Concept of relative permeability

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Concept of relative permeability
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Concept of relative permeability

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

P1
Fluid 1
Fluid 1
Fluid 2
Fluid 2
P2

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

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rel perm vs. saturation

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

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Different demonstrations
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Log scale
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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

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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

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Capillary end effect
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Capillary end effect

• Capillary pressure end effect gives rise to
  increasing wetting phase saturation towards
  outlet of the core

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Determination of relative permeability

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

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Empirical correlations

• Corey

• Brooks-Corey

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Normalizing oil relative permeability data
Slope is no
kro Log scale
Son, log scale
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Normalizing water relative permeability data
End point, krw0
Slope is nw
krw Log scale
Swn, log scale
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Model Fit
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Estimation of Sor
We choose Sor that gives straight line
kro Log scale
Son, log scale
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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