Temperature Conversion Formulas

There are several units of temperature used in the drilling industry and you sometimes need to convert one unit into another unit. So you need to know and be able to convert temperature from one unit to another temperature unit. This post demonstrates how to use temperature conversion formulas to convert one temperature unit to another unit.

1 – Convert temperature from °Fahrenheit (F) to °Celsius (C)

°C = ((°F – 32) x 5) ÷ 9

Example: Convert 80 °F to °C:

°C = ((80 – 32) x 5) ÷ 9

°C = 26.7

2 – Convert temperature from ° Celsius (C) to °Fahrenheit

°F = (°C x 9) ÷ 5 + 32

Example: Convert 30 °C to °F:

°F = (30 x 9) ÷ 5 + 32

°F = 86

3 – Convert temperature from ° Celsius (C) to °Kelvin (K)

°K = °C + 273.16

Example: Convert 30 °C to °K:

°K = 30 + 273.16

°K = 303.16

4 – Convert temperature from °Fahrenheit (F) to °Rankine (R)

°R = °F + 459.69

Example: Convert 150 °F to °R:

°R = 150 + 459.69

°R = 609.69

** The 1st and 2nd are the most frequently used in oil field.

Please find the Excel sheet for converting temperature.

Ref books: Lapeyrouse, N.J., 2002. Formulas and calculations for drilling, production and workover, Boston: Gulf Professional publishing.

Bourgoyne, A.J.T., Chenevert , M.E. & Millheim, K.K., 1986. SPE Textbook Series, Volume 2: Applied Drilling Engineering, Society of Petroleum Engineers.

Mitchell, R.F., Miska, S. & Aadny, B.S., 2011. Fundamentals of drilling engineering, Richardson, TX: Society of Petroleum Engineers.

Pressure and Force Relationship and Its Application

Relationship of pressure, force and cross sectional area is one of the most commonly used concepts in oilfield and we will review this concept and its application. Pressure is force divided by cross section area (see an image below).

Pressure = Force ÷ Area

We normally use pressure in many units such as psi (pound per square inch), Pascal, kg/m3, etc.

In drilling operation, we mostly use circular area so area can be calculated by this formula;

Area = ¶ x (radius)2 or ¶ x (diameter)2÷ 4

Where  ¶= 22/7 = 3.143, so we can write a formula above in easy way

Area = 3.143 x (radius)2 or 0.7857 x (diameter)2

Pressure calculation based on the relationship above is shown below;

Pressure = force ÷ (3.143 x (radius)2) or force ÷ (0.7857 x (diameter)2)

Example : For this example, we will use the oilfield unit so force is in lb, diameter is in square inch (in2), and diameter is in inch.

Let’s try to apply pressure and force relationship in drilling operation. We plan to bullhead well and we still have drill string in the hole.

Drill string weight in the air = 45,000 lb
Mud weight in hole = 12.0 ppg
Bit size = 8.5”
Drill pipe size = 5″

What is the maximum pressure at surface you can apply before drilling string will be hydraulically pushed out due to bull heading pressure?

Solution

Buoyancy factor = (65.5 – 12.0) ÷ 65.5 = 0.817

Buoyed weight of drill string = 45,000 x 0.817 = 36,765 lb

Area = 0.7857 x (diameter)2= 0.7857 x (8.5)2= 56.77 square inch

Pressure = 36,765 lb ÷ 56.77 square inch= 647 psi.

In order to perform safe bullheading operation with drill string in hole, you need to apply bullheading pressure less than 647 psi on surface.

Bull Heading

Bull Heading

Ref books: Lapeyrouse, N.J., 2002. Formulas and calculations for drilling, production and workover, Boston: Gulf Professional publishing.

Bourgoyne, A.J.T., Chenevert , M.E. & Millheim, K.K., 1986. SPE Textbook Series, Volume 2: Applied Drilling Engineering, Society of Petroleum Engineers.

Mitchell, R.F., Miska, S. & Aadny, B.S., 2011. Fundamentals of drilling engineering, Richardson, TX: Society of Petroleum Engineers.

