## 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.

Mud Pump (OilfieldPix.com, 2017)

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.

## Drill pipe pulled to lose hydrostatic pressure

You previously learn about hydrostatic pressure lose due to pulling out of hole . This article will use the same concept but we will determine how many feet of drill pipe pulled to lose certain amount of hydrostatic pressure in well bore.

## Oilfield Unit

Pipe pulled, ft = (hydrostatic pressure loss in psi × (casing cap in bbl/ft – pipe displacement in bbl/ft)) ÷ (mud weight in ppg × 0.052 × pipe displacement in bbl/ft)

Example: Determine the FEET of drill pipe that must be pulled to lose 200 psi overbalance using the following data:

Hydrostatic pressure loss = 200 psi
Casing capacity = 0.0873 bbl/ft
Pipe displacement = 0.01876 bbl/ft
Mud weight = 12.0 ppg
Pipe pulled  = 200 psi × (0.0873 – 0.01876) ÷ (12.0 ppg × 0.052 × 0.01876)
Pipe pulled = 1171 ft
You need to pull 1171 ft of dry pipe to lose 200 psi hydrostatic pressure.

## Metric Unit

Pipe pulled, m = (hydrostatic pressure loss in KPa× (casing cap in m3/m- pipe displacement in m3/m-)) ÷ (mud weight in kg/m3 × 0.00981× pipe displacement in m3/m)

Example: Determine how many meters of drill pipe that must be pulled to lose 1400 KPa overbalance using the following data:

Hydrostatic pressure loss = 1400 KPa
Casing capacity = 0.04554 m3/m
Pipe displacement = 0.00979 m3/m
Mud weight = 1440 kg/m3
Pipe pulled  = 1400× (0.04554 – 0.00979 ) ÷ (1440 × 0.00981 × 0.00979 )
Pipe pulled = 362 m
You need to pull 362 m of dry pipe to lose 1400 KPa hydrostatic pressure.

Please find the Excel Spreadsheet to calculate how many feet  or meter of drill pipe pulled to lose certain amount of hydrostatic pressure in well bore.

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.

## Formation Temperature Calculation

Formation temperature is one of the most critical parameters in drilling and workover operation and it varies by true vertical depth of wellbore.

The following formula shows relationship between formation temperature and true vertical depth of well.

Formation temperature = (ambient surface temperature ) + (temperature gradient x  Well TVD)

Where:

Formation temperature in F (Fahrenheit)

ambient surface temperature in F (Fahrenheit)

temperature gradient in F/ft (Fahrenheit / ft)

Well TVD in ft

Example: The temperature gradient in a specific area is 0.015 °F/ft of depth and the ambient surface temperature is 90 °F.

Determine the estimated formation temperature at a TVD of 12,000 ft:

Formation Temperature, °F = 90 °F + (0.015 °F/ft x 12,000 ft)

Formation Temperature, °F = 90 °F + 180 °F

Formation Temperature = 270 °F (estimated formation temperature)

Please find the Excel sheet used for estimating formation temperature.

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.

## Hydrostatic Pressure (HP) Decreases When POOH

When pulling out of hole, volume of steel will be out of hole and mud volume will replace the steel volume.  If we don’t fill hole, hydrostatic pressure will decrease.  This topic shows you how to calculate hydrostatic pressure loss while pulling out of hole without filling the wellbore.  Moreover, there is the Excel sheet for calculating pressure decrease due to pulling out of hole.

## Oilfield Unit

Step 1: Determine Total Volume of Steel Out of Hole

Total Volume of Steel Out of Hole = Length  of pipe pulled out × Pipe Displacement

Where,

Total Volume of Steel Out of Hole in bbl

Length  of pipe pulled out in ft

Pipe Displacement in bbl/ft

Step 2: Determine Hydrostatic Pressure Decrease

Hydrostatic Pressure Decrease = (Total Volume of Steel Out of Hole × 0.052 × mud weight) ÷ (casing capacity – pipe displacement)

Where,

Hydrostatic Pressure Decrease in psi

Total Volume of Steel Out of Hole in bbl

mud weight in ppg

casing capacity in bbl/ft

pipe displacement in bbl/ft

Example: Determine the hydrostatic pressure decrease when pulling pipe out of the hole:

Number of stands pulled = 10
Pipe displacement = 0.0055 bbl/ft
Average length per stand = 91 ft
Casing capacity = 0.0873 bbl/ft
Mud weight = 12.0 ppg

Step 1: Determine of pipe displacement in Barrels = 10 stands × 91 ft/std × 0.0055 bbl/ft displaced

Total Volume of Steel Out of Hole = 5.01 bbl

Step 2: Determine HP, psi decrease = 5.01 barrels × 0.052 × 12.0 ppg ÷ (0.0873 bbl/ft – 0.0055 bbl/ft)

Hydrostatic pressure decrease = 38.2 psi

## Metric Unit

Step 1: Determine Total Volume of Steel Out of Hole

Total Volume of Steel Out of Hole = Length  of pipe pulled out × Pipe Displacement

Where,

Total Volume of Steel Out of Hole in m3

Length  of pipe pulled out in m

Pipe Displacement in m3 /m

Step 2: Determine Hydrostatic Pressure Decrease

Hydrostatic Pressure Decrease = (Total Volume of Steel Out of Hole × 0.00981 × mud weight) ÷ (casing capacity – pipe displacement)

Where,

Hydrostatic Pressure Decrease in KPa

Total Volume of Steel Out of Hole in m3

mud weight in kg/m3

casing capacity in m3 /m

pipe displacement in m3 /m

Example: Determine the hydrostatic pressure decrease when pulling pipe out of the hole:

Number of stands pulled = 10
Pipe displacement = 0.00287 m3 /m
Average length per stand = 30 m
Casing capacity = 0.04554 m3 /m
Mud weight = 1440 kg/m3

Step 1: Determine of pipe displacement in m3 = 10 stands × 30 m/std × 0.00287 m3 /m pipe displacement

Total Volume of Steel Out of Hole 0.86  m3

Step 2: Determine HP, psi decrease = 0.86  m3 × 0.00981 × 1440 kg/m3 ÷ (0.04554 m3 /m- 0.00287 m3 /m)

Hydrostatic pressure decrease = 285 KPa

Please find the Excel sheet for calculating pressure decrease due to pulling out of hole.

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.