Differential Liberation (DL) Test

PVT Analysis of Reservoir Fluids › 2. Differential Liberation (DL)

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

Differential Liberation, also called Differential Vaporization or Differential Gas Liberation (and historically the "differential gas-oil ratio" experiment), is the second cornerstone depletion study run on a reservoir oil sample. Together with Constant Composition Expansion it forms the backbone of the black-oil PVT report and supplies the reservoir-condition fluid properties that drive material-balance and reservoir-simulation calculations.

Purpose↑ Contents

The DL test answers a specific reservoir question: as bottomhole pressure falls below the bubble point during primary depletion, gas liberates from the oil, the gas migrates upward (becoming more mobile than the oil once it exceeds the critical gas saturation), and is effectively removed from contact with the remaining liquid. DL reproduces this in-situ process where the liberated gas continuously leaves the system, so the overall composition of the cell changes at every stage. The test quantifies how the residual reservoir oil shrinks, loses dissolved gas, changes density, and changes viscosity as pressure drops, and it characterizes the composition and volumetric behavior of the gas evolved at each stage.

The DL results are used to: - Generate the saturated-region black-oil tables: solution gas-oil ratio \( R_{sd}(p) \), differential oil formation volume factor \( B_{od}(p) \), oil density \( \rho_o(p) \), oil viscosity \( \mu_o(p) \), and gas Z-factor and gas formation volume factor \( B_g(p) \). - Provide the residual-oil basis for converting differential data to separator/flash conditions (the field-applicable \( B_o \) and \( R_s \) are obtained by combining DL with separator tests). - Tune the equation of state (EOS) for compositional simulation by matching liberated-gas volumes, compositions, and liquid shrinkage stage by stage.

Physical principle↑ Contents

DL is a non-equilibrium-composition depletion: at each pressure step the system reaches phase equilibrium, then the equilibrium gas is expelled, so the total moles and total composition of the retained system decrease monotonically. This is the thermodynamic opposite of Constant Composition Expansion, where total composition is fixed.

At every step the two coexisting phases satisfy equilibrium, expressed through the equality of component fugacities \( f_i^L = f_i^V \), which is summarized by the K-values:

$$K_i = \frac{y_i}{x_i}$$

where \( K_i \) is the equilibrium ratio of component \( i \), \( y_i \) its mole fraction in the vapor (liberated gas), and \( x_i \) its mole fraction in the liquid (remaining oil). Because the light ends partition preferentially into the gas (\( K_i \) greater than 1 for methane, nitrogen, etc.), each gas-removal step strips light components from the oil, raising the average molecular weight, the density, and the viscosity of the residual liquid.

The governing reported quantities are defined as follows.

Solution (dissolved) gas-oil ratio, differential basis:

$$R_{sd}(p) = \frac{V_{gas,sc}(\text{remaining in solution at } p)}{V_{o,residual,sc}}$$

Here \( V_{gas,sc} \) is the volume of gas still dissolved in the oil at pressure \( p \), brought to standard conditions (60 \(\text{degF}\), 14.696 \(\text{psia}\)), and \( V_{o,residual,sc} \) is the residual oil volume measured at the end of the test and corrected to standard temperature. In practice \( R_{sd} \) at any stage is computed as the total gas liberated from that stage down to atmospheric, summed and referenced to the residual oil. Units: \(\text{scf/STB}\) (or \(\text{sm}^3/\text{sm}^3\)).

Differential oil formation volume factor:

$$B_{od}(p) = \frac{V_o(p,T_{res})}{V_{o,residual,sc}}$$

where \( V_o(p,T_{res}) \) is the oil volume in the cell at stage pressure \( p \) and reservoir temperature \( T_{res} \), and \( V_{o,residual,sc} \) is the residual oil at standard conditions. \( B_{od} \) is dimensionless (\(\text{rbbl/STB}\)). Note the residual-oil denominator: this is what distinguishes the differential factor from the flash factor and is why DL data must be adjusted before field use.

Oil density:

$$\rho_o(p) = \frac{m_o}{V_o(p,T_{res})}$$

with \( m_o \) the mass of oil in the cell (from the total charged mass minus the cumulative mass of removed gas) and \( V_o \) the measured liquid volume at \( p \) and \( T_{res} \). Units: \(\text{g/cm}^3\) or \(\text{lb/ft}^3\).

Gas deviation (compressibility) factor for each liberated increment:

$$Z = \frac{pV}{nRT}$$

where \( p \) is pressure, \( V \) the gas volume in the cell, \( n \) the moles of liberated gas, \( R \) the universal gas constant, and \( T \) absolute temperature. \( Z \) links the measured cell-volume gas to its standard-condition volume and underpins \( B_g \).

Gas formation volume factor:

$$B_g = \frac{V_{gas}(p,T_{res})}{V_{gas,sc}} = \frac{Z\,T_{res}\,p_{sc}}{Z_{sc}\,T_{sc}\,p}$$

with the standard-condition \( Z_{sc} \) taken as 1.0. Units: \(\text{rcf/scf}\) or \(\text{rbbl/scf}\).

