Module 8 Relative Permeability

Module 8:Relative Permeability

Synopsis

Page 2

• What is water-oil relative permeability and why does it matter?– endpoints and curves, fractional flow, what curve shapes mean

• Understand the jargon (and impress reservoir engineers)

• Wettability– water-wet, oil-wet and intermediate

• How do we measure it (in the lab)?

• How do we quality control and refine data?

Applications

Page 3

• To predict movement of fluid in the reservoir– e.g velocity of water and oil fronts

• To predict and bound ultimate recovery factor

• Application depends on reservoir type– gas-oil

– water-oil

– gas-water

Definitions

Page 4

• Absolute Permeability– permeability at 100% saturation of single fluid

• e.g. brine permeability, gas permeability

• Effective Permeability– permeability to one phase when 2 or more phases present

• e.g. ko(eff) at Swi

• Relative Permeability– ratio of effective permeability to a base (often absolute)

permeability• e.g. ko/ka or ko/ko at Swi

Requirements

Page 5

• Gas-Oil Relative Permeability (kg-ko)– solution gas drive

– gas cap drive

• Water-Oil Relative Permeability(kw-ko)– water injection

• Water - Gas Relative Permeability (kw-kg)– aquifer influx into gas reservoir

• Gas-Water Relative Permeability (kg-kw)– gas storage (gas re-injection into gas reservoir)

Jargon Buster!

Page 6

• Relative permeability curves are known as rel perms

• Endpoints are the (4) points at the ends of the curves

• The displacing phase is always first, i.e.:– kw-ko is water(w) displacing oil (o)

– kg-ko is gas (g) displacing oil (o)

– kg-kw is gas displacing water

Why shape is important

Page 7

• Measure air permeability ka = 100 mD

• Saturate core in water (brine)

• Desaturate to Swir Swir = 0.20 (20%– Centrifuge or porous plate

– Measure oil permeability ko @ Swir – endpoint• Ko = 80 mD

– Waterflood – collect water volume Sro = 0.25• Swr = 1-0.25 = 0.75

– Measure water permeability kw @Sro – endpoint• Kw = 24 mD

So = 1-Swir

Swirr

Oil = Sro

Sw = 1-Sro

Endpoints

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Water Saturation (-)

Rel

ativ

e Pe

rmea

bilit

y (-)

Swir = 0.20 Sro = 0.25

Endpoint- oil

kro’ = ko/ko @ Swir

= 80/80

= 1

Endpoint - water

krw’ = kw/ko @ Swir

= 24/80

= 0.30

Page 8

Endpoints

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Rel

ativ

e Pe

rmea

bilit

y (-)

Swir = 0.20 Sro = 0.25

Page 9

Curves - 1

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Rel

ativ

e Pe

rmea

bilit

y (-)

Swir = 0.20 Sro = 0.25

Page 10

Curves - 2

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Rel

ativ

e Pe

rmea

bilit

y (-)

Swir = 0.20 Sro = 0.25

Page 11

Curves - 3

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Rel

ativ

e Pe

rmea

bilit

y (-)

Swir = 0.20 Sro = 0.25

Page 12

Relative Permeability

• Non-linear function of Swet

• Competing forces– gravity forces

• minimised in lab tests

• e.g. water injected from bottom to top

– viscous forces• Darcy’s Law

– capillary forces• low flood rates

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Rel

ativ

e Pe

rmea

bilit

y (-)

