Module 8 Relative Permeability

Module 8: Relative Permeability

Synopsis • 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?

Page 2

Applications • 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

Page 3

Definitions • 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 Page 4

Requirements • 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) Page 5

Jargon Buster! • 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

Page 6

Why shape is important • Measure air permeability

ka = 100 mD

• Saturate core in water (brine) • Desaturate to Swir

Swir = 0.20 (20%

Swirr

– Centrifuge or porous plate – Measure oil permeability ko @ Swir – endpoint • Ko = 80 mD

– Waterflood – collect water volume

Sro = 0.25

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

Oil = Sro Sw = 1-Sro

• Swr = 1-0.25 = 0.75

Page 7

So = 1-Swir

Endpoints

Relative Permeability (-)

1.0 0.9

Endpoint- oil

0.8

kro’ = ko/ko @ Swir

0.7

= 80/80

0.6

=1 Swir = 0.20

Sro = 0.25

0.5 0.4

Endpoint - water

0.3

krw’ = kw/ko @ Swir

0.2

= 24/80 0.1

= 0.30 0.0 0.0

0.1

0.2

0.3

0.4

0.5 Water Saturation (-)

Page 8

0.6

0.7

0.8

0.9

1.0

Endpoints 1.0 0.9

Relative Permeability (-)

0.8 0.7 0.6

Swir = 0.20

Sro = 0.25

0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5 Water Saturation (-)

Page 9

0.6

0.7

0.8

0.9

1.0

Curves - 1 1.0 0.9

Relative Permeability (-)

0.8 0.7 0.6

Swir = 0.20

Sro = 0.25

0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5 Water Saturation (-)

Page 10

0.6

0.7

0.8

0.9

1.0

Curves - 2 1.0 0.9

Relative Permeability (-)

0.8 0.7 0.6

Swir = 0.20

Sro = 0.25

0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5 Water Saturation (-)

Page 11

0.6

0.7

0.8

0.9

1.0

Curves - 3 1.0 0.9

Relative Permeability (-)

0.8 0.7 0.6

Swir = 0.20

Sro = 0.25

0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5 Water Saturation (-)

Page 12

0.6

0.7

0.8

0.9

1.0

Relative Permeability 1

• Non-linear function of Swet

0.9

• Competing forces

0.8

0.7

• minimised in lab tests • e.g. water injected from bottom to top

– viscous forces • Darcy’s Law

Relative Permeability (-)

– gravity forces

0.6

kro

0.5

krw

0.4

0.3

0.2

0.1

– capillary forces

0 0

• low flood rates Page 13

0.2

0.4

0.6

Water Saturation (-)

0.8

1

Relative Permeability Curves – Key Features • 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

Page 14

• Unsteady-state

Buckley-Leverett, Welge, JBN

• Steady-state

Darcy

• Corey exponents:

No and Nw

Waterflood Interpretation

S

fw=1

• Welge

w

fw only after BT Average Saturation behind flood front

Swf , fw | S

wf

fw Sw at BT

fw =

Page 15

1

1 +

k ro µ . k rw µ

w o

Swc

Sw

1-Sor

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

fw =

1

k ro µ 1 + . k rw µ

k rw µo . M= k ro µ w

w o

M< 1: piston-like M > 1: unstable

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

Page 16

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

fw =

1

k ro µ w 1+ . k rw µ o

– W = PV water injected – Swa = average (plug) Sw – fw2 = 1-fo2

∆ pt =0 Ir = ∆ pt =i Page 17

dS wa = fo2 dW 1 ) f WI r = o2 1 k ro 2 d( ) W

d(

Injectivity Ratio Waterflood rate, q

Buckley Leverett Assumptions • 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

Page 18

Capillary End Effect • 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

Page 19

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 • Page 20

rate of ∆p increase reduces as krw increases

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 • 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) Page 22

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 krw = krw’(Swn)Nw

kro = SonNo

krw’ = end-point krw

1 − S w − Sro Son = = 1 − S wn 1 − S wi − Sro

S wn Page 24

S w − S wi = 1 − S wi − S ro

Normalisation Swn = 1 1 0.9

Water Relative Permeability (-)

0.8 0.7 krw at Sro krwn = 1

0.6

Sample 1

0.5

Sample 2

0.4 0.3

krwn = 1

0.2 0.1 0 0

0.1

0.2

0.3

0.4

0.5 Water Saturation (-)

Page 25

0.6

0.7

0.8

0.9

1

Corey Exponents • Depend on wettability 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

