Pore-scale modelling of WAG: impact of wettability

11

Pore-scale modelling of WAG:impact of wettability

Rink van Dijke and Ken Sorbie

Institute of Petroleum EngineeringHeriot-Watt University

WAG Workshop FORCE, Stavanger, 18 March 2009

2

• 3-phase (immiscible) flow processes, e.g.– water-alternating-gas injection (WAG): improved oil recovery

– NAPL in unsaturated zone: ground water remediation

• modelled with Darcy’s law:

• capillary pressure and relative permeability functions

– difficult to measure

– pore-scale modelling

Introduction

, , , ,r ii i

i

Kkq P i w o g

, ,, ,,i jc ij i j r i i jP S S k S SP P

33

Introduction• Pore-scale modelling:

– pore space structure:• connectivity (topology)• geometry (pore sizes and shapes)

– flow mechanisms:• capillary forces• conductance (viscous forces)

– wettability (contact angles)– incorporated in

• idealized network models (quasi-static “invasion percolation” or dynamic)

• capillary bundle models water, oil, gas

44

Introduction

• Capillary forces:– invasion of a single tube (cylinder):

– ‘rule’ for displacement of water by oil:

with capillary ‘entry’ pressure according to Young-Laplace: 2

,

cosow owc owP

r

,ow o w c owP P P P

oP wP

55

Introduction

• Wettability:– wettability of pore surface defined in terms of oil-

water contact angle (measured through water)

• water-wet if

• oil-wet if

SOLID SURFACE

wateroil

ow

0cos ow 0cos ow

66

Introduction

• Wettability:– in 3-phase flow contact angles:

• related by Bartell-Osterhof equation:

• constitute capillary entry pressures for gas-water and gas-oil displacements, e.g.

• determine presence of wetting films and spreading layers

, ,ow go gw

cos cos cosgw gw ow ow go go

2,

coso gwg

wwcP r

77

Introduction• Micromodel experiments:

– understand flow mechanisms– validate pore-scale network models

– Sohrabi et al. (HWU)

pore cross-section: wide and

shallow

250 m50 m

88

Outline: effects of wettability• Saturation-dependencies of three-phase capillary

pressures and relative permeabilities

• Intra-pore physics:– fluid configurations

– capillary entry pressures and layer criteria

– non-uniform wettability

• Network displacement mechanisms:– phase continuity and displacement chains

– WAG simulations

– comparison simulations and WAG micromodel experiments

• Concluding remarks

9

Saturation-dependencies

• Traditional example (Corey et al., 1956)

•Curved oil isoperms

•Straight water and gas isoperms

10

Saturation-dependencies• Traditional assumptions for saturation-dependencies

• Water-wet system: water wetting to oil wetting to gas water in small pores, gas in big pores

, , ,, , ,r w w r g g r o w gk S k S k S S

pore

occ

upan

cy

(num

ber

frac

tion)

pore size r

water oil gas

1111


• Wettability distributions in porous medium often correlated to pore size:– mixed-wet with larger pores oil-wet (MWL): may occur

after primary drainage and aging (similarly MWS)

r0

-1

1water-wet

oil-wet

cos ow

rwet

12

Saturation-dependencies• Paths in saturation space: gas flood into oil, followed by water flood into gas and oil

• capillary bundle model

oil water

gas

gas flood

water flood

I

III

II

water-wet oil-wet

13

Saturation-dependencies• Regions in saturation space: iso-capillary pressure

curves

II II

( )go oP S ( , )ow w oP S S

II

gas is “intermediate-wetting”

14

Saturation-dependencies• Regions in saturation space: iso-relative

permeability curves

II II, ( )r o ok S , ( , )r g w ok S S

gas is “intermediate-wetting”

II

15

• numerical example FW capillary bundle

gas isoperms

II

IIII

0.09

0.99


36 14 29 mN/m, ,gw go ow 0 6 0 1cos . , cos .wwet owetow ow

10 m 160 mmin min,r r

oil isoperms

0.01

0.91

1616

Intra-pore physics• Films and layers:

– water-wet micromodel: WAG flood

• water wetting films around both oil and gas• possible oil layers separating water and gas

1717

Intra-pore physics• Fluid configurations in angular pores:

