Category Archives: Drilling Engineering Calculations

D Exponent Calculation

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D exponent is an extrapolation of drilling parameters to get a trend while drilling into over-pressured zones. Usually, mud logger will correct all data, calculate d-exponent and plot the d exponent valve on the curve. The d-exponent can be utilized to detect transition from normal pressure regime to abnormal formation pressure. While drilling, if the change of trend is observed, rig supervisors must be cautious about this situation because this is one of the possible well control indications.

The “d” exponent described from the equation below:

d = log (R ÷ 60N) ÷ log (12W ÷ 1000D)

Where; R = penetration rate in feet per hour

d = exponent in drilling equation, dimensionless

N = rotary speed in rpm

W = weight on bit in kilo pound

D = bit size in inch

** Note: this equation is is valid for constant drilling fluid weight.

Example: Determine the d-exponent from following information.

Rate of penetration (R) = 90 ft/hr

Rotary drilling speed (N) = 110 rpm

Weight on bit (W) = 20 klb

Bit Diameter (D) = 8.5 in.

Solution: d = log [90÷ (60 x 110)] ÷ log [(12 x 20) ÷ (1000 x 8.5)] d = 1.20

Please find the Excel Sheet for calculating d-exponent.

References

(2010). Well Control for Completions and Interventions. 1st ed. Texas: Gulf Publishing.

Grace, R. (2003). Blowout and well control handbook [recurso electrónico]. 1st ed. Paises Bajos: Gulf Professional Pub.

Grace, R. and Cudd, B. (1994). Advanced blowout & well control. 1st ed. Houston: Gulf Publishing Company.

Watson, D., Brittenham, T. and Moore, P. (2003). Advanced well control. 1st ed. Richardson, Tex.: Society of Petroleum Engineers.

Weight of slug required for desired length of dry pipe with set volume of slug

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You can determine how much slug weight required in order to achieve desired length of dry pipe with certain slug volume that you will use.

slug lenght dry pipe

Oilfield Unit

Please follow these steps of calculation below;

Step 1 Determine Length of slug in drill pipe in ft:

Length of slug in drill pipe in ft = slug volume in bbl ÷ drill pipe capacity in bbl/ft

Step 2 Determine hydrostatic pressure required to give desired dry pipe drill pipe:

Hydrostatic Pressure in psi = mud weight in ppg × 0.052 × desired length of dry pipe

Step 3 Determine slug weight needed in ppg:

Slug weight in ppg = (Hydrostatic Prำssure (from step 2) ÷ 0.052 ÷ Length of slug in ft (step1)) + mud weight, ppg, in hole

Example: Determine slug weight required for the following data:

Desired length of dry pipe = 200 ft

Mud weight in hole = 12.0 ppg

Drill pipe capacity = 0.016 bbl/ft

Volume of slug = 20 bbl

Step 1 – Determine Length of slug inside drill pipe in ft:

Slug length = 20 bbl ÷ 0.016 bbl/ft

Slug length = 1250 ft

Step 2 – Determine hydrostatic pressure required to give desired dry pipe drill pipe

Hydrostatic Pressure in psi = 12.0 × 0.052 × 200

Hydrostatic Pressure in psi = 124.8 psi

Step 3 – Determine slug weight needed in ppg:

Slug weight in ppg = (124.8 ÷ 0.052 ÷ 1250) + 12.0

Slug weight in ppg = 13.9 ppg

Metric Unit

Please follow these steps of calculation below;

Step 1 Determine Length of slug in drill pipe in meter (m):

Length of slug in drill pipe in m = slug volume in m³ ÷ drill pipe capacity in m³/m

Step 2 Determine hydrostatic pressure required to give desired dry pipe drill pipe:

Hydrostatic Pressure in psi = mud weight in kg/m³ × 0.00981 × desired length of dry pipe in m

Step 3 Determine slug weight needed in ppg:

Slug weight in ppg = (Hydrostatic Pressure (from step 2) ÷ 0.00981÷ Length of slug in m (step1)) + mud weight, kg/m³, in hole

Example: Determine slug weight required for the following data:

Desired length of dry pipe = 120 m

Mud weight in hole = 1,400 kg/m³

Drill pipe capacity = 0.007824 m³/m

Volume of slug = 4.5 m³

Step 1 – Determine Length of slug inside drill pipe in ft:

Slug length = 4.5 m³÷ 0.007824 m³/m

Slug length = 575 m

Step 2 – Determine hydrostatic pressure required to give desired dry pipe drill pipe

Hydrostatic Pressure in psi = 1,400 × 0.00981 × 120

Hydrostatic Pressure in psi = 1,648 KPa

Step 3 – Determine slug weight needed in ppg:

Slug weight in ppg = (1,648 ÷ 0.00981 ÷ 575) + 1,400

Slug weight in ppg = 1692 kg/m³

Please find the excel sheet used to calculate Weight of slug required for a desired length of dry pipe with a set volume of slug.

Ref books: 

Lapeyrouse, N.J., 2002. Formulas and calculations for drilling, production and workover, Boston: Gulf Professional publishing.

Bourgoyne, A.J.T., Chenevert , M.E. & Millheim, K.K., 1986. SPE Textbook Series, Volume 2: Applied Drilling Engineering, Society of Petroleum Engineers.

Mitchell, R.F., Miska, S. & Aadny, B.S., 2011. Fundamentals of drilling engineering, Richardson, TX: Society of Petroleum Engineers.

What does the negative vertical section mean?

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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.

vertical-section-direction

The two factors that affect vertical section are as follows:

1. The Incremental horizontal displacement (? 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 ?HD

VS: Vertical Section

VSD: Vertical Section Direction

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

?HD: 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

Directional Drilling Books

Dogleg Severity Calculation Based on Tangential Method

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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)]}

directional survey photo

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

Directional Drilling Books

Dogleg Severity Calculation based on Radius of Curvature Method

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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.

directional survey photo

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

Directional Drilling Books