Uses: – interpolate & extrapolate data – lab data quality control Page 26

Gas-Oil Relative Permeability Pore-Scale Saturation Distribution

•

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 Page 27

• Sgc ~ 2% - 6%

Typical Gas-Oil Curves: Linear 1.0 0.9

Relative Permeability (-)

0.8 0.7

1-(Srog+Swi)

0.6

kro krg

0.5

Sgc

0.4 0.3 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Gas Saturation (fractional)

Page 28

Labs plot kr vs liquid saturation (So+Swi)

0.9

1.0

Typical Gas-Oil Curves: Semi-Log

Relative Permeability (-)

1

0.1

1-(Srog+Swi) kro krg

0.01

0.001 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Gas Saturation (fractional)

Page 29

0.7

0.8

0.9

1.0

Gas-Oil Curves • 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

Page 30

Gas-Oil Curves – Corey Method kro = Son No

• Oil relative permeability

1 − Sg − Swir − Srog Son = 1 − Swir − Srog

– normalised oil saturation

krg = Sgn Ng

• Gas relative permeability

Sgn =

– normalised gas saturation • Sgc:

Page 31

critical gas saturation Corey Exponent

Values

No

4 to 7

Ng

1.3 to 3.0

Sg − Sgc 1 − Swir − Srog − Sgc

Corey Gas-Oil Curves 1

Swir kro krg' Srog Sgc

Relative Permeability (-)

0.1

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

0.001

Sgc = 0.03

0.0001

0.00001 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Gas Saturation (-)

Page 32

0.7

0.8

0.9

1.0

0.15 1.00 1.00 0.0000 0.0300

Typical Lab Data - krg Krg too low 1

Srog too high

Relative Permeability, krg

0.1

Ng = 2.3; Swir = 0.15 Ng = 2.3; Swir = 0.20 11a-5 # 4 11a-5 # 31 11a-5 # 34 11a-5 #39 11a-7 BEA5 11a-7 BEA7 11a-7 BEB5 11a-7 BEC5

0.01

0.001 Composite Gas-Oil Curves Ng : No : Sgc: Srog: krg' :

0.0001

2.3 4.0 0.03 0.10 1.0

0.00001 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Swi+Sg (fraction)

Page 33

0.7

0.8

0.9

1.0

Laboratory Methods • 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?

Page 34

Test States • “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 Page 35

Test State • 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? Page 36

Irreducible Water Saturation (Swir) • 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 Page 37

– Swir uniform

Lab Variation in Swir (SPE28826) 30

Dynamic Displacement Porous Plate

25

Swi (%)

20 180 psi

15 ???

10

5

200 psi

0 Lab A

Page 38

Lab B

Lab C

Lab D

Centrifuge Tests • 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?

1.0

• Good for low kro data (near Sro) • Computer simulation used • Problems – uncontrolled imbibition at Swirr – mobilisation of trapped oil – sample fracturing Page 39

0.8

Relative Permeability (-)

– e.g. for gravity drainage

0.9

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5 Water Saturation (-)

0.6

0.7

0.8

0.9

1.0

Dynamic Displacement Tests • 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

Page 40

Unsteady-State Waterflood • Saturate in brine • Desaturate to Swirr • Oil permeability at Swirr (Darcy analysis) • Waterflood (matched viscosity) ⎛ µo ⎜⎜ ⎝ µw

⎛ µ ⎞ ⎟⎟ = ⎜⎜ o ⎝ µw ⎠ res

⎞ ⎟⎟ ⎠ lab

• Total Oil Recovery • kw at Srow (Darcy analysis) Page 41

Unsteady-State Relative Permeability • • • •

Saturate in brine Desaturate to Swirr Oil permeability at Swirr (Darcy analysis) Waterflood (adverse viscosity) ⎛ µo ⎞ ⎛ µo ⎞ ⎜ ⎟ >> ⎜ ⎟ ⎝ µ w ⎠ lab ⎝ µ w ⎠ res

• Incremental oil recovery measured • kw at Srow (Darcy analysis) • Relative permeability (JBN Analysis) Page 42

