1. Laboratory Measurement of Relative Permeability
Effective and Relative Permeabilities 1
Laboratory Measurement of Relative Permeability

2. Hysteresis Effect on Rel. Perm.
Effective and Relative Permeabilities 2
Hysteresis Effect on Rel. Perm.
Non-wetting phase
Wetting phase
Imbibition
krnw
krnw
krw
Drainage
Relative Permeability, %
Process begins with rock completely saturated with wetting phase, i.e., Swp = 100%
The wetting phase is displaced with the non-wetting phase (i.e., drainage process) until wetting phase ceases to flow.
At this point, the wetting phase saturation equals the minimum interstitial wetting phase saturation.
Then, the non-wetting phase is displaced with the wetting phase, (i.e., imbibition process) until the non-wetting phase ceases to flow.
At this point, the non-wetting phase saturation equals the equilibrium or residual non-wetting phase saturation.
The term “hysteresis” describes the process in which the relative permeabilities are different when measurements are made in different directions.
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. Effective and Relative Permeabilities 4
Review: Effective Permeability
Effective and Relative Permeabilities 4
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. STEADY-STATE RELATIVE PERMEABILITY TEST EQUIPMENT (HASSLER METHOD)
Effective and Relative Permeabilities 14
STEADY-STATE RELATIVE PERMEABILITY TEST EQUIPMENT (HASSLER METHOD)
Oil inlet
Oil burette To
atmosphere
Po
Gas
outlet
inlet
Pg Pc
Core
Porcelain
plate

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

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

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

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