Today we will take a look at the basic calculations that you might need to perform during hydraulic fracturing operations to find rates, pressure, and volumes.
Calculating Frac Gradient
Frac Gradient = (ISIP + hydrostatic pressure)/TVD
TVD – True vertical depth
ISIP – Instantaneous shut-in Pressure = Final injection pressure – Pressure drop due to friction
ISIP is taken right after pumps are shut down
The frac gradient is used to calculate the pressure needed to break the formation and initiate the fracture.
Related: What is Proppant in Oil and Gas?
Calculating Wellhead Pressure (WHP)
WHP = BHFP – hydrostatic pressure + friction pressure
Bottom Hole Fracturing Pressure (BHFP) = Frac Gradient x Depth (TVD)=ISIP + Hydrostatic pressure
Bottom Hole Pressure (BHP) = Hydrostatic pressure +WHP
Hydrostatic Pressure = fluid density x 0.00981 x Depth (TVD)
Friction Pressure = Friction gradient x Depth (TMD) + Perforation Friction +Near wellbore Friction
TMD – Total measured depth
Related: What is Hydraulic Fracturing?
Calculating Flush Volumes
Flush Volume = Perf Depth x Tubing Internal Capacity
Flush volume is usually equal to the full wellbore volume of fluid that is pumped to displace all the proppant.
Overflush means that more than the wellbore volume is pumped.
Calculating Sand and Slurry Rates
Slurry Rate = Clean Rate x (1 +(Proppant concentration/SG))
Slurry rate is the total rate combined of fluid, chemicals, and proppant
Clean Rate – the pumping rate before the proppant is added
Dirty Rate – the total slurry pumping rate with proppant
Proppant Concentration = ((Slurry Rate – Clean Rate)/Clean Rate) x SG (Proppant)
Proppant concentration is the sand concentration in the fracturing fluid
Sand Pumped = (Dirty Rate – Clean Rate) x SG of Sand
The specific gravity of sand is 2650 kg/m3
N2 Downhole Rate (m3/min) = N2 Rate (scm/min)/N2 Volume Factor (scm/min)
Horse Power Calculations
Pumping Power (kW)=(Pump rate (m3/min) x WHP (kPa))/60
Pumping Power (HP) =Pumping Power (kW) x 1.341
HP – Horse Power
Read next: Top 10 Chemicals Used In Hydraulic Fracturing Process
References:
http://www.fekete.com/SAN/TheoryAndEquations/WellTestTheoryEquations/ISIP.htm