Calculate Equivalent Circulation Density (ECD) with complex engineering equations

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:

1-determine n
2. Determine K:

2 determine k
3. Determine annular velocity (v) in ft/min:

3 annular velocity

4. Determine critical velocity (Vc) in ft/min:
4 determine vc

5. Pressure loss for laminar flow (Ps), psi:

5 Pressure loss for laminar flow

6. Pressure loss for turbulent flow (Ps), psi:
6 Pressure loss for turbulent flow

7. Determine equivalent circulating density (ECD), ppg:

7 ECD

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:

example 1-determine n

2. Determine K:

example 2 determine k
3. Determine annular velocity (v) in ft/min around drill pipe:

example 3 annular velocity around drill pipe

 

4. Determine critical velocity (Vc) in ft/min around drill pipe:

example 4 determine vc 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:

example 4 determine pressure loss around drill pipe

5. Determine annular velocity (v) in ft/min around drill collar:

example 5 annular velocity around drill collar

6. Determine critical velocity (Vc) in ft/min around drill collar:
example 6 determine vc 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:
example 6 determine pressure loss around drill collar

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:

Example 7 ECD

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.

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.

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.

Equivalent Circulating Density (ECD) in both Oilfield and Metric Unit

Equivalent Circulating Density (ECD) is the effective density that combines current mud density and annular pressure drop. ECD is vital for drilling engineering since it limits how depth of each section to be drilled and leads to losses.

The equivalent circulating density formula is shown below;

Oilfield Unit

Equivalent Circulating Density (ECD) = (Annular Pressure Loss ÷ 0.052 ÷ True Vertical Depth (TVD)) + (Current Mud Weight)

Equivalent Circulating Density (ECD) in ppg

Annular Pressure Loss in psi

True Vertical Depth (TVD) in ft

Current Mud Weight in pppg

Example:

Annular pressure loss = 400 psi
True Vertical Depth = 8,000 ft
Current mud weight in ppg = 10 ppg

ECD in ppg =   (400 psi ÷ 0.052 ÷ 8,000 ft) +10.0 ppg 

ECD = 11.0 ppg

Metric Unit

Equivalent Circulating Density (ECD) = (Annular Pressure Loss × 1000 ÷ 9.81÷ True Vertical Depth (TVD) ) + (Current Mud Weight)

Equivalent Circulating Density (ECD) in kg/m3

Annular Pressure Loss in KPa

True Vertical Depth (TVD) in m

Current Mud Weight in kg/m3

Example:

Annular pressure loss = 2760 KPa
True Vertical Depth = 2,440 m
Current mud weight in ppg = 1200  kg/m3

ECD in ppg =  (2,760 Kpa  × 1000 ÷ 9.81÷ 2,440 m )  + 1,200 kg/m3

ECD = 1,315 kg/m3

Please find the Excel sheet to calculate Equivalent Circulating Density (ECD) 

https://www.drillingformulas.com/wp-content/uploads/2009/04/7.Equivalent-Circulating-Density.xlsx

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 Engineer

Annular Velocity (AV) Calculation

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) ÷ (Dh2 – Dp2)

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) ÷ (102 – 52)
AV = 261 ft/mim

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

Annular Velocity  = Flow Rate × 1029.4÷ (Dh2 – Dp2)

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 ÷ (102 – 52)
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×(Dh2 – Dp2))

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×(2542 – 1272))
Annular Velocity = 78.9 m/min

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

Annular Velocity  = (Flow Rate × 4 ×106 ) ÷ (π×(Dh2 – Dp2))

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 ×106 ) ÷ (π×(102 – 52))
AV = 52.6 m/min

Flow Rate to Achieve Require Annular Velocity 

Oilfield Unit

Flow rate required in gpm = (Annular Velocity ) × (Dh2 – DP2) ÷ 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 × (102– 52) ÷ 24.5
Flow rate required in gpm = 367.4 gpm

Metric Unit

Flow rate required in gpm = (Annular Velocity × π) × (Dh2 – DP2) ÷ 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) × (2542– 1272) ÷ 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.

