**Annular Velocity (AV)** is how fast of fluid in 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.

**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) ÷ (Dh**^{2} – Dp^{2})

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) ÷ (10^{2} – 5^{2})

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÷ (Dh**^{2} – Dp^{2})

Example:

Flow rate (Q) = 13 bbl/min

Hole size = 10 in.

Drill pipe OD = 5 in.

AV = 13 bbl/min x 1029.4 ÷ (10^{2} – 5^{2})

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 formulas.

**Flow rate required in gpm = (AV in ft/min) x (Dh**^{2} – DP^{2}) ÷ 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 (10^{2}– 5^{2}) ÷ 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 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.