Calculate inner capacity of open hole/inside cylindrical objects

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

There are several formulas to calculate inner capacity depending on unit of inner capacity required. Please read and understand the formulas below:

Formula#1) Calculate inner capacity in bbl/ft


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


Example: Determine inner capacity in bbl/ft of a 6-1/8 in. hole:
Inner Capacity in bbl/ft = 6.1252÷1029.4
Inner Capacity in bbl/ft = 0. 0364 bbl/ft

Formula#2) Calculate inner capacity in ft/bbl

 

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

Example: Determine inner capacity in ft/bbl of 6-1/8 in. hole:
Inner Capacity in ft/bbl = 1029.4 ÷ 6.1252
Inner Capacity in = 27.439 ft/bbl

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

Formula#3) Calculate inner capacity in gal/ft


Inner Capacity in gal/ft = (ID in.)2 ÷24.51

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

Formula#4) Calculate inner capacity in ft/gal

 

Inner Capacity in ft/gal = 24.51 ÷ (ID in.)2

Example: Determine inner capacity in ft/gal of 6-1/8 in. hole:
Inner Capacity in ft/gal = 24.51 ÷ 6.1252
Inner Capacity in ft/gal = 0.6533 ft/gal

Determine the volume of mud to fill up the inner of the cylindrical objects by the following equation.

Inner Volume = Inner Capacity x Length

Example: Inner capacity =  0. 0364 bbl/ft

Length = 3000 ft

Volume = 0. 0364 x 3,000 = 109.2 bbl.

Please find the excel sheet on how to calculate inner 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 Annular Capacity

Annular capacity , which is one of basic values that you really need to understand, 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

a) Calculate annular capacity in bbl/ft

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

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 ft/bbl

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

Example: Hole size (Dh) = 6-1/8 in.
Drill pipe OD (Dp) = 3.5  in.
Annular capacity in ft/bbl = 1029.4 ÷ (6.125 2 – 3.5 2)
Annular capacity = 40.743 ft/bbl

c) Calculate annular capacity in gal/ft

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

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

d) Calculate annular capacity in ft/gal

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

Example: Hole size (Dh) = 6-1/8 in.
Drill pipe OD (Dp) = 3.5  in.
Annular capacity in ft/gal = 24.51 ÷  (6.125 2 – 3.5 2)
Annular capacity in ft/gal = 0.97 ft/gal

Annular volume can be determined by this following formula;

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

Note: annular volume can be expressed in several unit depending on unit that you use in the calculation.

Example:

Annular capacity = 0.0245 bbl/ft
Length of annulus = 1000 ft

Annular volume = 1000 x 0.0245 = 24.5 bbl.

** 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.

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

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.

Calcuate Annular Pressure Loss

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 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/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 x 10-7) x 13.0 x 8000 x 2992] ÷ (6.5 – 4.0)

P = 531.65 psi

Please find the Excel sheet to calculate annular pressure loss

PS, 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.

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.

Equivalent Circulating Density (ECD) in ppg

Equivalent Circulating Density (ECD) is the effective density that combines current mud density and annular pressure drop. ECD is vital for drilling engineering since it limits how depth of each section to be drilled and leads to losses.

semi

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 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 Engineer