Drilling Formulas and Drilling Calculations

This post will show you Lean about bottom hole pressure relationship because this concept is very important for well control concept.
The bottom hole pressure is sum of all the pressure acting on the bottom hole. We can describe the statement before as the following equation;

Bottom Hole Pressure (BHP) = Surface Pressure (SP) + Hydrostatic Pressure (HP)

The image below demonstrates the relationship of bottom hole pressure.

Note: BHP created by hydrostatic column of drilling fluid is the primary well control in drilling.

Looking more into details,

If BHP is more than FP (formation pressure), this situation is called “Overbalance”.

If BHP is equal to FP (formation pressure), this situation is called “Balance”.

If BHP is less than FP (formation pressure), this situation is called “Underbalance”.

For more understanding, please follow this example below demonstrating the relationship of BHP, SP and HP.

Bottom Hole Pressure (BHP) = Surface Pressure (SP) + Hydrostatic Pressure (HP)

We assume that formation pressure is normal pressure gradient of water gradient (0.465 psi/ft) so formation pressure at 8000’ TVD = 8000 ft x 0.465 psi/ft = 3720 psi. Click here to learn how to calculate hydrostatic pressure in oilfield.

The first case: Hydrostatic column is water which is equal to formation pressure gradient so SP is equal to 0 psi

The second case: BHP is still be water gradient but fluid column is oil (0.35 psi/ft) which is lower density than water gradient (0.465 psi/ft). Therefore, in order to balance BHP, we need Surface Pressure (SP) of 920 psi (SP = 3720 – (0.35 x 8000)).

The third case: BHP is still be water gradient but fluid column is gas (0.1 psi/ft) which is even lower density than water gradient (0.465 psi/ft). Therefore, in order to balance BHP, we need Surface Pressure (SP) of 2,920 psi (SP = 3720 – (0.1 x 8000)).

According to the example, Surface Pressure (SP) will compensate the lack of hydrostatic pressure (HP) in order to balance formation pressure (FP).

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You previously learn about hydrostatic pressure lose due to pulling out of hole . This post 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.

The calculations below have 2 cases of pulling out of hole, pull dry and pull wet. They are different in calculation because amount of drilling fluid out of hole is different. Please follow and understand each case of calculation.

#1: How many feet of pipe pulled DRY to lose certain amount of hydrostatic pressure
Feet = (hydrostatic pressure loss in psi x (casing cap in bbl/ft – pipe displacement in bbl/ft)) ÷ (mud weight in ppg x 0.052 x pipe displacement in bbl/ft)

Example: Determine the FEET of dry drill pipe that must be pulled to lose the 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
Ft = 200 psi x (0.0873 – 0.01876) ÷ (12.0 ppg x 0.052 x 0.01876)
Ft = 1171 ft
You need to pull 1171 ft of dry pipe to lose 200 psi hydrostatic pressure.

#2: How many feet of pipe pulled WET to lose certain amount of hydrostatic pressure

Feet = hydrostatic pressure loss in psi x (casing capacity in bbl/ft – drill pipe capacity in bbl/ft – drill pipe displacement in bbl/ft) ÷ {mud wt in ppg x 0.052 x (pipe displacement in bbl/ft + (% of volume in drill pipe out of hole ÷ 100) x pipe capacity in bbl/ft)}

Example: Determine the feet of WET pipe that must be pulled to lose the overbalance using the following data:

% of volume in drill pipe out of hole = 100
Hydrostatic pressure loss = 200 psi
Casing capacity = 0.0873 bbl/ft
Drill pipe capacity = 0.01876 bbl/ft
Drill pipe displacement = 0.0055 bbl/ft
Mud weight = 12.0 ppg

Feet = 200 psi x (0.0873 – 0.01876 – 0.0055 bbl/ft) ÷ {12.0 ppg x 0.052 x (0.0055 + (100÷100) x 0.01876 bbl/ft)}
Feet = 832.9 ft
You need to pull 833 ft of wet pipe to lose 200 psi hydrostatic pressure.

Please find how many feet of drill pipe pulled to lose certain amount of hydrostatic pressure in well bore.

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

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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. There are 2 cases of pulling pipe which are pull dry and pull wet. Each condition is different in calculation concept because mud volume to displace pipe volume is different.