krokrw

Page 13

Relative Permeability Curves – Key Features

Page 14

• Water-Oil Curves– irreducible water saturation (Swir) endpoint

• kro = 1.0 krw = 0.0

– residual oil saturation (Sro) endpoint• kro = 0.0 krw = maximum

– relative permeability curve shape• Unsteady-state Buckley-Leverett, Welge, JBN

• Steady-state Darcy

• Corey exponents: No and Nw

Waterflood Interpretation

• Welge

Page 15

Average Saturationbehind flood front

Sw at BT

o

w

rw

row

kkf

µµ.1

1

+=

fw only after BT

1-SorSwc

fw=1

Sw

Sw

S fwf w Swf, |

fw

Relative Permeability Interpretation

Page 16

• Welge/Buckley-Leverett fraction flow– gives ratio: kro/krw

• Decouple kro and krw from kro/krw– JBN, Jones and Roszelle, etc

w

o

ro

rw

kkM

µµ.=

o

w

rw

row

kkf

µµ.1

1

+=

M< 1: piston-like

M > 1: unstable

JBN Method Outline

Page 17

• Johnson, Bossler, Nauman (JBN)– Based on Buckley-Leverett/Welge

– W = PV water injected

– Swa = average (plug) Sw

– fw2 = 1-fo2

o

w

rw

row

kkf

µµ.1

1

+=

2owa f

dWdS

=

2

2

)1(

)1(

ro

or

kf

Wd

WId

=

it

tr p

pI=

=

∆∆

= 0 Injectivity RatioWaterflood rate, q

Buckley Leverett Assumptions

Page 18

• Fluids are immiscible

• Fluids are incompressible

• Flow is linear (1 Dimensional)

• Flow is uni-directional

• Porous medium is homogeneous

• Capillary effects are negligible

• Most are not met in most core floods

Capillary End Effect

Page 19

• If viscous force large (high rate)– Pc effects negligible

• If viscous force small (low rate)– Pc effects dominate flood behaviour

• Leverett– capillary boundary effects on short cores

– boundary effects negligible in reservoir

End Effect

• Pressure Trace for Flood– zero ∆p (no injection)– start of injection– water nears exit

• ∆p increases abruptly until Sw(exit) = 1-Sro and Pc nears zero

• suppresses krw– BT

• Sw(exit) = 1-Sro, Pc ~0– After BT

• rate of ∆p increase reduces as krw increases

Page 20

Scaling Coefficient

Breakthrough Recovery

(Rappaport & Leas)

Affected by Pc end effects

At lengths > 25 cm

Little effect on BT recovery

(LVµw > 1)

Hence composite samples

or high rates

Page 21

Capillary End Effects

Page 22

• Rapaport and Leas Scaling Coefficient– LVµw > 1(cm2/min.cp) : minimal end effect

• Overcome by:– flooding at high rate

• 300 ml/hour +

– using longer cores• difficult for reservoir core (limited by core geometry)• “butt” several cores together

– using capillary mixing sections• end-point saturations only in USS tests (weigh sample)

Composite Core Plug

Capillary end effects adsorbed by Cores 1 and 4

Page 23

Corey Exponents – Water/Oil Systems

• Define relative permeability curve shapes

• Based on normalised saturations

• No guarantee that real rock curves obey Corey

Page 24

kro = SonNo krw = krw’(Swn)Nw

krw’ = end-point krw

wnrowi

rowon S

SSSSS −=

−−−−

= 111

rowi

wiwwn SS

SSS−−

−=

1

Normalisation

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Wat

er R

elat

ive

Perm

eabi

lity

(-)

Sample 1Sample 2

krw at Srokrwn = 1

Swn = 1

krwn = 1

Page 25

Corey Exponents

• Depend on wettability

Uses:– interpolate & extrapolate data

– lab data quality control

Wettability No (kro) Nw (krw)

Water-Wet 2 to 4 5 to 8

Intermediate Wet 3 to 6 3 to 5

Oil-Wet 6 to 8 2 to 3

Page 26

Gas-Oil Relative Permeability

• Test performed at Swir

• Gas is non wetting– takes easiest flow path– kro drops rapidly as Sg

increases– krg higher than krw– Srog > Srow in lab tests

• end effects

– Srog < Srow in field

• Sgc ~ 2% - 6%

Pore-Scale Saturation Distribution

Page 27

Typical Gas-Oil Curves: Linear

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Gas Saturation (fractional)

Rel

ativ

e Pe

rmea

bilit

y (-)

krokrg

1-(Srog+Swi)

Sgc

Labs plot kr vs liquid saturation (So+Swi)Page 28

Typical Gas-Oil Curves: Semi-Log

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0.01

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1

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Gas Saturation (fractional)

Rel

ativ

e Pe

rmea

bilit

y (-)

krokrg

1-(Srog+Swi)

