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Joshi Isotropic Horizontal Well Effective Radius Formula

rwd=rehL/2a(1+1(L2a)2)(h2rw)h/Lr_{wd}=r_{eh}\frac{L/2}{a\left(1+\sqrt{1-\left(\frac{L}{2a}\right)^2}\right)\left(\frac{h}{2r_w}\right)^{h/L}}

Joshi Isotropic Horizontal Well Effective Radius calculates effective wellbore radius of horizontal well for well performance workflows in reservoir engineering.

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How engineers use this formula

Use this formula when the listed inputs (A, L, h, r_w) are known and the assumptions behind the cited well performance relationship match the engineering case being checked.

Assumptions

  • Input values are representative for the well, reservoir, fluid, or equipment case being evaluated.
  • The declared units match the field-unit constants used in the formula.
  • The cited formula applies to the selected petroleum engineering workflow.

Limitations

  • The calculation does not replace a full engineering model or operating procedure.
  • Accuracy depends on the source correlation, assumptions, input quality, and unit consistency.

Common mistakes

  • Mixing unit systems without converting the inputs.
  • Using default example values as field recommendations.
  • Applying the formula outside the source assumptions.

Default example

Using the default inputs, r_wd equals 721.784886 ft.

Aacre

160

Lft

2000

hft

50

r_wft

0.328

Inputs

A

acre

Drainage Area

L

ft

Horizontal Well Length

h

ft

Reservoir Thickness

r_w

ft

Wellbore Radius

Outputs

r_wd

ft

Effective Wellbore Radius of Horizontal Well

r_eh

intermediateft

Equivalent Horizontal Drainage Radius

a_joshi

intermediateft

Major Half-Axis of Drainage Ellipse

Source and review

reviewed

Joshi, S.D. Horizontal Well Technology, Page 90.

Source

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