Page 255 - Formulas and Calculations for Petroleum Engineering

248 Formulas and calculations for petroleum engineering

Output(s)

v z : Velocity (ft/s)

Formula(s)

2

r
r
ρ g R Þ 2
ð
2
v ¼ 1 +2 a ln
z 4 μ R R
Reference: Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons,
Chapter: 2, Page: 65.
4.97 Velocity distribution of flow through an annulus

Input(s)
po: Pressure at initial point (Pa)
pL: Pressure at point L (Pa)
R: Radius (m)
μ: Viscosity (kg/(ms))
L: Length (m)
r: Cylindrical Shell of Thickness (m)
2
1
K: Boltzmann Constant (m kg s 2 K )

Output(s)
vz: Velocity Distribution (m/s)

Formula(s)

0 1
r
ð po pLÞ R 2 B 2 1 K 2
R C
vz ¼ B 1 ln C
4 μ L @ R 1 r A
ln
K
Reference: Transport Phenomena, Second Edition, Bird, Page: 55.

4.98 Velocity of fluid in annulus

Input(s)
Q: Flow rate (gpm)
D o : Open Hole Diameter (in.)
D p : Outside Diameter of Pipe (in.)

Output(s)

v a : Velocity of Fluid in Annulus (ft/s)