Drilling Formulas and Drilling Calculations » Hydraulic Formulas

Drilling Formulas and Calculation Summary Page

DrillingFormulas.Com — Mon, 05 Jul 2010 03:04:14 +0000

I created summary page for drilling formulas and calculations (http://www.drillingformulas.com/drilling-formulas-and-calculation-sheets/). I wish these excel sheets would be helpful for you.

Amount of cuttings produced per foot of hole drilled
Annular Pressure Loss
Annular-Capacity
Annular-velocity
Bulk Density Calculation
Buoyancy Factor Oilfield
Convert Pressure to Equivalent Mud Weight
Convert-Specific-Gravity
Cost Per Foot Calculation
Critical RPM
D Exponent Calculation
D Exponent Corrected Calculation
Decrease Oil Water Ratio
Density of Oil Water Mixture
Depth of Washout
Dilution LGS control
Dilution LGS control – adding mud
Directional Survey Calculation – Angle Averaging Method
Directional Survey Calculation – Radius of Curvature Method
Dogleg Severity Calculation – Radius of Curvature Method
Dogleg Severity Calculation – Tangential Method
Drilling or Connection Ton-Mile
Drill-pipe-pulled-to-lose-certain-hydrostatic-pressure
Equivalent Circulating Density Calculation
Equivalent Circulating Density with engineering formula
Formation Integrity Test
Formation Temperature
Free Point Constant Calculation
Hydraulic Horse Power
Hydrostatic Pressure Calculation
Hydrostatic Pressure Decreases When POOH
Increase mud weight adding Barite
Increase mud weight adding calcium carbonate
Increase mud weight adding hematite
Increase Oil Water Ratio
Internal Capacity
Lag Time Calculation
Leak off test calculation
Light Weight Spot Pill
Loss hydrostatic due to filling water into annulus
Mix Different Fluid Density – Limit Space
Mix Different Fluid Density – Unlimit Space
Mud Volume Increase Due to Adding Barite
Mud Volume Increase Due to Adding Calcium Carbonate
Mud Volume Increase Due to Adding Hematite
Oil Water Ratio from a Retort Analysis
Pipe Displacement Calculation
Pressure and Force Calculation
Pressure Gradient Calculation
Pressure Required to Break Circulation In Annulus
Pressure Required to Break Circulation Inside Drill String
Pump Output (Duplex and Triplex)
Pump Pressure and Pump Stroke Relationship
Reduce Mud Weight by Dilution
Slug Calculation – Barrel of Slug Required
Slug Calculation – barrels of slug required for a desired length of dry pipe
Slug Calculation – Weight of Slug Required
Specific Gravity Calculation
Starting Volume for Weighting Up with Bartie
Starting Volume for Weighting Up with calcium carbonate
Starting Volume for Weighting Up with Hematite
Stuck Pipe Calculation – Not Know Free Point Constant
Stuck Pipe Calculation – Use Table for Free Point Constant
Temperature Conversion Formulas
Ton-Mile (TM) for Coring Operation
Ton-Mile (TM) for Making Short Trip
Ton-Mile (TM) for Round Trip
Ton-Mile (TM) for Setting Casing
Ton-Mile (TM) for Drilling or Connection

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

Pressure Loss and Equivalent Circulating Density Review – Reverse Circulation

DrillingFormulas.Com — Sun, 23 May 2010 17:28:53 +0000

We still have the same question as the previous post, Pressure Loss and Equivalent Circulating Density Review, but this case we will do reverser circulation, circulating from annulus to tubing , and see how much pressure and equivalent circulating density at bottom hole.

Data Given

Reverse circulate total of 3 time bottom up from annulus to tubing with 12.7 ppg mud at 10,000′MD/10,000 TVD.

Pump pressure = 1000 psi

Annulus friction loss = 50 psi

Inside tubing friction loss = 925 psi

Surface line friction loss = 25 psi

Determine pressure at bottom hole.

We still apply the concept of frictional pressure so reverse circulation is calculated by this following equation:

Pressure at bottom hole (reference at annulus side) = Hydrostatic Pressure + Pressure from pump- Annular Pressure Loss

Note: Hydrostatic pressure and pressure from pump force downward to bottom hole but annulus pressure forces upward direction.

Pressure in the well at 10,000’ = 1000 + (0.052×10,000×12.7) – 50 = 7554 psi

OR you can referrence to the tubing side as well.

Pressure at bottom hole (reference at tubing) = Hydrostatic Pressure + Annular Pressure Loss in tubing + surface line pressure loss
Note: All pressure force downward to bottom hole so all pressure term must be sum together.

Pressure at bottom hole (reference at tubing) = (0.052×10,000×12.7) + 925+25 = 7554 psi.

Determine Equivalent Circulating Density at bottom hole.

ECD = Current mud weight in PPG + (annular pressure loss /(0.052xTVD)) = Total Pressure at Bottom Hole /(0.052xTVD)

ECD =7554 / (0.052 x 10,000) = 14.53 PPG.

The point that I want you to think of between this example and the previous example, Pressure Loss and Equivalent Circulating Density Review, is about the different of bottom hole pressure and ECD between forward circulation and reverse circulation.
You will see that reverse circulation results in a lot of pressure at bottom hole. Hence, you must keep in mind this concept and try to figure out how much pressure at bottom hole should be for both forward circulation and reverse circulation. Otherwise, you can accidentally break wellbore due to high ECD.

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

Pressure Loss and Equivalent Circulating Density Review

DrillingFormulas.Com — Thu, 20 May 2010 02:58:34 +0000

This example that I got from my junior member is very simple but it helps you a lot to understand about how to determine pressure loss during normal circulation.

