Drilling formulas quick reference

Dogleg Severity (DLS)

Formula:

DLS=cos⁡−1(cos⁡(INC1)⋅cos⁡(INC2)+sin⁡(INC1)⋅sin⁡(INC2)⋅cos⁡(AZI2−AZI1))ΔMD×100\text{DLS} = \frac{\cos^{-1}(\cos(\text{INC}_1) \cdot \cos(\text{INC}_2) + \sin(\text{INC}_1) \cdot \sin(\text{INC}_2) \cdot \cos(\text{AZI}_2 - \text{AZI}_1))}{\Delta MD} \times 100DLS=ΔMDcos−1(cos(INC1​)⋅cos(INC2​)+sin(INC1​)⋅sin(INC2​)⋅cos(AZI2​−AZI1​))​×100

Units: degrees/100 ft or degrees/30 m
Use: Measures the curvature between two survey points.

Example:

• INC1 = 10°, AZI1 = 45°

• INC2 = 14°, AZI2 = 55°

• ΔMD = 100 ft
  → DLS ≈ 4.1°/100 ft

Build or Turn Rate

Formula (for build or turn separately):

Rate=INC2−INC1ΔMD×100\text{Rate} = \frac{\text{INC}_2 - \text{INC}_1}{\Delta MD} \times 100Rate=ΔMDINC2​−INC1​​×100

Example (Build Rate):

• INC1 = 10°, INC2 = 20°, ΔMD = 500 ft
  → Build Rate = 2°/100 ft

TVD from Inclined Section

Formula:

TVD=TVD1+cos⁡(INC)×ΔMD\text{TVD} = \text{TVD}_1 + \cos(\text{INC}) \times \Delta MDTVD=TVD1​+cos(INC)×ΔMD

Example:

• TVD₁ = 5,000 ft, INC = 30°, ΔMD = 100 ft
  → TVD₂ ≈ 5,000 + 86.6 = 5,086.6 ft

Horizontal Displacement (Northing & Easting)

Formula (simplified):

ΔN=ΔMD×sin⁡(INC)×cos⁡(AZI)\Delta N = \Delta MD \times \sin(\text{INC}) \times \cos(\text{AZI})ΔN=ΔMD×sin(INC)×cos(AZI) ΔE=ΔMD×sin⁡(INC)×sin⁡(AZI)\Delta E = \Delta MD \times \sin(\text{INC}) \times \sin(\text{AZI})ΔE=ΔMD×sin(INC)×sin(AZI)

Example:

• INC = 45°, AZI = 60°, ΔMD = 100 ft
  → ΔN ≈ 50 × 0.5 = 25 ft
  → ΔE ≈ 50 × 0.866 = 43.3 ft

Slide vs Rotate Footage Ratio

Formula:

Slide Ratio=Slide FootageTotal Footage×100\text{Slide Ratio} = \frac{\text{Slide Footage}}{\text{Total Footage}} \times 100Slide Ratio=Total FootageSlide Footage​×100

Example:

• Slide: 300 ft, Total: 800 ft
  → Slide Ratio = 37.5%

Build Rate Needed to Hit Target Inclination

Formula:

Required Build Rate=Target INC−Current INCAvailable MD×100\text{Required Build Rate} = \frac{\text{Target INC} - \text{Current INC}}{\text{Available MD}} \times 100Required Build Rate=Available MDTarget INC−Current INC​×100

Example:

• Target INC = 45°, Current INC = 15°, Available MD = 600 ft
  → Build Rate = 5°/100 ft

Radius of Curvature

Formula:

Radius (ft)=18000π×DLS (°/100 ft)\text{Radius (ft)} = \frac{18000}{\pi \times \text{DLS (°/100 ft)}}Radius (ft)=π×DLS (°/100 ft)18000​

Example:

• DLS = 3°/100 ft
  → Radius ≈ 1910 ft

TVD Error from Survey Tool

Formula:

TVD Error≈ΔMD×sin⁡(Tool Inclination Error)\text{TVD Error} \approx \Delta MD \times \sin(\text{Tool Inclination Error})TVD Error≈ΔMD×sin(Tool Inclination Error)

Example:

• ΔMD = 10,000 ft, error = 0.25°
  → TVD Error ≈ 10,000 × sin(0.25°) ≈ 43.6 ft

Time to Drill Section

Formula:

Time (hrs)=LengthROP\text{Time (hrs)} = \frac{\text{Length}}{\text{ROP}}Time (hrs)=ROPLength​

Example:

• Length = 1,000 ft, ROP = 50 ft/hr
  → Time = 20 hours

 Bit Projection (Slide/Rotate Split Planning)

If required to hit target angle in given footage:

Slide Footage=Required Angle ChangeToolface Build/Turn per 100 ft×100\text{Slide Footage} = \frac{\text{Required Angle Change}}{\text{Toolface Build/Turn per 100 ft}} \times 100Slide Footage=Toolface Build/Turn per 100 ftRequired Angle Change​×100

Example:
Need to build 12°, toolface performance = 4°/100 ft
→ Slide = 300 ft