Three PhaseRelative Permeability

Outline

• Application of 3-phase relative permeabilities• Saturation-dependencies of 3-phase relative

permeabilities– Occupancies and filling sequences– Dependency regions– Probabilistic model

• Ternary diagram– Iso-relative permeabilities (isoperm)

• Modeling of three phase relative permeability

Application of 3-phase relperm

• Main application in EOR projects, WAG, SWAG, etc.

• Equilibrium gas or separator gas injection.– 3-phase relperm measurement is difficult,

expensive and time consuming.– Two phase data is much more available.–Many methods have been developed to calculate

three phase relative permeability from two phase curves (water/oil curve and oil/gas curve).

Relative Permeability

Correlations Lab measurements

Three phase system

Corey’s model

Two phase system

Stone 1 and 2 models

Stone 1• Scaling technique• Input two sets of rel perm data• krow,krw=f(Sw)

• krog,krg=f(Sg)

• Find kro=f(Sw,Sg)

Stone 2• Does not require Sor

• Find kro=f(Sw,Sg)

3-Phase relative permeabilities

• Traditional assumptions for saturation-dependencies

• krw(Sw), krg(Sg), kro(Sw,Sg)

• Which is based on simple pore scale view of pore occupancy

• Traditional assumptions for saturation-dependencies

• krw(Sw), krg(Sg), kro(Sw,Sg)

• Water-wet system: Water in small pores, gas in big pores, oil in between

3-Phase relative permeabilities

• Similar to water-oil system, water occupancy depends only on water saturation, therfore krw(Sw)

3-Phase relative permeabilities

• Similar to gas-oil system, gas occupancy depends only on gas saturation, therfore krg(Sg)

3-Phase relative permeabilities

• Oil is in contact with water and gas. Therefore oil occupancy depends on gas and water occupancy.

kro(Sg, Sw)

3-Phase relative permeabilities

Ternary Diagram

• Plot Point for:

Sw=0.25

So=0.40

Sg=0.35

0.00 So 1.00

Iso-relative permeabilities (isoperm)

• Lines show constant kro (isoperm)– Not parallel to any

saturation lines

– kro is a function of both water and gas saturation

– Pore size distribution• Water: smallest• Gas: largest• Oil: intermediate pores

Iso-relative permeabilities (isoperm)

• Lines show constant krg (isoperm).– Approximately parallel

to gas saturation lines– Krg is a function of

gas saturation– Gas is in largest pores

Stone model 1

• Proposed method by Stone in 1970

• Sor: residual oil saturation

• Swir: irreducible water saturation

SoD

SwD

SgD

𝛽𝑤=k row

1−SwD

𝛽𝑔=k rog

1−SgD

kro

Stone model 2

• Stone's model 2 is a modified version of Stone 1. It is a better predictor than Stone 1 in high-oil saturation regions. It is more appropriate for water-wet systems and is not suited for intermediate wet systems.