Engineering lesson
Gas formation volume factor and expansion factor worked together
Gas formation volume factor can be derived from the ratio of reservoir and standard gas volumes for the same amount. Its reciprocal gives the complementary expansion factor after units are matched.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Derive the state ratio
From PV = ZnRT at two states, Bg = (ZrTr/Pr)/(ZsTs/Ps) when both volumes use the same volume unit. Every pressure and temperature must be absolute.
This worked lesson specifies both states and derives Bg. The separate expansion-factor lesson focuses on reciprocal units, preventing the two pages from being duplicate definitions.
Include standard-state assumptions
Standard pressure, standard temperature and standard Z belong in the calculation record. A field coefficient can embed selected standard conditions and volume conversions.
If different standard conditions are used, the coefficient or explicit ratio must change accordingly. A bare scf label can hide this distinction.
Check the two conversion directions
Multiply standard volume by Bg to obtain reservoir volume. Divide reservoir volume by Bg to recover standard volume. The reciprocal expansion factor gives the same reverse mapping.
The example keeps gas composition and Z assumptions fixed. It is a state-volume exercise, not a compositional separator calculation.
Explore the example
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
Select one of 5 recorded scenarios. Intermediate states are not interpolated.
Reservoir pressure (psia) = 3000. Bg (reservoir ft³/scf): 0.00480576923; Expansion (scf/reservoir ft³): 208.083233.
- Bg (reservoir ft³/scf)
Worked example
Bg from two explicit absolute states
Reservoir T = 600 °R and Z = 0.85; standard T = 520 °R, P = 14.7 psia, Z = 1. Reservoir pressure varies.
Relation and unit basis
Bg = Zr Tr Ps/(Pr Zs Ts); expansion = 1/Bg
Bg in reservoir ft³/scf when both volumes use cubic feet. This explicit state ratio differs slightly from rounded field coefficients.
1. Define the baseline
Reservoir pressure (psia) = 3000
Reservoir T = 600 °R and Z = 0.85; standard T = 520 °R, P = 14.7 psia, Z = 1. Reservoir pressure varies.
2. Select the relation
Bg = Zr Tr Ps/(Pr Zs Ts); expansion = 1/Bg
Bg in reservoir ft³/scf when both volumes use cubic feet. This explicit state ratio differs slightly from rounded field coefficients.
3. Substitute the values
Bg = 0.85 × 600 × 14.7/(3,000 × 520) = 0.00480576923 ft³/scf; reciprocal = 208.083233 scf/ft³
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
Bg (reservoir ft³/scf) = 0.00480576923; Expansion (scf/reservoir ft³) = 208.083233
Both state definitions are part of the factor; changing standards changes the explicit ratio.
Result and interpretation
Bg (reservoir ft³/scf) = 0.00480576923; Expansion (scf/reservoir ft³) = 208.083233
Both state definitions are part of the factor; changing standards changes the explicit ratio.
Pressure varies on an absolute basis while both temperatures and Z assumptions remain fixed.
Exact scenario data
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
| Reservoir pressure (psia) | Bg (reservoir ft³/scf) | Expansion (scf/reservoir ft³) |
|---|---|---|
| 500 | 0.02883462 | 34.68054 |
| 1,000 | 0.01441731 | 69.36108 |
| 2,000 | 0.007208654 | 138.7222 |
| 3,000 | 0.004805769 | 208.0832 |
| 5,000 | 0.002883462 | 346.8054 |
Scroll the table to see all columns. The highlighted row is the worked baseline. Downloads retain full numerical precision.
Test your understanding
Work through the question before revealing its answer. Use the stated assumptions and include units in every numerical step.
1. If Bg = 0.005 reservoir ft³/scf, what reservoir volume corresponds to 10,000 scf?
Show the worked answer
50 reservoir ft³. The reverse factor is 200 scf/reservoir ft³.
2. Reproduce the baseline Bg (reservoir ft³/scf) without rounding intermediate values.
Show the worked answer
Bg = 0.85 × 600 × 14.7/(3,000 × 520) = 0.00480576923 ft³/scf; reciprocal = 208.083233 scf/ft³. Bg (reservoir ft³/scf) = 0.00480576923. Both state definitions are part of the factor; changing standards changes the explicit ratio.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Reservoir pressure (psia) changes from 500 to 5000. Other controls remain as stated in the premise. Bg (reservoir ft³/scf) changes from 0.0288346154 to 0.00288346154.
4. What would be needed to apply this example to a different physical system?
Show the worked answer
Replace the synthetic controls with compatible documented inputs and check the relation's assumptions. Bg in reservoir ft³/scf when both volumes use cubic feet. This explicit state ratio differs slightly from rounded field coefficients. Both state definitions are part of the factor; changing standards changes the explicit ratio.
Before using the result
- Record both state definitions.
- Use absolute pressure and temperature.
- Match volume units before taking a reciprocal.
Both state definitions are part of the factor; changing standards changes the explicit ratio.
Continue learning
Start with the broader workflow guide · Related method guide
Sources and method
The explanation and synthetic examples are original PetroCalcHub teaching material. The references below support the definitions and model context. They do not supply field validation for the synthetic scenarios.