Drilling Formulas and Drilling Calculations

You have learn how to weight up with Barite and Calcium Carbonate from previous posts. Sometimes, you may need to weight up to extremely high weight therefore you may consider using Hematite , its average specific gravity +/- 4.8, to weight up your mud system. If you are interested in Hematite information, please take a look at Wiki.

The concept of weighting up calculation with Hematite is as same as the concept of weighting up with Barite and Calcium Carbonate. The only one thing change is weight factor used in the equation. Please follow the equation below for calculating how many sacks required to weight up per 100 bbl of original mud.
Sacks of Hematite per 100 bbl of mud = 1680 x (W2 – W1) ÷ (40 – W2)

Where; W1 = current mud weight in ppg

W2 = new mud weight in ppg

Example: Determine the number of sacks of Hematite per l00 bbl required to increase the density from 10.0 ppg (W1) to 13.0 ppg (W2):

Sacks of hematite per 100 bbl of mud = 1680 x (13.0 – 10.0) ÷ (40 – 13.0)

Sacks of hematite per 100 bbl of mud = 186.7 sacks

If you have total volume of 500 bbl of mud, calcium carbonate required to increase mud weight from 10.0 ppg to 13.0 ppg is 933.3 sacks (186.7×500/100).

Please find the Excel used for calculating how many sacks required in case of weighting up with Hematite.

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

You know how much volume will be increased due to adding calcium carbonate into the system; however, you sometimes are limited to total volume due to limit pit volume on the rig so you need to calculate starting volume to achieve the predetermined final volume of desired mud weight.
This formula below is used to determine the staring volume of mud (for calcium carbonate system).

Starting volume in bbl  = VF x (22.5 – W2) ÷ (22.5 – W1)

Where; W1 = current mud weight in ppg

W2 = new mud weight in ppg

VF = final volume of mud needed in bbl

Example: Determine the barrel of starting volume of 10.0 ppg (W1) mud required to achieve final volume of 100 bbl (VF) of 13.0 ppg (W2) mud with calcium carbonate:

Starting volume in bbl = VF x (22.5 – W2) ÷ (22.5 – W1)

Starting volume in bbl = 100 x (22.5 – 13.0) ÷ (22.5 – 10.0)

Starting volume = 76 bbl

In order to achieve  final mud volume of 100 bbl of 13.0 ppg mud weight up with calcium carbonate, you must have 76.0 bbl starting volume of 10.0 ppg mud.

Please find the Excel sheet for calculating Barrel of starting volume of original mud weight required to give a predetermined final volume of desired mud weight with CALCIUM CARBONATE.

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

The concept of mud volume increase due to adding calcium carbonate is as same as the mud volume increase by adding barite. The formula for calculating volume increment is just different only one factor which is 22.5 for calcium carbonate but 35 is used for barite case. Please follow the formula below for determining volume increase because of adding calcium carbonate.

Volume increase per 100 bbl of mud due to adding Calcium Carbonate = 100 x (W2 – W1) ÷ (22.5 – W2)

Where; W1 = current mud weight

W2 = new mud weight

Example: Determine the volume increase when increasing the density with calcium carbonate from 10.0 ppg (W1) to 13.0 ppg (W2):

Volume increase per 100 bbl of mud =100 x (13.0 – 10.0) ÷ (22.5 – 13.0)

Volume increase per 100 bbl of mud = 31.58 bbl

If you have total volume of 500 bbl of mud, the volume increase due to adding calcium carbonate will be equal to 157.9 bbl (31.58 x 500 ÷ 100).

Please find the Excel sheet for determine mud volume increase due to adding calcium carbonate.

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

Carbonate is weighing agent mostly used in horizontal well because it does not plug up formation. We can use the same weight up concept with barite to calculate how to weight up with carbonate. Follow a topic below to learn how to weight up with calcium carbonate.

NOTE: The maximum practical mud weight attainable with calcium carbonate is 14.0 ppg.

This formula below is used for calculating how many sacks of calcium carbonate required per 100 bbl of drilling fluid (Mud weight increase with calcium carbonate (SG – 2.7))

Sacks of calcium carbonate per 100 bbl of mud = 945 x (W2 – W1) ÷ (22.5 – W2)

Where; W1 = current mud weight

W2 = new mud weight

Example: Determine the number of sacks of calcium carbonate per l00 bbl required to increase the density from 10.0 ppg (W1) to 13.0 ppg (W2):
Sacks of calcium carbonate per 100 bbl of mud = 945 x(13.0 – 10.0) ÷ (22.5 – 13.0)

Sacks of calcium carbonate per 100 bbl of mud = 298.4 sacks
If you have total volume of 500 bbl of mud, calcium carbonate required to increase mud weight from 10.0 ppg to 13.0 ppg is 1,492 sacks (298.4×500/100).

