# Calculate Annular Pressure Loss

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

P = 531.65 psi

## Metric Unit

P= [(7.39 × 10-6) × MW × L × V2] ÷ (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 × (1652 – 1002) ÷ 4)

v = 88.7 m/min

Determine annular pressure losses, psi: P = [(7.39 × 10-6× 1560 × 2400 × 88.72] ÷ (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. 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. Working in the oil field and loving to share knowledge.

### 16 Responses to Calculate Annular Pressure Loss

1. mohand says:

its good to know the important of APL calculation because its related to many things ( ECD, BHP while circulation)
and that is important for engineer to know how to calculate it …

thanks for you effort

2. Jorge Barros says:

Dear Sir
About this article Annular PressureLloss on the datum you give the diameter of hole of 6 inch and OD of pipe 4 inch all calculations are done with figures for diameter of hole 8,5 inch and OD of pipe 5 inch, however, the results of calculations correspond to the datum.
With best regards.
Jorge Barros

• DrillingFormulas.Com says:

Hi Jorge,

Thanks for correcting my typo. I already correct as per your observation.

Thanks and best regards,
Drillingformulas.com Team

3. Paul Roland Umade says:

Doing a very great job,thanks a million.

4. SHAWN L. PERKINS says:

FIRST OFF….
THE CORRECT ANSWER IS; P=533, SECOND THE FORMULA IS ALL JACKED UP.
YOU ARE USING 4″ DRILL PIPE IN THE FORMULA WHICH YOU “NEVER” DO, BUT THEN YOU USED 5″ IN THE EQUATION WHEN YOU WORKED IT!!!!!

• DrillingFormulas.Com says:

Hi Shawn,

Hole size = 6.5 in.

Drill pipe OD = 4.0 in.

I did correct some mistake already. Thanks for feed back.

5. noob drilling enthusiast says:

Dear Sir,

I have a small doubt … The expression (L = length of annular in ft ) is in TVD or MD ? I wish to ask this because, if it is TVD, then for two similar wells (one horizontal and the other vertical) having same TVD hence would have equal annular pressure loss.

That would mean that an infinite horizontal well would have same ECD as that of a vertical well of same TVD.

Hope I was able to frame the question in correct form.

Thanks and Regards

• DrillingFormulas.Com says:

Length of annular is MD.

6. Francis Okoto says:

Dear Sir,
Can we use this expression to calculate the annular pressure loss during cement – especially during the displacement phase.

To do this, what would MW represent. The mud weight during displacement or the cement weight in the annulus

In such a case, would the Dp represent the casing.

• DrillingFormulas.Com says:

Since there will be several fluid density in the well, you may need to separate each fluid in the annuls and determine friction pressure loss for each fluid. Then you need to sum all the figures to get the annular pressure loss. This process is very tricky and it might be good idea to use the computer simulation to determine the annular pressure loss while pumping cement.

7. Francis Okoto says:

How can we relate this to cementing – especially during the displacement phase?

• DrillingFormulas.Com says:

Francis,

I will show this topic in the blog soon.

Regards,
Shyne

8. Qureshi says:

The annular velocity is in ft/mm, which is wrong. It has to be in ft/min 🙂

• DrillingFormulas.Com says:

Qureshi,

I’ve changed the unit. Thanks for helping us checking our typo mistake.

Regards,
Shyne

9. Ed says:

I have a question that states The calculation of APL is? Out of the 4 answers available we can assume that the answer is The average of mud return weights?

• DrillingFormulas.Com says:

Ed,

I don’t get what you would like to know. Can you give me more explanation about what you want to learn?

This site uses Akismet to reduce spam. Learn how your comment data is processed.