels and the interface position are no longer changing.
6. Withdraw a representative sample of the equilibrium vapor phase through the top port at constant pressure (compensate volume with the piston/displacement fluid to hold \( p \) essentially constant during sampling) and route it to the GC analytical train.
7. Withdraw a representative sample of the equilibrium liquid phase through the bottom port at constant pressure, taking care to draw only liquid (avoid entraining vapor near the interface), and route it to the analytical train (single-stage or multi-stage flash to atmospheric, with all flashed gas and residual liquid recombined analytically).
8. Analyze each phase by gas chromatography to obtain the full molar composition \( y_i \) of the vapor and \( x_i \) of the liquid through C7+ (extended to the heaviest reported pseudo-component), and normalize each composition to sum to unity.
9. Compute \( K_i = y_i / x_i \) for every component.
10. Check internal consistency: verify the component material balance against the known feed \( z_i \) and \( \beta \), and inspect the \( K_i \) versus carbon-number trend for monotonic, physically sensible behavior.
11. Repeat steps 2 through 10 at the other target pressures (and, if specified, temperatures) to map the \( K_i \) pressure (and temperature) dependence.
12. Tabulate results and pass the \( K_i \), phase compositions, and phase split to the EOS regression workflow.

Measured parameters↑ Contents

• System pressure \( p \) and temperature \( T \) of each equilibrium state.
• Equilibration time and interface stability/observations at each state.
• Vapor-phase molar composition \( y_i \) for all components/pseudo-components (GC).
• Liquid-phase molar composition \( x_i \) for all components/pseudo-components (GC).
• Where the rig allows: phase volumes (vapor volume and liquid volume in the cell) and the withdrawn sample quantities used to close the material balance.
• Densities and molar masses of the C7+ (or heaviest) fraction of each phase, from the analytical train, used in phase property checks.

Calculated / derived parameters↑ Contents

• Equilibrium ratio of each component: \( K_i = y_i / x_i \) (dimensionless).
• Vapor mole fraction (phase split) \( \beta = n_v / n \), obtained by solving the Rachford-Rice equation \( \sum_i \frac{z_i\,(K_i - 1)}{1 + \beta\,(K_i - 1)} = 0 \) for \( 0 \le \beta \le 1 \).
• Back-calculated phase compositions for consistency: \( x_i = z_i / (1 + \beta(K_i - 1)) \) and \( y_i = K_i\,x_i \).
• Gas-liquid split / molar ratio \( n_v / n_l = \beta / (1 - \beta) \).
• Convergence pressure estimate: the pressure at which the \( K_i \) versus pressure curves extrapolate to a common \( K = 1 \) (used to constrain correlations).
• EOS-consistency residuals: the difference between measured \( K_i \) and EOS-predicted \( \phi_i^l/\phi_i^v \), which is the objective function minimized during regression of binary interaction parameters and C7+ properties.

Reporting & typical curves↑ Contents

The deliverables are: a table of \( K_i \) for every component at each \( (p, T) \) state; the corresponding equilibrium vapor (\( y_i \)) and liquid (\( x_i \)) compositions; the phase split \( \beta \) (or gas-liquid molar ratio); and the data package formatted for EOS tuning. The signature plots are:

• \( \log K_i \) versus pressure at fixed temperature, one curve per component. Light components (C1, N2) plot high (\( K > 1 \)) and decline gently with pressure; heavy components plot low (\( K \ll 1 \)) and rise with pressure; all curves converge toward \( K = 1 \) at the convergence pressure. The crossing/convergence behavior is read to validate the data and to identify the convergence pressure.
• \( \log K_i \) versus carbon number (or versus \( 1/T_{bi} \) or component property) at fixed \( p \) and \( T \), which should be a smooth, monotonically decreasing trend; kinks or non-monotonic points flag sampling or analytical errors.
• Phase split \( \beta \) versus pressure, read to locate the dew point (\( \beta \to 1 \) from the two-phase side) and to quantify retrograde liquid build-up.

These curves are read jointly: a well-behaved data set shows smooth \( K_i \) versus pressure curves, monotonic \( K_i \) versus carbon-number trends, and a consistent convergence pressure. Departures indicate non-equilibrium sampling, phase carryover, or GC error.

Practical notes & pitfalls↑ Contents

• Sampling is the dominant error source. Drawing the vapor sample while liquid is entrained, or the liquid sample while gas is entrained near the interface, corrupts \( y_i \) and \( x_i \) directly and therefore \( K_i \). Sample from well clear of the interface and at constant pressure; isobaric withdrawal (piston compensation) prevents pressure drop that would re-equilibrate the system mid-sampling.
• Equilibration time must be sufficient and verified, not assumed. Gas condensates near the dew point and fluids with heavy ends equilibrate slowly; insufficient settling leaves a non-equilibrium split and biases \( K_i \) toward unity. Confirm by constant pressure at fixed volume and a stationary interface.
• Use mercury-free (piston-type) cells where possible. Mercury contamination biases GC and is an HSE hazard; if a mercury cell is used, guard against carryover into the analytical line.
• Account for dead volume in sampling lines, valves, and the GC sample loop. Unswept dead volume holds a previous, non-representative aliquot; purge sample lines thoroughly between phases and between pressure stages to avoid cross-contamination of the next sample.
• Extended C7+ analysis matters. Truncating the GC too early under-resolves the heavy fraction, which carries the lowest K-values and the most EOS-sensitive information; carry the analysis as far into the heavy end as the instrument allows and characterize the C7+ density and molar mass.
• Close the material balance. Always check that the measured \( y_i \), \( x_i \), and \( \beta \) reproduce the known feed \( z_i \); a failed balance is a red flag for sampling loss or analytical drift before the \( K_i \) are passed to regression.
• Maintain isothermal, isobaric stability during and after sampling; thermal gradients in the bath or pressure drift cause partial re-equilibration and smear the result.
• Near the critical/convergence region K-values become extremely composition-sensitive and the ideal \( K_i = p_i^{sat}/p \) approximation fails entirely; rely on the fugacity-based definition and treat measured near-convergence points with extra replication.