– water-wet pores, e.g. strongly water-wet: all close to 0

• water wetting films around both oil and gas• possible oil layers separating water and gas:

affected by oil spreading coefficient

– oil-wet pores, e.g. weakly oil-wet: close to 90 degrees, close

to 0• no oil wetting films around water• only oil wetting films around gas

– ensures phase continuity along pores

,S o gw ow goC

, ,ow go gw

,ow gw go

1818

Intra-pore physics• true 3-phase capillary entry pressures (improved

Y-L)

– gas-oil entry pressure depends on water wetting film pressure

– determined by free energy calculation (MS-P)– also criterion for (oil) layers

,c go owP P

bulk displacement

layer displacement

19

0

0.5

1

1.5

0 0.5 1 1.5

ow

go

Intra-pore physics• consistent relation 3-phase pressure differences

and occupancies

gor

owr

goP

owP

gas-oil bulk displacement (true varying)

oil-water bulk displacement

gas-oil bulk displacement, with layer (constant)

layer displacement

2020

Intra-pore physics

• mixed-wet bundle of triangular pores:

– small pores strongly water-wet

– large pores weakly oil-wet:

dr

wr

5 m 20 mdr 20 m 55 mdr

0 1cos .ow

2121

Intra-pore physics

• water injection– no difference true (3-phase)

and constant (2-phase) during invasion of water-wet pores

– huge differences during invasion of oil-wet pores

– true: simultaneous w->o and w->g

– volume effectoil films

o-g-w

constant

true

2222

• nonuniform wettability:– after primary - after imbibition

drainage

– strongly affects water flood Sor (Ryazanov et al., 2009)

Intra-pore physics

surface rendered oil-wet: aging(Kovscek)

wateroil

oil layers (2-phase)

2323

• non-uniform wettability

• layers in 3-phase configuration• consistent entry pressures and layer

criteria

Intra-pore physics

2424

-3

-2

-1

0

1

-7 -6 -5 -4 -3 -2 -1

P ow

Pg

wIntra-pore physics

high Pow drainage

gas injection

2525

Network displacement mechanisms

• phase continuity:– connectivity– films and layers (wettability)

– water-wet micromodel: WAG flood

2626


• connected, trapped and disconnected phases

– phase cluster map

trapped oil cluster

invading gas cluster

disconnected water cluster

water cluster connected to outlet

outlet inlet

disconnected oil cluster

oil cluster connected to outlet

disconnected gas cluster

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• multiple displacement chains displace disconnected clusters

• based on “target” pressure difference

• determining lowest target requires shortest path algorithm


trapped oil cluster

invading gas cluster

disconnected water cluster

water cluster connected to outlet

outlet inlet

disconnected oil cluster

ogr

gor

gwr

oil cluster connected to outlet

disconnected gas cluster

, , ,( ) ( ) ( )invading out targetg w gw c go go c og og c ow owP P P P r P r P r

e.g. gas->oil->gas->water

28

Network simulations

• 3-phase flow simulator 3PhWetNet: regular lattice, arbitrary wettability, capillary-dominated flow

• few free parameters describing essence of pore-scale displacements (needs “anchoring”)– coordination number z– pore size distribution– volume and conductance

exponents– wettability (contact angle

distribution)– film and layers (notional)

2929

Network simulations• Network model:

– parameters “anchored” to easy-to-obtain data: network structure and wettability

– example mixed-wet North Sea reservoir data

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Sg

Krg/

Kro

Kro

Krg

Sim - Kro

Sim - Krg

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Sw

Kro

/Krw

Krw

Kro

Sim - Krw - rw et=1

Sim - Kro - rw et=1

Sim - Krw - rw et=2

Sim - Kro - rw et=2

water-wet

mixed-wet (MWL)

gas flood water flood

3030

Network simulations

• Network model:– predict difficult-to-obtain data, e.g. 3-phase kr and Pc

10 90

8020

30 70

6040

50 50

4060

70 30

2080

90 10

102030405060708090wateroil

gas

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Sg

Krg

Swi = 0.1

Swi = 0.3

Swi = 0.5

Swi = 0.65

Swi = 0.7

three-phase gas injection displacement paths

three-phase gas relperms

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WAG network simulations

• mixed-wet• no films or layers• varying coordination

number z

• high residual, but additional recovery during WAG for z=3

z=5

z=3

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WAG network simulations• displacement statistics (chain lengths), z=5

• few multiple, many double displacements• continuing phase “movement” but no additional recovery