Loss of Hydrostatic Pressure due to Lost Return

In case of totally lost return, the annulus must be fully filled with fluid, normally water, as fast as we can. Water filled in annulus causes loss of hydrostatic pressure in the wellbore. This article demonstrates how to determine hydrostatic pressure reduction due to fully filling water into annulus.

Loss of Hydrostatic Pressure due to Lost Return

There are two main concepts, annular capacity and hydrostatic pressure, applied to determine loss of hydrostatic pressure.

Please follow concepts below.

Number of feet of water in annulus

Ft of water added = water added in bbl ÷ annular capacity in bbl/ft

Bottomhole (BHP) pressure reduction

In order to calculate bottom hole pressure reduction, we assume the column of water in annulus is true vertical depth (TVD).

BHP decrease in psi = (current mud weight in ppg – weight of water in ppg) x 0.052 x (ft of water added)

Note: this calculation may not be accurate if the well has high angle so you need to determine the actual TVD from directional survey data.

Equivalent Mud Weight at TD

EMW in ppg = current mud weight in ppg – (BHP decrease in psi ÷ 0.052 ÷ TVD ft of hole)

Example: Determine bottom hole pressure loss and equivalent mud weight at TD due to filling up water into annulus.

Mud weight = 13.0 ppg
Water added = 140 bbl required to fill annulus
Weight of water = 8.6 ppg **
Annular capacity = 0.1422 bbl/ft
Hole TVD = 6,000 ft

** If you fill lighter mud in hole instead of water, please adjust water weight to your mud weight.

Number of feet of water in annulus

Feet of water in annulus = 140 bbl ÷ 0.1422 bbl/ft

Feet = 984.5 ft

Bottomhole (BHP) pressure reduction

BHP reduction = (13.0 ppg – 8.6 ppg) x 0.052 x 984.5 ft

BHP reduction = 225.3 psi

Equivalent mud weight at TD

EMW in ppg = 13.0 – (225.3 psi ÷ (0.052 x 6,000 ft))

EMW = 12.3 ppg

Please find the Excel sheet for calculating how much pressure loss due to lost return

Ref books: Lapeyrouse, N.J., 2002. Formulas and calculations for drilling, production and workover, Boston: Gulf Professional publishing.

Bourgoyne, A.J.T., Chenevert , M.E. & Millheim, K.K., 1986. SPE Textbook Series, Volume 2: Applied Drilling Engineering, Society of Petroleum Engineers.

Mitchell, R.F., Miska, S. & Aadny, B.S., 2011. Fundamentals of drilling engineering, Richardson, TX: Society of Petroleum Engineers.

Depth of Washout Pipe

Washout in drill string can cause big problem later such as parted drill string. When we see stand pipe pressure decrease without changing any parameters as flow rate, mud properties, etc, you may need to consider following items before you decide to pull out of hole for washout.

1. Check surface line: You may need to close stand pipe valves or IBOP and then pressure up to see leaking in the surface. If you see pressure drop, you can fix the surface problem. Anyway you still need to test system again.

2. Check drillstring: You may pump the same flow rate and see how your MWD tool down hole response. If y MWD tool response gets weaker signal so it means that you have washout somewhere above MWD tool. If not, you may have washout below that such as bit, mud motor, etc.

You may consider finding washout depth by using two following formulas listed below:

Method 1: The concept of this method is to pump plugging material to plug the wash out. We will count how many strokes pump till pump pressure increases then we can calculate back where the washout is by applying internal capacity concept and pump output concept.

Depth of washout in ft= (strokes pumped till seeing pressure increase x pump output in bbl/stk) ÷ drill pipe capacity in bbl/ft

Determine washout depth from following information:

Internal drill pipe capacity = 0.00742 bbl/ft

Pump output = 0.0855 bbl/stk

Pressure increase was noticed after 400 strokes.

Depth of washout, ft = 400 stk x 0.0855 bbl/stk ÷ 0.00742 bbl/ft

Depth of washout = 4609 ft

Method 2: The concept of this method is to pump material that can be easily observed from drill pipe pass through wash out into annulus and over the surface. We can calculate the depth of washout bases on the combination volume of internal drill pipe volume and annulus volume.

