Page 260 - Formulas and Calculations for Petroleum Engineering

Production engineering formulas and calculations Chapter 4 253

4.108 Well flowing pressure under Pseudo-steady state flow for non-circular
reservoirs

Input(s)
p i : Initial Reservoir Pressure (psi)
k: Permeability (mD)
h: Thickness (ft)
B: Formation Volume Factor (bbl/STB)
μ: Viscosity (cP)
C A : Shape Factor (dimensionless)
r w : Wellbore Radius (ft)
Q: Flow Rate (STB/day)
c t : Total Compressibility (1/psi)
ø: Porosity (fraction)
2
t: Time (hour) A: Area (ft )

Output(s)
P wf : Well Flowing Pressure (psi)

Formula(s)

162:6 Q B μ 2:2458 A 0:23396 Q B t

P ¼ p log
wf i 2
k h C r w A h ø c t
A
Reference: Ahmed, T., McKinney, P.D. 2005. Advanced Reservoir Engineering, Gulf Publishing of Elsevier, Chapter: 1,
Page: 33.

4.109 Wellbore pressure loss due to friction during hydraulic fracturing (laminar flow)
Input(s)

v: Average Velocity (ft/s)
L: Pipe Length (ft)
d: Inner Diameter of Pipe (in.)
μ p : Plastic Viscosity (cP)
2
τ y : Yield Point of the Liquid (lb/100ft )

Output(s)

ΔP f : Pressure Loss in the wellbore Sourced by Frictions during Hydraulic Fracturing (psi)

Formula(s)

μ Lv τ L
y
p
ΔP ¼
f
2
1500 d 225 d
Reference: Saydam, T., (1967). Principles of Hydraulic Fracturing, ARI Publishing Co., Page: 30.