Engineering lesson
Gas deliverability pressure squared versus pseudopressure
Pressure-squared gas deliverability approximates gas-property behavior with a fitted relation. Pseudopressure instead integrates pressure-dependent viscosity and Z. Their coefficients and pressure variables are not interchangeable.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Identify the driving potential
The Rawlins–Schellhardt form uses a power of pr² − pwf² with a fitted coefficient and exponent. Pseudopressure uses an integral involving 2p/[μ(p)Z(p)].
When gas properties vary substantially, a pressure-squared approximation can lose the property weighting that pseudopressure retains. The suitability depends on fluid and pressure range.
Fit on the same definition used for prediction
A coefficient fitted to psi-squared potential cannot be copied into a pseudopressure formula. Its units and numerical meaning depend on the exponent and rate basis.
The numerical panel evaluates the site's pressure-squared calculator only. It does not invent a pseudopressure curve without a viscosity–Z property table.
Use absolute pressures and independent tests
Squaring gauge pressures does not preserve the same potential as squaring absolute pressures. Keep psia labels on both boundary pressures.
Deliverability fitting also needs suitable stabilized or interpreted test data. A converged fit to incompatible points is not evidence of a valid gas-flow model.
Explore the example
Replayed with the same equation record and calculation engine as /calculators/rawlins-schellhardt-gas-deliverability-rate. Original synthetic inputs; engine outputs are saved in the downloadable record.
Select one of 5 recorded scenarios. Intermediate states are not interpolated.
Flowing Bottom-Hole Pressure (psia) = 1500. q_g (MSCF/day): 87.2095957.
- q_g (MSCF/day)
Worked example
Rawlins-Schellhardt Gas Deliverability Rate
Fixed controls: C_rs = 0.0003 MSCF/day/psi^(2n); P_r = 3000 psia; n_rs = 0.8 dimensionless. P_wf is varied as shown.
Relation and unit basis
q_g = C_{RS}(P_r^2 - P_{wf}^2)^{n_{RS}}
C_rs: Rawlins-Schellhardt Deliverability Coefficient (MSCF/day/psi^(2n)). P_r: Average Reservoir Pressure (psia). P_wf: Flowing Bottom-Hole Pressure (psia). n_rs: Rawlins-Schellhardt Deliverability Exponent (dimensionless).
1. Define the baseline
Flowing Bottom-Hole Pressure (psia) = 1500
Fixed controls: C_rs = 0.0003 MSCF/day/psi^(2n); P_r = 3000 psia; n_rs = 0.8 dimensionless. P_wf is varied as shown.
2. Select the relation
q_g = C_{RS}(P_r^2 - P_{wf}^2)^{n_{RS}}
C_rs: Rawlins-Schellhardt Deliverability Coefficient (MSCF/day/psi^(2n)). P_r: Average Reservoir Pressure (psia). P_wf: Flowing Bottom-Hole Pressure (psia). n_rs: Rawlins-Schellhardt Deliverability Exponent (dimensionless).
3. Substitute the values
C_rs = 0.0003; P_r = 3000; P_wf = 1500; n_rs = 0.8 → q_g = 87.2095957 MSCF/day
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
q_g (MSCF/day) = 87.2095957
The pressure-squared relation uses absolute pressures and its own fitted coefficient; no pseudopressure property integral is supplied.
Result and interpretation
q_g (MSCF/day) = 87.2095957
The pressure-squared relation uses absolute pressures and its own fitted coefficient; no pseudopressure property integral is supplied.
The pressure-squared potential varies with flowing pressure. A pseudopressure prediction requires additional property data.
Exact scenario data
Replayed with the same equation record and calculation engine as /calculators/rawlins-schellhardt-gas-deliverability-rate. Original synthetic inputs; engine outputs are saved in the downloadable record.
| Flowing Bottom-Hole Pressure (psia) | q_g (MSCF/day) |
|---|---|
| 0 | 109.778 |
| 750 | 104.2539 |
| 1,500 | 87.2096 |
| 2,250 | 56.66276 |
| 3,000 | 0 |
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. Why does using gauge pressure matter even though the equation contains a pressure difference?
Show the worked answer
It is a difference of squares, not a simple pressure difference. The atmospheric offset does not cancel from the squared terms.
2. Reproduce the baseline q_g (MSCF/day) without rounding intermediate values.
Show the worked answer
C_rs = 0.0003; P_r = 3000; P_wf = 1500; n_rs = 0.8 → q_g = 87.2095957 MSCF/day. q_g (MSCF/day) = 87.2095957. The pressure-squared relation uses absolute pressures and its own fitted coefficient; no pseudopressure property integral is supplied.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Flowing Bottom-Hole Pressure (psia) changes from 0 to 3000. Other controls remain as stated in the premise. q_g (MSCF/day) changes from 109.777987 to 0.
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. C_rs: Rawlins-Schellhardt Deliverability Coefficient (MSCF/day/psi^(2n)). P_r: Average Reservoir Pressure (psia). P_wf: Flowing Bottom-Hole Pressure (psia). n_rs: Rawlins-Schellhardt Deliverability Exponent (dimensionless). The pressure-squared relation uses absolute pressures and its own fitted coefficient; no pseudopressure property integral is supplied.
Before using the result
- Use absolute boundary pressures.
- Keep coefficient units with the exponent.
- Do not substitute pseudopressure coefficients into pressure-squared form.
The pressure-squared relation uses absolute pressures and its own fitted coefficient; no pseudopressure property integral is supplied.
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.