Drilling Fluids - Frictional Pressure Loss

Formulas

Flow rate, flow regime, rheological properties, and conduit geometry are among the key parameters that impact frictional pressure losses in the drill string and annulus. The process to model these pressures, complex in its own right for Herschel-Bulkley fluids, is further complicated in HTHP and deepwater wells by the sensitivity of drilling fluid density and rheological properties to downhole temperatures and pressures

Yield Stress:

𝑇𝑦 = 2 ∗ 𝑅3 − 𝑅6

R3 – R3 Viscometer Reading (RPM)
R6 – R6 Viscometer Reading (RPM)

Plastic Viscosity:

𝑃𝑉 = 𝑅600 − 𝑅300

R600 – R300 Viscometer Reading (RPM)
R300 – R600 Viscometer Reading (RPM)

Yield Point of Drilling Fluid:

𝑌𝑃 = 𝑅300 – 𝑃𝑉

Flow Behavior Index (Herschel-Bulkley Fluids)

𝑁 = 3.32 ∗ 𝐿𝑜𝑔10((2 ∗ 𝑃𝑉 + 𝑌𝑃 − 𝑇𝑦) / (𝑃𝑉 + 𝑌𝑃 − 𝑇𝑦))

Consistency Factor (Herschel-Bulkley Fluids)

𝐾 = (𝑃𝑉 + 𝑌𝑃 − 𝑇𝑦) / (511 ^ 𝑁)

Flow Behavior Index (Power Low Fluids)

𝑛_𝑝 = 3.32 ∗ 𝐿𝑜𝑔10((2 ∗ 𝑃𝑉 + 𝑌𝑃) / (𝑃𝑉 + 𝑌𝑃))

Consistency Factor (Power Low Fluids)

𝑘𝑝 = (𝑃𝑉 + 𝑌𝑃) / (511 ^ 𝑛_𝑝 )

Frictional Pressure Loss in Drill Pipe:

Drilling Fluid Velocity Inside Pipe

Q = Flow Rate (gal/min)

Di = Internal Diameter of Drill Pipe (inch)

Shear Rate Correction

Reynolds Number

ρ = Drilling Fluid Density (gal/min)

Critical Reynolds Number

𝑁_𝐶𝑅𝑒𝑝𝑖𝑝𝑒 = 3470−1370𝑁

Fanning Friction Factor

Pressure Loss in Drill Pipe

L = Length of the Pipe or Annulus (ft)

Frictional Pressure Loss in Annulus:

Drilling Fluid Velocity Inside Annulus

Dh = Borehole Diameter (inch)
Dp = Outside Diameter of Drill Pipe (inch)

Shear Rate Correction

Reynolds Number

Critical Reynolds Number

𝑁_𝐶𝑅𝑒𝑝𝑖𝑝𝑒 = 3470 −1370𝑁

Fanning Friction Factor

Pressure Loss in Drill Pipe

L = Length of the Pipe or Annulus (ft)

Bit Pressure Loss:

Ndn1 = Number of Nozzle 1
Ndn2 = Number of Nozzle 2
Ndn3 = Number of Nozzle 3
dn1 = Nozzle 1 Size (1/32 inch)
dn2 = Nozzle 2 Size (1/32 inch)
dn3 = Nozzle 3 Size (1/32 inch)
Cv = Nozzle Discharge Coefficient

Total Frictional Pressure Losses:

𝑃_𝑡𝑜𝑡 = 𝑃_𝐷𝑆 + 𝑃_𝑎 + ∆𝑃_{𝑁𝑂𝑍𝑍𝐿𝐸}

Input Parameters

• R3 Viscometer Reading [RPM]
• R6 Viscometer Reading [RPM]
• R300 Viscometer Reading [RPM]
• R600 Viscometer Reading [RPM]
• Flow Rate [gal/min]
• Drilling Fluid Density [lb/gal]
• Internal Diameter of Drill Pipe [inch]
• Outside Diameter of Drill Pipe [inch]
• Bore Hole Diameter [inch]
• Length of Pipe Annulus [ft]

Bit Nozzle Input Parameters:

• Nozzle 1 Size [1/32 inch]
• Nozzle 2 Size [1/32 inch]
• Nozzle 3 Size [1/32 inch]
• Number of Nozzle 1
• Number of Nozzle 2
• Number of Nozzle 3
• Nozzle Discharge Coefficient

Outputs/Reports

• Yield Stress [lb/100ft2]
• Plastic Viscosity [cP]
• Yield Point of Drilling Fluid [lb/100ft2]
• Flow Behavior Index (Herschel-Bulkley Fluids)
• Consistency Factor (Herschel-Bulkley Fluids)
• Flow Behavior Index (Power Low Fluids)
• Consistency Factor (Power Low Fluids)

Frictional Pressure Loss in Drill Pipe:

• Drilling Fluid Velocity Inside Pipe [ft/min]
• Reynolds Number
• Fanning Friction Factor
• Pipe Pressure Loss [psi]

Frictional Pressure Loss in Annulus:

• Drilling Fluid Velocity Inside Annulus [ft/min]
• Reynolds Number
• Fanning Friction Factor
• Pressure Loss in Annulus [psi]
• Bit Pressure Loss [psi]
• Total Frictional Pressure Losses [psi]

Related Links

Horizontal Directional Drilling Miscellaneous