0.00

0.25

0.50

0.75

1.00

water 1 gas 1 water 2 gas 2 water 3 gas 3

chai

n le

ngth

frac

tion

5

4

3

2

1

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WAG network simulations• displacement statistics (types), z=5

• mainly 3 displacement types, corresponding to doubles, e.g. g->o and o->w during gas flood

0.00

0.25

0.50

0.75

1.00


dis

pla

cem

ent

typ

e fra

ctio

n

g->w

g->o

w->g

w->o

o->g

o->w

38

0.00

0.25

0.50

0.75

1.00

5 9 13 17 21

r (m)

po

re o

ccu

pa

ncy

fra

ctio

n

gas

water

oil

25


• WAG occupancy statistics (z=5): end gas flood 2

• oil and gas in both water-wet and oil-wet pores

39


• Chain lengths (z=3)

•

significant number of multiple chains0.00

0.25

0.50

0.75

1.00


chai

n le

ngth

frac

tion

5

4

3

2

1

0.00

0.25

0.50

0.75

1.00

chai

n le

ngth

frac

tion

5

4

3

2

1

z=5

40

0.00

0.25

0.50

0.75

1.00

disp

lace

men

t typ

e fr

actio

n

g->w

g->o

w->g

w->o

o->g

o->w


0.00

0.25

0.50

0.75

1.00


disp

lace

men

t typ

e fr

actio

n

g->w

g->o

w->g

w->o

o->g

o->w

additional types of displacementsg->o for water and o->g for gas floods

z=5

• Displacementtypes (z=3)

•

4141

WAG simulation micromodel experiment

• weakly wetted: little evidence of (continuous) water and oil wetting films (around water)

• spreading oil: assume oil layers and oil wetting films around gas

water-wet oil-wet

56 41 15gw ow go mN/m

4242

WAG simulation micromodel experiment• Fractionally-wet

– 50% water-wet & oil-wet pores– angles distributed between 60-120 degrees– oil layers and oil wetting films around gas

• Comparison simulated and experimental recoveries– recovery

ceases afterWAG 2

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

wf 1g 1w 2g 2w 3g 3w 4g 4w

Res

idu

al

oil

[%

]

Neutral-wet

More oil-wet

More water-wet

Case 7

0

10

20

30

40

50

60

wf 1g 1w 2g 2w 3g 3w 4g 4w

Oil

rec

ov

ery

%S

orw

Neutral-wet

More oil-wet

More water-wet

Case 7

4343

WAG simulation micromodel experiment• Displacement chain lengths

– many multiples (few films: low phase continuity)– multiples dying out after WAG 3

00.10.20.30.40.50.60.70.80.9

1

Fra

ctio

n

5

4

3

2

1

4444

• Type of displacements

– all types of displacements occur– many displacements involving oil movement– after WAG 3 mainly w->g, g->w

00.10.20.30.40.50.60.70.80.9

1

waterfl

ood

gasf

lood

1

waterfl

ood 1

gasfl

ood

2

waterfl

ood 2

gasfloo

d 3

waterfl

ood 3

gasflo

od 4

waterfl

ood 4

Fra

cti

on

g->w

g->o

w->g

w->o

o->g

o->w


4545


• fluid distributions aftergas flood 1

– narrow gas finger in both simulation and experiment

– significant amount of oil displaced

– multiple displacements: e.g. gas->oil->gas->water

4646


• fluid distributions after water flood 1

– water disperses gas

– slightly more extensive in experiment

4747


• fluid distributions after gas flood 2

– different gas finger appears

– additional oil production

4848


• fluid distributions after gas flood 3

– new gas finger in simulation

– some additional oil displaced (“jump” in recovery)

– after this flood mainly water displacing gas and vice versa

4949

Conclusions

• Mixed wettability leads to three types of pore occupancy and corresponding saturation-dependencies of three-phase capillary pressures and relative permeabilities: – difficult to capture in empirical model

• True three-phase capillary entry pressures and layer criteria essential for consistent and accurate modelling

• Phase continuity driver for WAG at pore-scale– strongly affected by network connectivity and presence films and layers:

precise wettability

– multiple displacement chains

– new fluid patterns during each cycle (micromodels)

– recovery ceases after few WAG floods, oil movement may continue

5050

Near-miscible WAG: micromodel

Continued gas injection in strongly water-wet experiment:

• Much oil displaced through film flow + mass transfer (?)

After 1 hour After 2 hours

Documents

Pore-scale modelling of WAG: impact of wettability