Original synthetic study
Why a small pressure datum mistake can distort a gas calculation
A pressure-datum error has a larger relative effect on a low-pressure gas calculation. At fixed Z and T, substituting gauge pressure for absolute pressure creates a relative density error of Patm/Pabs.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Isolate one input mistake
The study assumes 14.7 psia atmosphere, fixed molecular weight, fixed absolute temperature and fixed Z. It compares correct absolute-pressure density with the deliberately incorrect gauge-pressure substitution.
The two predictions use the same gas equation, so the difference is attributable to the pressure reference alone.
Normalize the error correctly
At 100 psia, using 85.3 as the pressure underestimates density by 14.7%. At much higher absolute pressure, the same omitted atmosphere is a smaller fraction.
This does not imply atmosphere is irrelevant at high pressure; it explains the scale of this one error with all other assumptions held fixed.
Keep the experiment distinct from Z uncertainty
Z generally changes with pressure. The constant-Z control makes the datum effect exactly proportional and should not be mistaken for a real-fluid sweep.
The downloaded table includes correct and incorrect pressures as well as relative error. Use the full calculator with a state-consistent Z for an actual density estimate.
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.
Absolute pressure (psia) = 100. Correct density (lb/ft³): 0.344006015; Wrong density (lb/ft³): 0.29343713; Underestimate (%): 14.7.
- Correct density (lb/ft³)
- Wrong density (lb/ft³)
Worked example
Gas density error from a missing atmosphere
Patm = 14.7 psia, T = 600 °R, Z = 0.85, molecular weight 18.82855 lb/lbmol, R = 10.732 field units.
Relation and unit basis
ρcorrect = Pabs M/(ZRT); ρwrong = (Pabs − 14.7)M/(ZRT)
The fixed-Z control isolates pressure reference. The wrong column is deliberately invalid as a state input.
1. Define the baseline
Absolute pressure (psia) = 100
Patm = 14.7 psia, T = 600 °R, Z = 0.85, molecular weight 18.82855 lb/lbmol, R = 10.732 field units.
2. Select the relation
ρcorrect = Pabs M/(ZRT); ρwrong = (Pabs − 14.7)M/(ZRT)
The fixed-Z control isolates pressure reference. The wrong column is deliberately invalid as a state input.
3. Substitute the values
At 100 psia the wrong pressure is 85.3; density ratio = 85.3/100 = 0.853, a 14.7% underestimate
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
Correct density (lb/ft³) = 0.344006015; Wrong density (lb/ft³) = 0.29343713; Underestimate (%) = 14.7
The relative datum error grows at low absolute pressure under these fixed-property controls.
Result and interpretation
Correct density (lb/ft³) = 0.344006015; Wrong density (lb/ft³) = 0.29343713; Underestimate (%) = 14.7
The relative datum error grows at low absolute pressure under these fixed-property controls.
The incorrect column is deliberately labelled. Its percentage error is measured against the correct absolute-pressure result.
Study data and reproduction
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
| Absolute pressure (psia) | Correct density (lb/ft³) | Wrong density (lb/ft³) | Underestimate (%) |
|---|---|---|---|
| 25 | 0.0860015 | 0.03543262 | 58.8 |
| 50 | 0.172003 | 0.1214341 | 29.4 |
| 100 | 0.344006 | 0.2934371 | 14.7 |
| 500 | 1.72003 | 1.669461 | 2.94 |
| 3,000 | 10.32018 | 10.26961 | 0.49 |
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. At 50 psia and 14.7 psia atmosphere, what relative density error comes from using gauge pressure?
Show the worked answer
A 29.4% underestimate at fixed Z and T, because 14.7/50 = 0.294.
2. Reproduce the baseline Correct density (lb/ft³) without rounding intermediate values.
Show the worked answer
At 100 psia the wrong pressure is 85.3; density ratio = 85.3/100 = 0.853, a 14.7% underestimate. Correct density (lb/ft³) = 0.344006015. The relative datum error grows at low absolute pressure under these fixed-property controls.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Absolute pressure (psia) changes from 25 to 3000. Other controls remain as stated in the premise. Correct density (lb/ft³) changes from 0.0860015037 to 10.3201804.
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. The fixed-Z control isolates pressure reference. The wrong column is deliberately invalid as a state input. The relative datum error grows at low absolute pressure under these fixed-property controls.
Before using the result
- Use the correct result as the reference.
- Keep atmosphere explicit.
- Separate datum error from real-gas model error.
The relative datum error grows at low absolute pressure under these fixed-property controls.
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.