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.