Volume of mud in bbl increase due to adding barite

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 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.

Calculate Annular Pressure Loss

From the previous articles, 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 roughly give you idea about how much annular pressure loss you will encounter. For this 2021 update, we’ve added the formula in both oilfield and metric unit.

Oilfield Unit

P= [(1.4327 × 10-7) × MW × L × V2] ÷ (Dh – Dp)

P = annular pressure losses, psi

MW = mud weight in ppg

L = length of annular in ft

V = annular velocity in ft/min

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) ÷ (6.52 – 4.02)

v = 299 ft/min

Determine annular pressure losses, psi: P = [(1.4327 × 10-7× 13.0 × 8000 × 2992] ÷ (6.5 – 4.0)

P = 531.65 psi

Metric Unit

P= [(7.39 × 10-6) × MW × L × V2] ÷ (Dh – Dp)

P = annular pressure losses, KPa

MW = mud weight in kg/m³

L = length of annular in m

V = annular velocity in m/min

Dh = hole or casing ID in mm

Dp = drill pipe or drill collar OD in mm

Example:

Mud weight = 1,560 kg/m³

Length = 2,400 m

Circulation rate = 1,200 l/m

Hole size = 165 mm

Drill pipe OD = 100 mm

Determine annular velocity, ft/mm: v = (1,000 × 1,200) ÷ (π × (1652 – 1002) ÷ 4)

v = 88.7 m/min

Determine annular pressure losses, psi: P = [(7.39 × 10-6× 1560 × 2400 × 88.72] ÷ (165 – 100)

P = 3,349 KPa

PS, This is the estimation for annular pressure. For more accurate, you may need to consult to a drilling fluid company to perform simulation since they have advanced software that can account for many parameters ie cutting loading, mud rheology, etc.

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.

Annular Velocity (AV) Calculation

Annular Velocity (AV) is how fast of fluid flow in  the annulus while pumping.

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 Formula

Oilfield Unit

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

Annular velocity = Flow Rate÷ Annular Capacity

where;

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/min

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

Annular velocity = (24.5 × Flow Rate) ÷ (Dh2 – Dp2)

where;
Annular velocity in ft/min
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 = 800 gpm
Hole size = 10 in.
Drill pipe OD = 5 in.
AV = (24.5 × 800) ÷ (102 – 52)
AV = 261 ft/mim

Formula#3: Annular velocity (AV) in ft/min

Annular Velocity  = Flow Rate × 1029.4÷ (Dh2 – Dp2)

Where;
Annular Velocity in ft/min
Flow Rate in bbl/min

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

Metric Unit

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

Annular velocity = Flow Rate÷ Annular Capacity

where;
Annular velocity in m/min
Flow rate in liters/min
Annular capacity in liters/m

Example:
Flow rate = 1600 liters/min
Annular capacity = 68 liters/m
Annular Velocity = 1600 liters/min÷ 68 liters/m
Annular Velocity = 23.5 m/min

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

Annular velocity = (4000× Flow Rate) ÷ (π×(Dh2 – Dp2))

where;
Annular velocity in m/min
Flow Rate in liters/min
Dh = inside diameter of casing or hole size in mm
Dp = outside diameter of pipe, tubing or collars in mm

Example:
Flow rate = 3000 liters/min
Hole size = 254 mm
Drill pipe OD = 127 mm
Annular Velocity = (4000 × 3000) ÷ (π×(2542 – 1272))
Annular Velocity = 78.9 m/min

Formula#3: Annular velocity (AV) in m/min

Annular Velocity  = (Flow Rate × 4 ×106 ) ÷ (π×(Dh2 – Dp2))

Where;
Annular Velocity in m/min
Flow Rate in m³/min
Dh = inside diameter of casing or hole size in mm
Dp = outside diameter of pipe, tubing or collars in mm

Example:
Flow rate = 2 m³/min
Hole size = 254 mm
Drill pipe OD = 127 mm
AV = (2 m³/min 4 ×106 ) ÷ (π×(102 – 52))
AV = 52.6 m/min

Flow Rate to Achieve Require Annular Velocity

Oilfield Unit

Flow rate required in gpm = (Annular Velocity ) × (Dh2 – DP2) ÷ 24.5

Where;
Flow rate in gpm
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 × (102– 52) ÷ 24.5
Flow rate required in gpm = 367.4 gpm

Metric Unit

Flow rate required in gpm = (Annular Velocity × π) × (Dh2 – DP2) ÷ 4000

Where;
Flow rate in liters/min
Annular Velocity in m/min
Dh = inside diameter of casing or hole size in mm
Dp = outside diameter of pipe, tubing or collars in mm

Example:
Desired annular velocity = 37 m/min
Hole size = 254 mm
Drill pipe OD = 127 mm
Flow rate required  = (37 × π) × (2542– 1272) ÷ 4,000
Flow rate required  = 1,406 liters/min

Stroke per Minute to Achieve Require Annular Velocity

Oilfield Unit

SPM = (Annular Velocity × Annular Capacity) ÷ Pump Output

Where;
Annular Velocity in ft/min
Annular Capacity in bbl/ft
Pump output in bbl/stk

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/min× 0.1261 bbl/ft) ÷ 0.136 bbl/stk
SPM = 111.3 spm

Metric Unit

SPM = (Annular Velocity × Annular Capacity) ÷ Pump Output

Where;
Annular Velocity in m/min
Annular Capacity in liters/m
Pump output in liters/stk

Example:
Desired annular velocity in m/min = 46 m/min
Hole size = 254 mm
Drill pipe OD = 127 mm
Annular capacity = 0.0380 m³/m
Pump output = 0.0156 m³/stk
SPM = (46 m/min × 0.0380 bbl/ft) ÷ 0.0156 m³/stk
SPM = 112 spm

Please find the Excel sheet  for calculating annular velocity

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.

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

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 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

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

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

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

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

Mud weight in ppg = pressure gradient in psi/ft ÷ 0.052

Example:
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

Mud weight in
lb/ft
3 = pressure gradient in psi/ft ÷ 0.006944

Example:
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

SG = pressure gradient, psi/ft ÷ 0.433

Example: