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 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.