Engineering lesson
Calculate radial pressure drop with skin included
In the stated steady radial model, skin adds to the dimensionless logarithmic resistance. Positive skin reduces rate for a fixed drawdown or increases required drawdown for a fixed rate.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Build the resistance denominator
The rate denominator contains ln(re/rw) + s, multiplied by viscosity and formation volume factor. The logarithm represents radial spreading; skin represents an additional near-well pressure contribution on this convention.
A negative skin reduces resistance, but the denominator must remain physically meaningful. A negative or vanishing total denominator is not a valid productivity prediction.
Choose rate or drawdown as the held quantity
For a fixed rate, solve the relation for pressure drop. For fixed boundary and bottomhole pressures, solve for rate. These are inverse uses of the same model, with different controlled inputs.
The example fixes drawdown at 500 psi and varies skin. It does not assume that the same fixed rate persists while the denominator changes.
Keep the volume basis consistent
The published field equation returns stock-tank liquid rate and includes Bo in reservoir barrels per stock-tank barrel. Omitting Bo changes the rate basis.
Skin is a lumped model parameter. One fitted value cannot by itself distinguish damage, completion geometry and other near-well effects.
Explore the example
Replayed with the same equation record and calculation engine as /calculators/steady-state-radial-liquid-flow-rate. Original synthetic inputs; engine outputs are saved in the downloadable record.
Select one of 5 recorded scenarios. Intermediate states are not interpolated.
Skin Factor (dimensionless) = 2. q_o (STB/day): 735.844574.
- q_o (STB/day)
Worked example
Steady-State Radial Liquid Flow Rate
Fixed controls: k = 100 mD; h = 50 ft; p_e = 3000 psi; p_wf = 2500 psi; mu_o = 2 cP; B_o = 1.2 bbl/STB; r_e = 1000 ft; r_w = 0.328 ft. s is varied as shown.
Relation and unit basis
q_o = 0.00708 k h (p_e - p_wf) / (mu_o B_o (ln(r_e / r_w) + s))
k: Permeability (mD). h: Net Pay Thickness (ft). p_e: External Boundary Pressure (psi). p_wf: Flowing Bottom-Hole Pressure (psi). mu_o: Oil Viscosity (cP). B_o: Oil Formation Volume Factor (bbl/STB). r_e: Drainage Radius (ft). r_w: Wellbore Radius (ft). s: Skin Factor (dimensionless).
1. Define the baseline
Skin Factor (dimensionless) = 2
Fixed controls: k = 100 mD; h = 50 ft; p_e = 3000 psi; p_wf = 2500 psi; mu_o = 2 cP; B_o = 1.2 bbl/STB; r_e = 1000 ft; r_w = 0.328 ft. s is varied as shown.
2. Select the relation
q_o = 0.00708 k h (p_e - p_wf) / (mu_o B_o (ln(r_e / r_w) + s))
k: Permeability (mD). h: Net Pay Thickness (ft). p_e: External Boundary Pressure (psi). p_wf: Flowing Bottom-Hole Pressure (psi). mu_o: Oil Viscosity (cP). B_o: Oil Formation Volume Factor (bbl/STB). r_e: Drainage Radius (ft). r_w: Wellbore Radius (ft). s: Skin Factor (dimensionless).
3. Substitute the values
k = 100; h = 50; p_e = 3000; p_wf = 2500; mu_o = 2; B_o = 1.2; r_e = 1000; r_w = 0.328; s = 2 → q_o = 735.844574 STB/day
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
q_o (STB/day) = 735.844574
Positive skin adds resistance at fixed drawdown; it is not a unique diagnosis of damage.
Result and interpretation
q_o (STB/day) = 735.844574
Positive skin adds resistance at fixed drawdown; it is not a unique diagnosis of damage.
Skin varies while drawdown, permeability, thickness, radii, viscosity and Bo remain fixed.
Exact scenario data
Replayed with the same equation record and calculation engine as /calculators/steady-state-radial-liquid-flow-rate. Original synthetic inputs; engine outputs are saved in the downloadable record.
| Skin Factor (dimensionless) | q_o (STB/day) |
|---|---|
| 0 | 919.2898 |
| 1 | 817.4012 |
| 2 | 735.8446 |
| 4 | 613.4333 |
| 8 | 460.2903 |
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 positive skin is removed at fixed drawdown, what happens to rate?
Show the worked answer
Rate increases because the resistance denominator decreases, provided the model and boundary assumptions still apply.
2. Reproduce the baseline q_o (STB/day) without rounding intermediate values.
Show the worked answer
k = 100; h = 50; p_e = 3000; p_wf = 2500; mu_o = 2; B_o = 1.2; r_e = 1000; r_w = 0.328; s = 2 → q_o = 735.844574 STB/day. q_o (STB/day) = 735.844574. Positive skin adds resistance at fixed drawdown; it is not a unique diagnosis of damage.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Skin Factor (dimensionless) changes from 0 to 8. Other controls remain as stated in the premise. q_o (STB/day) changes from 919.289848 to 460.290305.
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. k: Permeability (mD). h: Net Pay Thickness (ft). p_e: External Boundary Pressure (psi). p_wf: Flowing Bottom-Hole Pressure (psi). mu_o: Oil Viscosity (cP). B_o: Oil Formation Volume Factor (bbl/STB). r_e: Drainage Radius (ft). r_w: Wellbore Radius (ft). s: Skin Factor (dimensionless). Positive skin adds resistance at fixed drawdown; it is not a unique diagnosis of damage.
Before using the result
- Keep ln(re/rw) and skin on one convention.
- State whether rate or drawdown is fixed.
- Retain Bo for stock-tank rate.
Positive skin adds resistance at fixed drawdown; it is not a unique diagnosis of damage.
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.