Page 29

Gas-Oil Curves

Page 30

• Most lab data are artefacts– due to capillary end effects

• Tests should be carried out on long cores

– insufficient flood period

• Real gas-oil curves– Sgc ~ 3%

– Srog is low and approaches zero• Due to thin film and gravity drainage

– krg = 1 at Srog = 0

– well defined Corey exponents

Gas-Oil Curves – Corey Method

NoSonkro =

Page 31

• Oil relative permeability– normalised oil saturation

• Gas relative permeability– normalised gas saturation

• Sgc: critical gas saturation

SrogSwirSrogSwirSgSon

−−−−−

=1

1

SgcSrogSwirSgcSgSgn

−−−−

=1

NgSgnkrg =

Corey Exponent Values

No 4 to 7

Ng 1.3 to 3.0

Corey Gas-Oil Curves

Page 32

Swir 0.15kro 1.00krg' 1.00Srog 0.0000Sgc 0.0300

0.00001

0.0001

0.001

0.01

0.1

1

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Gas Saturation (-)

Rel

ativ

e Pe

rmea

bilit

y (-)

Kro No = 4krg Ng = 1.3kro No = 7krg Ng = 3.0

Sgc = 0.03

Typical Lab Data - krg

0.00001

0.0001

0.001

0.01

0.1

1

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Swi+Sg (fraction)

Rel

ativ

e Pe

rmea

bilit

y, k

rg Ng = 2.3; Swir = 0.15Ng = 2.3; Swir = 0.2011a-5 # 411a-5 # 3111a-5 # 3411a-5 #3911a-7 BEA511a-7 BEA711a-7 BEB511a-7 BEC5

Composite Gas-Oil Curves

Ng : 2.3No : 4.0Sgc: 0.03Srog: 0.10krg' : 1.0

Krg too low

Srog too high

Page 33

Laboratory Methods

Page 34

• Core Selection– all significant reservoir flow units

– often constrained by preserved core availability

– core CT scanning to select plugs

• Core Size– at least 25 cm long to overcome end effects

– butt samples (but several end effects?)

– flood at high rate to overcome end effects?

Test States

Page 35

• “Fresh” or “Preserved” State– tested “as is” (no cleaning)– probably too oil wet (e.g OBM, long term storage)– “Native” state term also used (defines “bland” mud)– Some labs’ “fresh state” is other labs’ “restored state”

• “Cleaned” State– Cleaned (soxhlet or miscible flush)– water-wet by definition (but could be oil-wet!!!!!!)

• “Restored” State (reservoir-appropriate wettability)– saturate in crude oil (live or dead)– age in oil at P & T to restore native wettability

Test State

Page 36

• Fresh-State Tests– too oil wet data unreliable

• Cleaned-State Tests– too water wet (or oil-wet) data unreliable

• Restored-State Tests– native wettability restored data reliable (?)– if GOR low can use dead crude ageing (cheaper)– if GOR high must use live crude ageing (expensive)– if wettability restored - use synthetic fluids at ambient– ensure cores water-wet prior to restoration

• Compare methods - are there differences?

Irreducible Water Saturation (Swir)

Page 37

• Swir essential for reliable waterflood data

• Dynamic displacement– flood with viscous oil then test oil

– rapid and can get primary drainage rel perms

– Swir too high and can be non-uniform

• Centrifuge– faster than others

– Swir can be non-uniform

• Porous Plate– slow, grain loss, loss of capillary contact

– Swir uniform

Lab Variation in Swir (SPE28826)

Page 38

Lab A Lab B Lab C Lab D0

5

10

15

20

25

30

Swi (

%)

Dynamic Displacement

Porous Plate

???

180 psi

200 psi

Centrifuge Tests

Page 39

• Displaced phase relative permeability only– oil-displacing-brine : krw drainage– brine-displacing-oil : kro imbibition– assume no hysteresis for krw imbibition

• oil-wet or neutral wet rocks?• Good for low kro data (near Sro)

– e.g. for gravity drainage• Computer simulation used• Problems

– uncontrolled imbibition at Swirr– mobilisation of trapped oil– sample fracturing

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Water Saturation (-)R

elat

ive

Perm

eabi

lity

(-)

Dynamic Displacement Tests

Page 40

• Test Methods– Waterflood (End-Points: ko at Swi, kw at Srow)

– Unsteady-State (relative permeability curves)

– Steady-State (relative permeability curves)

• Test Conditions– fresh state

– cleaned state

– restored state

– ambient or reservoir conditions

Unsteady-State Waterflood

Page 41

• Saturate in brine

• Desaturate to Swirr

• Oil permeability at Swirr (Darcy analysis)

• Waterflood (matched viscosity)

