New Three-Phase ModelingCapabilities in Eclipse

PhD meeting

NTNU

7th February, 2008

by

Odd Steve Hustad

StatoilHydro R&D, Trondheim

Gas Based Recovery Methods

Gas

Water Oil

Water flooding

Gas flooding

2

Outline

• Extensions to Stones first model (SPE 24116)

– Available in Eclipse version 2008_1

• The ODD3P model option

– Available in Eclipse version 2007_1, immiscible option

– Available in Eclipse version 2008_1, miscible option

3

Modifications to Stone’s first model Introducing the n-exponent

SPE 24116

n = 1 n = 4.5 n = 25

4

Exponent’s impact on saturation distribution during flow• Low exponent value keeps oil between gas and water

• High exponent value causes gas to bypass oil

• This exponent parameter will appear in the 2008 version of Eclipse as a gridblock and directional dependent parameter

n = 1 n = 4.5 n = 25

5

• Exponent value of 4 was sufficient to match oil recovery curve

• Oil iso-curves are more linear in compliance with Oak et al. (JPT, Aug. 1990)

SPE 24116

Modifications to Stone’s first model sufficient for modeling equilibrium gas injection

Note

Sgmax ~ 62%

6

Tertiary gas displacement experiments

• Vertical 1.2 m long Bentheimer Core, water-wet condition

• Gas injection from top of core after water injection from below

1) Equilibrium gas

2) Dry separator gas

• Oil’s bubble point at 313.5 bar and 91.9 °C

– Bo=1.62

– GOR=200.9

– μo=0.43 cP

– σgo=1.2 mN/m

SPE 24116

WaterWater,

Oil & Gas

Oil & Water

Equilibrium Gas or

Separator Gas

7

Some conclusions from experiments

• Significant phase behavior effects from vaporization

• Long after drainage, oil still draining at end of experiments

• Modeling flash process from reservoir to ambient conditions important for proper fluid description

• Capillary pressure and relative permeability are important parameters when modeling experiment

SPE 24116

8

The flash process

• Sufficient number of pseudo-components are required for proper molecular weight representation (composition) in modeling gas injection with an Equation-of-state (EOS)

SPE 24116

Flash Procedure Saturation Pressure• If too few pseudo-components are used in an EOS model, significant errors in modeling saturation pressure may occur

9

Preliminary simulations using Stone’s models

Equilibrium Gas Injection

•Modification required to Stone model

•Water recovery profile proved most difficult to history match

10

SPE 24116

Modifications to Stone’s first model insufficient for modeling dry gas injection• Water recovery not properly modeled for dry gas injection experiment

• Vaporization impacts capillary forces which are not properly represented

• Correct modeling of maximum gas saturation remain a challenge

11

ODD3P three-phase model option• Developed to extend Stone’s water-wet three-phase models

• The ODD3P model extends the capability to handle other wetting conditions through each three-phase property being dependent on two two-phase properties

• The ODD3P model is an extension to the IKU3P model option in compositional Eclipse

– Relevant papers: SPE 74705, SPE 75138 and RUTH Program Summary book

– Three-phase properties are now consistent at all two-phase boundaries

– Couples capillary pressure and relative permeability through saturation

•

– Primary, secondary and tertiary process data may be applied

– Dynamic gridblock dependent end-point saturations for all processes

– Hysteresis capability (for three sets of two-phase data)

– miscibility capability

( )[ ]ciri PSfk =

12

ODD3P model concept

( ) ( )( ) ( )( ) ( )

Rock Type (Table) data

;

;

;

Gridblock Data, , , ,

w w cow g g cgo

row row w rgo rgo g

rwo rwo w rog rog g

r r r r r rgro grw org orw wrg wro

S S P S S P

k k S k k S

k k S k k S

S S S S S and S

= =

= =

= =

( ( ( (

( ( ( (( (

( ( ( (( (

k r g

r w

k r g

k r g

r o k r

g , o , w

w rS o r

S g o

w rS o r

S r

w

k g

o

o

k wo w

( S S S )

