Pump Output Calculation for Duplex Pump and Triplex Pump

Rig pump output, normally in volume per stroke, of mud pumps on the rig is  one of important figures that we really need to know because we will use pump out put figures to calculate many parameters such as bottom up strokes,  wash out depth, tracking drilling fluid, etc. In this post, you will learn how to calculate pump out put for triplex pump and duplex pump in both Oilfield and Metric Unit. 

Triplex Mud Pump

Triplex Pump Output Formula

Oilfield Unit

Triplex Pump Output  = 0.000243 × (Liner Diameter ) 2 × (Stroke Length)

Where,

Triplex pump output in bbl/stk

Liner Diameter in inch

Stroke Length in inch

Example:

Determine the pump output in bbl/stk at 100% and 97% efficiency
Liner size = 6 inch
Stroke length = 12 inch

Triplex pump output @ 100% efficiency
Triplex pump output @ 100% = 0.000243 × 62 × 12
Triplex pump output @ 100% = 0.104976 bbl/stk

Triplex pump output @ 97% efficiency
Adjust the triplex pump output for 97% efficiency:
Triplex pump output @ 97% = 0.104976 × 0.97 bbl/stk
Triplex pump output @ 97% = 0.101827 bbl/stk

Metric Unit

Triplex Pump Output  = 2.3576 × 10-9× (Liner Diameter ) 2 × (Stroke Length)

Where,

Triplex pump output in m3/stk

Liner Diameter in mm

Stroke Length in mm

Example:

Determine the pump output in bbl/stk at 100% and 97% efficiency
Liner size = 152.4 mm
Stroke length = 304.8 mm

Triplex pump output @ 100 % efficiency

Triplex pump output @ 100% = 2.3576 × 10-9 × 152.42 × 304.8
Triplex pump output @ 100% = 0.016690 m3/stk

Triplex pump output @ 97% efficiency
Adjust the triplex pump output for 97% efficiency:
Triplex pump output @ 97% = 0.016690 × 0.97 m3/stk
Triplex pump output @ 97% = 0.016189 m3/stk

Duplex Mud Pump (Ref: http://www.sunmachinery.com/8214R_01.jpg)

Duplex Pump Output Formula

Oilfield Unit

Duplex Pump Output = 0.000162 × S × [2(D)2 – d2]

Where:

Duplex pump output in bbl/stk
D = liner diameter in inch
S = stroke length in inch
d = rod diameter in inch

Example:

Determine the duplex pump output in bbl/stk at 100% and 85% efficiency

Liner diameter = 6 inch
Stroke length = 12 inch
Rod diameter = 2.0 in.

Duplex pump output @ 100 % efficiency

Duplex pump output @ 100% = 0.000162 × 12 × [2 (6) 2 -22 ]
Duplex pump output @ 100% = 0.13219 bbl/stk

Duplex pump output @ 85% efficiency

Adjust pump output for 85% efficiency:
Duplex pump output @ 85% = 0.132192 × 0.85 bbl/stk
Duplex pump output @ 85% = 0.11236 bbl/stk

Metric Unit

Duplex Pump Output =1.57172 × 10-9 × S × [2(D)2 – d2]

Where:

Duplex pump output in m3/stk
D = liner diameter in mm
S = stroke length in mm
d = rod diameter in mm

Example: Determine the duplex pump output in m3/stk at 100% and 85% efficiency

Liner diameter = 152.4 mm
Stroke length = 304.8 mm
Rod diameter = 50.8 mm

Duplex pump output @ 100 % efficiency
Duplex pump output@ 100% = 1.57172 × 10-9 × 304.8 × [2 (152.4) 2 -50.82 ]
Duplex pump output@ 100% = 0.02102 m3/stk

Duplex pump output @ 85% efficiency

Duplex pump output@ 85% = 0.02102 × 0.85 m3/stk
Duplex pump output @ 85% = 0.01786 bbl/stk

Please find the Excel sheet to calculate triplex pump output and duplex pump output

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.

Formation Integrity Test (FIT) Procedure and Calculation

Formation Integrity Test is a method to test strength of formation and shoe by increasing Bottom Hole Pressure (BHP) to designed pressure. FIT is normally conducted to ensure that formation below a casing shoe will not be broken while drilling the next section with higher BHP or circulating gas influx in a well control situation. Normally, drilling engineers will design how much formation integrity test pressure required for each hole section.

The formula below demonstrates you how to calculate required FIT pressure.

Oilfield Unit

Pressure required for FIT = (Required FIT – Current Mud Weight) × 0.052 × True Vertical Depth of shoe

Where

Pressure required for FIT in psi

Required FIT in ppg

Current Mud Weight in ppg

True Vertical Depth of shoe in ft

Note: FIT pressure must be rounded down.