• Total Oil Recovery

• kw at Srow (Darcy analysis)

labw

o

resw

o⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛µµ

µµ

Unsteady-State Relative Permeability

• Saturate in brine• Desaturate to Swirr• Oil permeability at Swirr (Darcy analysis)• Waterflood (adverse viscosity)

• Incremental oil recovery measured• kw at Srow (Darcy analysis)• Relative permeability (JBN Analysis)

µµ

µµ

o

w lab

o

w res

⎛⎝⎜

⎞⎠⎟ >>

⎛⎝⎜

⎞⎠⎟

Page 42

Unsteady-State Procedures

Page 43

Water OilOnly oil produced

Measure oil volume

Just After Breakthrough

Measure oil + water volumes

Increasing Water Collected

Continue until 99.x% water

Unsteady-State

• Rel perm calculations require– fractional flow data at core outlet (JBN)– pressure data versus water injected

• Labs use high oil/water viscosity ratio– promote viscous fingering– provide fractional flow data after BT– allow calculation of rel perms

• Waterflood (matched viscosity ratio)– little or no oil after BT– little or no fractional flow (no rel perms)– end points only

Page 44

Effect of Adverse Viscosity Ratio

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Frac

tiona

l Flo

w, f

w

µo/µw = 30:1

Unstable flood front

Early BT

Prolonged 2 phase flow

Oil recovery lower µo/µw = 3:1

Stable flood front

BT delayed

Suppressed 2 phase flow

Oil recovery higher

Page 45

Unsteady-State Tests

Page 46

• Only post BT data are used for rel perm calculations– Sw range restricted if matched viscosities

• Advantages– appropriate Buckley-Leverett “shock-front”

– reservoir flow rates possible

– fast and low throughput (fines)

• Disadvantages– inlet and outlet boundary effects at lower rates

– complex interpretation

Steady-State Tests

Page 47

• Intermediate relative permeability curves– Saturate in brine

– Desaturate to Swir

– Oil permeability at Swir (Darcy analysis)

– Inject oil and water simultaneously in steps

– Determine So and Sw at steady state conditions

– kw at Srow (Darcy analysis)

– Relative Permeability (Darcy Analysis)

Steady-State Test Equipment

Oil and water out

∆p

Coreholder

Oil in

Water in

Mixing Sections

Page 48

Steady-State Procedures

Page 49

Summary

100% Oil: ko at Swirr

Ratio 1: ko & kw at Sw(1)

Ratio 2:: ko & kw at Sw(2)

….

….

Ratio n: ko & kw at Sw(n)

100% Water: kw at Sro

Steady-State versus Unsteady-State

Page 50

• Constant rate (SS) vs constant pressure (USS)– fluids usually re-circulated

• Generally high flood rates (SS)– end effects minimised, possible fines damage

• Easier analysis– Darcy vs JBN

• Slower– days versus hours

• Endpoints may not be representative• Saturation Measurement

– gravimetric (volumetric often not reliable)– NISM

Laboratory Tests

Page 51

• You can choose from:– matched or high oil-water viscosity ratio

– cleaned state, fresh state, restored-state tests

– ambient or reservoir condition

– high rate or low rate

– USS versus SS

• Laboratory variation expected– McPhee and Arthur (SPE 28826)

– Compared 4 labs using identical test methods

Oil Recovery

Lab A Lab B Lab C Lab D10

20

30

40

50

60

70O

il R

ecov

ery

(% O

IIP)

Fixed - 120 ml/hour

Preferred

120

Bump

360

120

Page 52

Gas-Oil and Gas-Water Relative Permeability

Page 53

• Unsteady-State – adverse mobility ratio (µg<<µo or µw)

– prolonged two phase flow data after breakthrough

– drainage tests reliable

– imbibition tests difficult

• Steady-State– kg-ko, kg-kw and kw-kg

– saturation determination difficult

– much slower

• Gas humidified to prevent mass transfer

Drainage Gas-Water Curves (steady-state)

• Steady-state test example

• Log-linear scale (very low krw)

• Krg’ > krw’

• Gas saturation increases

• Krg increases to 1

• Krw reduces to close to zero

Page 54

Water-Gas Relative Permeability

Page 55

• Aquifer influx (imbibition)

• Drainage gas-water curves can be used but – hysteresis expected for non-wetting phase (krg) curve

– no hysteresis for wetting phase (krw) curve• drainage krw curve same shape as imbibition krw curve

