Page 254 - Formulas and Calculations for Petroleum Engineering

Production engineering formulas and calculations Chapter 4 247

p s : Shut-in Pressure at any Shut-in Time (psi)
p w : Well Flowing Pressure at the Instant of Shut-in (psi)
Δt: Shut-in Time (day)
m: Slope of Cartesian Pressure Build-up Plot (psi/cycle)

Output(s)
S: Skin (dimensionless)

Formula(s)

! !

c p p 1
0:5
S ¼ 34:7 r ø μ t s w + 1
ew 0:5
k m ð ΔtÞ
Reference: Ahmed, T., McKinney, P.D. 2005. Advanced Reservoir Engineering, Gulf Publishing of Elsevier, Chapter: 1,
Page: 81.

4.95 Velocity distribution in the annular slit of a falling-cylinder viscometer

Input(s)
κ: Ratio of inner Radius to Outer Radius (fraction)
v o : Velocity (cm/s)
ξ: Radial Coordinate (dimensionless)

Output(s)
v z : Velocity Profile (cm/s)

Formula(s)

1

2 2
1 ξ 1+ κ Þ ln
ð
v ξ
z
¼
v 1
o 2 2 ln
ð 1 κ Þ 1+ κð Þ
κ
Reference: Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons,
Chapter: 2, Page: 70.
4.96 Velocity distribution in the narrow annular region in annular flow
with inner cylinder moving axially

Input(s)
ρ: Density (ppg)
2
g: Acceleration due to Gravity (ft/s )
R: Radius (ft)
r: Position from Point (ft)
a: Ratio of Distance of Rod from Centre (fraction)
μ: Viscosity (cP)