Drilling Formulas and Drilling Calculations

From the previous post, Equivalent Circulating Density (ECD) in ppg, you may want to know how to determine annular pressure loss in order to calculate Equivalent Circulating Density (ECD) in ppg. So use the following formula to calculate annular pressure loss. This formula will give you idea about how much pressure loss but if you want to get the more accurate, you may need to contact your drilling fluid company to do it for you because they have the actual database and more complex formula that may help you get the good number. Anyway this formula can give you an idea how much annular pressure loss you will encounter.

P= [(1.4327 x 10^-7) x MW x Lx V²] ÷ (Dh – Dp)

P = annular pressure losses, psi

MW = mud weight in ppg

L = length of annular in ft

V = annular velocity in ft/mm

Dh = hole or casing ID in inch

Dp = drill pipe or drill collar OD in inch

Example:

Mud weight = 13.0 ppg

Length = 8000 ft

Circulation rate = 320 gpm

Hole size = 6.5 in.

Drill pipe OD = 4.0 in.

Determine annular velocity, ft/mm: v = (24.5 x 320) ÷ (8.5² – 5.0²)

v = 299 ft/min

Determine annular pressure losses, psi: P = [(1.4327 x 10^-7) x 13.0 x 8000 x 299²] ÷ (8.5 – 5.0)

P = 531.65 psi

Please find the Excel sheet to calculate annular pressure loss

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

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Equivalent Circulating Density (ECD) is the effective density that combines current mud density and annular pressure drop. ECD is critical for drilling operations because it can caused losses due to high pressure loss in annulus. Moreover, ECD is very critical in both well control and losses aspects in the areas where have narrow room between pore pressure and fracture gradient.

The equivalent circulating density formula is shown below

Equivalent Circulating Density (ECD) in ppg = (annular pressure loss in psi) ÷ 0.052 ÷ true vertical depth (TVD) in ft + (current mud weight in ppg)

Example:
Annular pressure loss = 400 psi
True Vertical Depth = 8,000 ft
Current mud weight in ppg = 10 ppg

ECD in ppg = (400 psi ÷ 0.052 ÷ 8,000 ft) + 10.0 ppg
ECD = 11.0 ppg

Please find the Excel sheet to calculate equivalent circulating density (ECD)

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

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Annular Velocity (AV) is how fast of fluid in annulus is traveling. Three main factors affecting annular velocity are size of hole (bigger ID), size of drill pipe (smaller OD) and pump rate. This post will show you how to calculate annular velocity in feet per minute with different formulas.
Annular velocity (AV) in ft/min

Formula#1: Annular velocity (AV) in ft/min

Annular velocity in ft/min = Flow rate in bbl/min ÷ annular capacity in bbl/ft

Example:
Flow rate = 10 bbl/min
Annular capacity = 0.13 bbl/ft
AV = 10 bbl/min ÷ 0.13 bbl/ft
AV = 76.92 ft/mim

Formula#2: Annular velocity (AV) in ft/min

Annular velocity in ft/min = (24.5 x Q) ÷ (Dh² – Dp²)

where
Q = flow rate in gpm
Dh = inside diameter of casing or hole size in inch
Dp = outside diameter of pipe, tubing or collars in inch

Example:
Flow rate (Q) = 800 gpm
Hole size = 10 in.
Drill pipe OD = 5 in.
AV = (24.5 x 800) ÷ (10² – 5²)
AV = 261 ft/mim

Formula#3: Annular velocity (AV) in ft/min
Annular Velocity in ft/min = Flow rate (Q) in bbl/min x 1029.4÷ (Dh² – Dp²)

Example:
Flow rate (Q) = 13 bbl/min
Hole size = 10 in.
Drill pipe OD = 5 in.
AV = 13 bbl/min x 1029.4 ÷ (10² – 5²)
AV = 178.43 ft/min

You also can back calculate how much flow rate you want for desired annular velocity in feet per minute as per following fomulas.

