Gas Depletion Test (Stepwise)

PVT Analysis of Reservoir Fluids › 12. Gas Depletion (Stepwise Gas Depletion)

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

The Gas Depletion test reproduces, at the cell scale, the non-equilibrium material-balance history that a dry or wet gas reservoir undergoes as it is produced down its decline curve. Unlike a Constant Composition Expansion, where nothing leaves the cell, here gas is physically withdrawn at each pressure step, so the test couples a thermodynamic state determination with a production accounting that an equation-of-state (EOS) simulator cannot reproduce in a single equilibrium flash.

Purpose↑ Contents

The test answers the central question of gas-reservoir engineering: how do the volumetric and density properties of the reservoir gas evolve as reservoir pressure is drawn down and gas is removed from the system. Concretely it provides:

• The real-gas deviation factor (\(Z\)-factor) as a function of pressure, \(Z(p)\), the single most important input to gas-in-place and gas material-balance (\(p/Z\)) analysis.
• The gas formation volume factor \(B_g(p)\), which converts reservoir-condition volumes to surface (standard) volumes and vice versa.
• The cumulative volume of gas produced (withdrawn) versus pressure, i.e. a laboratory analogue of the recovery-versus-depletion relationship.
• Calibration data for tuning a gas-phase EOS so that simulator predictions match measured \(Z\) and \(B_g\) over the production pressure range.

For a dry gas with negligible retrograde condensation it characterizes the producible single-phase gas. For a wet or near-dewpoint gas it must be distinguished from a Constant Volume Depletion (CVD) study, which is the proper test once a second (liquid) phase drops out; Gas Depletion proper assumes the withdrawn fluid is essentially the equilibrium gas itself.

Physical principle↑ Contents

The governing relation is the real-gas equation of state:

$$pV = ZnRT$$

where \(p\) is absolute pressure, \(V\) is the gas volume, \(n\) is the number of moles of gas in that volume, \(R\) is the universal gas constant (\(8.314\ \text{J/(mol K)}\), or \(10.732\ \text{psia ft}^3\text{/(lbmol R)}\) in field units), \(T\) is absolute temperature (\(\text{K}\) or \(\text{R}\)), and \(Z\) is the dimensionless compressibility (deviation) factor. \(Z\) measures the departure of the real gas from ideal-gas behavior; \(Z = 1\) for an ideal gas, and for natural gases \(Z\) typically falls below 1 at moderate pressures (attractive forces dominate) and rises above 1 at high pressures (repulsive, finite-volume effects dominate). Rearranged for the measured quantities:

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

The gas formation volume factor is the ratio of a volume of gas at reservoir (cell) conditions to the volume the same quantity occupies at standard conditions:

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

Taking \(Z_{sc} \approx 1\) and substituting standard conditions, the compact form used in the source is:

$$B_g = \frac{Z R T}{p}$$ (per unit mole basis, reservoir volume per surface mole)

In the more practical reservoir-volume-per-standard-volume convention (field units, \(p_{sc} = 14.696\ \text{psia}\), \(T_{sc} = 519.67\ \text{R}\)):

$$B_g = 0.02827 \cdot \frac{Z T}{p}$$ [\(\text{rcf/scf}\), \(T\) in \(\text{R}\), \(p\) in \(\text{psia}\)]

or in metric:

$$B_g = 0.350958 \cdot \frac{Z T}{p}$$ [\(\text{rm}^3\text{/sm}^3\), \(T\) in \(\text{K}\), \(p\) in \(\text{kPa}\)]

The volume of gas measured in the cell, when converted to standard conditions, follows the ideal-gas combined law corrected by \(Z\):

$$V_{std} = V_{cell} \cdot \frac{p_{cell}}{p_{std}} \cdot \frac{T_{std}}{T_{cell}} \cdot \frac{Z_{std}}{Z_{cell}}$$

The source gives the uncorrected form \(V_{std} = V_{cell} \cdot (p_{cell}/p_{std}) \cdot (T_{std}/T_{cell})\); the \(Z\)-ratio is the rigorous correction and should be applied when \(Z_{cell}\) differs appreciably from unity.

