Dogleg Severity Calculator Formula

Dogleg severity (DLS) measures the rate of change of wellbore direction, expressed in degrees per 100 feet (or per 30 meters). It combines changes in both inclination and azimuth into a single value. DLS is critical for determining drill string fatigue, casing wear, key-seating risk, and the ability...

Overview

Theory

A dogleg is any change in the wellbore trajectory. Even if inclination and azimuth each change only slightly, the combined 3D change can produce significant DLS. The minimum curvature method is the industry standard (SPE) for calculating wellbore trajectory and DLS.

Formulas

Dogleg Severity — Minimum Curvature Method

cos(DL) = cos(I2 - I1) - sin(I1)*sin(I2)*(1 - cos(A2 - A1))

where DL = total dogleg angle over the survey interval, I1, I2 = inclination at stations 1 and 2, A1, A2 = azimuth at stations 1 and 2.

Then:

DLS = DL / ΔMD * 100 (°/100ft)

Radius of Curvature

R = 180 / (π * DLS) * 100 (ft)

Simplified (for small angles)

DLS ≈ sqrt((ΔI)^2 + (ΔA * sin(I_avg))^2) / ΔMD * 100

Maximum DLS Limits (Rules of Thumb)

Wellbore Section	Max DLS (°/100ft)
Vertical section	1 – 2
Build section	2 – 6 (conventional), 8 – 15 (motor/RSS)
Tangent/hold	1 – 3
Drop section	2 – 4
Horizontal landing	6 – 12

Fatigue Limit (Lubinski's Formula)

Maximum tensile stress due to bending:

σ_bending = 218 * OD * DLS (psi, for steel drill pipe)

For drill pipe fatigue life, combined bending + tension stress should not exceed the endurance limit (~20,000 psi for S-135 drill pipe with rotation).

Worked Example

Given: Station 1: MD = 5,000 ft, I = 15°, A = 120°. Station 2: MD = 5,100 ft, I = 18°, A = 125°.

Step 1: Calculate dogleg angle:

cos(DL) = cos(18 - 15) - sin(15)*sin(18)*(1 - cos(125 - 120))
        = cos(3°) - sin(15°)*sin(18°)*(1 - cos(5°))
        = 0.99863 - 0.2588*0.3090*(1 - 0.99619)
        = 0.99863 - 0.07997*0.00381
        = 0.99863 - 0.000305
        = 0.99832

DL = arccos(0.99832) = 3.32°

Step 2: DLS:

DLS = 3.32 / 100 * 100 = 3.32 °/100ft

Step 3: Radius of curvature:

R = 18,000 / (π * 3.32) = 18,000 / 10.43 = 1,726 ft

Valid Ranges

Parameter	Typical Range	Notes
DLS (conventional wells)	0 – 6 °/100ft	Higher in build/drop sections
DLS (ERD wells)	0 – 15 °/100ft	With RSS tools
DLS (casing running limit)	< 8 °/100ft	Depends on casing size
ΔMD between surveys	30 – 100 ft	Closer spacing = more accurate

Common Issues from High DLS

Drill string fatigue and washouts
Casing wear (especially at tool joints)
Key-seating and stuck pipe
Difficulty running completion tools and logging tools
Increased torque and drag

References

Bourgoyne, A.T. et al. (1986). Applied Drilling Engineering. SPE Textbook Series, Vol. 2.
Lubinski, A. (1953). "A Study of the Buckling of Rotary Drilling Strings." Drilling and Production Practice, API.
SPE — Minimum Curvature Method for wellbore survey calculations.
PetroWiki — Directional drilling: https://petrowiki.spe.org/Directional_survey

Dogleg Severity Calculator