S gg

r

S ow

g w

100%Gas

100%Water

100%Oil

Model Input – Two-Phase Data

SPE 74705

13

Eclipse keywords in PROPS section• ODD3P

– Specifies to use model

• EPSODD3P

– Specifies end-point saturation scaling preference, reference and threshold values for interfacial tension and capillary number

• PCODD3P, PCODD3PW & PCODD3PG

– Specifies the capillary pressure and saturation calculation control parameters

• PSORG, PSGRO, PSORW, PSWRO, PSGRW & PSWRG

– Primary end-point saturations for gridblocks

• HSORG, HSGRO, HSORW, HSWRO, HSGRW & HSWRG

– Hysteresis end-point saturations for gridblock

14

Eclipse keywords in REGIONS section• PSTNUM, ISTNUM & DSTNUM

– Primary, increasing (water) and decreasing saturation table numbers

• SDROG, SDRGO, SDROW, SDRWO, SDRGW & SDRWG

– Initial gridblock direction saturation indicators

15

Eclipse keywords in SOLUTION section• DBGODD3P

– Debugging information

16

Eclipse keywords in SUMMARY section• BSDROG, BSDRGO, BSDROW, BSDRWO, BSDRGW & BSDRWG

– Gridblock phase saturation direction indicators

• BSGNRM, BSONRM & BSWNRM

– Gridblock normalized saturations

• BSOGTN, BSGOTN, BSOWTN, BSWOTN, BSGWTN & BSWGTN

– Gridblock turning point saturations

• BSOGNH, BSGONH, BSOWNH, BSWONH, BSGWNH & BSWGNH

– Gridblock hysteresis normalized saturations

• BSOGNE, BSGONE, BSOWNE, BSWONE, BSGWNE & BSWGNE

– Gridblock equivalent opposite direction normalized saturations

• BSORGB, BSGROB, BSORWB, BSWROB, BSGRWB & BSWRGB

– Residual saturations to calculate normalized saturations

17

Eclipse keywords in SUMMARY section cont.

• BSORGP, BSGROP, BSORWP, BSWROP, BSGRWP & BSWRGP

– Process dependent residual saturations

• BIFTGO, BIFTWO & BIFTGW

– Gridblock interfacial tension values

• BKROGN, BKRGON, BKROWN, BKRWON, BKRGWN & BKRWGN

– Gridblock representative relative permeability

• BKROGH, BKRGOH, BKROWH, BKRWOH, BKRGWH & BKRWGH

– Gridblock turning point relative permeability

• BKROGE, BKRGOE, BKROWE, BKRWOE, BKRGWE & BKRWGE

– Gridblock equivalent relative permeability

• BKROGT, BKRGOT, BKROWT, BKRWOT, BKRGWT & BKRWGT

– Gridblock opposite direction turning point relative permeability

18

Tertiary gas injection recovery, varying wettability

Water-wet Mixed-wet

Oil-wet

Book:

RUTH Program SummaryNPD, Stavanger, 1997

19

Pore scale modeling (eCore)Thin section

Network model

flowsimulation

3D pore space

pore scale physicswettabilty measurementscryo ESEM

wogs

0,0 0,2 0,4 0,6 0,8 1,0So

1E-4

1E-3

1E-2

1E-1

1E+0

measuredpredictedaverage

0 0,2 0,4 0,6 0,8 1

Sw

1E-4

1E-3

1E-2

1E-1

1E+0

krw (exp)krw (sim)krw (avg)kro (exp)kro (sim)kro (avg)

Core-scale multi-phase flow parameters

k rw

or k

row

two-

phas

e m

odel

k r

ogth

ree-

phas

e m

odel

Technology offered by Numerical Rocks AS

SPE 52052

20

Modeling of mixed-wet core flooding experiments• Improved model for saturation functions is established – ODD3P – in reservoir

simulation software

• Numerical generated two-phase saturation functions can be established through the eCore technology

• Can Core flood modeling be done better?

