FRAC FORMULAS DAVID AAKRE TECHNOLOGIST

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)

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)

Blender Screw Geometry (Blender Screw Speed is Important!)

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

PUMP MATH:

Fluid End Geometry: Measure plunger Length. Diameter, count number of plungers

PUMP TAG could have all information you need. Radius= ½ diameter

Plunger Radius x Plunger Radius x 3.14= SQ inches of Circle

SQ inches of Circle x Stroke length x Number of Plungers= Cubic Inches of Liquid per revolution.

(Triplex pump has 3 plungers and Quinn has 5 plungers )

Cubic Inches of Rev / 231 = Gallons per revolution

Gallons Per rev / 42 = Barrels per revolution

Allison 9885 Transmission speed sensor Ratio 6.353:1

Barrels per Rev / 6.353 = Barrels per Rev of Transmission

Max Engine Rpms 1950 for most Frac Pumps

Max Pump Rate in 7th gear is =1950 rpms Max Engine speed x Barrels per Rev Transmission

Allison 9885 Gear Ratios: 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 1:1

6th gear Rate = Max Rate 7th Gear /1.27= Barrels per minute at Engine Speed 1950 in 6th gear

5th gear rate = Max Rate 7th gear/ 1.58 =

4th gear rate = Max Rate 7th gear/ 1.77=

3rd gear rate = Max Rate 7th gear / 2.20=

2nd gear rate = Max Rate 7th gear / 2.69 =

1st gear rate = Max Rate 7th gear / 3.75 =

Make a pump chart from engine speed 1200 rpm to 1950 rpm for all gears

1200 rpm x Barrels per rev transmission = 7th gear rate at 1200 rpms

You do the rest of chart : )

Never match your Mag meter rate to Truck Rate because your truck rate is based off mathematical equations at 100 percent efficiency. (Is your valves and packing perfect?

Blender Action Density Reaction

Screw Efficiency Increased Density Decrease

Screw Efficiency Decreased Density Increase

Bulk Density Increase Density Decrease

Bulk Density Decrease Density Increase

Fluid SG Increased Density Decrease

Fluid SG Decreased Density Increased

Sand SG Increased Density Decreased

Sand SG decreased Density Increased

Bucket Test: Simulate Rate 23.81 Set Point 1 or 2

GPM= set point x clean rate x .042= 1 x 23.81 x.042 =1 gpm (will get 1 gallon in 1 minute)

Halliburton uses Absolute volume to control density and screw speed to correct sand use.

Absolute Volume = 1 / (Specific gravity (sand) x .0022046226 x 3785.412) = how much of a gallon 1 lb. occupies.

Nitrogen Pump:Cold end size squared x stroke x .7854                              Divided by 231 = gallons per stroke    x3 = 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% efficiency.

TECH FORMULAS: David Aakre

Rate

Rate = Frequency (Input or Simulated) x Time Factor Meter Factor x Conversion Factor

Example: Simulate a 100 Hz signal into a channel that has a meter factor of 2.986 pulses/US Gal. Calculate the rate in m3/min. (meter factor such as given with a Turbine flow meter)

Rate = ____100 Hz x 60 sec/min______2.986p/gal US x 264.2 gal

Rate = 7.606

Conversion Factors

1 m3 = 264.1761 US gallons (Petroleum) 1 m3 = 6.28991 US Barrels (Petroleum)

Frequency

Frequency = Rate x Meter Factor x Conversion Factor 60

If you have a rate and meter factor, you can calculate the source frequency. You can then take a measurement from the instrument generating the signal to verify it as expected.

Scaling (Current 4-20ma)

A Technician must know how to take a raw signal (current or freq) and translate it into a measurement value. It is also necessary to convert measured values back into their raw signals.

Value = (Signal – 4) x (Rangemax – Rangemin) 16

Example: 15 K Frac pressure Transducer Range 15,000 to 0

Signal= 12 ma measured with digital meter in DC amps.

Value = (12-4)/16 x (15000-0)= 7500 PSI

Signal ma = (__Value__ x 16 ) + 4(Rangemax – Rangemin)

Example: 7500 PSI measured what is Milliamps for 15 K Pressure Transducer.

Signal Ma= (7500 x 16)/ 15000-0) +4 = 12 Ma

Slope = Max Range/ 16 Ma

Example: 15000/ 16 = 937.50

Use these formulas to calibrate instrumentation and test software with frequency generator like a PIE and 4-20 ma loop calibrator. Most instruments have two calibration points a low and Max. 4ma =0 and 20 ma = high range. Frequency is zero to max scale in Hertz (HZ).