Upscaling Flow Properties - Reservoir Model Design - page 119

1

Endpoint k ro

Total fluid
mobility

Endpoint k rw

k ro

k rw

0

1

Water Saturation

S wor

S wc

S or = 1 - S wor

Also called S wi

Fig. 4.5 Example oil-water relative permeability functions

Fig. 4.6 Example gas-oil
relative permeability
functions

1

Straight-line
approximation

k rog

k rg

0

1

Gas Saturation

S gc S gmax = 1 - S or - S wi

S gmax

arise from poor treatment or understanding of
these endpoints.
The most common functions used for relative
permeability are the Corey exponent functions:

Typical values for a water-wet light oil might be:

3 3

k ro ¼ 0 : 85 1 ð S wn Þ and k rw ¼ 0 : 3S w ðÞ

ð 4 : 9 Þ

x

k ro ¼ A1 ð S wn Þ ð 4 : 6 Þ

A similar set of functions can be used to
describe a gas-oil system (Fig. 4.6 ), where the
functions are bounded by the critical gas satura-
tion, S gc , and the maximum gas saturation, S gmax .
However, gas-oil relative permeability curves
tend to have less curvature (lower Corey
exponents) and sometimes straight-line functions

y

k rw ¼ BS w ðÞ ð 4 : 7 Þ

where S wn is the normalized saturation:

S wn ¼ ð S w S wc Þ= ð S wor S wc Þ ð 4 : 8 Þ