Drilling Formulas and Drilling Calculations

All types of ton-mile service should be calculated and recorded in order to obtain a true picture of the total service received from the rotary drilling line. There are several types of ton miles as follows;

1. Round trip ton-miles
2. Drilling or “connection” ton-miles
3. Coring ton-miles
4. Ton-miles setting casing
5. Short-trip ton-miles

For this time, I will show how to calculate round trip ton-mile.

Round Trip Ton-Miles Calculation

The formula for round trip ton-miles is listed below;

RTTM = (Wp x D x (Lp + D) + (2 x D) x (2 x Wb + Wc)) ÷ (5280 x 2000)

where
RTTM = Round Trip Ton-Miles
Wp = buoyed weight of drill pipe in lb/ft
D = hole measured depth in ft
Lp = Average length per stand of drill pipe in ft
Wb = weight of travelling block in lb
Wc = buoyed weight of BHA (drill collar + heavy weight drill pipe + BHA) in mud minus the buoyed weight of the same length of drill pipe in lb
** If you have BHA (mud motor, MWD, etc) and HWDP, you must add those weight into calculation as well not just only drill collar weight. **
2000 = number of pounds in one ton
5280 = number of feet in one mile

Example: Round trip ton-miles

Mud weight = 10.0 ppg
Average length per stand = 94 ft
Drill pipe weight = 13.3 lb/ft
Hole measure depth = 5500 ft
Drill collar length = 120 ft
Drill collar weight = 85 lb/ft
HWDP length = 49 lb/ft
HWDP weight = 450 ft
BHA weight from directional driller = 8,300 lb
BHA length = 94 ft
Travelling block assembly = 95,000 lb

Solution:

a) Buoyancy factor:
BF = (65.5 – 10.0) ÷ 65.5
BF = 0.847

b) Buoyed weight of drill pipe in mud, lb/ft (Wp):
Wp = 13.3 lb/ft x 0.847
Wp = 11.27 lb/ft

c) buoyed weight of BHA (drill collar + heavy weight drill pipe + BHA) in mud minus the buoyed weight of the same length of drill pipe in lb (Wc):

Wc = {[(120x85) + (49x450) + (8300)] x 0.847} – [(120+450+94) x13.3x 0.847]
Wc = 26,866 lb

Round trip ton-miles = [(11.27 x 5500 x (94+ 5500)) + (2 x 5500) x (2 x 95000 + 26,866)] ÷ (5280 x 2000)
RTTM = 258.75 ton-mile

Please find the excel sheet for round trip ton-miles calculation via click this link.

Referencer book:

Formulas and Calculations for Drilling, Production and Workover, Second Edition

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For subsea applications, hydrostatic pressure exerted by the hydraulic fluid must be accounted for calculation.

In this case, we assume water depth at 1500 ft, therefore hydrostatic pressure exerted by hydraulic fluid (hydraulic fluid pressure gradient = 0.445 psi/ft) = 0.445×1500 = 668 psi. Besides of that, the concept for calculation is as same as surface accumulator. So please take a look about how to calculate usable volume per bottle as following steps.

Step 1 Adjust all pressures for the hydrostatic pressure of the hydraulic fluid:

Pre-charge pressure = 1000 psi + 668 psi = 1668 psi

Minimum system pressure = 1200 psi + 668 psi = 1868 psi

Operating pressure = 3000 psi + 668 psi = 3668 psi

Step 2 Determine hydraulic fluid required to increase pressure from pre-charge pressure to minimum system pressure:

Boyle’s Law for ideal gase: P1 V1 = P2 V2

1668 psi x 10 = 1868 x V2

16,680 ÷1,868 = V2

V2 = 8.93 gal

It means that N2 will be compressed from 10 gal to 8.93 gal in order to reach minimum operating pressure. Therefore, 1.07 gal (10.0 – 8.93 = 1.07 gal) of hydraulic fluid is used for compressing to minimum system pressure.

