laboratory measurement of relative permeability - steady state method
TRANSCRIPT
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Laboratory Measurementof
Relative Permeability
- Steady State Method
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Hysteresis Effect on Rel. Perm.
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0 20 40 60 80 100
DrainageImbibitionkrnw
Wetting Phase Saturation, %PV
Rel
ativ
e P
erm
eab
ilit
y, %
Residual non-wettingphase saturation
Irreducible wetting phase saturation
Non-wetting phase
Wetting phase
krnw krw
What is kbase for this case?
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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
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• Oil
• Water
• Gas
L
Akq
o
ooo
L
Akq
w
www
L
Akq
g
ggg
Review: Effective PermeabilitySteady state, 1D, linear flow equation (Darcy units):
qn = volumetric flow rate for a specific phase, n
A = flow area
n = flow potential drop for phase, n (including pressure, gravity and capillary pressure terms)
n = fluid viscosity for phase n
L = flow length
Modified from NExT, 1999; Amyx, Bass, and Whiting, 1960; PETE 311 NOTES
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Rel. Perm. - Steady State• Purpose: determination of
– two phase relative permeability functions
– irreducible wetting phase saturation (drainage)
– residual non-wetting phase saturation (imbibition)
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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
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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
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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 ratio, qw/qnw
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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 wetting phase pressure drop
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STEADY-STATE RELATIVE PERMEABILITY TEST EQUIPMENT
(HASSLER METHOD)
Oil inlet
Oil burette
Toatmosphere
Po
Gasoutlet
Gasinlet
Pg Pc
Core
Porcelainplate
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PENN STATE METHOD FOR MEASURING STEADY-STATE RELATIVE
PERMEABILITY
x x x xx x x xx x x xx x x xx x x xx x x x
Differentialpressure taps
PackingnutThermometer
sectionEnd
Bronzescreen
sectionTest
sectionMixing
InletOutlet Highly permeabledisk
InletCopperorificeplate
Electrodes
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HAFFORD’S METHOD FOR MEASURING STEADY-STATE RELATIVE
PERMEABILITY
Oil pressure padOil
Gas
Gaspressuregauge
Gas meter
Oil burette
Oilpressure
Porous end plate
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DISPERSED FEED METHOD FOR MEASURING STEADY-STATE RELATIVE
PERMEABILITY
Lucite-mountedcore
Gas-pressuregauge Gas
Corematerial
Gas meter
Lucite
OilOil burette
Dispersingsection
Dispersingsection face