Laboratory Measurement of Relative Permeability - Capillary End Effect -Unsteady State Method

1. Laboratory MeasurementofRelative Permeability- Capillary End Effect-Unsteady State Method

2. Capillary End Effect • During immiscible displacement • In the bulk of the core plug • Pc= f (Swet) • At the outflow face • Pc= 0  Swet=1 • There must be a gradient of saturation from the the bulk of the core to the outflow face • This saturation gradient is the “Capillary End Effect”

3. Capillary End Effect • Comparison for low flow rate • Theoretical gradient (dashed line) • Experimental data (circles) • Saturation gradient extends over half of the length of the core plug

4. Capillary End Effect • Comparison for higher flow rate • Theoretical gradient (dashed line) • Experimental data (circles) • At higher flow rate, saturation gradient extends over only 1/5 of the length of the core plug

5. Capillary End Effect • Eliminating errors due to end effect in measurement of relative permeability functions • Measure saturation far enough away from outflow face (e.g. Penn State Method) • Use high flow rates to make error in measured saturation negligible

6. 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)

7. 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

8. 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

9. 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

10. 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

11. 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

12. Rel. Perm. - Unsteady State • Relative Permeability Ratio usually plotted semi-log • hysteresis due to saturation process (drainage, imbibition)