Original synthetic study
Three synthetic IPR curves from one test point
One rate–pressure test point can be matched by several inflow shapes. Agreement at that point does not establish equal absolute-open-flow predictions or equal rates elsewhere.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Define the shared test
The synthetic test uses reservoir pressure 3,000 psia and a rate of 700 STB/day at pwf = 1,500 psia. A straight line, Vogel curve and a simple quadratic-drawdown teaching curve are each scaled to pass through it.
The third curve is a deliberately defined mathematical alternative, not a named validated petroleum correlation.
Compare predictions away from the test
Matching one point determines only the scale once each shape is assumed. At other bottomhole pressures the curves separate, including at their zero-pressure intercepts.
This differs from a comparison normalized to the same qmax. The experiment holds an observed-style test point fixed instead.
Use additional evidence to choose shape
Multiple suitable tests, fluid phase behavior and reservoir assumptions are needed to assess a model. The study does not rank accuracy because no independent field observations are supplied.
The downloadable rows include all three explicit equations and scales so the matched condition can be checked directly.
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.
Pressure ratio pwf/pr = 0.5. Straight-line rate (STB/day): 700; Vogel rate (STB/day): 700; Synthetic quadratic rate (STB/day): 700.
- Straight-line rate (STB/day)
- Vogel rate (STB/day)
- Synthetic quadratic rate (STB/day)
Worked example
Three shapes matched to one test point
pr = 3,000 psia, test q = 700 STB/day at pwf = 1,500 psia. Models: line, Vogel, and explicitly synthetic q = A(1 − pwf/pr)².
Relation and unit basis
qline = 1,400(1 − r); qVogel = 1,000(1 − 0.2r − 0.8r²); qsynthetic = 2,800(1 − r)²
r = pwf/pr. The third function is a teaching alternative, not a validated named inflow correlation.
1. Define the baseline
Pressure ratio pwf/pr = 0.5
pr = 3,000 psia, test q = 700 STB/day at pwf = 1,500 psia. Models: line, Vogel, and explicitly synthetic q = A(1 − pwf/pr)².
2. Select the relation
qline = 1,400(1 − r); qVogel = 1,000(1 − 0.2r − 0.8r²); qsynthetic = 2,800(1 − r)²
r = pwf/pr. The third function is a teaching alternative, not a validated named inflow correlation.
3. Substitute the values
At r = 0.5: 1,400 × 0.5 = 700; 1,000 × 0.7 = 700; 2,800 × 0.25 = 700 STB/day
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
Straight-line rate (STB/day) = 700; Vogel rate (STB/day) = 700; Synthetic quadratic rate (STB/day) = 700
The matched test does not constrain the extrapolated intercept or the rest of the curve.
Result and interpretation
Straight-line rate (STB/day) = 700; Vogel rate (STB/day) = 700; Synthetic quadratic rate (STB/day) = 700
The matched test does not constrain the extrapolated intercept or the rest of the curve.
Check the common test at pwf/pr = 0.5 before comparing the extrapolated curves.
Study data and reproduction
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
| Pressure ratio pwf/pr | Straight-line rate (STB/day) | Vogel rate (STB/day) | Synthetic quadratic rate (STB/day) |
|---|---|---|---|
| 0 | 1,400 | 1,000 | 2,800 |
| 0.25 | 1,050 | 900 | 1,575 |
| 0.5 | 700 | 700 | 700 |
| 0.75 | 350 | 400 | 175 |
| 1 | 0 | 0 | 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. Can three curves match one point and still have different qmax values?
Show the worked answer
Yes. The assumed curve shape determines how the matching point scales to the intercept.
2. Reproduce the baseline Straight-line rate (STB/day) without rounding intermediate values.
Show the worked answer
At r = 0.5: 1,400 × 0.5 = 700; 1,000 × 0.7 = 700; 2,800 × 0.25 = 700 STB/day. Straight-line rate (STB/day) = 700. The matched test does not constrain the extrapolated intercept or the rest of the curve.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Pressure ratio pwf/pr changes from 0 to 1. Other controls remain as stated in the premise. Straight-line rate (STB/day) changes from 1400 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. r = pwf/pr. The third function is a teaching alternative, not a validated named inflow correlation. The matched test does not constrain the extrapolated intercept or the rest of the curve.
Before using the result
- Match the same test datum.
- Label the third curve as a teaching function.
- Avoid accuracy rankings without independent observations.
The matched test does not constrain the extrapolated intercept or the rest of the curve.
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.