Step 3 Determine hydraulic required increasing pressure from pre-charge to operating pressure:

P1 V1 = P2 V2

1668 psi x 10 gal = 3668 psi x V2

16,680 ÷ 3668 = V2

V2 = 4.55 gal

It means that N2 will be compressed from 10 gal to 4.55 gal in order to reach operating pressure. Therefore, 5.45 gal (10.0 – 4.55 = 5.45 gal) of hydraulic fluid is used for compressing to operating pressure.

Step 4 Determine usable fluid volume per bottle:

Usable volume per bottle = Total hydraulic fluid/bottle – Dead hydraulic fluid/bottle

Usable volume per bottle = 5.45 – 1.07

Usable volume per bottle = 4.38 gallons

Ref: Formulas and Calculations for drill, production and workover by Norton J. Lapeyrouse

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Accumulator (Koomey) is a unit used to hydraulically operate Rams BOP, Annular BOP, HCR and some hydraulic equipment. There are several of high pressure cylinders that store gas (in bladders) and hydraulic fluid or water under pressure for hydraulic activated systems. The primary purpose of this unit is to supply hydraulic power to the BOP stack in order to close/open BOP stack for both normal operational and emergency situation. Stored hydraulic in the system can provide hydraulic power to close BOP’s in well control operation, therefore, kick volume will be minimize. Accumulators should have sufficient volume to close/open all preventers and accumulator pressure must be maintained all time.

This post you will learn how to calculate usable volume per bottle by applying Boyle’s gas law:

Use following information as guideline for calculation:

Volume per bottle = 10 gal

Pre-charge pressure = 1000 psi

Operating pressure = 3000 psi

Minimum system pressure = 1200 psi

Pressure gradient of hydraulic fluid = 0.445 psi/ft

For surface application

Step 1 Determine hydraulic fluid required to increase pressure from pre-charge pressure to minimum:

Boyle’s Law for ideal gase: P1 V1 = P2 V2

P1 V1 = P2 V2

1000 psi x 10 gal = 1200 psi x V2

10,000 ÷ 1200 = V2

V2 = 8.3 gal

It means that N2 will be compressed from 10 gal to 8.3 gal in order to reach minimum operating pressure. Therefore, 1.7 gal (10.0 – 8.3 = 1.7 gal) of hydraulic fluid is used for compressing to minimum system pressure.

Step 2 Determine hydraulic required increasing pressure from pre-charge to operating pressure:

P1 V1 = P2 V2

1000 psi x 10 gals = 3000 psi x V2

10,000 ÷3000 = V2

V2= 3.3 gal

It means that N2 will be compressed from 10 gal to 3.3 gal. Therefore, 6.7 gal (10.0 – 3.3 = 6.7 gal) of hydraulic fluid is used for compressing to operating pressure.

Step 3 Determine usable fluid volume per bottle:

Usable volume per bottle = Hydraulic used to compress fluid to operating pressure – hydraulic volume used to compress fluid to minimum pressure

Usable volume per bottle = 6.7 – 1.7

Usable volume per bottle = 5.0 gallons

Ref: Formulas and Calculations for drill, production and workover by Norton J. Lapeyrouse

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Hydrostatic pressure is pressure that exert by density of fluid column. The relationship of hydrostatic pressure is shown in the equation below.

HP (Hydrostatic Pressure) = density x g (gravity acceleration) x h (True Vertical Depth, TVD)

In oilfield term, the formula above is modified so that people can use it easily. The formulas are as follows:

HP = Constant x MW x TVD

HP = 0.052 x MW (ppg) x TVD (ft) ** Most frequent used in the oilfield **

HP = 0.007 x MW (pcf) x TVD (ft)

HP = 0.00981 x MW (kg/m3) x TVD (m)

According to the equation, Hydrostatic Pressure is not a function of hole geometry. Only mud weight and True Vertical Depth (TVD) affect on Hydrostatic Pressure.  For example (a picture below); well A and well B have the same vertical depth. With the same mud density in hole, the bottom hole pressure due to hydrostatic pressure is the same. The only different between Well A and Well B is mud volume.

This concept is basic and very important for many aspects such as well control, balance cementing, u-tube, etc.

