Pump Output Calculation for Duplex Pump and Triplex Pump

Rig pump output, normally in bbl per stroke, of mud pumps on the rig is important figures that we really need to know because we will use pump out put figures to calculates many things 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.

Triplex Pump Output Formula

Triplex Pump Output in bbl/stk = 0.000243 x (liner diameter in inch) 2 X (stroke length in inch)

Example: Determine the pump output in bbl/stk at 100% and 97% efficiency
Linner size = 6 inch
Stroke length = 12 inch
Triplex pump output:
PO @ 100% = 0.000243 x 62 x 12
PO @ 100% = 0.104976 bbl/stk

Adjust the triplex pump output for 97% efficiency:
Decimal equivalent = 97 ÷ 100 = 0.97
PO @ 97% = 0.104976 bbl/stk x 0.97
PO @ 97% = 0.101827 bbl/stk

Duplex Pump Output Formula

Duplex Pump Output in bbl/stk = 0.000162 x S x [2(D)2 – d2]

Where:
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 efficiency = 100 %.
PO @ 100% = 0.000162 x 12 x [2 (6) 2 -22 ]
PO @ 100% = 0.13219 bbl/stk

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

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

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

Formation Integrity Test (FIT) Procedure and Calcualtion

Formation Integrity Test is the 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 in town will design how much formation integrity test pressure required mostly in ppg.

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

Pressure required for FIT (psi) = (Required FIT in ppg – Current Mud Weight in ppg) x 0.052 x True Vertical Depth of shoe in ft

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) x 0.052 x 4000 = 1102 psi

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 to calculate pressure required for formation integrity test.

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

Leak Off Test (Procedures and Calcuation)

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

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 increase 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.

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

Leak off test pressure can be calculated into equivalent mud weight in ppg as formula below:

Leak off test in equivalent mud weight (ppg) = (Leak off test pressure in psi) ÷ 0.052 ÷ (Casing Shoe TVD in ft) + (current mud weight in ppg)

Pressure gradient in psi/ft = (Leak off test pressure in psi) ÷ (Casing Shoe TVD in ft)

Example:

Leak off test pressure = 1600 psi
Casing shoe TVD = 4000 ft
Mud weight = 9.2 ppg

Leak off test in equivalent mud weight (ppg) = 1600 psi ÷ 0.052 ÷ 4000 ft + 9.2ppg ppg = 16.9

Pressure gradient = 1600 ÷ 4000 = 0.4 psi/ft

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

Please find the Excel sheet tocalculate leak off test

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

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

Referring to the previous post, 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). So you will learn how to how to convert specific gravity to mud weight (ppg and lb/ft3) and pressure gradient (psi/ft) by using simple formulas as follows:

1. Convert specific gravity to mud weight in pounds per gallon (ppg)
Convert specific gravity fomula: mud weight in ppg = specific gravity (SG) x 8.33
Example: specific gravity = 1.50
mud wt, ppg = 1.50 x 8.33
mud wt = 12.5 ppg

2. Convert specific gravity to mud weight in lb/ft3
Convert specific gravity fomula: Mud weight in lb/ft3 = specific gravity x 62.4
Example: specific gravity = 1.50
Mud weight in lb/ft3 = 1.50 x 62.4 lb/ft3
Mud weight in lb/ft3 = 93.6 lb/ft3

3. Convert specific gravity to pressure gradient in psi/ft
Convert specific gravity fomula: Pressure gradient in psi/ft = specific gravity (SG) x 0.433
Example: specific gravity = 1.5
Pressure gradient in psi/ft  = 1.5 x 0.433
Pressure gradient in psi/ft = 0.650 psi/ft

Please also find the Excel sheet regarding how to convert specific gravity (SG)

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

Calculate Specific Gravity (SG) in oilfield unit

You may need to calculate specific gravity from different density or pressure gradient units. This post demonstrates you about specific gravity calculation and specific gravity formulas frequently used in oilfield business.

1. Calculate specific gravity using mud weight in PPG

Specific gravity formula : SG = mud weight in ppg ÷ 8.33

Example:  Fluid = 13.0 ppg
SG = 13.0 ppg ÷ 8.33
SG = 1.56

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

Specific gravity formula : SG = pressure gradient in psi/ft ÷ 0.433

Example: pressure gradient = 0.50 psi/ft
SG = 0.50 psi/ft ÷ 0.433
SG = 1.15

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

Specific gravity formula : SG = mud weight in lb/ft3 ÷ 62.4

Example: Mud weight = 90 lb/ft3
SG = 90 lb/ft3÷ 62.4
SG = 1.44

Please also find the Excel Sheet: Specific Gravity Calculation Sheet

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