Flow rate required in gpm = (AV in ft/min) x (Dh² – DP²) ÷ 24.5

AV = desired annular velocity in ft/min
Dh = inside diameter of casing or hole size in inch
Dp = outside diameter of pipe, tubing or collars in inch

Example:
Desired annular velocity = 120 ft/mm
Hole size = 10 in
Drill pipe OD = 5 in.
Flow rate required in gpm = 120 x (10²- 5²) ÷ 24.5
Flow rate required in gpm = 367.4 gpm

Moreover, you can calculate strokes per minute (SPM) required for a given annular velocity in feet per minute as well. The idea is to use the formula above and devided by pump output in bbl/stk. Let’s review the fomula.

SPM = (AV in ft/min x annular capacity in bbl/ft) ÷ pump output in bbl/stk

AV = desired annular velocity in ft/min

Example
Desired annular velocity in ft/min = 120 ft/min
Dh = 12-1/4 in.
Dp = 4-1/2 in.
Annular capacity = 0.1261 bbl/ft
Pump output = 0.136 bbl/stk
SPM = (120 ft/mm x 0.1261 bbl/ft) ÷ 0.136 bbl/stk
SPM = 111.3 spm

Please find the Excel sheet  for calculating annular velocity

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

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Rig pump out put, normally in bbl per stroke, of mud pumps on the rig is important figures that we really need to know because we will use pump out put figures to calculates many things such as bottom up strokes,  wash out depth, tracking drilling fluid, etc. In this post, you will learn how to calculate pump out put for triplex pump and duplex pump.

Triplex Pump Output Formula

Triplex Pump Output in bbl/stk = 0.000243 x (liner diameter in inch) ² X (stroke length in inch)

Example: Determine the pump output in bbl/stk at 100% and 97% efficiency
Linner size = 6 inch
Stroke length = 12 inch
Triplex pump output:
PO @ 100% = 0.000243 x 6² x 12
PO @ 100% = 0.104976 bbl/stk

Adjust the triplex pump output for 97% efficiency:
Decimal equivalent = 97 ÷ 100 = 0.97
PO @ 97% = 0.104976 bbl/stk x 0.97
PO @ 97% = 0.101827 bbl/stk

Duplex Pump Output Formula

Duplex Pump Output in bbl/stk = 0.000162 x S x [2(D)² - d²]

Whrere:
D = liner diameter in inch
S = stroke length in inch
d = rod diameter in inch

Example: Determine the duplex pump output in bbl/stk at 100% and 85% efficiency

Liner diameter = 6 inch
Stroke length = 12 inch
Rod diameter = 2.0 in.

Duplex pump efficiency = 100 %.
PO @ 100% = 0.000162 x 12 x [2 (6) ² -12² ]
PO @ 100% = 0.13219 bbl/stk

Adjust pump output for 85% efficiency:
PO @ 85% = 0.132192 bbl/stk x 0.85
PO @ 85% = 0.11236 bbl/stk

Please find the Excel sheet to calculate triplex pump output and duplex pump output

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

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Formation Integrity Test is the method to test strength of formation and shoe by increasing Bottom Hole Pressure (BHP) to designed pressure. FIT is normally conducted to ensure that formation below show will not be broken while drilling the next section with higher BHP. Normally, engineers in town will design how much formation integrity test pressure required mostly in ppg.

Before forming formation integrity test, you should know pressure required for Formation Integrity Test. The formula showed below demonstrates you how to calculate required FIT pressure.

Pressure required for FIT (psi) = (Required FIT in ppg – Current Mud Weight in ppg) x 0.052 x True Vertical Depth of shoe in ft

Example:
Required FIT (ppg) = 14.5
Current mud weight (ppg) = 9.2
Shoe depth TVD (ft) = 4000 TVD
Pressure required for FIT = (14.5-9.2) x 0.052 x 4000 = 1102 psi
Formation Integrity Test (FIT) sguide line as follows: (note: this is just only guide line. You may need to follow your standard procedure in order to perform formation integrity test):

1. Drill out new formation few feet, circulate bottom up and collect sample to confirm that new formation is drilled to and then pull string into the casing.

