Drilling Formulas and Drilling Calculations

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 Drilling, Production and Workover, Second Edition

Formation temperature is one of the most critical in many drilling and workover operation and it varies by true vertical depth of wellbore. Therefore, it is very critical to determine correct formation temperature.

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

Formation temperature in °F = (ambient surface temperature in °F) + (temperature increase in °F per  TVD depth x TVD in ft)

Example: If the temperature increase in a specific area is 0.015 °F/ft of depth (temperature gradient) 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 book: Formulas and Calculations for Drilling, Production and Workover, Second Edition

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

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

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

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 Drilling, Production and Workover, Second Edition

Buoyancy Factor is the factor that is used to compensate loss of weight due to immersion in drilling fluid.

Before explaining any further, I will explain you about the basic concept of Buoyancy. Buoyancy is the upward force that keeps things afloat. The net upward buoyancy force equals to the amount of the weight of fluid displaced by the body volume. This force will make objects lighter when it immerses in fluid. For example, we feel ourselves lighter when we are in swimming pool because this is the effect of buoyancy.

In drilling operation, we need to know how much weight of string of drill pipe, completion string, etc in drilling fluid. Therefore,  Buoyancy Factor is value that we need to know and be able to calculate this value. Please follow the formulas below to calculate Buoyancy Factor in different mud weight units, ppg and lb/ft³.

Buoyancy Factor using mud weight in ppg

Buoyancy Factor (BF) = (65.5 – mud weight in ppg) ÷65.5

Example: Determine the buoyancy factor for a 13.0 ppg fluid:
BF = (65.5 – 13.0) ÷ 65.5
BF = 0.8015

Buoyancy Factor using mud weight in  lb/ft³

Buoyancy Factor (BF) = (489 – mud weight in lb/ft³) ÷489

Example: Determine the buoyancy factor for a 100 lb/ft³ fluid:
BF = (489 – 100) ÷489
BF = 0.7955

How to use the Buoyancy Factor

In order to figure out the actual weight of drilling string in mud, the air weight of drilling string times the buoyancy factor equal to actual weight in mud, called buoyed weight.

For example , determine the string weight in 13.0 ppg mud. Air weight of string is 350 klb.

The buoyancy factor for a 13.0 ppg fluid:
BF = (65.5 – 13.0) ÷ 65.5
BF = 0.8015

The bouyed weight of drill string in 13.0 ppg mud = 350 x 0.8015 = 280.5 Klb.

Please find the Excel sheet used to calculate Buoyancy Factor

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

After learning about capacity calculation, we can apply the capacity calculation to determine how much barrels of cutting produced per foot of hole drilled and total solid generated in pounds. Please read and understand the following formulas:

Use formular#1 and #2 for calculating amount of cutting generated per feet drilled.

Formula#1 for BARRELS of cuttings drilled per foot of hole drilled:

Barrels of cutting per foot drilled = Dh² x (1 – % porosity) ÷1029.4

Where: Dh is hole diameter.

Example: Determine barrels of cuttings drilled for one foot of 6-1/8 inch hole with 25% (0.25) porosity:

Barrels/footage drilled = 6.125² x (1 – 0.25) ÷1029.4
Barrels/footage drilled = 0.02733 bbl/footage drilled

Formula#2 for CUBIC FEET of cuttings drilled per foot of hole drilled:

Cubic feet of cutting per foot drilled = Dh² x 0.7854 x (1 – % porosity) ÷144
Where: Dh is hole diameter.

Example: Determine barrels of cuttings drilled for one foot of 6-1/8 inch hole with 25% (0.25) porosity

Cubic feet/footage drilled = 6.125² x 0.7854 x (1 – 0.15) ÷144
Cubic feet/footage drilled = 0.153462 cu ft/footage drilled

Moreover, you also apply simeple density and volume relationship to determine total solids generated. Use the following formula to calculate total solid generated.

