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Annulus Pressure Loss Due to Friction During Hydraulic Fracturing - Laminar Flow Formula

ΔPf=μpLv1000(d0di)2+τyL200(d0di)\Delta P_f=\frac{\mu_pLv}{1000(d_0-d_i)^2}+\frac{\tau_yL}{200(d_0-d_i)}

Annulus Pressure Loss Due to Friction During Hydraulic Fracturing - Laminar Flow calculates annulus friction pressure loss for hydraulic fracturing workflows in production engineering.

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How engineers use this formula

Use this formula when the listed inputs (v, L, d_0, d_i, mu_p, tau_y) are known and the assumptions behind the cited hydraulic fracturing relationship match the engineering case being checked.

Assumptions

  • Input values are representative for the well, reservoir, fluid, or equipment case being evaluated.
  • The declared units match the field-unit constants used in the formula.
  • The cited formula applies to the selected petroleum engineering workflow.

Limitations

  • The calculation does not replace a full engineering model or operating procedure.
  • Accuracy depends on the source correlation, assumptions, input quality, and unit consistency.

Common mistakes

  • Mixing unit systems without converting the inputs.
  • Using default example values as field recommendations.
  • Applying the formula outside the source assumptions.

Default example

Using the default inputs, DeltaP_f equals 311.22449 psi.

vft/s

20

Lft

5000

d_0in

8.5

d_iin

5

mu_pcP

25

tau_ylb/100 ft2

15

Inputs

v

ft/s

Average Fluid Velocity

L

ft

Pipe Length

d_0

in

Inner Diameter of Outer Pipe

d_i

in

Outer Diameter of Inner Pipe

mu_p

cP

Plastic Viscosity

tau_y

lb/100 ft2

Yield Point of the Liquid

Outputs

DeltaP_f

psi

Annulus Friction Pressure Loss

gap

in

Annular Diameter Difference

v

ft/s

Average Fluid Velocity

L

ft

Pipe Length

mu_p

cP

Plastic Viscosity

tau_y

lb/100 ft2

Yield Point of the Liquid

d_0

in

Inner Diameter of Outer Pipe

d_i

in

Outer Diameter of Inner Pipe

Source and review

reviewed

Principles of Hydraulic Fracturing, Saydam, T. (1967)

Saydam, T. 1967. Principles of Hydraulic Fracturing, ARI Publishing Co., Page 31.

Source

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