Daily Operations Report > Drillstrings Section > Bit Operations Tab
The following section describes generic equations and constants for several Bit hydraulics calculations in the Bits tab:
P Bit - Pressure Differential
Noz Vel - Nozzle or Jet Velocity
HHP - Hydraulic Horse Power
HHP/Area - Bit Hydraulic Horse Power per Bit Area
P Bit is the pressure differential or loss across the bit.
The equation for P Bit and derivation of the coefficient used in the equation are provided below:
Dp = r ´ Q2 / (2 ´ Cd2 ´ A2)
Where:
Dp = pressure drop across bit (psi or kPa)
r = fluid density (ppg or kg/m3)
Q = flow rate (gal/min or L/min)
Cd = jet discharge coefficient
A = total flow area (in2 or mm2)
Note: Cd is a dimensionless coefficient. It may be as high as 0.98, but most resource materials recommend using the conservative figure of 0.95. The following value is used in OpenWells® software for this calculation:
Cd = 0.95
The 2 ´ Cd2 factor is integrated into the conversion constant. Therefore, the intermediate calculation is just r ´ Q2/A2. This results in an intermediate result of:
For API: lbs ´ gal/(min2 x in4)
For SI: kg ´ L2/(m3 x min2 x mm4)
Therefore for API, convert lbs ´ gal/(min2 x in4) to psi:
Note: For the API calculation, convert pounds to a mass by dividing by the acceleration due to gravity. This is the "(lbs2/386.04in)" factor you see in the following conversion.
lbs x gal/(min x in4) ´ (231 in3/1 gal) ´ (1min2/3600s2) ´ (lbs2/386.04in )= 1/6016.20779221 psi
Now the denominator (6016.20779221) is multiplied by 2 ´ Cd2 to get 10859.2550649.
In SI, convert kg ´L2/(m3 x min2 x mm4) to kPa:
kg ´ L2/(m3 ´ min2 ´ mm4) ´ (10-6m6/1L2) ´ (1012mm4/1m4) ´ (1min2/3600s2) ´ (1kPa/1000(kg/(m ´ s2))) = 1/3.6 kPa
The denominator (3.6) is now multiplied by 2 ´ Cd2 to get 6.498
Noz Vel (Nozzle or Jet Velocity)
The calculation of Nozzle Velocity (nozzle or jet velocity) and derivation of the constant used in the calculation are provided below:
v = Q / A ´ const
Where:
v = velocity (ft/s or m/s)
Q = flow rate (gal/min or L/min)
A = area (in2 or mm2)
The intermediate result of the calculation is as follows:
For API: gal/(min x in2)
For SI: L/(min x mm2)
Therefore for API, convert gal/(min x in2) to ft/s:
1 gal/(min x in2) x (231 in3/gal) x (1min/60s) x (1 ft/12 in)=0.32083333333333 ft/s
Therefore for SI, convert L/(min x mm2) to m/s:
1 L/(min x mm2) x (0.001m3/L) x (1,000,000mm2/m2) x (1min/60s)=16.6666666667 m/s
The calculation of HHP, or hydraulic horsepower and derivation of the constant used in the calculation are provided below:
hp = Q ´ p / const
Where:
hp = horsepower (HP or kW/cm2)
Q = flow rate (gal/min or L/min)
p = pressure drop (lbs/in2 or kPa)
const = conversion factor to change (min/in2)/(gal/lbs) to horsepower
The intermediate result of the calculation is as follows:
For API: (gal x lbs)/(min x in2)
For SI: (L x kPa)/min
Therefore for API, convert (gal x lbs)/(min x in2) to HP:
1 (gal x lbs)/(min x in2) x (231in3/gal) x (1ft/12in) x (33000HP/(1ft x lbs/min))=1/1714.28571429 HP
For SI, convert (L x kPa)/min to kW:
1 (L x kPa)/min x (1000(N/m2)/1kPa) x (0.001m3/L) x (1 min/60sec) x (1kW/1000 (N x m/s))=1/60000 kW
Note: Standard API documentation usually rounds this number to 1714. In OpenWells, this calculation is left as precise as possible so that there will be little or no discrepancy between what is calculated for different unit sets.
HHP/Area (Bit Hydraulic Horsepower per Bit Area)
The calculation of HSI, or bit hydraulic horsepower per bit area, is provided below:
HSI = hp / A
Where:
HSI = HHP/in2
hp = horsepower (HP or kW/cm2)
A = total flow bit cross sectional area (in2 or mm2)
The calculation of Impact Force is provided below:
Impact Force = (p / gc) VQ
Where:
Impact Force = measured in lbf
p = Density of Fluid (lb/ft3)
gc = Gravitational constant, 32.17 ft/sec2
Q = Circulation rate (ft3/sec)
V = Velocity through the bit (ft/sec)
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