Wcg = 350 x Ch x L x (l – porosity) x Cutting density

Wcg = solids generated in pounds
Ch = capacity of hole in bbl/ft
L = footage drilled in ft
Cutting density = cutting density in gm/cc

Example: Determine the total pounds of solids generated in drilling 100 ft of  6-1/8 inch hole (0.03644 bbl/ft). Density of cuttings = 2.20 gm/cc. Porosity = 25%:
Wcg = 350 x 0.03644 x 100 x (1 – 0.25) x 2.2
Wcg = 2104.41 pounds

Please find the excel sheet how to calculate how much cuttings drilled per foot of hole drilled and total solids generated

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

Pipe displacement, normally in bbl/ft, is steel volume to displace fluid volume.  When we either pull out of hole or trip in hole for any kind of pipes such as drill pipe, casing or tubing, you should know how much fluid to displace steel volume.

For example, when we pull out of hole, a trip sheet must be monitored all time. We must know how much fluid will fill the hole each stand of drill pipe pulled out. If the volume of displacement less than theoretical displacement value, we may have problem due to swabbing formation into wellbore.

This post will demonstrate how to calculate plain pipe displacement with this following formula:

Pipe Displacement in bbl/ft = (OD in² – ID in² ) ÷ 1029.4

Where,
OD is out side diameter of pipe.
ID is inside diameter of pipe.

This formula is good for plain pipe diplacment such as casing and tubing. It’s not accurate enough for drill pipe because this formula does not account for tool joint displacement therefore you need drill pipe specification sheet for its displacement.

Example: Determine inner capacity in bbl/ft of 9-5/8” casing 40 ppf, OD = 9.625 in, ID = 8.835 in

Pipe Displacement of 9-5/8” casing 40 ppf in bbl/ft = (9.625² – 8.835² ) ÷1029.4
Pipe Displacement of 9-5/8” casing 40 ppf in bbl/ft = 0.01417 bbl/ft

Please find the excel sheet how to calculate pipe displacement

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

From the previous post, you learn how to calculate annular capacity and this post shows you how to use the same principle to calculate inner capacity of  open hole / inside cylindrical objects such as tubulars, drill pipe, drill collars, tubing, casing etc.

There are several formulas to calculate inner capacity depending on unit of inner capacity required. Please read and understand the formulas below:

Formula#1) Calculate inner capacity in bbl/ft

Inner Capacity in bbl/ft = (ID in.)² ÷1029.4

Example: Determine inner capacity in bbl/ft of a 6-1/8 in. hole:
Inner Capacity in bbl/ft = 6.125²÷1029.4
Inner Capacity in bbl/ft = 0. 0364 bbl/ft

Formula#2) Calculate inner capacity in ft/bbl²

Example: Determine inner capacity in ft/bbl of 6-1/8 in. hole:
Inner Capacity in ft/bbl = 1029.4 ÷ 6.125²
Inner Capacity in = 27.439 ft/bbl

Inner Capacity in ft/bbl = 1029.4 ÷ (ID in.)

Formula#3) Calculate inner capacity in gal/ft

Inner Capacity in gal/ft = (ID in.)² ÷24.51

Example: Determine inner capacity in gal/ft of 6-1/8 in. hole:
Inner Capacity in gal/ft = 6.125²÷ 24.51
Inner Capacity in = 1.53 gal/ft

Formula#4) Calculate inner capacity in ft/gal

Inner Capacity in ft/gal = 24.51 ÷ (ID in.)²

Example: Determine inner capacity in ft/gal of 6-1/8 in. hole:
Inner Capacity in ft/gal = 24.51 ÷ 6.125²
Inner Capacity in ft/gal = 0.6533 ft/gal

Please find the excel sheet on how to calculate inner capacity.

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

Annular capacity is one of basic values that you really need to understand. This post demonstrates you how to calculate annular capacity between casing or hole and drill pipe, tubing, or casing. There are several formulas as shown below to calculate annular capacity depending on unit of annular capacity required.

