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Fracture Area from Saydam Leakoff Function Formula

Af=qiWf4πCL2(exD2erfc(xD)+2xDπ1)A_f=\frac{q_iW_f}{4\pi C_L^2}\left(e^{x_D^2}\operatorname{erfc}(x_D)+\frac{2x_D}{\sqrt{\pi}}-1\right)

Fracture Area from Saydam Leakoff Function calculates hydraulic fracture area for hydraulic fracturing workflows in production engineering.

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How engineers use this formula

Use this formula when the listed inputs (q_i, W_f, t, C_L) 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, A_f equals 7,999.683022 m2.

q_im3/min

2

W_fm

0.006

tmin

60

C_Lm/sqrt(min)

0.0004

Inputs

q_i

m3/min

Injection Rate

W_f

m

Fracture Width

t

min

Injection Time

C_L

m/sqrt(min)

Fracture Fluid Leakoff Coefficient

Outputs

A_f

m2

Hydraulic Fracture Area

q_i

m3/min

Injection Rate

x_D

dimensionless

Saydam Leakoff Parameter

F_L

dimensionless

Saydam Leakoff Function

Source and review

reviewed

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

Saydam, T. 1967. Principles of Hydraulic Fracturing, ARI Publishing Co., Page 12.

source conflict
Source

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