Ratio-Metric Blender Auger Equations

David AakreTechnologist

Need to Measure Augers to Find Pitch Volume. Use a Tape Measure.

• Auger Flight: The flat part that coils around the shaft of the auger.

• Auger Pitch: The distance between two flights of the auger.

• Auger Shaft: The shaft in middle of auger.

• Pitch Volume: The volume of the space between two flights of the auger.

Pitch Volume Formula3.14 x (Auger Flight Radius)² x Auger Pitch = Pitch volumeTo make Cubic Foot / rev Divide answer by 1728 inches cubed

Example Calculating Pitch Volume 12 inch Screw 3.14x(4.15)² x 12 = 648.94 inches cubed/ rev648.94/1728 = .3755 feet cubed / rev Software formula rounded it to .380 feet cubed / rev

Pounds Per Revolution

• Pounds Per Revolution: The amount of sand used in one revolution

• Pounds Per Revolution Formula:• Lbs./ Rev =Pitch Volume x Sand Bulk Density

• Each Sand type has a different Bulk Density

Example Calculating LB s / Rev Ottawa Sand20/40 Lbs. /rev = .380 feet cubed x 100 lb./feet cubed = 38lb / rev

Software calculated it in Above picture for 12 inch Screw. ( 38 lb/rev)

Encoder on Top End of Screw. Pulses Per Minute is listed On Encoder

Pulses Per Pound

• Pulses Per Pound can be looked at how many times the screw turns in one minute.

• Encoder Pulses / lbs. per revolution• Example 600Pulses / 38 lbs. = 15.789• So 15.789 Pul/ lb. can be 15.789 rotations per

minute or Screw Speed.

Auger Information on a Different Software. Frac Formulas Work!!!

Blender Auger Equations• Auger flight- flat part that coils around the shaft on Auger• Auger Pitch- The distance between two flights on Auger• Auger Shaft- The shaft in middle of an Auger• Pitch Volume = 3.14 x (Auger flight Radius) ² x Auger Pitch• To make Cubic Foot / rev Divide answer by 1728 inches cubed• • Pounds per Revolution= Pitch Volume x Sand Bulk Density (lbs. /Ft³)• Revolutions per Minute = (Encoder) lbs. / min / Pound per revolution • Encoder Pulses per minute listed on sensor which sits on top of Augers

or Screws (measures screw speed).• Stewart & Stevenson Encoder 525 PPM• Halliburton Encoder 600 PPM

Frac Formulas

• Max rate = ID ²x 2.3314

• Line Volume = .0009714 x ID² X Depth

• Fluid Gradient: Pressure exerted per unit depth of a fluid

• Fluid Density (lbs. /Gal) x .05195 = Fluid Gradient

• Hydrostatic Pressure= True vertical Depth (TVD) x Fluid Gradient

• Bottom Hole pressure (BHP) = Hydrostatic + Well Head Pressure ( Use instant shut in pressure if pumping complete)

• Frac Gradient= PSI per foot of depth, = BHP/True vertical Depth (Mid perf depth on a vertical Well)• Horsepower = (well head pressure x rate)/ 40.8

• Pipe Time = Line volume / Rate

Blender Equations

• Weight of clean water = 8.33334 lbs. per gallon

• Oil field Barrel = 42 Gallons

• Gallons to Barrels = Gallons / 42

• Barrels to Gallons = Barrels x 42

• Set Points Based off Mega Gallon principle (1000 Gal) 42 gal/ 1000 gal = .042• Clean Rate is the Suction Rate on Blender – Mag Meter or Turbine Flow Meter

• Gallons per Minute = Clean Rate x .042 x Concentration (Set Point)• Gel Loading = Gel Weight lbs. / 4 40lbs/4= 10 GPT• Base Fluid Density =Weight lbs. / volume Gal (use Hydrometer)

Blender Equations Cont.• Absolute Volume = 1 / (Specific gravity x .0022046226 x 3785.412) = how

much of a gallon 1 lb. occupies.

• Specific Gravity= Grams per cc Take @ 60 F for every 5 degrees difference +/- .001

• Bulk Density = (Specific Gravity (g/cc)-1) x 62.42796• Clean Volume = Base Fluid Volume Gallons (clean water)• Sand Volume (gals) = Total Sand x Absolute Volume Factor• Slurry Volume = Clean Volume + Sand Volume = Slurry Gallons• Total Sand = Clean Volume (gal) x Sand Concentration (Lbs. /gal)• Slurry Density = Base Fluid Density + Prop Concentration / volume factor• Volume Factor = 1 + (Prop concentration x Absolute volume factor)

Absolute volume Factor Calculation

1/(2.654) x .0022046226 x 3785.412 =.0452 gal/lb

Calculating Density

The Density Meters Prove Your Math is Correct On Blender : )

David AakreTechnologist