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Production engineering formulas and calculations Chapter 4 215
Output(s)
K L : Dimensionless Fracture Length (dimensionless)
K u : Reciprocal Dimensionless Fracture Width (dimensionless)
K s : Dimensionless Fluid-Loss Coefficient (dimensionless)
K ηL : Dimensionless Variable (dimensionless)
Formula(s)
p ffiffi
K ¼ CLh=i t
L
p ffiffi
K ¼ C t=w w
u
p ffiffi
K ¼ C t=V
s spt
i 3
μ
K ¼ 21:8
ηL
hC 2 Et
Reference: Williams, B. B., Gidley, J. L., & Schechter, R. S. (1979). Acidizing fundamentals. Henry L. Doherty Memorial
Fund of AIME, Society of Petroleum Engineers of AIME, Page: 40.
4.25 Downhole operating pressure (hydraulic fracturing)
Input(s)
ΔP f : Pressure Loss Sourced by Friction (psi)
ΔP p : Pressure Loss sourced by Perforations(psi)
ΔP h : Hydrostatic Pressure Change (psi)
P inj : Injection Pressure (psi)
D: Fracture Elevation Depth (ft)
G f : Fracture Gradient (psi/ft)
Output(s)
P F : Downhole Operating Pressure (psi)
Formula(s)
P ¼ G D
F f
P + ΔP ΔP ΔP p
f
h
inj
G ¼
f
D
Reference: Saydam, T., (1967). Principles of Hydraulic Fracturing, ARI Publishing Co., Page: 25.
4.26 Entrance hole size (perforation)
Input(s)
σ y : Yield Strength of Casing of Interest (ksi)
σ yr : Yield Strength of Reference Casing (ksi)
d r : Entrance Hole Diameter in Reference Casing (in.)