• Imbibition tests require– low rate imbibition waterflood kw-kg test

• capillary forces dominate

– CCI tests for residual gas saturation

– Hybrid test

Imbibition Tests

Page 56

• Waterflood– low rate waterflood from Swi to Sgr

– obtain krg and krw on imbibition

– Sgr too low (viscous force dominates)

• Counter-Current Imbibition Test– Sgr dominated by capillary forces– immerse sample in wetting phase (from Sgi)– monitor sample weight during imbibition– Determine Sgr from crossplot

129.90 g129.90 g

CCI: Experimental Data

Air-Toluene CCI: Plug 10706: Sgi = 88.8%

Square Root Time (secs)

Gas

Sat

urat

ion

(%)

30

35

40

45

50

55

60

65

70

0 10 20 30 40 50 60

Sgr = 33.5%

Page 57

Trapped or Residual Gas Saturation

Page 58

Sgr vs Sgi – North Sea

Low rate waterflood

Repeatability of CCI tests

Imbibition Kw-Kg

Drainage

Imbibition

Swi

krw

Sw

kr

0 1

1

0

krg

1-Sgr

krw@Sgr

Page 59

Relative Permeability Controls

Page 60

• Wettability

• Saturation History

• Rock Texture (pore size)

• Viscosity Ratio

• Flow Rate

Wettability

Page 61

Wettability

Page 62

Wettability

Page 63

• Waterflood of Water-Wet Rock– front moves at uniform rate– oil displaced into larger pores and produced– water moves along pore walls– oil trapped at centre of large pores - “snap-off”– BT delayed– oil production essentially complete at BT

• Waterflood of Oil-Wet Rock– water invades smaller pores– earlier BT– oil remains continuous– oil produced at low rate after BT– krw higher - fewer water channels blocked by oil

Effects of Wettability

Page 64

• Water-Wet– better kro– lower krw– krw = kro > 50%– better flood performance

• Oil-Wet– poorer kro– higher krw– kro = krw < 50%– poorer flood performance

Wettability Effects: Brent Field

Preserved Core

Neutral to oil-wet

low kro - high krw

Extracted Core

Water wet

high kro - low krw

Page 65

Importance of Wettability - Example

Page 66

• Water Wet– No = 2 Nw = 8 Swir = 0.20

– Sro = 0.30, krw’ = 0.25, ultimate recovery = 0.625 OIIP

• Intermediate Wet– No = 4 Nw = 4 Swir = 0.15


• Oil Wet– No = 8 Nw = 2 Swir = 0.10


µo/µw = 3:1

Relative Permeability Curves

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Rel

ativ

e Pe

rmea

bilit

y (-)

WW kroWW krw

Page 67


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Rel

ativ

e Pe

rmea

bilit

y (-)

WW kroWW krwIW kroIW krw

Page 68


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Rel

ativ

e Pe

rmea

bilit

y (-)

WW kroWW krwIW kroIW krwOW kroOW krw

Page 69

Fractional Flow Curves

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Frac

tiona

l Flo

w, f

w (-

)

WW fw

Water WetSOR = 0.33

Recovery = 0.59

Page 70


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Frac

tiona

l Flo

w, f

w (-

)

WW fwIW fw

IWSOR = 0.44

Recovery = 0.482

Page 71


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Frac

tiona

l Flo

w, f

w (-

)

WW fwIW fwOW fw

Oil WetSOR = 0.63

Recovery = 0.300

Page 72

Costs of Wettability UncertaintyPV 120 MMbblsOil Price 30 US$/bbls

Parameter Water-Wet IW Oil wetSwi 0.200 0.150 0.100Ultimate Sro 0.300 0.250 0.200Ultimate Recovery Factor 0.625 0.706 0.778SOR 0.330 0.440 0.630Actual Recovery Factor 0.588 0.482 0.300STOIIP (MMbbls) 96 102 108Ultimate Recovery (bbls) 60 72 84Actual Recovery (bbls) 56 49 32"Loss" (MM US$) 108 684 1548

• It is really, really important to get wettability right!!!

Page 73

Page 74

Rock Texture

Viscosity Ratio

Page 75

krw and kro - no effect ?

End-Points - viscosity dependent

Hence:

use high viscosity ratio for curves

use matched for end-points

Not valid for neutral-wet rocks (?)