Note: Dh is bigger ID and Dp is smaller OD. The examples below will show the Dh as hole size and Dp is drill pipe OD

a) Calculate annular capacity in bbl/ft

Annular capacity in bbl/ft =  (Dh² – Dp²) ÷1029.4

Example: Hole size (Dh) = 6-1/8 in.
Drill pipe OD (Dp) = 3.5  in.
Annular capacity in bbl/ft = (6.125² – 3.5 ²) ÷1029.4
Annular capacity = 0.0245 bbl/ft

b) Calculate annular capacity in ft/bbl

Annular capacity in ft/bbl = 1029.4 ÷ (Dh² – Dp²)

Example: Hole size (Dh) = 6-1/8 in.
Drill pipe OD (Dp) = 3.5  in.
Annular capacity in ft/bbl = 1029.4 ÷ (6.125 ² – 3.5 ²)
Annular capacity = 40.743 ft/bbl

c) Calculate annular capacity in gal/ft

Annular capacity in gal/ft = (Dh² – Dp²) ÷ 24.51

Example: Hole size (Dh) = 6-1/8 in.
Drill pipe OD (Dp) = 3.5  in.
Annular capacity in gal/ft = (6.125 ² – 3.5²) ÷24.51
Annular capacity = 1.031 gal/ft

d) Calculate annular capacity in ft/gal

Annular capacity, ft/gal = 24.51 ÷ (Dh² – Dp²)

Example: Hole size (Dh) = 6-1/8 in.
Drill pipe OD (Dp) = 3.5  in.
Annular capacity in ft/gal = 24.51 ÷  (6.125 ² – 3.5 ²)
Annular capacity in ft/gal = 0.97 ft/gal

After obtaining annular capacity, we can calculate annular volume by this following formula;

Annular volume in bbl  = annular capacity (bbl/ft) x length of annulus (ft)

Note: annular volume can be expressed in several unit depending on unit that you use in the calculation.

Example:

Annular capacity = 0.0245 bbl/ft
Length of annulus = 1000 ft

Annular volume = 1000 x 0.0245 = 24.5 bbl.

** Please remember that if you have several annular profile, you must calculate volume based on each annular profile in order to get total annular volume.

Please find the Excel sheet for calculating annular capacity.

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

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 the simple equation that I post before. Please follow steps how to calculate annular pressure loss and ECD.

1. Determine n:
2. Determine K:  
3. Determine annular velocity (v) in ft/min: v = (24.5 x Q) ÷ (Dh² – Dp²)

4. Determine critical velocity (Vc) in ft/min:

5. Pressure loss for laminar flow (Ps), psi:

6. Pressure loss for turbulent flow (Ps), psi:

7. Determine equivalent circulating density (ECD), ppg:

ECD in ppg = Ps ÷ 0.052 ÷ TVD in ft + MW in ppg

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 = 30
Θ600 = 60
Plastic viscosity = 22 cps
Circulation rate = 320 gpm
Hole diameter = 8.5 in.
Drill collar OD = 6.5 in.
Drill pipe OD = 5.0 in
Drill collar length = 650 ft
Drill pipe length = 11,500 ft
True vertical depth = 12,150 ft

1. Determine n:

2. Determine K:
3. Determine annular velocity (v) in ft/min around drill pipe: v = (24.5 x 320) ÷ (8.5² – 5² ) = 165.9 ft/min

4. Determine critical velocity (Vc) in ft/min around drill pipe:

The annular velocity around drill pipe is more than the critical velocity around drill pipe so this is turbulent flow. The equation #6 (for turbulent flow) must be applied in this case.

Pressure loss for turbulent flow (Ps), psi:

5. Determine annular velocity (v) in ft/min around drill collar: v = (24.5 x 320) ÷ (8.5² – 6.5²) = 261.3 ft/min

6. Determine critical velocity (Vc) in ft/min around drill collar:

The annular velocity around drill collar is less than the critical velocity around drill collar so this is laminar flow. The equation #5 (for laminar flow) must be applied in this case.

Pressure loss for laminar flow (Ps), psi:

Total annular pressure loss = annular pressure loss around drill pipe + annular pressure loss around drill collar

Ps=69.2+12.7 = 81.9 psi

7. Determine equivalent circulating density (ECD), ppg:

ECD in ppg = (81.9 ÷ 0.052 ÷ 12,150) + 9.5 = 9.63 ppg

Please find the Excel sheet for calculating ECD (engineering calculation)

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