## 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: Formulas and Calculations for Drilling, Production and Workover, Second Edition

## Pump Pressure and Pump Stroke Relationship There are relationships 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:

## 1st 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

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.

## Hydraulic Horse Power (HHP) Calculation 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 by this 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).

## 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

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

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. 