Laboratory Measurementof

Relative Permeability

- Steady State Method

Hysteresis Effect on Rel. Perm.

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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?

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

• 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

Rel. Perm. - Steady State• Purpose: determination of

– two phase relative permeability functions

– irreducible wetting phase saturation (drainage)

– residual non-wetting phase saturation (imbibition)

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

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

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

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

STEADY-STATE RELATIVE PERMEABILITY TEST EQUIPMENT

(HASSLER METHOD)

Oil inlet

Oil burette

Toatmosphere

Po

Gasoutlet

Gasinlet

Pg Pc

Core

Porcelainplate

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

HAFFORD’S METHOD FOR MEASURING STEADY-STATE RELATIVE

PERMEABILITY

Oil pressure padOil

Gas

Gaspressuregauge

Gas meter

Oil burette

Oilpressure

Porous end plate

DISPERSED FEED METHOD FOR MEASURING STEADY-STATE RELATIVE

PERMEABILITY

Lucite-mountedcore

Gas-pressuregauge Gas

Corematerial

Gas meter

Lucite

OilOil burette

Dispersingsection

Dispersingsection face