This document provides formulas and explanations for calculating frac job parameters such as fluid rates, pressures, horsepower requirements, and blender equations. Key points include: 1. Formulas are given for calculating maximum frac rate, line volume, fluid gradient, bottomhole pressure, frac gradient, horsepower, and pipe time. 2. Modes of monitoring bottomhole pressure during fracturing are described. 3. Equations are outlined for calculating parameters related to blender operations like fluid and proppant volumes and densities. 4. Pump math formulas are defined for calculating fluid volumes per revolution and maximum pump rates based on engine speeds and transmission gear ratios. 5. Steps for bucket testing chemical pumps to validate

1. FRAC FORMULAS DAVID AAKRE TECHNOLOGIST
Max rate = ID ²x 2.3314
Line Volume = .0009714xID²X Depth
FluidGradient: Pressureexerted per unit depth of a fluid
Fluid Density (lbs. /Gal) x .05195 =Fluid Gradient
Hydrostatic Pressure=TrueverticalDepth (TVD) x Fluid Gradient
BottomHole pressure (BHP) =Hydrostatic + Well Head Pressure( Use instant
shutin pressureif pumping complete)
4 modes of BHP monitoring while fracing: 1 pressureincreases gradually
(Fracturecontained). 2. Straightline pressure(fluid loss causing less efficient
fractureextensions). 3. Rapid risein pressure(screen out). 4 rapid declines in
pressure(narrow fracturewidth)
Frac Gradient=PSI per foot of depth, = BHP/Truevertical Depth (Mid perf
depth on a vertical Well) OR FG =ISIP/TVD + .433
ISIP- Instantaneous shutin pressurerecorded when rate goes to zero at end of
flush, All friction equals zero.
Horsepower =(well head pressurex rate)/ 40.8
Pipe Time = Line volume / Rate
Blender Equations:
Weight of cleanwater = 8.33334 lbs. per gallon
Oil fieldBarrel =42 Gallons
Gallons to Barrels =Gallons / 42
Barrels toGallons = Barrels x 42
Set Points Based off Mega Gallon principle (1000 Gal) 42 gal/ 1000 gal = .042

2. Clean Rate is the Suction Rate on Blender – Mag Meter or Turbine Flow Meter
Gallons per Minute = CleanRate x .042 x Concentration(Set Point)
Gel Loading = Gel Weight lbs. / 4 40lbs/4=10 GPT
Base FluidDensity =Weightlbs. / volume Gal (useHydrometer)
Absolute Volume = 1 / (Specific gravity x .0022046226 x3785.412) =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
CleanVolume = Base Fluid Volume Gallons (clean water)
Sand Volume (gals) = Total Sand x AbsoluteVolume 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 volumefactor)
Blender Screw Geometry (Blender ScrewSpeedis Important!)
Auger flight- flat part that coils around the shafton Auger
Auger Pitch- The distance between two flights on Auger
Auger Shaft- The shaftin middle of an Auger
PitchVolume = 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)

3. 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
Total screw Rate= (clean rate x42 x PPG)/Lbs per rev
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=

4. 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 TruckRate because yourtruckrate 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
FluidSG Increased Density Decrease
FluidSG Decreased Density Increased
Sand SG Increased Density Decreased
Sand SG decreased Density Increased
Bulk Density Decrease – Screw Speed Increases
Bulk Density Increases- Screw Speed decreases
Specific gravity Increases-Screw speed Increases
Specific gravity Decreases-Screw speed decrease
Fluid SGS decrease- Screw speed decrease

5. Fluid SGS Increase- Screw speed Increase
Screw Efficiency Increased-Screw Speed decrease
Screw Efficiency decreased- Screw speed Increase
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)
Density Back Calculation using absolute volume.
Absolute Volume can be changed in some
software to affect screw speed and density.

6. 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______
2.986 p/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)

7. 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

8. 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).
How to Bucket Test Chemical Pumps:
• Ramp Motorto full Speed on Blender
• Prime up pump with manualcontrol and get all air out and
check connections. Make sure you have steady stream.
Never Run a Dry pump burn it up.
• Select Auto to turn pump On to test Closed loop system.
Use set point One or two. Simulate Suction Rate to 23.81.
Need a suction rate for pumps to turn On. Gpm= Set point
x .042 x suction rate. IMPORTANT FORMULA
• Mass Meter shouldbe lining out on set point 1 or 2 gpm
and not jumping around.
• Make sure you have two buckets, one graduatedwith one
to five gallonmarks.
• When you have a steady stream in Auto, transfer chemical
hose to graduatedbucket starting timer for one minute for
set pointone or two.
• In one minute you should have one gallonin graduated
bucket with set point of one. Two gallonsin graduated
bucket with set point of 2.

9. • If You have one gallonin bucket match yourtach up ( mag
pick up and gear) or write down rpms for pump at that set
point. During job you can match tach up by writing down
rpms for each pump while at treating suction rate.
• If you did not get One gallonin one minute you might have
to zero mass meter or adjust the PID tuning.
• Zero Mass Meter: shut in Mass meter with fluid in it. Find
zero buttonin software or On transmitter. Zero and re-
bucket test. BAD PackingOn Pump causes air issues.
• After Zeroing the Mass meter and bucket testing and still
havingproblem you might haveto Auto tune pump or
adjust the Multiplierfor the pump.
• The pump could be wearing out and the way to test pump is
to see if it can reach maximum and minimum rate for that
style of pump. Use Mass meter or Tack rpms to test. If that
is not available use a mechanics tack meter that uses
reflective tape that is put on pump shaft.