The defining feature of the test is its irreversible, open-system character. After each withdrawal the moles in the cell change discontinuously: \(n_{i+1} = n_i - \Delta n_{produced,i}\). Because mass is removed between equilibrium states, the overall process is path-dependent and cannot be captured by a single closed-system flash; this is why, as the source notes, the test is not reproducible by a simple simulator equilibrium calculation and must be run as a stepwise material balance.

Apparatus and conditions↑ Contents

• A high-pressure, high-temperature PVT cell, typically a windowed or mercury-free piston (positive-displacement) cell rated to or above initial reservoir pressure, with a calibrated volume readout (cathetometer on a visual cell, or a servo-controlled piston position).
• An air bath or jacket holding the cell at constant reservoir temperature \(T\) throughout the run (the test is isothermal).
• A pressure-control system: in a mercury-free design the back-pressure piston is withdrawn to lower pressure; the displaced/withdrawn gas is routed out of the cell.
• A gas withdrawal and metering train: a separator or gasometer plus a wet-test or mass-flow meter that measures the volume of withdrawn gas reduced to standard conditions, and optionally a gas chromatograph if effluent composition is to be tracked.
• Accurate pressure transducers and a temperature sensor traceable to calibration.

Held constant: temperature \(T\) (reservoir temperature). Varied: pressure \(p\), stepped downward from initial reservoir pressure to a specified abandonment-type minimum. Recorded as dependent quantities at each step: residual gas volume in the cell, withdrawn gas volume, and the derived \(Z\) and \(B_g\).

Procedure↑ Contents

1. Charge the PVT cell with a representative gas sample and bring the cell to reservoir temperature \(T\); allow full thermal equilibration.
2. Pressurize (or compress with the piston) to the initial pressure corresponding to reservoir conditions, \(p_1\), and record the equilibrium cell volume \(V_1\).
3. Determine or confirm the initial moles \(n_1\) in the cell from a known charge or from \(pV = ZnRT\) using an independently measured \(Z_1\).
4. Lower the pressure to the first depletion step \(p_2\) by expanding the cell / withdrawing the piston, and bleed (withdraw) gas out of the cell through the metering train so that a controlled portion of the gas phase leaves the system.
5. Close the withdrawal valve and allow the remaining gas to re-equilibrate at \(p_2\) and \(T\); record the residual (equilibrium) cell volume \(V_2\).
6. Measure the volume of the withdrawn gas reduced to standard conditions, \(\Delta V_{std,1}\), on the gasometer / wet-test meter; if compositional tracking is required, sample the effluent for chromatography.
7. Record \(p_2\), \(V_2\), \(T\), and the cumulative withdrawn standard volume.
8. Compute \(Z_2\) and \(B_{g,2}\) at this step from the measured \(p\), \(V\), \(T\) and the current mole inventory.
9. Update the mole inventory: \(n_2 = n_1 - \Delta n_{produced,1}\), where \(\Delta n_{produced,1} = \frac{p_{std}\,\Delta V_{std,1}}{R T_{std}}\).
10. Repeat steps 4 through 9 for each successive pressure step (\(p_3\), \(p_4\), \(\ldots\)) down to the specified minimum / abandonment pressure.
11. At the final step, record the residual gas volume and total cumulative produced gas.
12. Reduce all data and construct the \(Z(p)\), \(B_g(p)\), and cumulative-produced-gas-versus-pressure curves.

Measured parameters↑ Contents

Recorded directly at each pressure step \(i\):

• Step pressure \(p_i\) (the equilibrium pressure after re-stabilization).
• Cell temperature \(T\) (constant, logged to confirm isothermal conditions).
• Residual equilibrium gas volume in the cell \(V_i\).
• Withdrawn gas volume at cell conditions and, via the meter, reduced to standard conditions \(\Delta V_{std,i}\).
• Cumulative withdrawn gas at standard conditions, sum of \(\Delta V_{std}\) up to step \(i\).
• Optionally, effluent gas composition (mole fractions) from chromatography.

Calculated / derived parameters↑ Contents

• Deviation factor at each step: $$Z_i = \frac{p_i V_i}{n_i R T}$$ with \(n_i\) the current mole inventory in the cell after prior withdrawals.

• Gas formation volume factor: $$B_{g,i} = \frac{Z_i R T}{p_i}$$ (reservoir volume per mole) or, in surface-referenced field/metric form, \(B_{g,i} = 0.02827\,Z_i T/p_i\) (\(\text{rcf/scf}\)) or \(0.350958\,Z_i T/p_i\) (\(\text{rm}^3\text{/sm}^3\)).

