Pipe Displacement Calculation

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Pipe displacement, normally in bbl/ft or m3/m, is steel volume  per length of steel pipe.  When we either pull out of hole or trip in hole for any kind of pipes such as drill pipe, casing or tubing, you should know how much fluid to displace steel volume.

For example, when we pull out of hole, a trip sheet must be monitored all time. We must know how much fluid will fill the hole each stand of drill pipe pulled out. If the volume of displacement less than theoretical displacement value, we may have problem due to swabbing formation into wellbore.

This article will demonstrate how to calculate plain pipe displacement with this following formula:

Oilfield Unit

Pipe Displacement in bbl/ft = (OD2 – ID2 ) ÷ 1029.4

Where;
OD in inch
ID in inch

Where,
OD is out side diameter of pipe in inch.
ID is inside diameter of pipe in inch.

This formula is for plain pipe diplacment such as casing and tubing. It is not for closed-end displacement. It’s not accurate enough for drill pipe because this formula does not account for tool joint displacement therefore you need drill pipe specification sheet for its displacement.

Example: Determine pipe displacement in bbl/ft of 9-5/8” casing 40 ppf, OD = 9.625 in, ID = 8.835 in

Pipe Displacement of 9-5/8” casing 40 ppf in bbl/ft = (9.6252 – 8.8352 ) ÷1029.4
Pipe Displacement of 9-5/8” casing 40 ppf in bbl/ft = 0.01417 bbl/ft

Metric Unit

Annular capacity in m3/m =  (OD2 – ID2) ÷1,273,240

Where;
OD in mm
ID in mm

Example: Determine pipe displacement in bbl/ft of 9-5/8” casing 40 ppf, OD = 244.475 mm, ID = 244.409 mm

Pipe Displacement of 9-5/8” casing 40 ppf in m3/m = (244.4752 – 244.4092 ) ÷1,273,240
Pipe Displacement of 9-5/8” casing 40 ppf in m3//m = 0.0074

Please find Pipe Displacement Calculation Oilfield and Metric Unit Excel sheet

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 inner capacity of open hole/inside cylindrical objects (Internal Capacity Factor)

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From the previous post, you learn how to calculate annular capacity and this article shows you how to use the same principle to calculate internal capacity factor of  open hole & inside cylindrical objects such as tubular, drill pipe, drill collars, tubing, casing, etc.

There are several formulas to calculate inner capacity depending on unit of inner capacity required. The formula are listed below;

Oilfield Unit

Calculate Internal Capacity Factor in bbl/ft


Inner Capacity in bbl/ft = (ID)2 ÷1029.4

Where;
Internal Diameter (ID) in inch

Example:

Determine Internal Capacity Factor in bbl/ft of a 6-1/8 in. hole:
Internal Capacity Factor in bbl/ft = 6.1252÷1029.4
Internal Capacity Factor in bbl/ft = 0. 0364 bbl/ft

Calculate Internal Capacity Factor in gal/ft


Inner Capacity in gal/ft = (ID in.)2 ÷24.51
Where;
Internal Diameter (ID) in inch

Example:

Determine Inner Capacity Factor in gal/ft of 6-1/8 in. hole:
Internal Capacity Factor in gal/ft = 6.1252÷ 24.51
Internal Capacity Factor in gal/ft = 1.53 gal/ft

Metric Unit

Calculate Internal Capacity Factor in cu-meter/meter (m3/m)

Annular capacity in m3/m =  (ID2) ÷1,273,240

Where;
Internal Diameter (ID) in mm

Example:

Hole size (ID) = 155.56  mm.
Internal Capacity Factor in m3/m = (155.562 ) ÷1,273,240
Internal Capacity Factor in m3/m = 0.0190 m3/m

Calculate Internal Capacity Factor in liter/meter (l/m)

Annular capacity in m3/m =  (ID2) ÷1,273.24

Where;
Internal Diameter (ID) in mm

Example:

Hole size (ID) = 155.56  mm.
Internal Capacity Factor in l/m = (155.562 ) ÷1,273.24
Internal Capacity Factor in l/m = 19.0 l/m

Volume can be determined by this following formula;

Oilfield Unit

Volume = Internal Capacity Factor x Length

Where;

Volume in bbl

Internal Capacity Factor in bbl/ft

Length in ft

Example:

Internal Capacity Factor =  0. 0364 bbl/ft

Hole Length = 3,000 ft

Volume = 0. 0364 x 3,000 = 109.2 bbl.

Metric Unit

Volume = Internal Capacity Factor x Length

Where;

Volume in cu.meter

Internal Capacity Factor in cu.meter/meter

Length in meter

Example:

Internal Capacity Factor in m3/m = 0.0190 m3/m

Hole Length = 3,000 m

Volume = 0. 0190 x 3,000 = 57 m3

Download Free Excel Spread Sheet

Please find the excel sheet on how to calculate internal capacity factor.

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 Capacity

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Annular capacity  is volume of fluid between two diameter of cylindrical objects per length or length per volume. This article demonstrates you how to calculate annular capacity between casing or hole and drill pipe, tubing, or casing. There are several formulas as shown below to calculate annular capacity depending on unit of annular capacity required.