Unsteady-State Procedures Water

Oil Only oil produced Measure oil volume

Just After Breakthrough Measure oil + water volumes

Increasing Water Collected Continue until 99.x% water

Page 43

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 1.0 0.9

µo/µw = 30:1

0.8

Unstable flood front Early BT

Fractional Flow, fw

0.7

Prolonged 2 phase flow 0.6

µo/µw = 3:1

Oil recovery lower

Stable flood front

0.5

BT delayed

0.4

Suppressed 2 phase flow 0.3

Oil recovery higher 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5 Water Saturation (-)

Page 45

0.6

0.7

0.8

0.9

1.0

Unsteady-State Tests • 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 Page 46

Steady-State Tests • 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)

Page 47

Steady-State Test Equipment ∆p

Oil in

Water in

Mixing Sections

Page 48

Coreholder

Oil and water out

Steady-State Procedures 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

Page 49

Steady-State versus Unsteady-State • 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 Page 50

Laboratory Tests • 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 Page 51

Oil Recovery 70 Fixed - 120 ml/hour

Oil Recovery (% OIIP)

60

Preferred 360

50

120

40

30

120

20 Bump 10 Lab A

Page 52

Lab B

Lab C

Lab D

Gas-Oil and Gas-Water Relative Permeability • 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 Page 53

Drainage Gas-Water Curves (steady-state)

Page 54

•

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

Water-Gas Relative Permeability • 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 Page 55

Imbibition Tests • Waterflood – low rate waterflood from Swi to Sgr – obtain krg and krw on imbibition – Sgr too low (viscous force dominates)

• Counter-Current Imbibition Test – – – –

Page 56

Sgr dominated by capillary forces immerse sample in wetting phase (from Sgi) monitor sample weight during imbibition Determine Sgr from crossplot

129.90 g

CCI: Experimental Data Air-Toluene CCI: Plug 10706: Sgi = 88.8% 70 65

Gas Saturation (%)

60 55 50 Sgr = 33.5%

45 40 35 30 0

10

20

30 Square Root Time (se c s)

Page 57

40

50

60

Trapped or Residual Gas Saturation

Sgr vs Sgi – North Sea

Low rate waterflood

Page 58

Repeatability of CCI tests

Imbibition Kw-Kg 1

krw@Sgr

Drainage

krg

kr

1-Sgr

Imbibition

Swi

krw 0 Page 59

0

Sw

1

Relative Permeability Controls • Wettability • Saturation History • Rock Texture (pore size) • Viscosity Ratio • Flow Rate

Page 60

Wettability

Page 61

Wettability

Page 62

Wettability • 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 – – – – – Page 63

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 • Water-Wet – – – –

better kro lower krw krw = kro > 50% better flood performance

• Oil-Wet – – – –

Page 64

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 • 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

– Sro = 0.25, krw’ = 0.5, ultimate recovery = 0.706 OIIP

• Oil Wet – No = 8

Nw = 2

Swir = 0.10

– Sro = 0.20, krw’ = 0.75, ultimate recovery = 0.778 OIIP Page 66

µo/µw = 3:1

Relative Permeability Curves 1.0 0.9

Relative Permeability (-)

0.8 0.7 0.6 WW kro WW krw

0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Water Saturation (-)

Page 67

0.7

0.8

0.9

1.0

Relative Permeability Curves 1.0 0.9

Relative Permeability (-)

0.8 0.7 0.6 WW kro WW krw IW kro IW krw

0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Water Saturation (-)

Page 68

0.7

0.8

0.9

1.0

Relative Permeability Curves 1.0 0.9

Relative Permeability (-)

0.8 0.7 0.6

WW kro WW krw IW kro IW krw OW kro OW krw

0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Water Saturation (-)

Page 69

0.7

0.8

0.9

1.0

Fractional Flow Curves 1.0 0.9 0.8

Water Wet SOR = 0.33 Recovery = 0.59

Fractional Flow, fw (-)

0.7 0.6 0.5

WW fw

0.4 0.3 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Water Saturation (-)

Page 70

0.7

0.8

0.9

1.0

Fractional Flow Curves 1.0 0.9 0.8

Fractional Flow, fw (-)

0.7 0.6

IW SOR = 0.44 Recovery = 0.482

0.5

WW fw IW fw

0.4 0.3 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Water Saturation (-)

Page 71

0.7

0.8

0.9

1.0

Fractional Flow Curves 1.0 0.9 0.8 Oil Wet SOR = 0.63 Recovery = 0.300

Fractional Flow, fw (-)

0.7 0.6

WW fw IW fw OW fw

0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Water Saturation (-)