• Moles produced per step (material balance): $$\Delta n_{produced,i} = \frac{p_{std}\,\Delta V_{std,i}}{R T_{std}}$$

• Updated cell mole inventory: $$n_{i+1} = n_i - \Delta n_{produced,i}$$

• Withdrawn gas reduced to standard conditions (when computed from cell readings rather than metered): $$V_{std,i} = V_{cell,i} \cdot \frac{p_{cell,i}}{p_{std}} \cdot \frac{T_{std}}{T_{cell}} \cdot \frac{Z_{std}}{Z_{cell,i}}$$

• Cumulative gas produced as a fraction of original moles in the cell: $$\frac{G_p}{G} = \frac{n_1 - n_i}{n_1}$$

• \(p/Z\) at each step, \(p_i/Z_i\), the variable that plots linearly against cumulative production for a volumetric (tank-type) gas system and is the basis of \(p/Z\) material-balance gas-in-place estimation.

Reporting and typical curves↑ Contents

The standard deliverables are a tabulation by pressure step (\(p\), \(T\), residual cell volume, withdrawn standard volume, cumulative produced, \(Z\), \(B_g\), \(p/Z\)) and the following plots:

• \(Z\) versus \(p\): read directly as the deviation-factor profile; it usually shows a minimum at intermediate pressure and recovery toward and above unity at high pressure. This curve is the primary EOS-calibration target.
• \(B_g\) versus \(p\): monotonically increasing as pressure falls (gas expands toward the surface volume), read to convert reservoir to surface volumes at any depletion pressure; on a \(B_g\)-versus-\(1/p\) basis it is nearly linear when \(Z\) is slowly varying.
• \(p\) versus \(V\) (the pressure-volume trace of the cell): used as a consistency check and to locate any change of slope that would signal a phase change.
• Cumulative produced gas (or \(G_p/G\)) versus pressure, and the \(p/Z\) versus cumulative-production line: the latter is read by extrapolating to \(p/Z = 0\) (or to abandonment \(p/Z\)) to estimate original and recoverable gas in place for a volumetric reservoir.

The full data set is then handed to the EOS-tuning workflow as the gas-model calibration data referenced in the source.

Practical notes and pitfalls↑ Contents

• Sampling and representativeness: the charged gas must be a genuine reservoir-representative sample at or above initial pressure; restoration to single phase before charging is essential, and for wet gases verify the sample is above its dewpoint so the test does not silently become a condensate study.
• Choose the right test: if a liquid phase drops out during depletion (retrograde condensate, near-critical gas), Gas Depletion is no longer the correct protocol; switch to Constant Volume Depletion, which holds cell volume constant after each withdrawal and is the recognized standard for gas-condensate depletion.
• Equilibration time: allow full pressure and thermal re-stabilization after each withdrawal before reading \(V\) and \(p\); reading too early biases \(Z\) and \(B_g\). Maintain strict isothermal control, since \(Z\) and \(B_g\) are temperature-sensitive and the test is defined at fixed \(T\).
• Mole-balance bookkeeping: the dominant source of error is the running material balance. Each withdrawn volume must be accurately reduced to standard conditions (apply the \(Z_{std}/Z_{cell}\) correction; do not use the bare ideal-gas reduction at high pressure) and subtracted from the inventory, or the computed \(Z\) at later steps drifts.
• Dead volume: account for all non-measured volumes (valves, lines, meter manifold) in both the residual-volume and withdrawn-volume accounting; uncorrected dead volume systematically corrupts \(B_g\) and the cumulative-produced curve.
• Mercury-free operation: modern HSE practice favors mercury-free piston cells; if a legacy mercury cell is used, track mercury position carefully and observe handling controls, since mercury interface errors map directly into volume errors.
• Withdrawal control: bleed gas slowly and meter steadily so the effluent stays single-phase and representative; flashing or entrainment during a too-rapid blowdown distorts both the metered standard volume and any effluent composition.
• Validation: cross-check measured \(Z\) against a correlation (for example Standing-Katz via pseudo-reduced properties) and confirm the \(p/Z\) trend is physically monotonic; a non-monotonic \(p/Z\) usually flags a leak, a missed phase change, or a mole-balance error rather than real reservoir behavior.