Note: Dh is bigger ID and Dp is smaller OD. The examples below will show the Dh as hole size and Dp is drill pipe OD

Oilfield Unit

a) Calculate annular capacity in bbl/ft

Annular capacity in bbl/ft =  (Dh2 – Dp2) ÷1029.4

Where;
Dh in inch
Dp in inch

Example: Hole size (Dh) = 6-1/8 in.
Drill pipe OD (Dp) = 3.5  in.
Annular capacity in bbl/ft = (6.1252 – 3.5 2) ÷1029.4
Annular capacity = 0.0245 bbl/ft

b) Calculate annular capacity in gal/ft

Annular capacity in gal/ft = (Dh2 – Dp2) ÷ 24.51

Where;
Dh in inch
Dp in inch

Example:
Hole size (Dh) = 6-1/8 in.
Drill pipe OD (Dp) = 3.5  in.
Annular capacity in gal/ft = (6.125 2 – 3.52) ÷24.51
Annular capacity = 1.031 gal/ft

Metric Unit

c) Calculate annular capacity in cu-meter/meter (m3/m)

Annular capacity in m3/m =  (Dh2 – Dp2) ÷1,273,240

Where;
Dh in mm
Dp in mm

Example:
Hole size (Dh) = 155.56 mm.
Drill pipe OD (Dp) = 88.90  mm.
Annular capacity in m3/m = (155.562 – 88.90 2) ÷1,273,240
Annular capacity = 0.0128 m3/m

d) Calculate annular capacity in litre/meter (l/m)

Annular capacity in l/m =  (Dh2 – Dp2) ÷1,273.24

Where;
Dh in mm
Dp in mm

Example:
Hole size (Dh) = 155.56 mm.
Drill pipe OD (Dp) = 88.90  mm.
Annular capacity in l/m = (155.562 – 88.90 2) ÷1,273.24
Annular capacity =12.8 l/m

Annular volume can be determined by this following formula;

Oilfield Unit

Annular volume in bbl  = annular capacity (bbl/ft) x length of annulus (ft)

Example:

Annular capacity = 0.0245 bbl/ft
Length of annulus = 1000 ft
Annular volume = 1000 x 0.0245 = 24.5 bbl.

Metric Unit

Annular volume in m3 = annular capacity (m3/m) x length of annulus (m)

Example:

Annular capacity = 0.0128 m3/m
Length of annulus = 330 m
Annular volume = 330 x 0.0128 = 4.224 m3.

** Please remember that if you have several annular profile, you must calculate volume based on each annular profile in order to get total annular volume.

Download Free Excel Spread Sheet

This is 2020 update with Metric Unit – Please find the Excel sheet for calculating annular capacity.

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 Equivalent Circulation Density (ECD) with complex engineering equations

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These formulas below are used for complex calculation for annular pressure loss and equivalent circulating density. I think this calculation will give you more accurate result than a simple equation. Please follow the following steps how to calculate annular pressure loss and ECD.

1. Determine n:

1-determine n
2. Determine K:

2 determine k
3. Determine annular velocity (v) in ft/min:

3 annular velocity

4. Determine critical velocity (Vc) in ft/min:
4 determine vc

5. Pressure loss for laminar flow (Ps), psi:

5 Pressure loss for laminar flow

6. Pressure loss for turbulent flow (Ps), psi:
6 Pressure loss for turbulent flow

7. Determine equivalent circulating density (ECD), ppg:

7 ECD

Abbreviation meaning

θ300: viscometer dial reading at 300 rpm
θ600: viscometer dial reading at 600 rpm
Q: Flow rate in gpm
Dh: Diameter of hole
Dp: Diameter of drill pipe, drill collar or BHA in ft
v: annular velocity in ft/min
L: length of drill pipe, drill collar or BHA in ft
MW: Mud Weight
PV: Plastic viscosity

Example: Equivalent circulating density (ECD) in ppg by using following data:

Mud weight = 9.5 ppg
θ300 = 40
θ600 = 60
Plastic viscosity = 20 cps
Circulation rate = 650 gpm
Hole diameter = 8.5 in.
Drill collar OD = 6.75 in.
Drill pipe OD = 5.0 in
Drill collar length = 600 ft
Drill pipe length = 10,000 ft
True vertical depth = 9,000 ft

1. Determine n:

example 1-determine n

2. Determine K:

example 2 determine k
3. Determine annular velocity (v) in ft/min around drill pipe:

example 3 annular velocity around drill pipe

 

4. Determine critical velocity (Vc) in ft/min around drill pipe:

example 4 determine vc around drill pipe

The annular velocity around drill pipe is less than the critical velocity around drill pipe so this is laminar flow. The equation #5 (for laminar flow) must be applied in this case.

Pressure loss for turbulent flow (Ps), psi:

example 4 determine pressure loss around drill pipe

5. Determine annular velocity (v) in ft/min around drill collar:

example 5 annular velocity around drill collar

6. Determine critical velocity (Vc) in ft/min around drill collar:
example 6 determine vc around drill collar

The annular velocity around drill collar is more than the critical velocity around drill collar so this is turbulent flow. The equation #6 (for turbulent flow) must be applied in this case.

Pressure loss for laminar flow (Ps), psi:
example 6 determine pressure loss around drill collar

Total annular pressure loss = annular pressure loss around drill pipe + annular pressure loss around drill collar

Ps=271.3+81.5 = 352.8psi

7. Determine equivalent circulating density (ECD), ppg:

Example 7 ECD

Please find the Excel sheet for calculating ECD (engineering calculation)

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

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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.

Download the spreadsheet from the link below.

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.