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 × 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 **×** 10^{-7}) **× **13.0 **×** 8000 **×** 299^{2}] ÷ (6.5 – 4.0)

P = 531.65 psi

## Metric Unit

**P= [(7.39 × 10**^{-6}) × MW × L × V^{2}] ÷ (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 **× **(165^{2} – 100^{2}) ÷ 4)

v = 88.7 m/min

Determine annular pressure losses, psi: P = [(7.39 **×** 10^{-6}) **× **1560 **×** 2400 **×** 88.7^{2}] ÷ (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.