Saturation HistoryPrimary Drainage Primary Imbibition100 %

Page 76

0 %

kr

0 % 100 %Sw

0 %

kr

0 % 100 %Sw

Swi Sro

NW

W

No hysteresis in wetting phaseNW

W

Flow Rate

Page 77

• Reservoir Frontal Advance Rate– about 1 ft/day

• Typical Laboratory Rates– about 1500 ft/day for 1.5” core samples

• Why not use reservoir rates ?– slow and time consuming

– capillary end effects

– capillary forces become significant c.f. viscous forces

– Buckley-Leverett (and JBN) invalidated

Flow Parameters

Nck

vLendo

≈σ φµ

Nc v w=µσ

RateRate NNcendcend(ml/h)(ml/h)44 2.32.3120120 0.070.07360360 0.020.02400400 0.020.02ReservoirReservoir 00

RateRate NcNc(ml/h)(ml/h)44 1.2 x101.2 x10--77

120120 3.6 x 3.6 x 1010--66

360360 1.1 x 1.1 x 1010--55

400400 1.2 x 1.2 x 1010--55

ReservoirReservoir 1010--77

For reservoir-appropriate data Nclab ~ NcreservoirIf Ncend > 0.1 kro and krw decrease as Ncend increases

Relative Permeabilities are Rate-Dependent

End Effect Capillary Number Flood Capillary Number

Page 78

Bump Flood

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


Rel

ativ

e Pe

rmea

bilit

y (-)

Low Rate krw'

Bump Flood krw'

High Rate krw ???

Page 79

Flow Rate Considerations

Page 80

• Imbibition (waterflood of water-wet rock)– Sro function of Soi: Sro is rate dependent– oil production essentially complete at BT– krw suppressed by Pcend and rate dependent– bump flood does not produce much oil but removes Pcend and

krw increases significantly– high rates acceptable but only if rock is homogeneous at pore

level• Considerations

– ensure Swi is representative– low rate floods for Sro: bump for krw– steady-state tests


Page 81

• Drainage (Waterflood of Oil-Wet Rock)– end effects present at low rate– Sro, krw dependent on capillary/viscous force ratio– high rate: significant production after BT– reduced recovery at BT compared with water-wet

• Considerations– high rate floods (minimum Dp = 50 psid) to minimise end effects– steady-state tests with ISSM– low rates with ISSM and simulation


Page 82

• Neutral/Intermediate– Sro and kro & krw are rate dependent

– “bump” flood produces oil from throughout sample, not just from ends

– ISSM necessary to distinguish between end effects and sweep

• Recommendations– data acquired at representative rates

– (e.g. near wellbore, grid block rates)

JBN Validity

Page 83

• High Viscosity Ratio– viscous fingering invalidates 1D flow assumption

• Low Rate– end effects invalidate JBN

• Most USS tests viewed with caution– if Ncend significant

– if Nc not representative

– if JBN method used

• Use coreflood simulation

Test Recommendations

Page 84

• Wettability Conditioning– flood rate selected on basis of wettability

– Amott and USBM tests required

– Wettability pre-study• reservoir wettability?

• fresh-state, cleaned-state, restored-state wettabilities

– beware “fresh-state” tests (often waste of time)

– reservoir condition tests most representative• but expensive and difficult

Wettability Restoration

• Hot soxhlet does not make cores water wet!

• Restored-state cores too oil wet

• Lose 10% OIIP potential recovery

-1.0

0.0

1.0

-1.0 0.0 1.0

Amott

USB

M

Original SCAL plugsHot Sox CleanedFlush Cleaned

STRONGLYWATER-WET

STRONGLYOIL-WET

Page 85

Key Steps in Test Design

Page 86

• Establishing Swi– must be representative

– use capillary desaturation if at all possible• remember many labs can’t do this correctly

– “fresh-state” Swirr is fixed

• Viscosity Ratio– matched viscosity ratio for end-points

– investigate viscosity dependency for rel perms

– normalise then denormalise to matched end-points

Key Steps In Test Design

Page 87

• Flood Rate– depends on wettability

– determine rate-appropriate end-points

– steady-state or Corey exponents for rel perm curves

• Saturation Determination– conventional

• grain loss, flow processes unknown

– NISM• can reveal heterogeneity, end effects, etc

Use of NISM

Page 88

• Examples from North Sea

• Core Laboratories SMAX System– low rate waterflood followed by bump flood

– X-ray scanning along length of core

– end-points

– some plugs scanned during waterflood

• Fresh-State Tests– core drilled with oil-based mud

X-Ray Scanner

Sw(NaI)X

-ray

ads

orpt

ion

0% 100%

X-rays emittedX-rays detectedScanning Bed

Coreholder

(invisible to X-rays)