• Old core flooding experiments with mixed wettability revisited:

– Establishing “irreducible” water saturation

– Water displacement

– Gas displacement

21

Displacement experimentsComposite core and numerical model

• Vertical composite core of six core plugs

• Three gridblocks representing each core

• Pore volume of 143.57 cm3

• Two gridblocks were added to represent the end-pieces having zero capillary pressure

• Each end gridblock has a pore volume of 1 cm3

0.26

0.27

0.28

0.29

0.3

0.31

0.32

0.33

0.34

1.183

33.5

500

5.916

78.4

003

11.00

0313

.6003

15.98

3318

.1503

20.31

7322

.7503

25.45

0328

.1503

30.68

3333

.0503

35.41

7337

.1333

38.20

0339

.2673

Center depths from top of core (cm)

Poro

sity

(fra

ctio

n)

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

Gas

per

mea

bilit

y (m

d)

Porosity (fraction)

Gas Permeability (md)

22

Oil-water Relative permeability• Observe the crossing hysteresis relative permeability curves to oil from eCore• Oil-water relative permeability is the same for all the cores• Sorw is 6.8% and Swro is 23.82%

0.0

0.2

0.4

0.6

0.8

1.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Water saturation

Oil-

wat

er re

lativ

e pe

rmea

bilit

y

RPWORPWOIRPWODRPOWRPOWIRPOWDHistory matched krwHistory matched krow

0.000000001

0.00000001

0.0000001

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Water saturation

Oil-

wat

er re

lativ

e pe

rmea

bilit

y

RPWORPWOIRPWODRPOWRPOWIRPOWDHistory matched krwHistory matched krow

23

Gas-oil relative permeability• Secondary drainage (network) curves have been estimated• Note difference in estimated data through history matching• The gas-oil relative permeability curves are the same for all the cores, and these are at Swro

• Sorg is 5.8% and Sgro is 31%, both at Swro of 23.82%

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

Gas saturation (fraction)

Rel

ativ

e pe

rmea

bilit

y

RPGOI - estimatedRPOGI - estimatedRPGODRPOGDRPGOPRPOGPHistory matched krogHistory matched krg

0.00000001

0.0000001

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Gas saturation (fraction)

Rel

ativ

e pe

rmea

bilit

y

RPGOI - estimatedRPOGI - estimatedRPGODRPOGDRPGOPRPOGPHistory matched krogHistory matched krg

24

Capillary pressures• The cores are assumed of fine grained sandstone and gas-oil data are at Swro

• Capillary pressure curves are scaled according to Leverett J-function formulation from core to core. Curves for one core are illustrated here

• History matched data are significantly different

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Water saturation

Oil-

wat

er c

apill

ary

pres

sure

(bar

)

SWI

SWD

SW

History matched Pcow

0.001

0.01

0.1

1

10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Gas saturation (fraction)

Cap

illar

y pr

essu

re (b

ar)

SGD

SGI - added

SGP

History matched Pcgo

25

Comparing gas-oil saturation functions• The presence of irreducible water does not impact the relative permeability data,

except near the end-point saturations.• Maximum gas saturation is lower in the presence of water• Slightly higher gas-oil J-function values are obtained at low gas saturation (<20%)

and different near the maximum gas saturation.• Residual gas saturation is slightly lower in the presence of water (0.8% points lower).

0.00000001

0.0000001

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Gas saturation (fraction)

Gas

-oil

rela

tive

perm

eabi

lity

krgoi krogi krgodkrogd krgop krogpkrog(Sgd) @ Swir krgo(Sgd) @ Swir krog(Sgp) @ Swirkrgo(Sgp) @ Swir

0.01

0.1

1

10

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Gas saturation (fraction)

Gas

-oil

J-fu

nctio

n

Sgi

Sgd

Sgp

Sgd @ Swir

Sgp @ Swir

26

Primary Drainage• Initial composite core water saturation was 45% and 44.8% for the water flood and

gas flood experiment• With direct use of network model data a match was achieved. No history matching

or alterations performed!• Initial water saturation of 45% and 44.8% corresponds to 2.5 and 4.5 pore volumes

of oil injected

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0 1 2 3 4 5 6 7 8

Pore Volumes Injected

Cor

e av

erag

e w

ater

sat

urat

ion

Ave. Sw

Ave Sw= 0.45 at 2.46 PVI

Ave Sw= 0.448 at 4.5 PVI

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0 5 10 15 20 25 30 35 40 45

Distance from top of core (cm)

