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 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
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.
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