Pressure Required to Break Circulation in Annulus

From the previous post, we learn about how to determine break circulating pressure inside drill string. This post we will learn about how to calculate pressure required to break circulation in annulas.

Formula to calculate pressure required overcoming the mud’s gel strength in the annulus as follow:

Pgs = y ÷ [300 x (Dh, in. – Dp, in.)] x L

where Pgs = pressure required to break gel strength, psi

L = length of drill string, ft

y = 10 mm. gel strength of drilling fluid, lb/100 sq ft

Dh = hole diameter, in.

Dp = pipe diameter, in.

Let’s take a look at the example below and understand how to determine pressure required to break circulation in the annulus by using following information

L = 11,500 ft

y = 12 lb/100 sq ft

Dh = 6.5 in.

Dp = 4.0 in.

Referring to the formula above, all parameters can simply input into the formula to get the break circulation pressure in the annulus.

Pgs = 12 ÷ [300 x (6.5 – 4.0)] x 11,500 ft

Pgs = 184.0 psi

Please find the Excel sheet for calculating the pressure required for break circulation in the annulus.

Ref book: Drilling Formula Book Formulas and Calculations for Drilling, Production and Workover, Second Edition

Pressure Required to Break Circulation Inside Drillstring

When we need to break circulation after mud in static condition, we need certain pressure to break mud gel strength. You may see that higher gel strength of mud, the higher pressure is required breaking circulation. So this post demonstrates how to determine pressure required breaking mud gel strength inside a drillstring.

Formula to calculate pressure required overcoming the mud’s gel strength inside the drill string as follow:

Pgs = (y ÷ 300 ÷ d) L

where Pgs = pressure required to break gel strength in psi

y = 10 mm gel strength of drilling fluid in lb/100 sq ft

d = inside diameter of drill pipe in inch

L = length of drill string in ft

Determine pressure required to break circulation inside the drill string by using following information

y = 12 lb/100 sq ft

d = 3.32 inch

L= 11,500 ft

Pgs = (12 ÷ 300 ÷ 3.32) x 11,500 ft

Pgs = 138.6 psi

Therefore, approximately 139 psi would be required to break circulation inside drill string.

Please find the Excel sheet for calculating the pressure required for break circulation inside drill string.

Ref book: Drilling Formula Book Formulas and Calculations for Drilling, Production and Workover, Second Edition

Pressure and Force Relationship and Its Application

Relationship of pressure, force and cross sectional area is one of the most commonly used concepts in oilfield and we will review this concept and its application. Pressure is force divided by cross section area (see an image below).

Pressure = Force ÷ Area

We normally use pressure in many units such as psi (pound per square inch), Pascal, kg/m3, etc.

In drilling operation, we mostly use circular area so area can be calculated by this formula;

Area = π x (radius)2 or π x (diameter)2÷ 4

Where  π= 22/7 = 3.143, so we can write a formula above in easy way

Area = 3.143 x (radius)2 or 0.7857 x (diameter)2

Pressure calculation based on the relationship above is shown below;

Pressure = force ÷ (3.143 x (radius)2) or force ÷ (0.7857 x (diameter)2)

Example : For this example, we will use the oilfield unit so force is in lb, diameter is in square inch (in2), and diameter is in inch.

Let’s try to apply pressure and force relationship in drilling operation. We plan to bullhead well and we still have drill string in the hole.

Drill string weight in the air = 45,000 lb
Mud weight in hole = 12.0 ppg
Bit size = 8.5”
Drill pipe size = 5″

What is the maximum pressure at surface you can apply before drilling string will be hydraulically pushed out due to bull heading pressure?

Solution

Buoyancy factor = (65.5 – 12.0) ÷ 65.5 = 0.817

Buoyed weight of drill string = 45,000 x 0.817 = 36,765 lb

Area = 0.7857 x (diameter)2= 0.7857 x (8.5)2= 56.77 square inch

Pressure = 36,765 lb ÷ 56.77 square inch= 647 psi.

In order to perform safe bullheading operation with drill string in hole, you need to apply bullheading pressure less than 647 psi on surface.

Bull Heading

Bull Heading

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.

Critical RPM to Avoid Excessive Vibration

When you operate top drive, you may need to know critical RPM that you can go. If you rotate pipe more than the critical RPM, it will create a lot of vibration that can cause failure in your drilling equipment such as drill pipe, TDS, etc.

In order to find out how much critical RPM, you may need high-tech simulation but sometimes you don’t really have that information supplied from town. So you really need to be able to roughly estimate how much critical RPM is ( at least you get a idea for this limitation). This formula below shows you how to estimate the critical RPM and it has accuracy of 15% roughly.

Critical RPM = 33,055 x (OD2 + ID2) 1/2 ÷ (L)2

Where;
OD = drill pipe outside diameter in inch
ID = drill pipe inside diameter in inch
L = length of one joint of drill pipe in feet

Example: Determine critical RPM from these following information

L = length of one joint of drill pipe = 32 ft
OD = drill pipe outside diameter = 4.0 in.
ID = drill pipe inside diameter = 3.5 in.

Critical RPM = 33,055 x (42+ 3.52)1/2 ÷ (32)2

Critical RPM = 172 RPM

Please remember this is ONLY estimation of the critical RPM. If you have your service companies or you have specific programs to determine it, please use the value from those programs because it should consider many parameters than this simple formula. USE IT IN CASE OF YOU HAVE NOTHING AVAILABLE TO CALCULATE THE CRITICAL RPM.

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 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.