This is one of well control series. To be continue 

Ref: Well Control Handbook

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The original “d” exponent is good for constant mud weight but in reality several drilling operations drill with various mud weights in hole due to weight up. In order to account for mud weight variation, so modification of d exponent, called “corrected d exponent”, has been made to correct for mud weight changes.

The corrected d-exponent is listed below.

dc = log (R ÷ 60N) ÷ log (12W ÷ 1000D) x (MW1 ÷ MW2)

Where;

dc = corrected “d” exponent

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

MW1 = initial mud weight in ppg

MW2 = actual mud weight in ppg

Example: Determine the corrected 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

MW1 = 9.0 ppg

MW2 = 12.0 ppg

Solution: dc = log [90÷ (60 x 110)] ÷ log [(12 x 20) ÷ (1000 x 8.5)] x (9.0 ÷ 12.0)

dc = 1.20 x 0.75

dc = 0.9

** Please remember that single d exponent or corrected d exponent valve does not help identify abnormal pressure. The trend of d exponent will help drilling personnel detect high formation pressure zones while drilling.

Ref book: Formulas and Calculations for drill, production and workover by Norton J. Lapeyrouse

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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.

Ref book: Formulas and Calculations for drill, production and workover by Norton J. Lapeyrouse

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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. 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 x 0.052 x desired length of dry pipe

Step 3 Determine slug weight needed in ppg:

Slug weight in ppg = (Hydrostatic Prssure (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

Slug length = 1250 ft

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

Hydrostatic Prssure in psi = 12.0 x 0.052 x 200

Hydrostatic Prssure 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 = 13.92 ppg

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 book: Formulas and Calculations for drill, production and workover by Norton J. Lapeyrouse

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What is slug? Slug: It is heavy mud which is used to push lighter mud weight down before pulling drill pipe out of hole. Slug is used when pipe became wet while pulling out of hole.

Normally, 1.5 to 2 PPG over current mud weight is a rule of thumb to decide how much weight of slug should be. For example, current mud weight is 10 PPG. Slug weight should be about 11.5 to 12 PPG. Generally, slug is pumped to push mud down approximate 200 ft and slug volume can be calculated by applying a concept of U-tube (See Figure below).

Volume of slug required for required length of dry pipe can be calculated by this following equations:

Step 1: Determine hydrostatic pressure required to give desired drop inside drill pipe:

Hydrostatic Pressure in psi = mud weight in ppg x 0.052 x ft of dry pipe

Step 2: Determine difference in pressure gradient between slug weight and mud weight:

Pressure gradient difference in psi/ft = (slug weight in ppg – mud weight in ppg) x 0.052

Step 3: Determine length of slug in drill pipe:

Slug length in ft = Hydrostatic Pressure in psi (in step 1) ÷ Pressure gradient difference in psi/ft (step 2)

Step 4 Slug volume required in barrels:

Slug volume in barrel = Slug length in ft x drill pipe capacity in bbl/ft

Example: Determine the barrels of slug required for the following:

Desired length of dry pipe = 200 ft

Drill pipe capacity = 0.016 bbl/ft

Mud weight = 10.0 ppg

Slug weight = 11.5 ppg

Step 1 Hydrostatic pressure required:

Hydrostatic Prssure in psi = 10.0 ppg x 0.052 x 200 ft

Hydrostatic Prssure in psi = 104 psi

Step 2 differences in pressure gradient between slug weight and mud weight:

Pressure gradient difference in psi/ft = (11.5 ppg – 10.5 ppg) x 0.052

Pressure gradient difference in psi/ft = 0.078 psi/ft

Step 3 length of slug in drill pipe:

Slug length in ft = 104psi ÷ 0.078

Slug length in ft = 1,333 ft

Step 4 Slug volume required in barrels:

Slug volume required = 1333 ft x 0.016 bbl/ft

Slug volume required = 21.3 bbl

Please find the Excel sheet for calculating barrels of slug required for desired length of dry pipe.

Ref book: Formulas and Calculations for drill, production and workover by Norton J. Lapeyrouse

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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 drill, production and workover by Norton J. Lapeyrouse

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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)]}

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 drill, production and workover by Norton J. Lapeyrouse

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