X-ray Emitter

(Detector Behind)

Page 89

NISM Flood Scans• SMAX Example 1

– uniform Swirr

– oil-wet(?) end effect

– bump flood removes end effect

– some oil removed from body of plug

– neutral-slightly oil-wet

Page 90

NISM Flood Scans

• SMAX Example 2– short sample

– end effect extends through entire sample length

– significant oil produced from body of core on bump flood

– moderate-strongly oil-wet

– data wholly unreliable due to pre-dominant end effect. Need coreflood simulation

Page 91

NISM Flood Scans

• SMAX Example 3– scanned during flood

– minimal end effect

– stable flood front until BT• vertical profile

– bump flood produces oil from body of core

– neutral wet

– data reliable

Page 92

NISM Flood Scans

Page 93

• SMAX Example 4– Sample 175 (fresh-state)

– scanned during waterflood

– unstable flood front• oil wetting effects

– oil-wet end effect

– bump produces incremental oil from body of core but does not remove end effect

– neutral to oil-wet

– data unreliable

NISM Flood Scans

• SMAX Example 5– Sample 175 re-run after

cleaning

– increase in Swirr compared to fresh-state test

– no/minimal end effects

– moderate-strongly water-wet

Page 94

NISM Flood Scans

• SMAX Example 6– heterogeneous coarse sand– variation in Swirr– Sro variation parallels Swirr– end effect masked by

heterogeneity (?)– very low recovery at low rate

(‘thief’zones in plug?)– bump flood produces

significant oil from body of core

– neutral-wet

Page 95

Key Steps in Test Design

Page 96

• Relative Permeability Interpretation– key Buckley-Leverett assumptions invalidated by most short

corefloods

• Interpretation Model must allow for:– capillarity

– viscous instability

– wettability

• Simulation required– e.g. SENDRA, SCORES

Simulation Data Input

Page 97

• Flood data (continuous)– injection rates and volumes

– production rates

– differential pressure

• Fluid properties– viscosity, IFT, density

• Imbibition Pc curve (option)

• ISSM or NISM Scans (option)

• Beware – several non-unique solutions possible

History Matching

• Pressure and production

1.66 cc/min

0 100 200 300 400 500 600 700 800

0,1 1,0 10,0 100,0 1000,0 10000,0Time (min)

Diff

eren

tial P

ress

ure

(kPa

)

0,0

1,0

2,0

3,0

4,0

5,0

6,0

Oil

Prod

uctio

n (c

c)

Measured differential pressureSimulated differential pressureMeasured oil productionSimulated oil production

Page 98

History Matching

• Saturation profiles

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.0 0.2 0.4 0.6 0.8 1.0

Normalized Core Length

Wat

er S

atur

atio

n

Page 99

Simulation Example – JBN Curves

Page 100

Relative Permeabilty CurvesPre-Simulation

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Water saturation

Rel

ativ

e Pe

rmea

bilit

y

KrwKrolow rate end pointhigh rate end point

Simulation Example – Simulated Curves

Page 101

Relative Permeabilty CurvesPost Simulation

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Water saturation

Rel

ativ

e Pe

rmea

bilit

y

KrwKrolow rate end pointhigh rate end pointKrw SimulationKro Simulation

Quality Control

Page 102

• Most abused measurement in core analysis

• Wide and unacceptable laboratory variation

• Quality Control essential– test design– detailed test specifications and milestones– contractor supervision– modify test programme if required

• Benefits– better data– more cost effective

Water-Oil Relative Permeability Refining

Page 103

• Key Steps– curve shapes

– Sro determination and refinement

– refine krw’

– determine Corey exponents

– refine measured curves

– normalise and average

• Uses Corey approach– rock curves may not obey Corey behaviour

Curve Shapes

Page 104

Water-Oil Rel. Perms.

