Drilling Formulas and Drilling Calculations

The tangential method is the simplest calculation among other directional survey calculations.

The tangential method formulas are listed below;

Tangential Method Calculation formula

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The Minimum Curvature Method smooths two straight-line segments of the Balanced Tangential Method by using the Ratio Factor (RF).

The formulas for the Minimum Curvature Method are listed below;

β must be in radians

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I have some directional calculations that I’ve shared with you. However, some of them are not shared yet so I will try to share all directional drilling formulas that may be helpful for you in the future.

Today, I would like to show you about Balanced Tangential Method Calculation. This calculation method treats half of the measured distance (MD/2) as being tangent to I1 and Az1 and the remainder of the measured distance (MD/2) as being tangent to I2 and Az2.

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I created summary page for drilling formulas and calculations (http://www.drillingformulas.com/drilling-formulas-and-calculation-sheets/). I wish these excel sheets would be helpful for you.

Amount of cuttings produced per foot of hole drilled
Annular Pressure Loss
Annular-Capacity
Annular-velocity
Bulk Density Calculation
Buoyancy Factor Oilfield
Convert Pressure to Equivalent Mud Weight
Convert-Specific-Gravity
Cost Per Foot Calculation
Critical RPM
D Exponent Calculation
D Exponent Corrected Calculation
Decrease Oil Water Ratio
Density of Oil Water Mixture
Depth of Washout
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Vertical Section is the horizontal distance of wellbore that moves in the direction of the target per each station or in total.  For instance, in the figure below, vertical section is the distance from survey to survey point and it’s measured in the same direction of the vertical section direction.

The two factors that affect vertical section are as follows:

1. The Incremental horizontal displacement (Δ HD)

2. Vertical section direction (VSD) is the azimuth that is used to reference to the vertical section. Normally, VSD is the azimuth of the last target.

The simple mathematics as Average Angle Method calculation demonstrates the relationship of the VS as below:

VS = cos (VSD – Az avg) X ΔHD

VS: Vertical Section

VSD: Vertical Section Direction

Az avg: Average Azimuth between 2 points (Az1 + Az2) ÷2

ΔHD: Delta Horizontal Displacement

In order to get the Positive Vertical Section or Zero Vertical Section, a well path must have difference of angle between VSD and Az avg, (VSD – Az avg), within a range of +90 to -90 degree. On the other hands, the negative Vertical Section can occur because the difference of angle between VSD and A zavg, (VSD – Az avg), is out of range of +90 to -90 degree AZI.

Ref book: Formulas and Calculations for Drilling, Production and Workover, Second Edition

From the previous post, I posted about how to calculate dogleg severity based on Radius of Curvature Method. What’s more, there is another way to calculate dogleg severity based on the concept of Tangential Method.

The following formula provides dogleg severity in degrees/100 ft and is based on the Tangential Method:

Dogleg severity (DLS) = 100 ÷ {MD x [(sin I1 x sin I2) x (sin Az1 x sin Az2 + cos Az1 x cos Az2) + (cos I1 x cos I2)]}

where

DLS = dogleg severity in degrees/l00 ft

MD = measured depth between survey points, ft

I1 = inclination (angle) at upper survey in degrees

I2 = inclination (angle) at lower in degrees

Az1= Azimuth direction at upper survey

Az2 = Azimuth direction at lower survey

Calculation example for dogleg severity based on Tangential Method

Survey 1

Depth = 7500 ft

Inclination = 45 degree (I1)

Azimuth = 130 degree (Az1)

Survey 2

Depth = 7595 ft

Inclination = 52 degree (I2)

Azimuth = 139 degree (Az2)

Dogleg severity (DLS) = 100 ÷ {95 x [(sin 45 x sin 52) x (sin 130 x sin 139 + cos 130 x cos 139) + (cos 45 x cos 52)]}

Dogleg severity (DLS) = 1.07 degree/100 ft

Please find the Excel sheet for calculating dogleg severity with the concept of Tangential Method
Ref book: Formulas and Calculations for Drilling, Production and Workover, Second Edition

Dogleg severity (DLS) is a normalized estimation, normally described in degrees per 100 feet or degree per 30 meters, of the overall well bore curvature between two consecutive directional surveys. Regarding a planned well path, dogleg severity may be synonymous about build and/or turn. The following formula provides dogleg severity in degrees/100 ft  based on the Radius of Curvature Method.

Dogleg severity (DLS) = {cos^-1 [(cos I1 x cos I2) + (sin I1 x sin I2) x cos (Az2 - Az1)]} x (100 ÷ MD)

Where;

DLS = dogleg severity in degrees/l00 ft

MD = Measured Depth between survey points in ft

I1 = Inclination (angle) at upper survey in degrees

I2 = Inclination (angle) at lower in degrees

Az1= Azimuth direction at upper survey

Az2 = Azimuth direction at lower survey

Example for dogleg severity based on Radius of Curvature Method

Survey 1

Depth = 7500 ft

Inclination = 45 degree (I1)

Azimuth = 130degree (Az1)

Survey 2

Depth = 7595 ft

Inclination = 52 degree (I2)

Azimuth = 139 degree (Az2)

Dogleg severity (DLS) = {cos^-1 [(cos 45 x cos 52) + (sin 45 x sin 52) x cos (139 - 130)]} x (100 ÷ 95)

Dogleg severity (DLS) =  10.22 degree/100 ft

Please find the Excel sheet used to calculate dogleg severity based on Radius of Curvature Method.

Ref book: Formulas and Calculations for Drilling, Production and Workover, Second Edition

Radius of Curvature Method is the most famous method for directional survey calculation. You can calculate North, East and TVD between directional surveys based on the Radius of Curvature Method as per formula below:

Where;

MD = measured depth between surveys in ft

I1 = inclination (angle) at upper survey in degrees

I2 = inclination (angle) at lower in degrees

Az1= Azimuth direction at upper survey

Az2 = Azimuth direction at lower survey

Calculation example for Radius of Curvature Method

Survey 1

Depth = 7500 ft

Inclination = 45 degree (I1)

Azimuth = 130degree (A1)

Survey 2

Depth = 7595 ft

Inclination = 52 degree (I2)

Azimuth = 139 degree (A2)

MD = 7595 – 7500 = 95 ft

As per the calculation above,

North = -49.97 ft

East = 50.66 ft

TVD = 62.91 ft

Please find the Excel sheet used for directional survey calculation with Radius of Curvature Method.

Ref book: Formulas and Calculations for Drilling, Production and Workover, Second Edition

You can calculate North, East and TVD between directional surveys based on the Angle Averaging Method as per formula below:

Where;

MD = measured depth between surveys in ft

I1 = inclination (angle) at upper survey in degrees

I2 = inclination (angle) at lower in degrees

Az1= Azimuth direction at upper survey

Az2 = Azimuth direction at lower survey

Calculation example for Angle Averaging Method

Survey 1

Depth = 7500 ft

Inclination = 45 degree

Azimuth = 130degree

Survey 2

Depth = 7595 ft

Inclination = 52 degree

Azimuth = 139 degree

As per formula above,

North = -49.87 ft

East = 50.74 ft

TVD = 62.95 ft

Please find the Excel sheet used for directional survey calculation with Angle Averaging Method

Ref book: Formulas and Calculations for Drilling, Production and Workover, Second Edition