Information given is listed below;

Circulate at 3 bottom up through open end tubing (Down tubing and up annulus) with 12.7 ppg mud.

Pump pressure = 1000 psi

Annulus friction loss = 50 psi

Inside tubing friction loss = 925 psi

Surface line friction loss = 25 psi

Calculate the pressure in the well at 10,000’ (tubing tail). What would ECD at 10,000’ TVD be?

The concept of calculation that you should know : total pressure at bottom = pumping pressure + hydrostatic pressure – pressure loss in the opposite way of fluid flowing.

Then,

If I reference to tubing site, I will get the equation like this.

Pressure at bottom hole= Hydrostatic Pressure at bottom hole + Pressure from pump- Pressure Loss in surface line – Pressure loss in tubing

Pressure in the well at 10,000’ = 0.052×12.7×10000 + 1000 – 25 – 925 = 6654 psi

If I reference to annulus site, I will get the equation like this.

Pressure at bottom hole= Hydrostatic Pressure at bottom hole +Annular pressure loss

Note: Hydrostatic pressure and annular pressure loss force downward.

Pressure in the well at 10,000’ = 0.052×12.7×10000+ 50 = 6654 psi

Note: It doesn’t matter which site of u-tube you refer to the bottom hole pressure is still the same.
ECD (Equivalent Circulating Density) is calculated by this following equation:

ECD = Current mud weight in PPG + (annular pressure loss /(0.052xTVD))

ECD = 12.7 + (50/(0.052 x 10000))

ECD = 12.8 ppg

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

How much pressure will we see at cement head in case of float shoe fail?

DrillingFormulas.Com — Sun, 16 May 2010 18:19:30 +0000

I still have the simple but interesting question about hydrostatic pressure which you can apply this calculation into drilling/cementing operation. The question I got about how much pressure we will see at cement head in case of float shoe fail.

Given situation as shown in figure above. This situation is in vertical well.

1) Inside 16” shoe, from 0’ to 1975’ = 9.3 ppg mud

From 1975’ to 2000’ = 16.0 ppg mud

2) Outside 16” shoe, From 0’ to 1500’ = 11.6 ppg cement (lead)

From 1500’ to 2000’ = 16.0 ppg cement (tail)

Given the conditions above and assuming the cement is still liquid, how much pressure will we see at cement head in case of float shoe fail?

** Note : you need to understand how to calculate hydrostatic pressure in order to fully understand this question **

Using U-tube concept: Bottom hole pressure both sides are the same.

Let’s work out at annulus side which is heavier due to cement in the annulus

Pressure at bottom hole in annulus = hydrostatic pressure of lead cement + hydrostatic pressure of tail cement

Pressure at bottom hole in annulus = 0.052×11.6×1500 + 0.052x16x(2000-1500) =1320.8 psi

Since, hydrostatic pressure in the annulus is more than hydrostatic pressure in 16″ casing; therefore, there will be pressure in the cement head in order to balance u-tube.

We can simply write equation as follows;

Bottom hole pressure = hydrostatic pressure inside 16” casing + surface pressure at cement head

1320.8 = 0.052x16x(2000-1975) + 0.052×9.3×1975 + surface pressure at cement head

Surface pressure at cement head = 1321 – 976 = 345 psi

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

Review Hydrostatic Pressure and U-Tube Concept

DrillingFormulas.Com — Wed, 12 May 2010 01:00:42 +0000

I just got the question from my junior asking me about relationship between hydrostatic pressure and U-tube. I think this might be good idea for us to review these 2 important concepts.

Referring to the figure below, the well is shut in and there are 2 gauges showing different numbers. Gauge#1 shows 600 psi and gauge#2 shows 100 psi.

One side we have water (8.5 ppg ) and mud 10.7 ppg and anther side has mud 10.7 ppg and mud 13.3 ppg. All depths are in TVD.

You know that the gauge #1 is reading correctly.

(1) Is gauge #2 correct?

In order to check the function of the gauge no.2, the concept of U-tube pressure balance is utilized.

Pressure at the bottom hole is calculated by this following equation:

BHP = Pressure gauge#1+ Hydraulic Pressure at gauge#1 side

BHP = 600 + 8.5×0.052×2500 + 10.7×0.052x(4000-2500)

BHP= 2539.6 psi

Pressure at the gauge#2 must balance BHP and is calculated by this following equation:

Pressure gauge2 = BHP – Hydraulic Pressure at gauge#2 side

Pressure gauge2 =2539.6-13.3×0.052×1,000-10.7×0.052×3,000

Pressure gauge2 =178.8 psi

Pressure gauge#2 must be about 180 psi; however, pressure gauge#2 is only 100 ps for this reason the Gauge #2 is not correct.

(2) If not, what should it read?

It should read about 180 psi.

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

Pressure Required to Break Circulation in Annlus

DrillingFormulas.Com — Wed, 26 Aug 2009 00:59:14 +0000

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 Drilling, Production and Workover, Second Edition

Pressure Required to Break Circulation Inside Drillstring

DrillingFormulas.Com — Sat, 22 Aug 2009 22:30:18 +0000

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 Drilling, Production and Workover, Second Edition

Pump Pressure and Pump Stroke Relationship

DrillingFormulas.Com — Wed, 03 Jun 2009 03:41:09 +0000

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 Drilling, Production and Workover, Second Edition

Hydraulic Horse Power Calculation

DrillingFormulas.Com — Mon, 25 May 2009 23:35:07 +0000

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

Calcuate Annular Pressure Loss

DrillingFormulas.Com — Tue, 28 Apr 2009 22:36:55 +0000

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 Drilling, Production and Workover, Second Edition