Drilling Formulas and Drilling Calculations

Drilling fluid properties are essential information that everybody should understand.

Density: Mud density is the weight per unit volume of mud and normally it is reported in Pound Per Gallon (PPG). Mud density is used for providing hydrostatic pressure to control well for drilling operation.

Viscosity: It is defined as the internal resistance of fluid flow. There are 2 types of viscosity which are Funnel Viscosity and Plastic Viscosity.

1) Funnel Viscosity: It is time, in seconds for one quart of mud to flow through a Marsh funnel which has a capacity of 946 cm3 (See Figure 1). A quart of water exits the funnel in 26 seconds. This is not a true viscosity, but serves as a qualitative measure of how thick the mud sample is. The funnel viscosity is useful only for relative comparisons.

Figure 1 Marsh Funnel

2) Plastic Viscosity (PV): A parameter of the Bingham plastic rheological model (See Figure 3). PV is the slope of the shear stress-shear rate plot above the yield point (See Figure 4). Viscometer is equipment to measure Plastic Viscosity (See Figure 2). Plastic Viscosity is derived from the 600 rpm reading minus the 300 rpm reading and PV is in centipoises (cp). A low PV indicates that the mud is capable of drilling rapidly because of the low viscosity of mud exiting at the bit. High PV is caused by a viscous base fluid and by excess colloidal solids. To lower PV, a reduction in solids content can be achieved by dilution.

There are many rheology models shown in Figure 3. Normally Bingham Plastic Model is used to describe mud properties as Plastic Viscosity and Yield Point (See Figure 4).

Figure 2 Viscometer

Figure 3 Rheology Model

Figure 4 Bingham Plastic Model describes PY and VP

Yield Point: Physical meaning is the resistance to initial flow, or the stress required starting fluid movement. The Bingham plastic fluid plots as a straight line on a shear-rate (x-axis) versus shear stress (y-axis) plot, in which YP is the zero-shear-rate intercept (PV is the slope of the line). YP is calculated from 300-rpm and 600-rpm viscometer dial readings by subtracting PV from the 300-rpm dial reading and it is reported as lbf/100 ft2. YP is used to evaluate the ability of mud to lift cuttings out of the annulus. A higher YP implies that drilling fluid has ability to carry cuttings better than a fluid of similar density but lower YP.

Gel Strength: It is the ability of fluid to suspend fluid while mud is in static condition. Before testing gel strength, mud must be agitated for awhile in order to prevent precipitation and then let mud is in static condition for a certain limited time (10 seconds, 10 minutes or maybe 30 minutes) and then open the viscometer at 3 rpm and read the maximum reading value. In a morning report, there are 3 values of gel strength, which are Gel 10sec (lbf/100 ft2), Gel 10 mins (lbf/100 ft2) and Gel 30 mins (lbf/100 ft2).

Ph: This value tells the acid of drilling fluid. Ph paper is used to measure Ph.

Electrical Stability (ES): This value reflects to the stability of emulsion of SDF. If water disperses well in oil phase (good emulsion), the resistivity of drilling fluid will be higher. In contrast, if water disperses badly in oil phase (bad emulsion), the resistivity of drilling fluid will be lower. As the concept above, applied Ohm’s law (V=IR), electricity from the electrical stability meter is emitted in to mud and voltage is measured by the electrical probe. Normally if the measured voltage is higher than 500 volt, the electrical stability is good.

Figure 5 Electrical Stability Meter

CaCl2 Concentration: Cl+ can prevent formation swell hence this value must be maintained. It is measured by a titration test by using silver nitrate as titrant with potassium chromate as the endpoint indicator and when titration reaches the equilibrium point mud will change into red.

Retort Test: There are 2 values that are Saraline Water Ratio (SWR) and Solid Content (LGS, Barite) obtained from this testing. Mud is retorted in retort test skid at 950 F for 2 hrs. High temperature can vaporize liquid phase into gas phase and then gas phase will be transferred to a condenser and condense in liquid form. Liquid is stored in a tube that has a level indicator to see how much of water and oil (saraline) extracted. Moreover, solid left in the retort reflects the solid content in mud.

Figure 6 Retort Test Skid

HTHP Fluid Loss: This test is conducted for testing fluid loss behavior of mud. Mud is pressed through filter paper located in the HTHP filter press at 300 F with differential pressure at 500 psi for 30 mins. Thickness of filter cake stuck in filter paper should be less than 2 ml.

Figure 7 HTHP filter press

Ref: Drilling Fluids Books

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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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You may not know that drilling fluid or mud has several important functions helping us achieve goal to drill well. I would like to share about the functions of drilling fluid as follows;

1. Transport cutting and dispose to surface - The drilling fluid brings the drilled material to the ground surface either by mud rheology and velocity.

2. Clean drill bits – As drilling fluid exits the bit jets, fluid velocity removes cutting from the bit teeth and bit body. This prevents bit ball up situation.

3. Provide hydrostatic pressure to control well while drilling – Hydrostatic pressure provided from drilling fluid is the primary well control. Mud weight should be high enough to control formation pressure while drilling.

4. Prevent excessive mud loss - While drilling, clay particle will form a thin layer over porous zones called “mud cake” or “filter cake”. Mud cake acts as barrier to prevent excessive drilling fluid loss into formation and provides wellbore stability.

5. Prevent formation damage by using reservoir drill-in fluid – While drilling long reach zone in horizontal wells, the special drilling fluid will be utilized in order to prevent formation damage.

6. Provide hydraulic pressure to downhole assembly (BHA) as mud motor, measuring while drilling (MWD), logging while drilling (LWD), etc – Without enough hydraulic power, downhole tool will not be properly operated, hence, drilling fluid plays essential role to provide power to sophisticated downhole tool.

7. Facilitate downhole measurement as open hole logging, MWD, LWD, mud logging, etc – Mud will assist tool to measure everything downhole.

8. Lubricate drill string and BHA and cool the bit. The drill bit and BHA become hot due to friction during the drilling process. When the drilling fluid passes through the bit and exits the jets/nozzles, some extra heat is removed via mud.

Ref: Drilling Fluids 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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