0.0001

0.001

0.01

0.1

1

0 0.2 0.4 0.6 0.8 1

Sw

Kr Kro

Krw

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Sw

Kr

KroKrw

Cartesian

Good data – convex upwards

Semi-log

Good data – concave down

Sro Determination

Page 105

• Compute Son

– high, medium and low Sro

• low rate, bump, centrifuge Sro

• Plot Son vs kro (log-log)

• Sro too low

– curves down

• Sro too high

– curves up

• Sro just right

– straight line

0.0001

0.001

0.01

0.1

1

0.0100.1001.000Son = (1-Sw-Sor)/(1-Swi-Sor)

Kro

Sor = 0.40Sor = 0.20Sor = 0.35

Refine krw’Refined krw’

• Use refined Sro

• Plot krw versus Swn

• Fit line to last few points

– least affected by end effects

• Determine refined krw’

Page 106

0.01

0.1

1

0.1 1

Swn = 1-Son

Krw

Determine Best Fit Coreys

• Use refined Sro and krw’

• Determine instantaneous Coreys

• Plot vs Sw

• Take No and Nw from flat sections

– Least influenced by end effects

)log()0.1log()log()'log(*

wnSkrwkrwNw

−−

=

)log()log(*

onSkroNo =

0

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6 0.8 1

Sw

No'

& N

w'

NoNw

Page 107

Refine Measured Data

• Endpoints

– Refined krw’ and Sro

• Corey Exponents

– No and Nw (stable)

• Corey Curves

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Sw

Rel

ativ

e Pe

rmea

bilit

y

Refined Kro

Refined Krw

Original Kro

Original Krw

Norefined Sonkro =)(

Nwrefined Swnkrwkrw ')( =

Page 108

Normalisation Equations

Page 109

• Water-Oil Data

• Gas - Oil Data

endrw

rwrwn k

kk =endro

ronro k

kk =rowwi

wiwnw SS

SSS−−−

=1

gcrogwi

gcggn SSS

SSS

−−−

−=

1endro

ronro k

kk =

endrg

rgrgn k

kk =

Example - kro Normalisation

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


Oil

Rel

ativ

e Pe

rmea

bilit

y (-)

Sample 1Sample 2Swirr

Swn = 0

Sw = 1-SroSwn = 1

Page 110

Example - krw Normalisation

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


Wat

er R

elat

ive

Perm

eabi

lity

(-)

Sample 1Sample 2

krw at Srokrwn = 1

Page 111

Normalise and Compare Data - kron

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Normalised Water Saturation (-)

Nor

mal

ised

Oil

Rel

ativ

e Pe

rmea

bilit

y (-) 1

23456789101112131415

Different Rock Types ?Different Wettabilities?

Steady State

Page 112

Normalise and Compare Data - krwn

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Normalised Water Saturation (-)

Nor

mal

ised

Wat

er R

elat

ive

Perm

eabi

lity

(-)

1234567891112131415

Page 113

Denormalisation

Page 114

• Group data by zone, HU, lithology etc

• Determine Swir (e.g. logs, saturation-height model)

• Determine ultimate Sro– e.g. from centrifuge core tests

• Determine krw’ at ultimate Sro– e.g. from centrifuge core tests

• Denormalise to these end-points

• Truncate denormalised curves at ROS– depends on location in reservoir

Denormalisation Equations

• Water Oil

• Gas-Oil

Denormalised Endpoints

Water-Oil

•Swi

•kro (@Swi)

•krw (@1-Srow)

From correlations & average data

rwnendrwrwdn

ronendrorodn

wirowiwndnw

kkkkkk

SSSSS

..

)1(

=

=

+−−=

rgnendrgrgdn

ronoendrodn

gcgcrogwigndng

kkkkkk

SSSSSS

..

)1(

==

+−−−=

Page 115

Summary – Getting the Best Rel Perms

Page 116

• Ensure samples are representative of poro-perm distribution

• Ensure Swir representative (e.g. porous plate, centrifuge)

• Ensure representative wettability (restored-state?)

• Use ISSM (at least for a few tests)

• Ensure matched viscosity ratio

• Low rate then bump flood

• Centrifuge – ultimate Sro and maximum krw’– Tail ok kro curve if gravity drainage significant

• Use coreflood simulation or Coreys for intermediate kr

Module 8 Relative Permeability

Documents

relative permeability

fractional

oil relative

relative permeability

water relative

centrifuge

relative permeability

gravity drainage