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
Saturation-dependencies
• 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
Saturation-dependencies
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
Network displacement mechanisms
• 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
27
• multiple displacement chains displace disconnected clusters
• based on “target” pressure difference
• determining lowest target requires shortest path algorithm
Network displacement mechanisms
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
31
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
32
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
33
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
water 1 gas 1 water 2 gas 2 water 3 gas 3
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 network simulations
• WAG occupancy statistics (z=5): end gas flood 2
• oil and gas in both water-wet and oil-wet pores
39
WAG network simulations
• Chain lengths (z=3)
•
significant number of multiple chains0.00
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
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
WAG network simulations
0.00
0.25
0.50
0.75
1.00
water 1 gas 1 water 2 gas 2 water 3 gas 3
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
WAG simulation micromodel experiment
4545
WAG simulation micromodel experiment
• 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
WAG simulation micromodel experiment
• fluid distributions after water flood 1
– water disperses gas
– slightly more extensive in experiment
4747
WAG simulation micromodel experiment
• fluid distributions after gas flood 2
– different gas finger appears
– additional oil production
4848
WAG simulation micromodel experiment
• 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