This post shows you how to calculate hydrostatic pressure loss for both cases of pulling pipe, pull dry and pull wet. Moreover, there is the Excel sheet for calculating pressure decrease due to pulling out of hole.

Case#1: When pulling DRY pipe

When pulling dry, we will consider volume of steel out of hole only.

Step 1:Determine of pipe displacement in Barrels = number of stands pulled X average length per stand, X pipe displacement ft displaced inbbl/ft

Step 2:Determine hydrostatic pressure in psi decrease = barrels displaced x 0.052 x mud weight, ppg ÷ (casing capacity in bbl/ft – pipe displacement in bbl/ft)

Example: Determine the hydrostatic pressure decrease when pulling DRY 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 x 91 ft/std x 0.0055 bbl/ft displaced
Barrels displaced = 5.01 bbl
Step 2: Determine HP, psi decrease = 5.01 barrels x 0.052 x 12.0 ppg ÷ (0.0873 bbl/ft – 0.0055 bbl/ft)
HP decrease = 38.2 psi

Case#2: When pulling WET pipe

When pulling wet, we will consider volume of steel out of hole and volume of mud in drillpipe as well. Threfore, pulling wet will decrease hydrostatic more than pulling dry pipe.

Step 1: Barrels displaced = number of stands pulled per stand in ft
X average length X {pipe disp inbbl/ft + {(% volume in drill pipe out of hole ÷ 100) X pipe cap in bbl/ft)}

Step 2: Determine hydrostatic pressure in psi decrease = barrels displaced x 0.052 x mud weight, ppg ÷ ((casing capacity in bbl/ft) – (Pipe disp in bbl/ft + pipe cap in bbl/ft))

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

% of volume in drill pipe out of hole = 100
Number of stands pulled = 10
Pipe displacement = 0.0055 bbl/ft
Average length per stand = 91 ft
Pipe capacity = 0.01876 bbl/ft
Mud weight = 12.0 ppg
Casing capacity = 0.0873 bbl/ft

Step 1 Barrels displaced = 10 stands x 91 ft/std x {(.0055 bbl/ft + (100 ÷ 100) x 0.01876 bbl/ft)}
Barrels displaced = 22.08 bbl

Step 2 hydrostatic pressure in psi decrease = 22.0766 barrels x 0.052 x 12.0 ppg ÷ ((0.0873 bbl/ft) – (0.0055 bbl/ft + 0.01876 bbl/ft))
HP decrease, psi = 218.52 psi

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

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.

Hydrostatic pressure is created by fluid column. Two factors affecting hydrostatic pressure  are mud weight and True Vertical Depth. So this post will demonstrate how to calculate hydrostatic pressure in different oilfield units.

1. Calculate hydrostatic pressure in psi by using mud weight  in PPG and feet as the units of True Vertical Depth.

Hydrostatic pressure equation:
HP = mud weight in ppg x 0.052 x True Vertical Depth (TVD) in ft

Example: mud weight = 12.0 ppg
True Vertical Depth = 10,000 ft
HP = 12.0 ppg x 0.052 x 10,000 ft
HP = 6,240 psi

2. Calculate hydrostatic pressure in psi by using pressure gradient in psi/ft and feet as the units of True Vertical Depth.

Hydrostatic pressure equation:
HP = Pressure gradient in psi/ft x True Vertical Depth (TVD) in ft

Example: Pressure Ggradient = 0.5 psi/ft
True Vertical Depth = 10,000 ft
HP = 0.5 psi/ft x 10,000 ft
HP = 5,000 psi

3 Calculate hydrostatic pressure in psi by using mud weight in lb/ft³ and feet as the units of True Vertical Depth.

Hydrostatic pressure equation:
HP = 0.006944 x mud weight, lb/ft³ x TVD, ft

Example: mud weight = 80 lb/ft³ true vertical depth = 10,000 ft
HP = 0.006944 x 80 lb/ft³ x 10,000 ft
HP = 5,555 psi

4. Calculate hydrostatic pressure in psi by using mud weight in PPG and meters as unit of True Vertical Depth.

Hydrostatic pressure equation:
HP = mud weight, ppg x 0.052 x TVD in meters x 3.281

Example: Mud weight = 12.0 ppg true vertical depth = 5000 meters
HP = 12.0 ppg x 0.052 x 5000 x 3.281
HP = 10,237 psi

Download the Excel sheet for calculating hydrostatic pressure

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