Oil viscosity \( \mu_o \) is measured directly (commonly with a rolling-ball or electromagnetic capillary viscometer integrated with the cell); if a falling/rolling-body instrument is used the working relation is \( \mu = K\,t\,(\rho_b - \rho_f) \), where \( K \) is the instrument constant, \( t \) the travel time of the body, \( \rho_b \) the body density, and \( \rho_f \) the fluid density. Units: \(\text{cP}\) (\(\text{mPa·s}\)).

Apparatus and conditions↑ Contents

• A high-pressure, high-temperature visual or blind PVT cell (windowed glass-mercury cell, or a modern mercury-free piston/floating-piston cell with a cathetometer, capacitance, or piston-position volume readout) rated above the bubble-point pressure and held at constant reservoir temperature \( T_{res} \) in an air bath or liquid bath.
• A calibrated gasometer / gas burette (or wet-test meter) at controlled conditions to measure the volume of each liberated gas increment, with provision to bring readings to standard conditions.
• A volumetric pump (positive-displacement) to control and read cell volume and pressure, and a magnetic or rocking agitation system to accelerate equilibration.
• Density measurement (cell volume plus mass balance, or an in-line densitometer such as an oscillating U-tube) and an integrated viscometer if \( \mu_o(p) \) is required.
• Gas chromatograph (and possibly residual-oil distillation) to analyze the composition of each liberated gas increment and of the final residual oil.

Held constant: temperature (\( T_{res} \) throughout). Varied: pressure, decreased in discrete steps from the bubble point to atmospheric. Removed at each step: the liberated gas (this is the defining feature versus CCE).

Procedure↑ Contents

1. Charge the cell with a representative, single-phase (above-bubble-point) oil sample, and bring it to reservoir temperature; allow thermal equilibration.
2. Raise/set the pressure to the bubble-point (saturation) pressure \( p_b \) and establish thermodynamic equilibrium; record the oil volume at \( p_b \) (this is \( V_{ob} \), the reference saturated volume).
3. Lower the pressure to the first predetermined sub-bubble-point stage by withdrawing the displacing fluid/expanding the piston, at constant temperature, so that free gas evolves.
4. Agitate and allow the system to reach equilibrium: wait until pressure and volume stabilize and the gas and liquid have fully separated. Equilibration time grows for viscous/heavy oils and near critical fluids.
5. Holding the stage pressure constant, displace all the liberated free gas out of the cell into the gasometer while keeping the oil in the cell (constant-pressure gas removal). Measure the removed gas volume at cell conditions.
6. Measure the removed gas volume at standard conditions (via the gasometer / wet-test meter), and take a sample for gas-chromatographic composition and gas gravity; from these compute the moles and mass removed.
7. With the gas gone, agitate the remaining liquid, then record the equilibrium oil volume \( V_o(p,T_{res}) \), the oil density, and (if specified) the oil viscosity at that stage.
8. Repeat steps 3 through 7 at each successive lower pressure stage (typically 6 to 12 stages spaced to resolve the curvature of \( R_{sd} \) and \( B_{od} \)) down to atmospheric pressure.
9. At the final atmospheric stage, expel the last gas increment, then record the dead/residual oil volume at cell temperature.
10. Cool the residual oil to standard temperature (60 \(\text{degF}\)) and measure its volume to obtain \( V_{o,residual,sc} \); also measure residual-oil density (API gravity) and, if required, its composition. This residual oil is the denominator (stock-tank-oil basis) for all differential factors.
11. Reconcile a material balance (gas removed plus residual oil mass versus original charge) and check overall component recovery.

Measured parameters↑ Contents

At each pressure stage the lab records: - Stage pressure \( p \) and the constant temperature \( T_{res} \). - Oil (liquid) volume in the cell \( V_o(p,T_{res}) \) after gas removal and re-equilibration. - Volume of liberated gas, at cell conditions and at standard conditions, for that stage. - Oil density \( \rho_o(p) \) (from mass balance and measured volume, or in-line meter). - Oil viscosity \( \mu_o(p) \), if measured. - Liberated-gas composition and specific gravity (gas gravity \( \gamma_g \)) per stage, by GC.

At the end of the test: residual oil volume at cell temperature and at standard temperature, residual-oil density / API gravity, and residual-oil composition.

