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 (-)

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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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Swir = 0.20 Sro = 0.25

Page 9

Curves - 1

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Swir = 0.20 Sro = 0.25

Page 10

Curves - 2

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Swir = 0.20 Sro = 0.25

Page 11

Curves - 3

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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 Darcys Law

capillary forces low flood rates

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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

.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

.=

o

w

rw

row

kkf

.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

.1

1

+=

2owa f

dWdS =

2

2

)1(

)1(

ro

or

kf

Wd

WId

=it

tr p

pI==

= 0 Injectivity Ratio

Waterflood 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

(LVw > 1)Hence composite samples

or high rates

Page 21

Capillary End Effects

Page 22

Rapaport and Leas Scaling Coefficient LVw > 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 SSS

SSS == 1

11

rowi

wiwwn SS

SSS =

1

Normalisation

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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)

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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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Gas Saturation (fractional)

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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

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1

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Gas Saturation (-)

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

Sgc = 0.03

Typical Lab Data - krg

0.00001

0.0001

0.001

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1

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Swi+Sg (fraction)

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g 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

S

w

i

(

%

)

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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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

=

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)

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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o/w = 30:1Unstable flood front

Early BT

Prolonged 2 phase flow

Oil recovery lower o/w = 3:1Stable 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

Summary100% Oil: ko at SwirrRatio 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

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50

60

70O

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)

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 (g

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)

G

a

s

S

a

t

u

r

a

t

i

o

n

(

%

)

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

k

r

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 krwExtracted 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


o/w = 3:1

Relative Permeability Curves

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WW kroWW krw

Page 67


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WW kroWW krwIW kroIW krw

Page 68


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WW kroWW krwIW kroIW krwOW kroOW krw

Page 69

Fractional Flow Curves

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WW fw

Water WetSOR = 0.33

Recovery = 0.59

Page 70


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WW fwIW fw

IWSOR = 0.44

Recovery = 0.482

Page 71


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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

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 %Sw0 %

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

vLend o Nc

v w= 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--77120120 3.6 x 3.6 x 1010--66360360 1.1 x 1.1 x 1010--55400400 1.2 x 1.2 x 1010--55ReservoirReservoir 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

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0.5

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1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


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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

U

S

B

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 cant 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

-

r

a

y

a

d

s

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r

p

t

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n

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

(thiefzones 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)

D

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(

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0,0

1,0

2,0

3,0

4,0

5,0

6,0

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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

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Page 99

Simulation Example JBN Curves

Page 100

Relative Permeabilty CurvesPre-Simulation

0

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Water saturation

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KrwKrolow rate end pointhigh rate end point

Simulation Example Simulated Curves

Page 101

Relative Permeabilty CurvesPost Simulation

0

0.1

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0.5

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1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Water saturation

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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

K

r KroKrw

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

K

r

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)

K

r

o

Sor = 0.40Sor = 0.20Sor = 0.35

Refine krwRefined 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

K

r

w

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

N

o

'

&

N

w

'

NoNw

Page 107

Refine Measured Data

Endpoints

Refined krw and Sro

Corey Exponents

No and Nw (stable)

Corey Curves

0.0

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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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

=1

endro

ronro k

kk =endrg

rgrgn k

kk =

Example - kro Normalisation

0

0.1

0.2

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0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


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Sample 1Sample 2Swirr

Swn = 0

Sw = 1-SroSwn = 1

Page 110

Example - krw Normalisation

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Sample 1Sample 2

krw at Srokrwn = 1

Page 111

Normalise and Compare Data - kron

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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 (-)

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123456789101112131415

Different Rock Types ?Different Wettabilities?

Steady State

Page 112

Normalise and Compare Data - krwn

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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 (-)

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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

Swikro (@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 PermeabilitySynopsisApplicationsDefinitionsRequirementsJargon Buster!Why shape is importantEndpointsEndpointsCurves - 1Curves - 2Curves - 3Relative PermeabilityRelative Permeability Curves Key FeaturesWaterflood InterpretationRelative Permeability InterpretationJBN Method OutlineBuckley Leverett AssumptionsCapillary End EffectEnd EffectScaling CoefficientCapillary End EffectsComposite Core PlugCorey Exponents Water/Oil SystemsNormalisationCorey ExponentsGas-Oil Relative PermeabilityTypical Gas-Oil Curves: LinearTypical Gas-Oil Curves: Semi-LogGas-Oil CurvesGas-Oil Curves Corey MethodCorey Gas-Oil CurvesTypical Lab Data - krgLaboratory MethodsTest StatesTest StateIrreducible Water Saturation (Swir)Lab Variation in Swir (SPE28826)Centrifuge TestsDynamic Displacement TestsUnsteady-State WaterfloodUnsteady-State Relative PermeabilityUnsteady-State ProceduresUnsteady-StateEffect of Adverse Viscosity RatioUnsteady-State TestsSteady-State TestsSteady-State Test EquipmentSteady-State ProceduresSteady-State versus Unsteady-StateLaboratory TestsOil RecoveryGas-Oil and Gas-Water Relative PermeabilityDrainage Gas-Water Curves (steady-state)Water-Gas Relative PermeabilityImbibition TestsCCI: Experimental DataTrapped or Residual Gas SaturationImbibition Kw-KgRelative Permeability ControlsWettabilityWettabilityWettabilityEffects of WettabilityWettability Effects: Brent FieldImportance of Wettability - ExampleRelative Permeability CurvesRelative Permeability CurvesRelative Permeability CurvesFractional Flow CurvesFractional Flow CurvesFractional Flow CurvesCosts of Wettability UncertaintyRock TextureViscosity RatioSaturation HistoryFlow RateFlow ParametersBump FloodFlow Rate ConsiderationsFlow Rate ConsiderationsFlow Rate ConsiderationsJBN ValidityTest RecommendationsWettability RestorationKey Steps in Test DesignKey Steps In Test DesignUse of NISMX-Ray ScannerNISM Flood ScansNISM Flood ScansNISM Flood ScansNISM Flood ScansNISM Flood ScansNISM Flood ScansKey Steps in Test DesignSimulation Data InputHistory MatchingHistory MatchingSimulation Example JBN CurvesSimulation Example Simulated CurvesQuality ControlWater-Oil Relative Permeability RefiningCurve ShapesSro DeterminationRefine krwDetermine Best Fit CoreysRefine Measured DataNormalisation EquationsExample - kro NormalisationExample - krw NormalisationNormalise and Compare Data - kronNormalise and Compare Data - krwnDenormalisationDenormalisation EquationsSummary Getting the Best Rel Perms

module 8 relative permeability

Documents

measure water permeability

gasoil relative permeability

brine permeability

water brine

swir swir

water volume sro

swir endpoint ko

g velocity of water