Drilling Formulas and Drilling Calculations

A “Kick” or “Wellbore Influx” is undesirable flow of formation fluid into the wellbore and it happens when formation pressure is more than hydrostatic pressure in wellbore.

Several causes of Kick (Wellbore Influx) are listed below:

1. Lack of knowledge and experience of personnel (Human error)– Lacking of well-trained personnel can cause well control incident because they don’t have any ideas what can cause well control problem. For example, personnel may accidentally pump lighter fluid into wellbore and if the fluid is light enough, reservoir pressure can overcome hydrostatic pressure.

2. Light density fluid in wellbore - It results in decreasing hydrostatic pressure. There are several reasons that can cause this issue such as

• Light pills, sweep, spacer in hole

• Accidental dilution of drilling fluid

• Gas cut mud

3. Abnormal pressure – If abnormally high pressure zones are over current mud weight in the well, eventually kick will occur.

4. Unable to keep the hole full all the time while drilling and tripping. If hole is not full with drilling fluid, overall hydrostatic pressure will decrease.

5. Severe lost circulation – Due to lost circulation in formation, if  the well could not be kept fully filled all the time, hydrostatic pressure will be decreased.

Lost circulation usually caused when the hydrostatic pressure of drilling fluid exceeds formation pressure. There are several factors that can cause lost circulation such as

• Mud properties – mud weight is too heavy and too viscous.

• High Equivalent Circulating Density

• High surge pressure due to tripping in hole so fast

• Drilling into weak formation strength zone

6. Swabbing causes reducing wellbore hydrostatic pressure.

Swabbing is the condition that happens when anything in a hole such as drill string, logging tool, completion sting, etc is pulled and it brings out decreasing hydrostatic pressure. Anyway, swabbing can be recognized while pulling out of hole by closely monitoring hole fill in trip sheet.

Reference : Well Control Books

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Understand Boyle’s Gas Law

Boyle’s law states that at constant temperature, the absolute pressure and the volume of a gas are inversely proportional in case of constant temperature within a closed system. It may sound pretty hard to understand what it is.

Well, we can describe the statement above into simple mathematics as following formula:

Boyle’s Gas Law: P x V = constant

Or express Boyle’s law in another term: P1 x V1 = P2 x V2

Where; P = Pressure and V = Volume

It sounds easy a little bit to understand.

Let’s apply Boyle’s law into our drilling business

Calculate the volume of gas you will have on the surface, 14.7 psi for atmospheric pressure, when 1 bbl of gas kick is circulated out from reservoir where has formation pressure of 3,000 psi.

Boyle’s Gas Law: P1 x V1 = P2 x V2

P1= 3000 psi (reservoir pressure)

V1 = 1 bbl (volume at bottom hole)

P2 = 14.7 psi (atmosphere pressure)

V2 = ? (volume at surface)

P1 x V1 = P2 x V2

3000 x 1 = 14.7 x V2

V2 = 204 bbl

Ref: Well Control Books

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After learning about U-tube concept, let’s get a example in order to understand clearly about physical meaning of U-tube. This is very important concept so you need to clear about it.

Mud weight inside drill pipe is 9.8 PPG is all the way to bit and mud weight in the annulus is 9.2 PPG all the way to surface. Hole depth is 10,000’MD/8500’TVD. The well is shut in and drill pipe pressure is equal to 0 psi. Determine casing pressure.

According to U-tube concept, both sides (casing and drill pipe) have the same bottom hole pressure so we can write the equation to describe the U-tube concept as shown below;

SP (casing) + HP (casing) = BHP = SP (drill pipe) + HP (drill pipe)

At drill pipe side: BHP = 0 psi (Drill pipe Pressure) + 0.052×9.8×8,500 (Hydrostatic Pressure at drill pipe side) = 4,331 psi

At casing side: BHP = 4,331 psi = (Casing Pressure) + 0.052×9.2×8,500 (Hydrostatic Pressure at casing)

With this relationship (SP (casing) + HP (casing) = BHP = SP (drill pipe) + HP (drill pipe) ),we can solve casing pressure.