Calculated / derived parameters↑ Contents

• Solution gas-oil ratio (differential), \( R_{sd}(p) = \dfrac{V_{gas,sc}(\text{in solution at } p)}{V_{o,residual,sc}} \), obtained by summing the gas liberated from stage \( p \) down to atmospheric and dividing by the residual-oil standard volume; units \(\text{scf/STB}\).
• Differential oil FVF, \( B_{od}(p) = \dfrac{V_o(p,T_{res})}{V_{o,residual,sc}} \); dimensionless (\(\text{rbbl/STB}\)).
• Oil density, \( \rho_o(p) = \dfrac{m_o}{V_o(p,T_{res})} \), with \( m_o \) updated each stage by subtracting the removed gas mass; units \(\text{g/cm}^3\) or \(\text{lb/ft}^3\).
• Gas deviation factor, \( Z = \dfrac{pV}{nRT} \), per liberated increment.
• Gas FVF, \( B_g = \dfrac{Z\,T_{res}\,p_{sc}}{T_{sc}\,p} \), units \(\text{rcf/scf}\) or \(\text{rbbl/scf}\).
• Gas gravity per stage, \( \gamma_g = \dfrac{M_{gas}}{M_{air}} = \dfrac{M_{gas}}{28.97} \), from the GC-derived gas molecular weight.
• Total formation volume factor (two-phase), \( B_t = B_{od} + B_g(R_{sdb} - R_{sd}) \), where \( R_{sdb} \) is the dissolved GOR at the bubble point; this captures the combined liquid-plus-evolved-gas volume below \( p_b \).
• Oil isothermal compressibility above \( p_b \) (if combined with CCE), \( c_o = -\dfrac{1}{V}\left(\dfrac{\partial V}{\partial p}\right)_T \).
• Oil viscosity correlated against \( p \) where directly measured.

When the field separator scheme is known, the differential factors are converted to field (flash) basis using the separator-test bubble-point flash factors, for example \( B_o = B_{od} \cdot \dfrac{B_{ofb}}{B_{odb}} \) and \( R_s = R_{sb} - (R_{sdb} - R_{sd})\dfrac{B_{ofb}}{B_{odb}} \), where the subscript \( b \) denotes bubble-point values and subscript \( f \) denotes the flash (separator) basis. This correction prevents the systematic over-shrinkage error that results from using raw DL data directly in volumetric calculations.

Reporting and typical curves↑ Contents

The DL report presents a stage-by-stage table (pressure, \( B_{od} \), \( R_{sd} \), gas \( Z \), \( B_g \), gas gravity, oil density, oil viscosity, \( B_t \)) plus the standard plots: - \( R_{sd} \) versus \( p \): monotonically increasing with pressure, flattening to the constant \( R_{sdb} \) above the bubble point; the slope reflects gas-evolution rate. - \( B_{od} \) versus \( p \): rises from the residual value of about 1.0 at atmospheric to a maximum at \( p_b \), then (when CCE is appended above \( p_b \)) declines slightly with further pressure due to liquid compressibility. The peak locates the bubble point. - \( \rho_o \) versus \( p \): increases as pressure drops below \( p_b \) because light ends are stripped out (the liquid gets heavier), even though above \( p_b \) density falls slightly with rising pressure. - \( \mu_o \) versus \( p \): U-shaped, minimum at the bubble point; below \( p_b \) viscosity climbs as dissolved gas is lost, above \( p_b \) it climbs with compression. - \( Z \) and \( B_g \) versus \( p \): gas-phase volumetrics for the liberated gas.

Reading the curves: the bubble point is read at the \( B_{od} \) peak / \( R_{sd} \) plateau onset; the shrinkage on going from reservoir to stock tank is \( B_{odb} \); and the slope \( \dfrac{dR_{sd}}{dp} \) feeds material-balance gas-cap and solution-gas drive calculations.

Practical notes and pitfalls↑ Contents

• Sample validity is everything: the charge must be representative and truly monophasic above \( p_b \) (validated by an opening CCE), or the entire \( R_{sd}/B_{od} \) set is biased. Check the measured \( p_b \) against the CCE bubble point.
• Constant-pressure gas removal must be exact: gas is expelled while holding stage pressure, with the oil kept in the cell. Pulling gas at falling pressure or co-producing oil corrupts both the liberated-gas volume and the residual oil.
• Equilibration time: under-equilibrated stages give too little liberated gas and too-high \( B_{od} \); heavy and waxy oils, foamy oils, and near-critical fluids need long settling and vigorous agitation. Watch for foam/emulsion at the interface.
• Mercury-free practice: classical Hg cells give precise volumes but pose toxicity and disposal hazards and can amalgamate; modern piston/floating-piston cells avoid mercury but require careful piston-friction and seal-leak control and accurate dead-volume calibration.
• Dead volume: gas trapped in lines, valves, and the gasometer manifold must be calibrated and subtracted from every gas reading; uncorrected dead volume inflates \( R_{sd} \).
• Residual-oil basis error: all differential factors are referenced to residual oil measured at standard temperature, not to separator stock-tank oil. Using DL \( B_o \) and \( R_s \) directly in reservoir volumetrics overstates shrinkage; always combine with separator tests for field-applicable values.
• Mass-balance closure: track the mass and moles removed as gas each stage; a poor overall material balance or component recovery signals leaks, incomplete gas removal, or volume-measurement drift.
• Standard-condition reduction: be explicit and consistent about the standard \( p_{sc} \) and \( T_{sc} \) used, and apply real-gas (\( Z \)) correction when converting cell-condition gas to standard volumes, especially for the higher-pressure, richer early increments.