Page 105 - Introduction to Petroleum Engineering

90 MULTIPHASE FLOW
5.4 MOBILITY AND FRACTIONAL FLOW

Equations 5.6 and 5.7 are the foundation for definitions of mobility, relative mobility,
mobility ratio, and fractional flow. Mobility for oil and water are defined as

S
kk ro ( )
λ = o (5.8)
o
µ o
kk rw ( )
S
λ = w (5.9)
w
µ w
Viscous oil typically has a low mobility relative to water and will flow with a lower
velocity than water when subjected to the same pressure gradient.
Relative mobilities are defined as follows:

k ro ( )
S
λ = o (5.10)
ro
µ o
S
k rw ( )
λ = w (5.11)
rw
µ w
Mobility ratio is used for assessing effectiveness of a displacement in porous
media. In general, mobility ratio is the mobility of the displacing fluid divided by the
mobility of the fluid being displaced. As an example, consider a water flood of an oil
reservoir. Water is injected into the reservoir to displace oil and provide pressure
support. In this case, the mobility ratio M is

kk ( ) /µ k ( ) /µ
S
S
M = rw or w = rw or w (5.12)
kk ( S ) /µ o k ( S ) /µ o
ro
wirr
wirr
ro
If M is greater than 1, the displacement is “unfavorable” because a less mobile fluid
is being pushed by a more mobile fluid. In a “favorable” displacement, the displacing
fluid is less mobile than the displaced fluid.
Water fractional flow is the fraction of water flowing through the reservoir during
a water–oil displacement process:
q
f = w (5.13)
w
q + q o
w
By contrast, water cut (WCT) introduced in Chapter 1 is the rate of water produced
at the surface divided by total liquid production rate at the surface:

 q 
WCT =  w  (5.14)
 q w + q o  surface

WCT should not be confused with water fractional flow.