1. Laboratory MeasurementofRelative Permeability

2. Hysteresis Effect on Rel. Perm. Non-wetting phase Wetting phase Imbibition krnw krnw krw Drainage Relative Permeability, % Irreducible wetting phase saturation Residual non-wetting phase saturation Wetting Phase Saturation, %PV

3. Hysteresis Effect on Rel. Perm. • During drainage, the wetting phase ceases to flow at the irreducible wetting phase saturation • This determines the maximum possible non-wetting phase saturation • Common Examples: • Petroleum accumulation (secondary migration) • Formation of secondary gas cap • During imbibition, the non-wetting phase becomes discontinuous and ceases to flow when the non-wetting phase saturation reaches the residual non-wetting phase saturation • This determines the minimum possible non-wetting phase saturation displacement by the wetting phase • Common Example: waterflooding water wet reservoir

4. Review: Effective Permeability Steady state, 1D, linear flow equation (Darcy units): qn= volumetric flow rate for a specific phase, n A = flow area Fn = flow potential drop for phase, n (including pressure, gravity and capillary pressure terms) n = fluid viscosity for phase n L = flow length • Oil • Water • Gas Modified from NExT, 1999; Amyx, Bass, and Whiting, 1960; PETE 311 NOTES

5. Rel. Perm. - Steady State • Purpose: determination of • two phase relative permeability functions • irreducible wetting phase saturation (drainage) • residual non-wetting phase saturation (imbibition)

6. Rel. Perm. - Steady State • Process (oil/water, water wet case): • simultaneously inject constant rates of oil and water until steady state behavior is observed • production will be constant at same oil and water rates as injection • pressure drop for each phase will be constant • determine saturation of core sample • usually by resistivity or weighing • this is typically not the same as the injection ratio • change injection ratio and repeat

7. Rel. Perm. - Steady State • Imbibition Relative Permeability Functions • Stage 1: Preparation for drainage • core saturated with wetting phase • steady state injection of wetting phase used to determine absolute permeability • Stage 2: Irreducible wetting phase • inject non-wetting phase until steady state, measure saturation • no wetting phase will be produced at steady state

8. Rel. Perm. - Steady State • Imbibition Relative Permeability Functions (continued) • Stage 3 (A-C): determination of points on imbibition relative permeability function • steady state injection at constant rates of wetting and non-wetting phase • Initially ratio qw/qnw is small • measure saturation and phase pressure drops at steady state • saturation ratio will in general, not be the same as injection ratio • repeat with increasing rate ratio, qw/qnw

9. Rel. Perm. - Steady State • Imbibition Relative Permeability Functions (continued) • Stage 4: determination of residual non-wetting phase saturation • inject wetting phase until steady state behavior observed • measure saturation and pressure drop

10. 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”

11. 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

12. 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

13. 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

14. Gas outlet Gas inlet Po Pg Pc Core Oil inlet To atmosphere Porcelain plate Oil burette STEADY-STATE RELATIVE PERMEABILITY TEST EQUIPMENT (HASSLER METHOD)

15. Inlet Packing nut Copper orifice plate Thermometer Electrodes x x x x x x x x x x x x x x x x x x x x x x x x Mixing Test End section section section Differential pressure taps Highly permeable disk Outlet Inlet Bronze screen PENN STATE METHOD FOR MEASURING STEADY-STATE RELATIVE PERMEABILITY

16. Gas Gas pressure gauge Porous end plate Oil pressure Oil pressure pad Gas meter Oil Oil burette HAFFORD’S METHOD FOR MEASURING STEADY-STATE RELATIVE PERMEABILITY

17. Gas-pressure gauge Gas meter Gas Lucite Core material Dispersing section Lucite-mounted core Oil Oil burette Dispersing section face DISPERSED FEED METHOD FOR MEASURING STEADY-STATE RELATIVE PERMEABILITY

18. Saturation by Weighing(Review) • Determine mass of fluid • Solve from Mass Balance mfluid = moil + mwater = Vp(1 - Sw)ro + VpSwrw