Please find the Excel sheet for calculating how many sacks of calcium carbonate required per 100 bbl of drilling fluid.

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

You know how much volume will be increased due to adding barite into the system; however, you sometimes are limited to total volume due to limit pit volume on the rig so you need to calculate starting volume to achieve the predetermined final volume of desired mud weight. This formula below is used to determine the star volume of mud in case of weighting up with Barite.

Starting volume in bbl = VF x (35 – W2) ÷ (35 – W1)

Where; W1 = current mud weigth in ppg

W2 = new mud weight in ppg

VF = final volume in bbl

Example: Determine the starting volume (bbl) of 10.0 ppg (W1) mud required to achieve 100 bbl (VF) of 13.0 ppg (W2) mud with barite:

Starting volume in bbl = 100 x (35 – 13.0) ÷ (35 – 10.0)

Starting volume in bbl= 88.0 bbl

In order to achieve 100 bbl of 13.0 ppg mud weight up with barite, you must have 88.0 bbl starting volume of 10.0 ppg mud.

Please find the Excel sheet for calculating Barrel of starting volume of original mud weight required to give a predetermined final volume of desired mud weight with barite.

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

After adding barite to increase mud weight in the system, total mud volume will increase due to volume of dry barite. This formula below shows you how to determine volume of mud increase in bbl per 100 bbl of original mud.

Volume increase per 100 bbl of mud = 100 x (W2 – W1) ÷ (35 – W2)

Where;

W1 = current mud weight
W2 = new mud weight

Example: Determine the volume increase when increasing the density with barite from 10.0 ppg (W1) to 13.0 ppg (W2):

Volume increase per 100 bbl of mud = 100 x (13.0 – 10.0) ÷ (35 – 13.0)
Volume increase per 100 bbl of mud = 13.64 bbl

If you have total volume of 500 bbl of mud, the volume increase due to adding barite will be equal to 68.2 bbl (13.64 x 500 ÷ 100).

Please find the Excel sheet for calculating volume of mud in bbl increase due to adding Barite.

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

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 Drilling, Production and Workover, Second Edition

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 Drilling, Production and Workover, Second Edition

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 Drilling, Production and Workover, Second Edition

This post you will learn how to calculate and convert pressure gradient in different units. Please see simple oil field formulas shown each topic below:

1. Calculate pressure gradient in psi/ft from mud weight in ppg

Pressure gradient calculation formula:
Pressure gradient in psi/ft = mud weight in ppg x 0.052

Example:
Mud weigt = 9.0 ppg
Pressure gradient in psi/ft = 9.0 x 0.052
Pressure gradient in psi/ft = 0.468 psi/ft

2. Calculate pressure gradient in psi/ft  from mud weight in lb/ft³

Pressure gradient calculation formula:
Pressure gradient in psi/ft = mud weight in lb/ft³ x 0.006944

Example:
Mud weight = 80 lb/ft³
Pressure gradient in psi/ft  = 80 lb/ft³ x 0.006944
Pressure gradient  = 0.55552  psi/ft

OR

Pressure gradient in psi/ft t = mud weight in lb/ft³ ÷ 144

Example:
Mud weight = 80 lb/ft³
Pressure gradient in psi/ft  = 80 lb/ft³ ÷ 144
Pressure gradient  = 0.55556 psi/ft

3. Calculate pressure gradient in psi/ft from specific gravity (SG)

Pressure gradient calculation formula:
Pressure gradient in psi/ft = mud weight in SG x 0.433

Example:
Fluid specific gravity = 2
Pressure gradient in psi/ft = 2.0 x 0.433
Pressure gradient = 0.866 psi/ft

4. Convert pressure gradient in psi/ft to mud weight in ppg

Pressure gradient coversion formula:
Mud weight in ppg = pressure gradient in psi/ft ÷ 0.052

Example:
Pressure gradient = 0.5 psi/ft
Mud weight in ppg = 0.5 psi/ft ÷ 0.052
Mud weight = 9.615 ppg

5. Convert pressure gradient in psi/ft to mud weight in lb/ft³

Pressure gradient coversion formula:
Mud weight in lb/ft³ = pressure gradient in psi/ft ÷ 0.006944

Example:
Pressure gradient = 0.5 psi/ft
Mud weight in lb/ft³ = 0.5 psi/ft ÷ 0.006944
Mud weight = 72 lb/ft³

6. Convert pressure gradient in psi/ft to mud weight in SG

Pressure gradient coversion formula:
SG = pressure gradient, psi/ft ÷ 0.433

Example: Pressure gradient =0.5 psi/ft
SG = 0.5 psi/ft ÷ 0.433
SG = 1.1547

Please find the Excel sheet in the following link: Pressure Gradient Calculation Sheet

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