Page 226 - Formulas and Calculations for Petroleum Engineering

Production engineering formulas and calculations Chapter 4 219

Formula(s)

q W x 2 2x
i
AtðÞ ¼ 2 e erfc xðÞ + p 1
ffiffiffi
4π C π
Z ∞
2 t 2
erfc xðÞ ¼ ffiffiffip e dt
π
x
p ffiffiffiffi
πt
x ¼ 2C
W
Reference: Saydam, T., (1967). Principles of Hydraulic Fracturing, ARI Publishing Co., Page: 12.

4.34 Fracture coefficient of a hydraulically fractured reservoir

Input(s)
3
m: Slope of the Production Decline Curve (ft /min)
2
A f : Fractured Surface Area (ft )

Output(s)
C f : Fracture Coefficient of a Hydraulically Fractured Well (ft/min)

Formula(s)

0:0164 m
C ¼
f
A
f
Reference: Saydam, T., (1967). Principles of Hydraulic Fracturing, ARI Publishing Co., Page: 99.

4.35 Fracture fluid coefficient for reservoir-controlled liquids

Input(s)
k: Effective Permeability (Darcy)
Ø: Effective Porosity (%)
μ: Viscosity of Reservoir Fluid (cP)
ΔP: Pressure difference in Fracture Face (psi)
1
c f : Isothermal Compressibility of Reservoir Fluid (psi )
c: Conversion Coefficient (dimensionless)

Output(s)

C r : Fracture Fluid Coefficient for Viscosity-Controlled Liquids (dimensionless)

Formula(s)

k c Ø 2
1
C ¼ c ΔP f
r μ

Reference: Saydam, T., (1967). Principles of Hydraulic Fracturing, ARI Publishing Co., Page: 20.