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Relative Permeability: Effective Permeability - Lecture Slides | PETE 2031, Study notes of Engineering

Louisiana State University (LSU) - System OfficeEngineering
Prof. S. Kam

Material Type: Notes; Professor: Kam; Class: RESERVOIR ROCK PROP; Subject: Petroleum Engineering; University: Louisiana State University; Term: Fall 2009;

Typology: Study notes

Pre 2010

Uploaded on 12/08/2009

taylor-dewalch
taylor-dewalch 🇺🇸

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1
Relative Permeability
Effective Permeability
•Multiphase flow in porous media- Darcy’s law still applies
•“ Effective permeability” : permeability of one fluid in the
presence of other fluids in porous media
Relative permeability
where kjis the effective permeability of phase j.
(Absolute permeability is no longer valid.)
Note that k > kjalways.
dx
dPAk
qo
o
o
o
μ
−=
dx
dPAk
qg
g
g
g
μ
−=
dx
dPAk
qw
w
w
w
μ
−=
pf3
pf4
pf5
pf8
pf9
pfa

Partial preview of the text

Download Relative Permeability: Effective Permeability - Lecture Slides | PETE 2031 and more Study notes Engineering in PDF only on Docsity!

Effective Permeability

  • Multiphase flow in porous media- Darcy’s law still applies
  • “ Effective permeability” : permeability of one fluid in the presence of other fluids in porous media

Relative permeability

where k j is the effective permeability of phase j.

(Absolute permeability is no longer valid.)

Note that k > k j always.

dx

kAdP q o o

o

o =− μ

dx

kAdP q g g

g g

dx

kAdP q w w

w w =− μ

Relative Permeability

  • It is more convenient to use relative permeability. k (^) rj = k (^) j/k , the relative permeability of phase j

dx

kk AdP q o o

ro o =− μ

dx

kk AdP q g g

rg g =− μ

dx

kk AdP q w w

rw

w =− μ

  • Therefore, relative permeability represents fraction to the absolute permeability.

Saturation

  • Pore space in a reservoir rock occupied by multiple phases.
  • Saturation (Sj):
    • Volume of each phase in the pore space
    • Relative permeability is a function of saturation.
  • Does not include fluids’ interaction at the interface (i.e., saturation does not tell the distribution of fluid in p.m.) (see interfacial phenomena, capillary pressure)
  • i.e., Sw = volume of water / pore volume = Vw / Vp
    • For a reservoir above bubble point pressure (BPP), Sw + So = 1.
  • For a reservoir below BPP, Sw + So + Sg = 1.

Relative permeability

Effect of Wettability: Pore-level description

Invasion of non-wetting phase into wetting-phase saturated medium

Invasion of wetting phase into non- wetting-phase saturated medium “Drainage” “Imbibition”

Relative permeability

Wettability (concepts)

  • Wetting phase “coats” the surface of rock grains.
  • Wetting phase fills smaller pores first; larger pores occupied by nonwetting phase.
  • In pores, wetting phase occupies corners and crevices; nonwetting

phase occupies centers. Therefore, wetting phase prefers pore

throat than pore body.

Rock

BOT (Bundle-of-Tubes) model

Wetting phase

Effect of Wettability: Pore-level description

Relative permeability

Non-wetting Saturation

Immobile Wetting Saturation (usually water) Flow Direction

Wetting Saturation

Immobile Non-wetting Saturation (usually oil)

Residual Wetting Phase Distribution Residual Non-wetting Phase Distribution

Normalizing relative perm

n

wi or

w or ro S S

S S

k B ⎥ ⎦

m

wi or

w wi rw

S S

S S

k A ⎥

  • Relative permeability curve depends on S (^) wi and Sor.
  • Need normalization to get rid of these effects.

, (^1) wi or

w wi S S

S S Defining S − −

−

n ro

m then , krw = AS and k = B ( 1 − S )

Parameters (A, B, m, and n) are the intercepts and

slopes of relative permeability vs. normalized

saturation (S) plot. “Corey-type relative permeability”

Normalizing relative perm

Relative permeability

0

1

0 0.5 1 Water Saturation, Sw

Relative perm, Kr

(^) krw kro

0

1

0 0.5 1 Nomalized Water Saturation, S

Relative perm, Kr

(^) krw kro

1 0 0.5 1

Water Saturation, Sw

Relative perm, Kr krw kro

Normalizing relative perm

krw = ASm ; k ro = B ( 1 − S ) n ;

therefore log( krw )= log( A )+ m log( S ) therefore log( kro )=log( B )+ n log( 1 − S )

y = 2.9881x - 0.

-2.

-1.

-0.

0 -1 -0.5 0

log (1- S)

log (Relative perm), log (Kr)

log(kro)

y = 1.9996x - 0. -2.

-1.

-0.

0 -1 -0.5 0

log (Nomalized Water Sat.), log S

log (Relative perm), log (Kr)

log (krw)

Topics in Advanced Level

Relative permeability

Relative permeability