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This article discusses the method of measuring relative permeability in core plugs under unsteady-state conditions. It covers stages of saturation, production rates, imbibition ratios, analysis procedures, and assumptions involved. Hysteresis effects and plotting techniques are also explored.
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Rel. Perm. - Unsteady State • Unsteady State Method for relative permeability provides • Relative permeability ratio (kr,nonwet/kr,wet) as a function of wetting phase saturation (Swet) • Irreducible wetting phase saturation (drainage) • Residual nonwetting phase saturation (imbibition)
Rel. Perm. - Unsteady State Saturation in Core Plug Production Rates • Imbibition Relative Permeability Ratio Function • Stage 1: Preparation for drainage • core saturated with wetting phase • Stage 2: Irreducible wetting phase (drainage) • inject non-wetting phase until steady state, measure saturation • no wetting phase will be produced after steady state
Rel. Perm. - Unsteady State Saturation in Core Plug Production Rates • Imbibition Relative Permeability Ratio Function • Stages 3-6: Inject wetting phase • Stage 3 (A) Wetting phase has not yet reached outflow face • only nonwetting phase produced at outflow face • Stage 4 (B) Wetting phase just reaches outflow face, called breakthrough • wetting phase will be produced at outflow face
Rel. Perm. - Unsteady State Saturation in Core Plug Production Rates • Imbibition Relative Permeability Ratio Function • Stages 3-6: Inject wetting phase • Stage 5 (C) As injection of wetting phase continues, production of nonwetting phase decreases (unsteady state) • Important to take many data points during this decrease • cummulative nonwetting phase produced • production rate for both phases
Rel. Perm. - Unsteady State Saturation in Core Plug Production Rates • Imbibition Relative Permeability Ratio Function • Stages 3-6: Inject wetting phase • Stage 6 (D) Eventually, no more nonwetting phase is produced, allowing residual nonwetting phase saturation to be determined
Rel. Perm. - Unsteady State • Analysis Procedure • Assumptions • immiscible displacement • incompressible fluids • linear, 1-D flow • capillary pressure neglected • Determination of average saturation • cumulative nonwetting phase production • Determination of relative permeability ratio from fractional flow • fwet = qwet/qtotal ; where qtotal = qwet + qnonwet • production rate measured at outflow face
Rel. Perm. - Unsteady State • Analysis Procedure • Assumptions • immiscible displacement • incompressible fluids • linear, 1-D flow • capillary pressure neglected • Determination of average saturation • cumulative nonwetting phase production • Determination of relative permeability ratio from fractional flow • fwet = qwet/qtotal ; where qtotal = qwet + qnonwet • production rate measured at outflow face
Rel. Perm. - Unsteady State • Relative Permeability Ratio usually plotted semi-log • hysteresis due to saturation process (drainage, imbibition)