Page 72

0.7

0.8

0.9

1.0

Costs of Wettability Uncertainty PV Oil Price Parameter Swi Ultimate Sro Ultimate Recovery Factor SOR Actual Recovery Factor STOIIP (MMbbls) Ultimate Recovery (bbls) Actual Recovery (bbls) "Loss" (MM US$)

Water-Wet 0.200 0.300 0.625 0.330 0.588 96 60 56 108

120 MMbbls 30 US$/bbls IW 0.150 0.250 0.706 0.440 0.482 102 72 49 684

Oil wet 0.100 0.200 0.778 0.630 0.300 108 84 32 1548

• It is really, really important to get wettability right!!! Page 73

Rock Texture

Page 74

Viscosity Ratio 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 (?)

Page 75

Saturation History Primary Drainage

100 %

Primary Imbibition

No hysteresis in wetting phase

NW

NW

kr

kr Sro

W

Swi

W 0%

0% 0%

Page 76

Sw

100 %

0%

Sw

100 %

Flow Rate • 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 Page 77

Flow Parameters End Effect Capillary Number

Nc end

σ φk ≈ µ o vL

Rate (ml/h) 4 120 360 400 Reservoir

Ncend 2.3 0.07 0.02 0.02 0

Flood Capillary Number

Nc = Rate (ml/h) 4 120 360 400 Reservoir

vµ

σ

w

Nc 1.2 x10-7 10-6 3.6 x 1010-5 1.1 x 1010-5 1.2 x 1010-7

For reservoir-appropriate data Nclab ~ Ncreservoir If Ncend > 0.1 kro and krw decrease as Ncend increases Page 78

Relative Permeabilities are Rate-Dependent

Bump Flood 1.0 0.9

Relative Permeability (-)

0.8 0.7 0.6 0.5 High Rate krw ??? 0.4 0.3

Bump Flood krw'

0.2 Low Rate krw'

0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5 Water Saturation (-)

Page 79

0.6

0.7

0.8

0.9

1.0

Flow Rate Considerations • 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 80

Flow Rate Considerations • 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 81

Flow Rate Considerations • 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)

Page 82

JBN Validity • 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 Page 83

Test Recommendations • 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 Page 84

Wettability Restoration •

Hot soxhlet does not make cores water wet! Restored-state cores too oil wet

•

Lose 10% OIIP potential recovery

STRONGLY WATER-WET

USBM

•

1.0

0.0

Original SCAL plugs Hot Sox Cleaned Flush Cleaned

STRONGLY OIL-WET -1.0 -1.0

0.0

Amott

Page 85

1.0

Key Steps in Test Design • 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 Page 86

Key Steps In Test Design • 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 Page 87

Use of NISM • 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

Page 88

X-Ray Scanner Coreholder X-rays detected

X-rays emitted

Scanning Bed

X-ray adsorption

(invisible to Xrays)

X-ray Emitter (Detector Behind) Page 89

0 %

Sw(NaI)

100%

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 • 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 Page 93

– 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 waterwet

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 • 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 Page 96

Simulation Data Input • 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 Page 97

History Matching • Pressure and production 1.66 cc/min 6,0

700

5,0

600 4,0

500 400

Measured differential pressure Simulated differential pressure

300

2,0

Measured oil production 200

Simulated oil production 1,0

100 0

0,0 0,1

Page 98

3,0

1,0

10,0 100,0 Time (min)

1000,0

10000,0

Oil Production (cc)

Differential Pressure (kPa)

800

History Matching • Saturation profiles 0.8

Water Saturation

0.7 0.6 0.5 0.4 0.3 0.2 0.0 Page 99

0.2

0.4

0.6

Normalized Core Length

0.8

1.0

Simulation Example – JBN Curves Relative Permeabilty Curves Pre-Simulation 1 0.9

Relative Permeability

0.8 0.7 0.6

Krw Kro low rate end point high rate end point

0.5 0.4 0.3 0.2 0.1 0 0

0.1

0.2

0.3

0.4

0.5

0.6

Water saturation Page 100

0.7

0.8

0.9

1

Simulation Example – Simulated Curves Relative Permeabilty Curves Post Simulation 1 0.9

Relative Permeability

0.8 0.7 Krw Kro low rate end point high rate end point Krw Simulation Kro Simulation

0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.1

0.2

0.3

0.4

0.5

0.6

Water saturation Page 101

0.7

0.8

0.9

1

Quality Control • 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 Page 102

Water-Oil Relative Permeability Refining • 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 Page 103

