Three Phase Relative 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 k row,k rw =f(S w ) k rog,k rg =f(S g ) Find k ro =f(S w,S g ) Stone 2 Does not require S or Find k ro =f(S w,S g )

3-Phase relative permeabilities Traditional assumptions for saturation-dependencies k rw (S w ), k rg (S g ), k ro (S w,S g ) Which is based on simple pore scale view of pore occupancy

Traditional assumptions for saturation-dependencies k rw (S w ), k rg (S g ), k ro (S w,S g ) 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 k rw (S w ) 3-Phase relative permeabilities

Similar to gas-oil system, gas occupancy depends only on gas saturation, therfore k rg (S g ) 3-Phase relative permeabilities

Oil is in contact with water and gas. Therefore oil occupancy depends on gas and water occupancy. k ro (S g, S w ) 3-Phase relative permeabilities

Ternary Diagram Plot Point for: S w =0.25 S o =0.40 S g = S o 1.00

Iso-relative permeabilities (isoperm) Lines show constant k ro (isoperm) – Not parallel to any saturation lines – k ro 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 k rg (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 S or : residual oil saturation S wir : irreducible water saturation

Stone model 2