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Directional Drilling Equations

Browse 33 directional drilling petroleum engineering equations with formulas, inputs, outputs, units, and sources.

Directional drilling calculations support survey interpretation, dogleg severity, build and turn planning, closure, displacement, and trajectory quality checks.

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Drilling EngineeringDirectional Drilling

Average Angle Survey Displacements

\Delta N=\Delta MD\sin\left(\frac{I_1+I_2}{2}\right)\cos\left(\frac{A_1+A_2}{2}\right)

Drilling EngineeringDirectional Drilling

Balanced Tangential Survey Displacements

\Delta N=\frac{\Delta MD}{2}(\sin I_1\cos A_1+\sin I_2\cos A_2)

Drilling EngineeringDirectional Drilling

Borehole Torsion by Cylindrical Helical Method

t=k_h\left(1+\frac{2k_v^2}{k^2}\right)\sin\left(\frac{a\pi}{180}\right)\cos\left(\frac{a\pi}{180}\right)

Drilling EngineeringDirectional Drilling

Build or Drop Rate from Inclination Change

BUR=\frac{(I_2-I_1)100}{\Delta MD}

Drilling EngineeringDirectional Drilling

Build Rate Component from Dogleg Severity and Toolface

BUR=DLS_{req}\cos(TF)

Drilling EngineeringDirectional Drilling

Build Section Measured Depth from Build Rate

\Delta MD=\frac{I_2-I_1}{BUR/100}

Drilling EngineeringDirectional Drilling

Closure Distance and Direction

CD=\sqrt{N^2+E^2}

Drilling EngineeringDirectional Drilling

Curvature Radius for a Borehole

R=\frac{180C}{3.1415k}

Drilling EngineeringDirectional Drilling

Directional Curvature for a Deviated Well

DC = \Delta\phi\frac{100}{\Delta L}

Drilling EngineeringDirectional Drilling

Dogleg Angle - Minimum Curvature Method

\beta=\cos^{-1}[\cos I_1\cos I_2+\sin I_1\sin I_2\cos(A_2-A_1)]

Drilling EngineeringDirectional Drilling

Dogleg Severity - Minimum Curvature Method

DLS=\frac{\beta_{deg}100}{\Delta MD}

Drilling EngineeringDirectional Drilling

EOU Clearance Distance for Wellbore Collision Avoidance

E_{clear}=C_C-(R_{ref}+R_{off})

Drilling EngineeringDirectional Drilling

Horizontal Section Inclination from Bed Dip and Thickness

I_h=90^\circ-dip-\sin^{-1}\left(\frac{h_{res}}{L_h}\right)

Drilling EngineeringDirectional Drilling

Horizontal Wellbore Center-to-Center Separation

S_h=\sqrt{\Delta N^2+\Delta E^2}

Drilling EngineeringDirectional Drilling

Kickoff Point from Target TVD and Build Sections

KOP=TVD_{target}-\Delta TVD_{build1}-\Delta TVD_{tangent}-\Delta TVD_{build2}

Drilling EngineeringDirectional Drilling

Maximum Slanted Well Length in Reservoir Thickness

L=\frac{h}{\cos(\alpha\pi/180)}

Drilling EngineeringDirectional Drilling

Minimum Allowable Separation Distance from Separation Factor

MASD=SF_{min}(R_{ref}+R_{off})

Drilling EngineeringDirectional Drilling

Minimum Curvature Ratio Factor

RF=\frac{2}{\beta}\tan\left(\frac{\beta}{2}\right)

Drilling EngineeringDirectional Drilling

Minimum Curvature Survey Displacements

\Delta N=\frac{\Delta MD}{2}(\sin I_1\cos A_1+\sin I_2\cos A_2)RF

Drilling EngineeringDirectional Drilling

Projected Turn Rate from Azimuth Change

TR=\frac{(A_2-A_1)\sin\left(\frac{I_1+I_2}{2}\right)100}{\Delta MD}

Drilling EngineeringDirectional Drilling

Radius of Curvature from Dogleg Severity

R_c=\frac{180}{\pi DLS}100

Drilling EngineeringDirectional Drilling

Radius-of-Curvature Build Section Departure

\Delta DEP=\frac{180\Delta MD(\cos I_1-\cos I_2)}{\pi(I_2-I_1)}

Drilling EngineeringDirectional Drilling

Radius-of-Curvature Build Section TVD Gain

\Delta TVD=\frac{180\Delta MD(\sin I_2-\sin I_1)}{\pi(I_2-I_1)}

Drilling EngineeringDirectional Drilling

Required Dogleg Severity from Build and Turn Components

DLS_{req}=\sqrt{BUR^2+TR^2}

Drilling EngineeringDirectional Drilling

Sliding Percentage from Required and Motor Dogleg Severity

S_{slide}=\frac{DLS_{req}}{DLS_{motor}}100

Drilling EngineeringDirectional Drilling

Tangential Survey Displacements

\Delta N=\Delta MD\sin I_2\cos A_2

Drilling EngineeringDirectional Drilling

Target TVD Increase from Bed Dip and Departure

\Delta TVD_{target}=DEP\tan(dip)

Drilling EngineeringDirectional Drilling

Three-Dimensional Wellbore Center-to-Center Separation

S_{3D}=\sqrt{\Delta N^2+\Delta E^2+\Delta TVD^2}

Drilling EngineeringDirectional Drilling

Toolface Angle from Build and Turn Components

TF=\operatorname{atan2}(TR,BUR)

Drilling EngineeringDirectional Drilling

Turn Rate Component from Dogleg Severity and Toolface

TR=DLS_{req}\sin(TF)

Drilling EngineeringDirectional Drilling

Vertical Curvature for Deviated Wells

VC = (I_b - I_a)\frac{100}{\Delta L}

Drilling EngineeringDirectional Drilling

Wellbore Separation Factor from EOU Radii

SF=\frac{C_C}{R_{ref}+R_{off}}

Drilling EngineeringDirectional Drilling

Wellbore Separation Ratio to Minimum Allowable Distance

R_{MASD}=\frac{C_C}{MASD}