**Pipe displacement**, normally in bbl/ft, is steel volume to displace fluid volume. 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.

**Pipe displacement**, normally in bbl/ft, is steel volume to displace fluid volume. 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.

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.)**

Example: Determine inner capacity in bbl/ft of a 6-1/8 in. hole:

Inner Capacity in bbl/ft = 6.125

Inner Capacity in bbl/ft = 0. 0364 bbl/ft

**Formula#2) Calculate inner capacity in ft/bbl**^{
}Example: Determine inner capacity in ft/bbl of 6-1/8 in. hole:

Inner Capacity in ft/bbl = 1029.4 ÷ 6.125^{2}

Inner Capacity in = 27.439 ft/bbl

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

**Formula#3) Calculate inner capacity in gal/ft
**

Example: Determine inner capacity in gal/ft of 6-1/8 in. hole:

Inner Capacity in gal/ft = 6.125

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 ÷ 6.125^{2}

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 Lenght**

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

**Annular capacity **is one of basic values that you really need to understand. This post 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
**

Drill pipe OD (Dp) = 3.5 in.

Annular capacity in bbl/ft = (6.125

Annular capacity = 0.0245 bbl/ft

**b) Calculate annular capacity in ft/bbl
**

Drill pipe OD (Dp) = 3.5 in.

Annular capacity in ft/bbl = 1029.4 ÷ (6.125

Annular capacity = 40.743 ft/bbl

**c) Calculate annular capacity in gal/ft
**

Drill pipe OD (Dp) = 3.5 in.

Annular capacity in gal/ft = (6.125

Annular capacity = 1.031 gal/ft

**d) Calculate annular capacity in ft/gal**

Annular capacity, ft/gal = 24.51 ÷ (Dh^{2} – Dp^{2})

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

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:

2. Determine K:

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

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

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

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

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

**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:

2. Determine K:

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

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

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

6. Determine critical velocity (Vc) in ft/min 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:

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:

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

**Ref book: ** **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 annular pressure loss you will encounter.

**P= [(1.4327 x 10 ^{-7}) x MW x Lx V^{2}] ÷ (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) ÷ (6.5^{2} – 4.0^{2})

v = 299 ft/min

Determine annular pressure losses, psi: P = [(1.4327 x 10^{-7}) x 13.0 x 8000 x 299^{2}] ÷ (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 book: ** **Formulas and Calculations for Drilling, Production and Workover, Second Edition**

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