Note: The materials can be easily observed when it comes across the shakers are as follows: carbide, corn starch, glass beads, bright colored paint, etc.

Depth of washout in ft = (strokes pumped till observed material on surface x pump output in bbl/stk) ÷ (drill pipe capacity in bbl/ft + annular capacity in bbl/ft)

Determine depth of washout from following information:

Internal drill pipe capacity = 0.00742 bbl/ft

Pump output = 0.0855 bbl/stk

Annulus capacity = 0.0455 bbl/ft

The material pumped down the drill pipe was noticed coming over the shaker after 2500 strokes.

Depth of washout, ft = (2500 x 0.0855) ÷ (0.00742+0.0455)

Depth of washout = 4039 ft

If you want to subtract volume from bell nipple to shale shaker, you can subtract the volume out of total volume pumped. Therefore the formula will be

Depth of washout, ft = (strokes pumped till observed material on surface x pump output in bbl/stk – volume (bbl) from bell nipple to shale shaker) ÷ (drill pipe capacity in bbl/ft + annular capacity in bbl/ft)

Example: Internal drill pipe capacity capacity = 0.00742 bbl/ft

Pump output = 0.0855 bbl/stk

Annulus capacity = 0.0455 bbl/ft

The material pumped down the drill pipe was noticed coming over the shaker after 2500 strokes.

Volume from bell nipple to shale shaker = 10 bbl

Depth of washout in ft = (2500 x 0.0855 – 10) ÷ (0.00742+0.0455)

Depth of washout = 3850 ft

ANYWAY PLEASE REMEMBER. If you know that your wash out is down hole, practically, we need to pull out of hole ASAP after we determine washout situation. The more you pump, more washout will be occurred.

Please find the excel sheet for calculating depth of washout

Ref books: Lapeyrouse, N.J., 2002. Formulas and calculations for drilling, production and workover, Boston: Gulf Professional publishing.

Bourgoyne, A.J.T., Chenevert , M.E. & Millheim, K.K., 1986. SPE Textbook Series, Volume 2: Applied Drilling Engineering, Society of Petroleum Engineers.

Mitchell, R.F., Miska, S. & Aadny, B.S., 2011. Fundamentals of drilling engineering, Richardson, TX: Society of Petroleum Engineer

Critical RPM to Avoid Excessive Vibration

When you operate top drive, you may need to know critical RPM that you can go. If you rotate pipe more than the critical RPM, it will create a lot of vibration that can cause failure in your drilling equipment such as drill pipe, TDS, etc.

In order to find out how much critical RPM, you may need high-tech simulation but sometimes you don’t really have that information supplied from town. So you really need to be able to roughly estimate how much critical RPM is ( at least you get a idea for this limitation). This formula below shows you how to estimate the critical RPM and it has accuracy of 15% roughly.

Critical RPM = 33,055 x (OD2 + ID2) 1/2 ÷ (L)2

Where;
OD = drill pipe outside diameter in inch
ID = drill pipe inside diameter in inch
L = length of one joint of drill pipe in feet

Example: Determine critical RPM from these following information

L = length of one joint of drill pipe = 32 ft
OD = drill pipe outside diameter = 4.0 in.
ID = drill pipe inside diameter = 3.5 in.

Critical RPM = 33,055 x (42+ 3.52)1/2 ÷ (32)2

Critical RPM = 172 RPM

Please remember this is ONLY estimation of the critical RPM. If you have your service companies or you have specific programs to determine it, please use the value from those programs because it should consider many parameters than this simple formula. USE IT IN CASE OF YOU HAVE NOTHING AVAILABLE TO CALCULATE THE CRITICAL RPM.

Ref books: Lapeyrouse, N.J., 2002. Formulas and calculations for drilling, production and workover, Boston: Gulf Professional publishing.

Bourgoyne, A.J.T., Chenevert , M.E. & Millheim, K.K., 1986. SPE Textbook Series, Volume 2: Applied Drilling Engineering, Society of Petroleum Engineers.

Mitchell, R.F., Miska, S. & Aadny, B.S., 2011. Fundamentals of drilling engineering, Richardson, TX: Society of Petroleum Engineers.