**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) ÷ (Dh**^{2} – Dp^{2})

**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) ÷ (10^{2} – 5^{2})

AV = 261 ft/mim

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

**Annular Velocity = Flow Rate × 1029.4÷ (Dh**^{2} – Dp^{2})

**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 ÷ (10^{2} – 5^{2})

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×(Dh**^{2} – Dp^{2}))

**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×(254^{2} – 127^{2}))

Annular Velocity = 78.9 m/min

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

**Annular Velocity = (Flow Rate × 4 ×10**^{6} ) ÷ (π×(Dh^{2} – Dp^{2}))

**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 ×10^{6} ) ÷ (π×(10^{2} – 5^{2}))

AV = 52.6 m/min

# Flow Rate to Achieve Require Annular Velocity

## Oilfield Unit

**Flow rate required in gpm = (Annular Velocity ) × (Dh**^{2} – DP^{2}) ÷ 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 × (10^{2}– 5^{2}) ÷ 24.5

Flow rate required in gpm = 367.4 gpm

## Metric Unit

**Flow rate required in gpm = (Annular Velocity × π) × (Dh**^{2} – DP^{2}) ÷ 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) × (254^{2}– 127^{2}) ÷ 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.