Page 138 - Formulas and Calculations for Petroleum Engineering

Drilling engineering formulas and calculations Chapter 2 131

2.132 Mass rate of flow through annulus

Input(s)
po: Pressure at initial point (Pa)
pL: Pressure at point L (Pa)
R: Radius (m)
3
r: Density (kg/m )
mu: Viscosity (kg/(ms))
L: Length (m)
1
2
K: Boltzmann Constant (m kg s 2 K )
Output(s)

C: Mass Rate of Flow (kg/s)

Formula(s)

0 1
4 2 2
ð ð
p po pLÞ R r B 4 1 K Þ C
C ¼ B 1 K C
8 m L @ 1 A
ln
K
Reference: Transport Phenomena, Second Edition, Bird, Chapter 2.

2.133 Matching conditions at the cake-to-rock interface—Formation invasion
Input(s)

P i_wall : Pressure value at Cake to Rock Interface (psi)
: Pressure value at previous grid of Cake to Rock Interface (psi)
P i wall 1
: Pressure value at the following grid of Cake to Rock Interface (psi)
P i wall+1
k c : Permeability of the Mudcake (mD)
k r : Permeability of the Rock (mD)

Output(s)
(k c + k r )P i_wall : Relationship for matching conditions at the Cake-to-Rock interface (mD psi)

Formula(s)

ð k + k ÞP ¼ k P + k P
c r i_wall c i wall 1 r i wall +1

Reference: Chin, W. C. (1995). Formation Invasion, Page: 147.

2.134 Maximum allowable mud weight

Input(s)

mw: Mud weight (ppg)
tvd: True Vertical Depth of Casing Shoe (ft)
P l : Leak-off Pressure (psi)