4331 = Casing Pressure + 4066

Casing Pressure = 4331 – 4066 = 265 psi

Ref: Well Control Book

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We can likely use the behavior of one of the fluid columns to describe behavior regarding what is happening in another side of fluid column, if two fluid columns are connected at bottom. Basically, this situation is simply described in common oil filed name as “U Tube”.

In oil field especially drilling business, “U Tube” can be considered as a string of pipe (drill pipe and tubing) is in a wellbore and fluids are able to pass inside of string of pipe (drill pipe and tubing) and the annulus (area between wellbore and string of pipe). The figure below demonstrates “U Tube” in our drilling business.

Why is U-Tube very important?

It is very vital to keep a basic concept of U-Tube in mind.

If there are two different fluids between inside of string and annulus, fluids always flow from a higher pressure area to a lower pressure.

If the system is NOT closed, lighter fluid will be flown out and it will be stopped when system pressure is stabilized (see figure below).

If the system is closed, pressure must be the same at the bottom point where both sides of U-tube are connected. Therefore, drill pipe pressure and casing pressure (annulus pressure) will be responded based on fluid in each side and formation pressure at bottom hole (see figure below).

Please always remember that U-Tube concept can be widely applied in many drilling and workover application such as well control, cementing, etc.

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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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Can you imagine if primary and secondary well control are failed? Well is flowing all the time so how can we deal with this situation? For this situation, you must use Tertiary Well Control.

Tertiary Well Control is specific method used to control well in case of failure of primary and secondary well control. These following examples are tertiary well control:

• Drill relief wells to hit adjacent well that is flowing and kill the well with heavy mud. Note: this case you can study from PTTEP Austraila Blow Out Incident. They use this method to control the well that was firing on the platform.
• Dynamic kill by rapidly pumping of heavy mud to control well with Equivalent Circulating Density (ECD)
• Pump barite or gunk to plug wellbore to stop flowing
• Pump cement to plug wellbore

Etc

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Referring to the previous section, primary well control is hydrostatic pressure bore that prevents reservoir influx while performing drilling operations (drilling, tripping, running casing/completion, etc). When primary well control is failed, it causes kick (wellbore influx) coming into wellbore. Therefore, this situation needs special equipment which is called “Blow Out Preventer” or BOP to control kick.

Well, we can call that “Blow Out Preventer” or BOP is Secondary Well Control. Please also remember that BOP must be used with specific procedures to control kick such as driller method, wait and weight, lubricate and bleed and bull heading. Without well control practices for using BOP’s, it will just be only heavy equipment on the rig.

There are several types of “Blow Out Preventer” (BOP) which have different applications. I will talk about BOP categories later.

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Primary Well Control is hydrostatic pressure provided by drilling fluid more than formation pressure but less than fracture gradient while drilling. If hydrostatic pressure is less than reservoir pressure, reservoir fluid may influx into wellbore. This situation is called “Loss Primary Well Control”.

Not only is hydrostatic pressure more than formation pressure, but also hydrostatic pressure must not exceed fracture gradient. If your mud in hole is too heavy causing broken wellbore, you will face with loss circulation problem (may be partially lost or total lost circulation). When fluid is losing into formation, mud level in well bore will be decreased that will result in reducing hydrostatic pressure. In worst case scenario, you will lose the primary well control and wellbore influx or kill will enter into wellbore.

Typically, slightly overbalance of hydrostatic pressure over reservoir pressure is normally desired. You must keep in mind about the basic of maintaining primary well control that you must maintain hole with drilling fluid that will be heavy enough to overbalance formation pressure but not fracture formation.

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For subsea applications, hydrostatic pressure exerted by the hydraulic fluid must be accounted for calculation.

In this case, we assume water depth at 1500 ft, therefore hydrostatic pressure exerted by hydraulic fluid (hydraulic fluid pressure gradient = 0.445 psi/ft) = 0.445×1500 = 668 psi. Besides of that, the concept for calculation is as same as surface accumulator. So please take a look about how to calculate usable volume per bottle as following steps.