2. Close annular preventer or pipe rams, line up a pump, normally a cement pump, and circulate through an open choke line to ensure that surface line is fully filled with drilling fluid.

3. Gradually pump small amount of drilling fluid into well with constant pump stroke. Record total pump strokes, drill pipe pressure and casing pressure. Pump until casing pressure reaches the pressure required for formatin integrity test. Hold pressure for few minutes to confirm pressure.

4. Bleed off pressure and open up the well. Then proceed drilling operation.

Please find the Excel sheet to calculate pressure required for formation integrity test.

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

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Leak Off Test is conducted in order to find the fracture gradient of certain formation. The results of the leak off test also dictate the maximum equivalent mud weight that should be applied to the well during drilling operations.

Leak Off Test (LOT) guide line procedures are as follows  (note: this is just only guide line. You may need to follow your standard procedure in order to perform leak off test):

1.Drill out new formation few feet, circulate bottom up and collect sample to confirm that new formation is drilled to and then pull string into the casing.

2.Close annular preventer or pipe rams, line up a pump, normally a cement pump, and circulate through an open choke line to ensure that surface line is fully filled with drilling fluid.

3.Gradually pump small amount of drilling fluid into well with constant pump stroke. Record total pump strokes, drill pipe pressure and casing pressure. Drill pipe pressure and casing pressure will increase continually while pumping mud in hole. When plot a graph between strokes pumped and pressure, if formation is not broken, a graph will demonstrate straight line relationship. When pressure exceeds formation strength, formation will be broken and let drilling fluid permeate into formation, therefore a trend of drill pipe/casing  pressure will deviate from straight line that mean formation is broken and is injected by drilling fluid. We may call pressure when deviated from straight line as leak off test pressure.

Note:  the way people call leak off test pressure depends on each company standard practices.

Leak off test pressure can be calculated into equivalent mud weight in ppg as formula below:

Leak off test in equivalent mud weight (ppg) = (Leak off test pressure in psi) ÷ 0.052 ÷ (Casing Shoe TVD in ft) + (current mud weight in ppg)

Pressure gradient in psi/ft = (Leak off test pressure in psi) ÷ (Casing Shoe TVD in ft)

Example:

Leak off test pressure = 1600 psi
Casing shoe TVD = 4000 ft
Mud weight = 9.2 ppg

Leak off test in equivalent mud weight (ppg) = 1600 psi ÷ 0.052 ÷ 4000 ft + 9.2ppg ppg = 16.9

Pressure gradient = 1600 ÷ 4000 = 0.4 psi/ft

4.Bleed off pressure and open up the well. Then proceed drilling operation.

Please find the Excel sheet to calculate leak off test

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

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Referring to the previous post, Calculate Specific Gravity (SG) in oilfield unit , you get specific gravity (SG) from mud weight (ppg and lb/ft³) and pressure gradient (psi/ft) but you may need to reverse calculation from specific gravity (SG) to mud weight or pressure gradient (psi/ft). So you will learn how to how to convert specific gravity to mud weight (ppg and lb/ft³) and pressure gradient (psi/ft) by using simple formulas as follows:

1. Convert specific gravity to mud weight in pounds per gallon (ppg)
Convert specific gravity fomula: mud weight in ppg = specific gravity (SG) x 8.33
Example: specific gravity = 1.50
mud wt, ppg = 1.50 x 8.33
mud wt = 12.5 ppg

2. Convert specific gravity to mud weight in lb/ft³
Convert specific gravity fomula: Mud weight in lb/ft3 = specific gravity x 62.4
Example: specific gravity = 1.50
Mud weight in lb/ft³ = 1.50 x 62.4 lb/ft³
Mud weight in lb/ft³ = 93.6 lb/ft³

3. Convert specific gravity to pressure gradient in psi/ft
Convert specific gravity fomula: Pressure gradient in psi/ft = specific gravity (SG) x 0.433
Example: specific gravity = 1.5
Pressure gradient in psi/ft  = 1.5 x 0.433
Pressure gradient in psi/ft = 0.650 psi/ft

Please also find the Excel sheet regarding how to convert specific gravity (SG)

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

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You may need to calculate specific gravity from different density or pressure gradient units. This post demonstrates you about specific gravity calculation and specific gravity formulas frequently used in oilfield business.

