Drilling Formulas and Drilling Calculations

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 = 11,150 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 11,150 ft

Pgs = 184.0 psi

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

Ref book: Formulas and Calculations for drill, production and workover by Norton J. Lapeyrouse

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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= 11,150 ft

Pgs = (12 ÷ 300 ÷ 3.32) x 11,150 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: Formulas and Calculations for drill, production and workover by Norton J. Lapeyrouse

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There is relationship between pump pressure and pump stroke that you really need to understand and be able to determine pump pressure after adjusting new pump stroke. There are 2 formulas used to determine pump pressure as shown in the detail below:

1^st formula for estimating new circulating pressure (simple and handy for field use)

New circulating pressure in psi = present circulating pressure in psi x (new pump rate in spm ÷ old pump rate in spm) ²

Example: Determine the new circulating pressure, psi using the following data:
Present circulating pressure = 2500 psi
Old pump rate = 40 spm
New pump rate = 25 spm
New circulating pressure in psi = 2500 psi x (25 spm ÷ 40 spm) ²
New circulating pressure = 976.6 psi

2nd formula for estimating new circulating pressure (more complex)

For the 1st formula, the factor “2” is used but it’s just the round up figure. If you want more accurate figure, you need to figure out an exact figure. So the 2nd formula has one additional formula to calculate the factor based on 2 pressure readings at different pump rate.  Please follow these steps to determine new circulating pressure

1. Determine the factor ”n” and  the formula to determine factor “n” is below:

Factor (n) = log (pressure 1 ÷ pressure 2) ÷ log (pump rate 1÷pump rate 2)
2. Determine new circulating pressure with this following formula.

New circulating pressure in psi = present circulating pressure in psi x (new pump rate in spm ÷ old pump rate in spm) ⁿ

Note: factor “n” comes from the first step of calculation.

Example: Determine the factor “n” from 2 pump pressure reading
Pressure 1 = 2700 psi at 320 gpm
Pressure 2 = 500 psi at 130 gpm
Factor (n)   = log (2700 psi ÷ 500 psi) ÷ log (320 gpm ÷ 130 gpm)
Factor (n) = 1.872

Example: Determine new circulating pressure by using these following information and the factor “n” from above example:
Present circulating pressure = 2500 psi
Old pump rate = 40 spm
New pump rate = 25 spm
New circulating pressure, psi = 2500 psi x (25 spm ÷ 40 spm) ^1.872
New circulating pressure = 1037 psi

Please find the Excel sheet used to calculate new circulating pressure based on pump pressure and pump stroke relationship.

Ref book: Formulas and Calculations for drill, production and workover by Norton J. Lapeyrouse

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Hydraulic Horse Power is a measure of the energy per unit of time that is being expended across the bit nozzles. It is commonly calculated with the equation HHP=P*Q/1714, where P stands for pressure in pounds per square in., Q stands for flow rate in gallons per minute, and 1714 is a conversion factor necessary to yield HHP in terms of horsepower. Bit manufacturers often recommend that fluid hydraulics energy across the bit nozzles be in a particular HHP range, for example 2.0 to 7.0 HHP, to ensure adequate bit tooth and bottom-of-hole cleaning (the minimum HHP) and to avoid premature erosion of the bit itself (the maximum HHP).
Ref: http://www.glossary.oilfield.slb.com

Hydraulic Horse Power (HPP) formula as follow:

HHP= (P x Q) ÷1714

where HHP = hydraulic horsepower
P = circulating pressure, psi
Q = circulating rate, gpm

Example : Determine Hydraulic Horse Power with these following data:

circulating pressure = 3500 psi
circulating rate = 800 gpm
HHP= (3500 x 800) ÷1714
HHP = 1633.6

Ref book: Formulas and Calculations for drill, production and workover by Norton J. Lapeyrouse

Please find the Excel sheet for calculating Hydraulic Horse Power (HHP)

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From the previous post, 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 give you idea about how much pressure loss but if you want to get the more accurate, you may need to contact your drilling fluid company to do it for you because they have the actual database and more complex formula that may help you get the good number. Anyway this formula can give you an idea how much annular pressure loss you will encounter.

P= [(1.4327 x 10^-7) x MW x Lx V²] ÷ (Dh – Dp)

P = annular pressure losses, psi

MW = mud weight in ppg

L = length of annular in ft

V = annular velocity in ft/mm

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) ÷ (8.5² – 5.0²)

v = 299 ft/min

Determine annular pressure losses, psi: P = [(1.4327 x 10^-7) x 13.0 x 8000 x 299²] ÷ (8.5 – 5.0)

P = 531.65 psi

Please find the Excel sheet to calculate annular pressure loss

Ref book: Formulas and Calculations for drill, production and workover by Norton J. Lapeyrouse

Note: If you don’t want to miss any post from drillingformulas.com, please consider subscribing to our mail list. So you will not miss our posts.