How To Use Simple Math To Find Frac Pump Rate Barrels/ Minute.

Example is from a Weir 4inch QWS 2500 Pump

Pump Plunger Geometry

• Plunger Radius X Plunger Radius X 3.142) = Sq. Inches of Circle (Sq. Inches of Circle) X (Stroke Length) X (Number of Plungers) = Cubic Inches of Liquid Per Revolution Cubic Inches of Liquid Per Revolution / 231 = Gallons Per Revolution

Weir 4 Inch Pump Calculations

• With a tape measure or from tag on pump find pump plunger diameter in this case it is 4 inches. Plunger radius would be 4/2 = 2 inches

• Measure with tape plunger stroke length which is 8 inches.

• Count the number of plungers in this example a Weir 4 inch Quin has 5 plungers.

Use Math Equations To Find Gallons Per Revolution

• 2 x 2 x 3.14 = 12.56 Sq inches of Circle

• 12.56 x 8 x 5 = 502.4 Cubic Inches of Fluid per revolution.

• 502.4 / 231 = 2.17 gallons per revolution

• Convert to Barrels per revolution

• 2.17 / 42 barrels = .0517 barrels per rev.

Allison 9885 Transmission Speed Sensor Ratio 6.353: 1

• The transmission drive shaft will turn 6. 353 for one revolution of pump.

• How many Barrels will we pump in one revolution of Transmission drive shaft.

• Divide .0518 / 6.353 = .008155 Barrels/ rev.

• Note 6.353: 1 can also be called pump ratio.

• In most cases you will use this ratio 6.353:1

How To Calculate Pump Rate for Each Allison 9885 Transmission Gear

• Need to know Max speed of Engine used on Pump truck.

• On MTU, CAT, and Cummins Industry Motors for frac pumps the max engine speed is 1950 rpms.

• Next you need to know gear ratio’s for the transmission you are using.

Allison Gear Ratios

Allison 9885 Gear Ratio’s

Gear 1 = 3.75 : 1

Gear 2 = 2.69 : 1

Gear 3 = 2.20 : 1

Gear 4 = 1.77 : 1

Gear 5 = 1.58 : 1

Gear 6 = 1.27 : 1

Gear 7 = 1.00 : 1

Calculate Max Pump Rate for Seventh Gear Using Max Engine Speed.

• Max engine speed 1950 rpm’s

• 4 inch Weir Barrels per revolution for this transmission calculated earlier was .00815

• Seventh Gear Rate = Max Engine speed x .00815

• 1950 x .00815 = 15.90 barrels per minute

• The max rate for this pump with this transmission and Engine is 15.9 Barrels / min

How to Calculate Pump Rate for All Gears

• Max pump rate is 15.9 barrels / min at 1950 max engine speed in seventh gear.

• Use transmission gear ratios to find rate for gears 6 through one.

• Divide 15.9 barrels per min. / 1.27 six gear ratio = 12.52 barrels per minute.

• 5 th gear barrels per minute would be 15. 9 barrels per minute divided by 1.58 = 10.06

Build a Pump Rate Chart for Engine Speeds up to 1950 for Each Gear

Summary

• Now you know how to use simple math equations to calculate Rate for Pumps.

• The Pump truck control software such as AccuFrac , NOV Rolligon, or Halliburton ACE use these exact math equations to find pump rate.

• I have attached with Power Point a 4 inch Weir Quin pump chart with pump information.

Ace Grizzly 4 inch pump with five plungers Example.

Weir Pump Information

Nitrogen Pump Formula

• Cold end size squared x stroke x .7854

• Divided by 231 = gallons per stroke x3 ( # plungers) = gallons per revolution

• x 93.11 = scf per revolution we normally multiply any results by .90 for efficiency factor

• your pump should be .0271 x 3 = .08155 gpr or 6.833 scf/rev @ 90% efficient

David Aakre

Technologist