1. Calculate specific gravity using mud weight in PPG

Specific gravity formula : SG = mud weight in ppg ÷ 8.33

Example:  Fluid = 13.0 ppg
SG = 13.0 ppg ÷ 8.33
SG = 1.56

2. Calculate specific gravity using pressure gradient in psi/ft

Specific gravity formula : SG = pressure gradient in psi/ft ÷ 0.433

Example: pressure gradient = 0.50 psi/ft
SG = 0.50 psi/ft ÷ 0.433
SG = 1.15

3. Calculate specific gravity using mud weight in lb/ft³

Specific gravity formula : SG = mud weight in lb/ft³ ÷ 62.4

Example: Mud weight = 90 lb/ft³
SG = 90 lb/ft³÷ 62.4
SG = 1.44

Please also find the Excel Sheet: Specific Gravity Calculation Sheet

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

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Learn how to convert pressure into equivalent mud weight in PPG as per following formulas.

1. Convert pressure in psi  unit into equivalent mud weight in ppg by using feet as the unit of measurement

Equivalent Mud Weight, ppg = pressure in psi ÷ 0.052 ÷ True Vertical Depth (TVD) in ft
Example: pressure = 5000 psi true vertical depth = 8000 ft
Equivalent mud weight, ppg = 5000 psi ÷ 0.052 ÷ 8000 ft
Equivalent mud weight, ppg = 12.0 ppg
2. Convert pressure in psi  unit into equivalent mud weight in ppg by using meters as the unit of measurement

Equivalent Mud Weight in ppg = Pressure in psi ÷ 0.052 ÷ True Vertical Depth (TVD) in meters ÷  3.281

Example: pressure = 5000 psi
True Vertical Depth = 2500 meters
Equivalent mud weight, ppg = 5000 psi ÷ 0.052 ÷ 2500 m ÷ 3.281
Equivalent mud weight, ppg = 11.7 ppg

Please find the Excel sheet for converting pressure into equivalent mud weight.

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

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Hydrostatic pressure is created by fluid column. Two factors affecting hydrostatic pressure  are mud weight and True Vertical Depth. So this post will demonstrate how to calculate hydrostatic pressure in different oilfield units.

1. Calculate hydrostatic pressure in psi by using mud weight  in PPG and feet as the units of True Vertical Depth.

Hydrostatic pressure equation:
HP = mud weight in ppg x 0.052 x True Vertical Depth (TVD) in ft

Example: mud weight = 12.0 ppg
True Vertical Depth = 10,000 ft
HP = 12.0 ppg x 0.052 x 10,000 ft
HP = 6,240 psi

2. Calculate hydrostatic pressure in psi by using pressure gradient in psi/ft and feet as the units of True Vertical Depth.

Hydrostatic pressure equation:
HP = Pressure gradient in psi/ft x True Vertical Depth (TVD) in ft

Example: Pressure Ggradient = 0.5 psi/ft
True Vertical Depth = 10,000 ft
HP = 0.5 psi/ft x 10,000 ft
HP = 5,000 psi

3 Calculate hydrostatic pressure in psi by using mud weight in lb/ft³ and feet as the units of True Vertical Depth.

Hydrostatic pressure equation:
HP = 0.006944 x mud weight, lb/ft³ x TVD, ft

Example: mud weight = 80 lb/ft³ true vertical depth = 10,000 ft
HP = 0.006944 x 80 lb/ft³ x 10,000 ft
HP = 5,555 psi

4. Calculate hydrostatic pressure in psi by using mud weight in PPG and meters as unit of True Vertical Depth.

Hydrostatic pressure equation:
HP = mud weight, ppg x 0.052 x TVD in meters x 3.281

Example: Mud weight = 12.0 ppg true vertical depth = 5000 meters
HP = 12.0 ppg x 0.052 x 5000 x 3.281
HP = 10,237 psi

Download the Excel sheet for calculating hydrostatic pressure

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