Example:
Required FIT (ppg) = 14.5
Current mud weight (ppg) = 9.2
Shoe depth TVD (ft) = 4000 TVD
Pressure required for FIT = (14.5-9.2) × 0.052 × 4000 = 1,102 psi

Metric Unit

Pressure required for FIT = (Required FIT – Current Mud Weight) × 0.00981 × True Vertical Depth of shoe

Where

Pressure required for FIT in KPa

Required FIT in Kg/m3

Current Mud Weight in Kg/m3

True Vertical Depth of shoe in m

Note: FIT pressure must be rounded down.

Example:
Required FIT (Kg/m3) = 1740
Current mud weight (Kg/m3) = 1100
Shoe depth TVD (m) = 1300 m
Pressure required for FIT = (1740-1300) × 0.00981 × 1300 = 8,161 KPa

Formation Integrity Test (FIT) guideline is listed below: (note: this is just only guide line. You may need to follow your standard procedure in order to perform formation integrity test):

1. Drill out new formation few feet, circulate bottom up and collect sample to confirm that new formation is drilled to and then pull string into the casing.

2. Close annular preventer or pipe rams, line up a pump, normally a cement pump, and circulate through an open choke line to ensure that surface line is fully filled with drilling fluid.

3.Stop the pump and close a choke valve.

4. Gradually pump small amount of drilling fluid into well with constant pump stroke. Record total pump strokes, drill pipe pressure and casing pressure. Pump until casing pressure reaches the pressure required for formatin integrity test. Hold pressure for few minutes to confirm pressure.

5. Bleed off pressure and open up the well. Then proceed drilling operation.

Please find the Excel sheet – calculate pressure required for formation integrity test.

 

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.

Leak Off Test (Procedures and Calculation)

Leak Off Test is conducted in order to find the fracture gradient of certain formation at casing shoe depth. The results of the leak off test also dictate the maximum equivalent mud weight that should be applied to the well during drilling operations.

Oilfield Unit

Leak Off  Test pressure in mud density

Leak off test in equivalent mud weight = (Leak Off Test pressure ÷ 0.052 ÷ Casing Shoe TVD ) + (Current Mud Weight)

Where;

Leak off test in equivalent mud weight in ppg

Leak Off Test pressure in psi

Casing Shoe TVD in ft

Current Mud Weight in ppg

Note: Always round down for LOT calculation

Example:

Leak off test pressure = 1,600 psi
Casing shoe TVD = 4,000 ft
Mud weight = 9.2 ppg
Leak off test in equivalent mud weight (ppg) = (1,600 psi ÷ 0.052 ÷ 4,000 ft )+ 9.2ppg  = 16.8 ppg

Metric Unit

Leak Off  Test pressure in mud density

Leak off test in equivalent mud weight  = (Leak Off Test pressure ÷ 0.00981 ÷ Casing Shoe TVD ) + (Current Mud Weight)

Where;

Leak off test in equivalent mud weight in kg/m3

Leak Off Test pressure in KPa

Casing Shoe TVD in m

Current Mud Weight in kg/m3

Note: Always round down for LOT calculation

Example:

Leak off test pressure = 1,740 KPa
Casing shoe TVD = 1,300 m
Mud weight = 1,100 Kg/m3
Leak off test in equivalent mud weight (Kg/m3) = (1,740 KPa ÷ 0.00981 ÷ 1,300 m)+ 1,100 Kg/m3 = 1,236 Kg/m3

Leak Off Test (LOT) guide line procedures are as follows  (note: this is just only guide line).

You may need to follow your standard procedure in order to perform leak off test):

1.Drill out new formation few feet, circulate bottom up and collect sample to confirm that new formation is drilled to and then pull string into the casing.

2.Close annular preventer or pipe rams, line up a pump, normally a cement pump, and circulate through an open choke line to ensure that surface line is fully filled with drilling fluid.

3.Stop the pump and close a choke valve.

4.Gradually pump small amount of drilling fluid into well with constant pump stroke. Record total pump strokes, drill pipe pressure and casing pressure. Drill pipe pressure and casing pressure will be increased continually while pumping mud in hole. When plot a graph between strokes pumped and pressure, if formation is not broken, a graph will demonstrate straight line relationship. When pressure exceeds formation strength, formation will be broken and let drilling fluid permeate into formation, therefore a trend of drill pipe/casing  pressure will deviate from straight line that mean formation is broken and is injected by drilling fluid. We may call pressure when deviated from straight line as leak off test pressure.

5.Bleed off pressure and open up the well. Then proceed drilling operation.

Note:  the way people call leak off test pressure depends on each company standard practices.