Curve Shapes 1 0.9

Semi-log

0.8 0.7

Good data – concave down

Kr

0.6 0.5 0.4

Kro Krw

0.3

Water-Oil Rel. Perms. 0.2 0.1

1

0

0

0.2

0.4

0.6

0.8

1

0.1

Cartesian Good data – convex upwards

Kr

Sw

Kro

0.01

Krw

0.001

0.0001 0

0.2

0.4

0.6 Sw

Page 104

0.8

1

Sro Determination •

Compute Son – high, medium and low Sro 1

•

low rate, bump, centrifuge Sro 0.1

Plot Son vs kro (log-log) 0.01

•

Sro too low 0.001

– curves down •

Sro too high

1.000

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

– curves up •

Sro just right – straight line

Page 105

0.0001 0.010

Kro

•

Sor = 0.40 Sor = 0.20 Sor = 0.35

Refine krw’ Refined krw’

Use refined Sro

•

Plot krw versus Swn

•

Fit line to last few points – least affected by end effects

•

1

Krw

•

0.1

Determine refined krw’ 0.01 0.1

1 Swn = 1-Son

Page 106

Determine Best Fit Coreys Use refined Sro and krw’

•

Determine instantaneous Coreys log(krw' ) − log(krw) Nw* = log(1.0) − log(S wn )

log(kro ) No* = log(Son )

3.5 3 2.5 No' & Nw'

•

2

No Nw

1.5 1 0.5 0

•

Plot vs Sw

•

Take No and Nw from flat sections – Least influenced by end effects

Page 107

0

0.2

0.4

0.6 Sw

0.8

1

Refine Measured Data •

Endpoints – Refined krw’ and Sro

1.0 0.9

•

Corey Exponents

0.8

– No and Nw (stable) •

Corey Curves

kro( refined ) = Son

No

Relative Permeability

0.7 0.6

Refined Kro Refined Krw

0.5

Original Kro Original Krw

0.4 0.3 0.2 0.1 0.0 0

krw( refined ) = krw' Swn Nw Page 108

0.1

0.2

0.3

0.4

0.5 Sw

0.6

0.7

0.8

0.9

1

Normalisation Equations • Water-Oil Data

Sw − Swi Swn = 1 − Swi − Srow

k ro n =

k ro k ro end

krw krwn = krwend

• Gas - Oil Data Sgn =

Page 109

Sg −Sgc 1−Swi −Srog−Sgc

k ro n =

k ro k ro end

krgn =

krg krgend

Example - kro Normalisation

1 0.9

Oil Relative Permeability (-)

0.8 0.7 0.6 Sw = 1-Sro Swn = 1

0.5 Swirr Swn = 0 0.4

Sample 1 Sample 2

0.3 0.2 0.1 0 0

0.1

0.2

0.3

0.4

0.5 Water Saturation (-)

Page 110

0.6

0.7

0.8

0.9

1

Example - krw Normalisation

1 0.9

Water Relative Permeability (-)

0.8 0.7 krw at Sro krwn = 1

0.6

Sample 1

0.5

Sample 2

0.4 0.3 0.2 0.1 0 0

0.1

0.2

0.3

0.4

0.5 Water Saturation (-)

Page 111

0.6

0.7

0.8

0.9

1

Normalise and Compare Data - kron 1.0

Normalised Oil Relative Permeability (-)

0.9 0.8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.7 0.6 0.5

Different Rock Types ? Different Wettabilities?

0.4 0.3

Steady State

0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Normalised Water Saturation (-)

Page 112

0.7

0.8

0.9

1.0

Normalise and Compare Data - krwn 1.0

Normalised Water Relative Permeability (-)

0.9 0.8 1 2 3 4 5 6 7 8 9 11 12 13 14 15

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Normalised Water Saturation (-)

Page 113

0.7

0.8

0.9

1.0

Denormalisation • 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 Page 114

Denormalisation Equations • Water Oil

S w dn = S wn (1 − S wi − S ro ) + S wi

Denormalised Endpoints

k rodn = k ro end .k ron k rwdn = k rw end .k rwn

Water-Oil •Swi •kro (@Swi) •krw (@1-Srow)

• Gas-Oil S = S (1 − S − S − S ) + S g dn gn wi rog gc gc

k rodn = koend .k ron k rgdn = k rg end .k rgn Page 115

From correlations & average data

Summary – Getting the Best Rel Perms • 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 Page 116