Pump Output Calculation for Duplex Pump and Triplex Pump

Rig pump output, normally in volume per stroke, of mud pumps on the rig is  one of important figures that we really need to know because we will use pump out put figures to calculate many parameters such as bottom up strokes,  wash out depth, tracking drilling fluid, etc. In this post, you will learn how to calculate pump out put for triplex pump and duplex pump in both Oilfield and Metric Unit. 

Triplex Mud Pump

Triplex Pump Output Formula

Oilfield Unit

Triplex Pump Output  = 0.000243 × (Liner Diameter ) 2 × (Stroke Length)

Where,

Triplex pump output in bbl/stk

Liner Diameter in inch

Stroke Length in inch

Example:

Determine the pump output in bbl/stk at 100% and 97% efficiency
Liner size = 6 inch
Stroke length = 12 inch

Triplex pump output @ 100% efficiency
Triplex pump output @ 100% = 0.000243 × 62 × 12
Triplex pump output @ 100% = 0.104976 bbl/stk

Triplex pump output @ 97% efficiency
Adjust the triplex pump output for 97% efficiency:
Triplex pump output @ 97% = 0.104976 × 0.97 bbl/stk
Triplex pump output @ 97% = 0.101827 bbl/stk

Metric Unit

Triplex Pump Output  = 2.3576 × 10-9× (Liner Diameter ) 2 × (Stroke Length)

Where,

Triplex pump output in m3/stk

Liner Diameter in mm

Stroke Length in mm

Example:

Determine the pump output in bbl/stk at 100% and 97% efficiency
Liner size = 152.4 mm
Stroke length = 304.8 mm

Triplex pump output @ 100 % efficiency

Triplex pump output @ 100% = 2.3576 × 10-9 × 152.42 × 304.8
Triplex pump output @ 100% = 0.016690 m3/stk

Triplex pump output @ 97% efficiency
Adjust the triplex pump output for 97% efficiency:
Triplex pump output @ 97% = 0.016690 × 0.97 m3/stk
Triplex pump output @ 97% = 0.016189 m3/stk

Duplex Mud Pump (Ref: http://www.sunmachinery.com/8214R_01.jpg)

Duplex Pump Output Formula

Oilfield Unit

Duplex Pump Output = 0.000162 × S × [2(D)2 – d2]

Where:

Duplex pump output in bbl/stk
D = liner diameter in inch
S = stroke length in inch
d = rod diameter in inch

Example:

Determine the duplex pump output in bbl/stk at 100% and 85% efficiency

Liner diameter = 6 inch
Stroke length = 12 inch
Rod diameter = 2.0 in.

Duplex pump output @ 100 % efficiency

Duplex pump output @ 100% = 0.000162 × 12 × [2 (6) 2 -22 ]
Duplex pump output @ 100% = 0.13219 bbl/stk

Duplex pump output @ 85% efficiency

Adjust pump output for 85% efficiency:
Duplex pump output @ 85% = 0.132192 × 0.85 bbl/stk
Duplex pump output @ 85% = 0.11236 bbl/stk

Metric Unit

Duplex Pump Output =1.57172 × 10-9 × S × [2(D)2 – d2]

Where:

Duplex pump output in m3/stk
D = liner diameter in mm
S = stroke length in mm
d = rod diameter in mm

Example: Determine the duplex pump output in m3/stk at 100% and 85% efficiency

Liner diameter = 152.4 mm
Stroke length = 304.8 mm
Rod diameter = 50.8 mm

Duplex pump output @ 100 % efficiency
Duplex pump output@ 100% = 1.57172 × 10-9 × 304.8 × [2 (152.4) 2 -50.82 ]
Duplex pump output@ 100% = 0.02102 m3/stk

Duplex pump output @ 85% efficiency

Duplex pump output@ 85% = 0.02102 × 0.85 m3/stk
Duplex pump output @ 85% = 0.01786 bbl/stk

Please find the Excel sheet to calculate triplex pump output and duplex pump output

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.