Step 1 Adjust all pressures for the hydrostatic pressure of the hydraulic fluid:

Pre-charge pressure = 1000 psi + 668 psi = 1668 psi

Minimum system pressure = 1200 psi + 668 psi = 1868 psi

Operating pressure = 3000 psi + 668 psi = 3668 psi

Step 2 Determine hydraulic fluid required to increase pressure from pre-charge pressure to minimum system pressure:

Boyle’s Law for ideal gase: P1 V1 = P2 V2

1668 psi x 10 = 1868 x V2

16,680 ÷1,868 = V2

V2 = 8.93 gal

It means that N2 will be compressed from 10 gal to 8.93 gal in order to reach minimum operating pressure. Therefore, 1.07 gal (10.0 – 8.93 = 1.07 gal) of hydraulic fluid is used for compressing to minimum system pressure.

Step 3 Determine hydraulic required increasing pressure from pre-charge to operating pressure:

P1 V1 = P2 V2

1668 psi x 10 gal = 3668 psi x V2

16,680 ÷ 3668 = V2

V2 = 4.55 gal

It means that N2 will be compressed from 10 gal to 4.55 gal in order to reach operating pressure. Therefore, 5.45 gal (10.0 – 4.55 = 5.45 gal) of hydraulic fluid is used for compressing to operating pressure.

Step 4 Determine usable fluid volume per bottle:

Usable volume per bottle = Total hydraulic fluid/bottle – Dead hydraulic fluid/bottle

Usable volume per bottle = 5.45 – 1.07

Usable volume per bottle = 4.38 gallons

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

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Accumulator (Koomey) is a unit used to hydraulically operate Rams BOP, Annular BOP, HCR and some hydraulic equipment. There are several of high pressure cylinders that store gas (in bladders) and hydraulic fluid or water under pressure for hydraulic activated systems. The primary purpose of this unit is to supply hydraulic power to the BOP stack in order to close/open BOP stack for both normal operational and emergency situation. Stored hydraulic in the system can provide hydraulic power to close BOP’s in well control operation, therefore, kick volume will be minimize. Accumulators should have sufficient volume to close/open all preventers and accumulator pressure must be maintained all time.

This post you will learn how to calculate usable volume per bottle by applying Boyle’s gas law:

Use following information as guideline for calculation:

Volume per bottle = 10 gal

Pre-charge pressure = 1000 psi

Operating pressure = 3000 psi

Minimum system pressure = 1200 psi

Pressure gradient of hydraulic fluid = 0.445 psi/ft

For surface application

Step 1 Determine hydraulic fluid required to increase pressure from pre-charge pressure to minimum:

Boyle’s Law for ideal gase: P1 V1 = P2 V2

P1 V1 = P2 V2

1000 psi x 10 gal = 1200 psi x V2

10,000 ÷ 1200 = V2

V2 = 8.3 gal

It means that N2 will be compressed from 10 gal to 8.3 gal in order to reach minimum operating pressure. Therefore, 1.7 gal (10.0 – 8.3 = 1.7 gal) of hydraulic fluid is used for compressing to minimum system pressure.

Step 2 Determine hydraulic required increasing pressure from pre-charge to operating pressure:

P1 V1 = P2 V2

1000 psi x 10 gals = 3000 psi x V2

10,000 ÷3000 = V2

V2= 3.3 gal

It means that N2 will be compressed from 10 gal to 3.3 gal. Therefore, 6.7 gal (10.0 – 3.3 = 6.7 gal) of hydraulic fluid is used for compressing to operating pressure.

Step 3 Determine usable fluid volume per bottle:

Usable volume per bottle = Hydraulic used to compress fluid to operating pressure – hydraulic volume used to compress fluid to minimum pressure

Usable volume per bottle = 6.7 – 1.7

Usable volume per bottle = 5.0 gallons

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

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