Please find the Excel sheet to calculate leak off test

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.

Convert specific gravity to mud weight (ppg and lb/ft3) and pressure gradient (psi/ft)

Referring to the previous article, Calculate Specific Gravity (SG) in oilfield unit , you get specific gravity (SG) from mud weight (ppg and lb/ft3) and pressure gradient (psi/ft) but you may need to reverse calculation from specific gravity (SG) to mud weight or pressure gradient (psi/ft). In this article, you will learn how to how to convert specific gravity to mud weight  and pressure gradient in both oilfield and metric unit by using simple formulas as follows:

Convert Specific Gravity to Mud Weight In Oilfield Unit

1. Convert specific gravity to mud weight in pounds per gallon (ppg)

Mud weight in ppg = specific gravity (SG) × 8.33



Example: specific gravity = 1.50
mud wt, ppg = 1.50 × 8.33
mud wt = 12.5 ppg

2. Convert specific gravity to mud weight in lb/ft3

Mud weight in lb/ft3 = specific gravity × 62.4


Example: specific gravity = 1.50
Mud weight in lb/ft3 = 1.50 × 62.4 lb/ft3
Mud weight in lb/ft3 = 93.6 lb/ft3

3. Convert specific gravity to pressure gradient in psi/ft

Pressure gradient in psi/ft = specific gravity (SG) × 0.433

Example: specific gravity = 1.5
Pressure gradient in psi/ft  = 1.5 × 0.433
Pressure gradient in psi/ft = 0.650 psi/ft

Convert Specific Gravity to Mud Weight In Metric Unit

4. Convert specific gravity to mud weight in kg/m3

Mud weight in kg/m3 = specific gravity × 1000

Example: specific gravity = 1.5

Mud weight in kg/m3 = 1.5 × 1,000

Mud weight in kg/m3 = 1,500

5. Convert specific gravity to mud weight in g/cc

Mud weight in g/cc = specific gravity × 1.0

Example: specific gravity = 1.5

Mud weight in  g/cc = 1.5 × 1.0

Mud weight in g/cc  = 1.5

6. Convert specific gravity to pressure gradient in kPa/m

Pressure gradient in kPa/m = specific gravity (SG) × 9.81

Example: specific gravity = 1.5
Pressure gradient in kPa/m  = 1.5 × 9.81
Pressure gradient in kPa/m = 14.7

Please also find the Excel sheet  for  this topic.

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.

Calculate Specific Gravity (SG) in oilfield unit

This article demonstrates how to calculate Specific Gravity (SG) from different density or pressure gradient  in both oilfield and metric unit.

Calculate Specific Gravity from Mud Weight In Oilfield Unit

1. Calculate specific gravity using mud weight in PPG

Specific Gravity (SG) = mud weight in ppg ÷ 8.33

Example: 
Mud weight = 13.0 ppg
Specific Gravity (SG) = 13.0 ppg ÷ 8.33
Specific Gravity (SG)= 1.56

2. Calculate specific gravity using pressure gradient in psi/ft

 Specific Gravity (SG) = pressure gradient in psi/ft ÷ 0.433

Example:

Pressure gradient = 0.50 psi/ft
Specific Gravity (SG) = 0.50 psi/ft ÷ 0.433
Specific Gravity (SG) = 1.15

3. Calculate specific gravity using mud weight in lb/ft3

Specific Gravity (SG) = mud weight in lb/ft3 ÷ 62.4

Example:

Mud weight = 90 lb/ft3
Specific Gravity (SG)= 90 lb/ft3÷ 62.4
Specific Gravity (SG) = 1.44

Calculate Specific Gravity from Mud Weight In Metric Unit

4. Calculate specific gravity using mud weight in kg/m3

 Specific Gravity (SG) = mud weight in kg/m3÷ 1000

Example: 
Mud density = 1200 kg/m3
Specific Gravity (SG) = 1200 kg/m3÷ 1000
Specific Gravity (SG)= 1.2

5. Calculate specific gravity using mud weight in g/cc

 Specific Gravity (SG) = mud weight in g/cc÷ 1.0

Example: 
Mud density = 1.2 g/cc
Specific Gravity (SG) = 1.2 g/cc÷ 1000
Specific Gravity (SG)= 1.2

6. Calculate specific gravity using pressure gradient in kPa/m

 Specific Gravity (SG) = pressure gradient in kPa/m ÷ 9.81

Example: 
Pressure gradient = 10 kPa/m
Specific Gravity (SG) = 10 kPa/m÷ 9.81
Specific Gravity (SG)= 1.02

Please also find the Excel sheet  for  this topic – Specific Gravity Calculation Sheet

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.