Concept of relative permeability

Concept of relative permeability

1 11

1

k A Pq

L

If two fluids flow simultaneously in a porous medium, the permeability of each fluid is reduced by the presence of the other one!

Fluid 1

Fluid 2Fluid 2

Fluid 1P1

P2

2 22

2

k A Pq

L

k1 and k2 are effective permeabilities and modified by saturations of the fluids

rel perm vs. saturation

r

kk

K

kr is called relative permeability and depends on saturation (also rock type and geometry and fluid properties)

End-points

Curvatures

Different demonstrations

Log scale

General comments on rel perms

Relative permeabilities only provide the general description of the process not the mechanism!

It is a very simple tool to describe multi-phase flow in porous media

Often used as fitting parameters in history-matching exercises

Absolute permeability does not depend on wettability while rel perms do

Like capillary pressure there are two drainage rel perms and imbibition rel perms

Gas-oil relative permeability

Gas flows above a critical gas saturation (Sgc)

When pressure drops below bubble point pressure, gas bubbles appear in oil, however they must coalesce and form a gas phase before gas can really move

Sgc = 0 – 8%

Capillary end effect

Capillary end effect Capillary pressure end effect gives rise to

increasing wetting phase saturation towards outlet of the core

Determination of relative permeability

Steady-state method: Fluids are injected with fixed flowrate into core until equilibrium is reached.

Unsteady-state method:

Empirical correlations

Corey:

0 wnrw rw ek k S 0 1 no

ro ro ek k S

1

w wc

eor wc

S SS

S S

Brooks-Corey:

2 30

/rw rw ek k S 2 2 1

0 1 1 /ro ro e ek k S S

Normalizing oil relative permeability data

1

1

w or

onwi or

S SS

S S

kroLog scale

Son, log scale

Slope is no

Normalizing water relative permeability data

1

w wi

wnwi or

S SS

S S

krwLog scale

Swn, log scale

Slope is nw

End point, krw0

Model Fit

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Water Saturation, fraction

Rel

ativ

e Pe

rmea

bilit

ies,

fra

ctio

n

Water

Oil

Water Fit

Oil Fit

0.00

0.01

0.10

1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Water Saturation, fraction

Rel

ativ

e Pe

rmea

bilit

ies,

fra

ctio

nWater

Oil

Water Fit

Oil Fit

Estimation of Sor

1

1

w or

onwi or

S SS

S S

kroLog scale

Son, log scale

We choose Sor that gives straight line

Different wettabilities

wettability no nw krw0

Water-wet 2-3 4-6 0.1-0.4

Intermediate 3-5 2-4 0.5-0.9

Oil wet 6-8 1.5-3 0.8-1.0