Engineering lesson
Horizontal versus vertical well productivity under stated assumptions
Horizontal and vertical productivity comparisons require matched rock, fluid and drainage assumptions. A longer well can improve access, but anisotropy, thickness and drainage geometry affect the gain.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
State the common reservoir before comparing wells
The Joshi model uses horizontal and vertical permeability, pay thickness, horizontal length, drainage area and well radius. A vertical radial reference needs its own consistent drainage radius and boundary definition.
Comparing two calculator defaults without matching these assumptions can attribute a difference in reservoir size or fluid properties to well orientation.
Anisotropy changes vertical access
Low vertical permeability limits how readily fluid moves toward a horizontal well from above and below. Equal horizontal permeability therefore does not imply equal productivity gain across formations.
The worked sensitivity keeps the horizontal well and fluid fixed while changing kv. It evaluates the published Joshi geometry rather than claiming a universal horizontal-to-vertical multiplier.
Keep the result as an inflow estimate
A productivity index does not predict the operating rate without drawdown and outflow conditions. Completion restrictions, pressure-dependent effects and reservoir boundaries may need additional models.
The linked broader Joshi guide gives the full method context. This lesson owns the matched-input comparison and the anisotropy interpretation.
Explore the example
Replayed with the same equation record and calculation engine as /calculators/joshi-horizontal-well-productivity-index. Original synthetic inputs; engine outputs are saved in the downloadable record.
Select one of 5 recorded scenarios. Intermediate states are not interpolated.
Vertical Permeability (mD) = 10. J_h (STB/day/psi): 7.5062339.
- J_h (STB/day/psi)
Worked example
Joshi Horizontal Well Productivity Index
Fixed controls: k_h = 100 mD; h = 50 ft; L = 1000 ft; A_ac = 40 acres; r_w = 0.328 ft; mu_o = 2 cP; B_o = 1.2 bbl/STB; s = 0 dimensionless. k_v is varied as shown.
Relation and unit basis
J_h = 0.00708 k_h h / [mu_o B_o (ln R_h + beta h/L ln(beta h / 2 r_w) + s)]
k_h: Horizontal Permeability (mD). k_v: Vertical Permeability (mD). h: Net Pay Thickness (ft). L: Horizontal Well Length (ft). A_ac: Drainage Area (acres). r_w: Wellbore Radius (ft). mu_o: Oil Viscosity (cP). B_o: Oil Formation Volume Factor (bbl/STB). s: Skin Factor (dimensionless).
1. Define the baseline
Vertical Permeability (mD) = 10
Fixed controls: k_h = 100 mD; h = 50 ft; L = 1000 ft; A_ac = 40 acres; r_w = 0.328 ft; mu_o = 2 cP; B_o = 1.2 bbl/STB; s = 0 dimensionless. k_v is varied as shown.
2. Select the relation
J_h = 0.00708 k_h h / [mu_o B_o (ln R_h + beta h/L ln(beta h / 2 r_w) + s)]
k_h: Horizontal Permeability (mD). k_v: Vertical Permeability (mD). h: Net Pay Thickness (ft). L: Horizontal Well Length (ft). A_ac: Drainage Area (acres). r_w: Wellbore Radius (ft). mu_o: Oil Viscosity (cP). B_o: Oil Formation Volume Factor (bbl/STB). s: Skin Factor (dimensionless).
3. Substitute the values
k_h = 100; k_v = 10; h = 50; L = 1000; A_ac = 40; r_w = 0.328; mu_o = 2; B_o = 1.2; s = 0 → J_h = 7.5062339 STB/day/psi
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
J_h (STB/day/psi) = 7.5062339
This is Joshi horizontal PI with fixed kh and geometry; it is not a horizontal-to-vertical rate multiplier.
Result and interpretation
J_h (STB/day/psi) = 7.5062339
This is Joshi horizontal PI with fixed kh and geometry; it is not a horizontal-to-vertical rate multiplier.
Vary vertical permeability with horizontal permeability fixed. The result is horizontal-well PI, not a complete production forecast.
Exact scenario data
Replayed with the same equation record and calculation engine as /calculators/joshi-horizontal-well-productivity-index. Original synthetic inputs; engine outputs are saved in the downloadable record.
| Vertical Permeability (mD) | J_h (STB/day/psi) |
|---|---|
| 1 | 3.340207 |
| 5 | 6.141349 |
| 10 | 7.506234 |
| 25 | 9.216046 |
| 100 | 11.22122 |
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. Does doubling horizontal length guarantee twice the production rate?
Show the worked answer
No. Productivity changes through the geometry model, while operating rate also depends on available drawdown and outflow.
2. Reproduce the baseline J_h (STB/day/psi) without rounding intermediate values.
Show the worked answer
k_h = 100; k_v = 10; h = 50; L = 1000; A_ac = 40; r_w = 0.328; mu_o = 2; B_o = 1.2; s = 0 → J_h = 7.5062339 STB/day/psi. J_h (STB/day/psi) = 7.5062339. This is Joshi horizontal PI with fixed kh and geometry; it is not a horizontal-to-vertical rate multiplier.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Vertical Permeability (mD) changes from 1 to 100. Other controls remain as stated in the premise. J_h (STB/day/psi) changes from 3.34020682 to 11.2212202.
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_h: Horizontal Permeability (mD). k_v: Vertical Permeability (mD). h: Net Pay Thickness (ft). L: Horizontal Well Length (ft). A_ac: Drainage Area (acres). r_w: Wellbore Radius (ft). mu_o: Oil Viscosity (cP). B_o: Oil Formation Volume Factor (bbl/STB). s: Skin Factor (dimensionless). This is Joshi horizontal PI with fixed kh and geometry; it is not a horizontal-to-vertical rate multiplier.
Before using the result
- Match drainage and fluid assumptions.
- Record kh and kv separately.
- Distinguish PI from operating rate.
This is Joshi horizontal PI with fixed kh and geometry; it is not a horizontal-to-vertical rate multiplier.
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.