Wat

er s

atur

atio

n (fr

actio

n)

Ave. Sw=0.4614 at 1.0659 PVI

Ave. Sw=0.4518 at 2.041 PVI

Ave. Sw=0.4503 at 2.4589 PVI

Ave. Sw=0.4477 at 6.9652 PVI

27

Water flooding• Oil-water Pc-curve had to be

modified/scaled by a factor 0.626• Application of Leverett J-function may

be questioned

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0 5 10 15 20 25 30 35 40 45

Distance from top of core (cm)

Wat

er s

atur

atio

n (fr

actio

n)

Ave. So=0.4499 at 0.1 PVI

Ave. So=0.379 at 0.2 PVI

Ave. So=0.3547 at 0.4 PVI

Ave. So=0.347 at 3 PVI

• The Amott wettability index of 0.1 may not be representative

• Good match of recovery curve was achieved with minor adjustments

• Zero capillary pressure will result in optimistic recovery

Water flooding LFR medium core

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.5 1 1.5 2 2.5 3 3.5

Pore volume injected

Oil

reco

very

(fra

ctio

n PV

)

Fig. 11Fig. 6No Pcow scaling, Sorw = 0.068Pcow scaled by 0.001, Pcow~0Pcow scaled by 0.626

28

Gas Flooding

• Omitting capillary pressure in Stone’s first model results in optimistic recovery• Too low oil recovery with eCore data and ODD3P model with no adjustments• Reducing oil-water capillary pressure gave more correct oil recovery level and

adjusting gas-oil capillary pressure had little impact • A fair match was achieved with ODD3P when the capillary pressure was turned off

in the solution of the pressure equation. This example show significant CPU time improvement

• Simulated scenarios used Stone’s first model and ODD3P model–Only primary data applied in Stone’s first model (no hysteresis)

–All eCore data applied using ODD3P model

• Stone’s first model “matched” the oil recovery, but the input gas-oil capillary pressure had to be adjusted by a factor 4!

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Pore volume injected

Oil

reco

very

(fra

ctio

n PV

)

Fig. 22Primary data only: Pcow*0.626, Pcgo*4.0, Stone 1Primary data only: Pcgo=Pcow=0, Stone 1Pc used as is with no adjustments, Swir=0, odd3pPcow*0.537, No Pcgo adjustment, Swir=0, odd3pPc turned off in pressure eq'n, Swir=0, odd3p

29

Gas Flooding cont.

• The simulated final gas saturation show large gradient with the composite core

• The initial water saturation is redistributed when gas enters the core with less end effects

• The gas displaces mainly the oil volume and not the water volume during the gas displacement.

• The gas injection process does not leave primary curve due to breakthrough (short-circuiting flow) and high end-point hysteresis saturation (Srg>30%)

• The laboratory boundary conditions seem to have little impact on the saturation end-effects (i.e. large gradients near the outlet) due to the wetting conditions

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1.2 3.6 5.9 8.4 11.0 13.6 16.0 18.2 20.3 22.8 25.5 28.2 30.7 33.1 35.4 37.1 38.2 39.3

Distance from top inlet (cm)

Sat

urat

ion

(%)

Final Sg

Final So

Final Sw

0

0.1

0.2

0.3

0.4

0.5

0.6

0 5 10 15 20 25 30 35 40

Distance from top of core (cm)

Sat

urat

ion

(frac

tion)

Initial Sw Final Sw

Final So Final Sg

30

Concluding remarks• Reservoir simulation technology improvements by StatoilHydro innovation

• StatoilHydro is approaching predictive capability when modeling core displacement experiments

• Work is ongoing to validate eCore technology for modeling core flooding experiments using ODD3P

• Further research still required

– Need more data containing multi-phase flow

• Lack good experimental data with different wettability, miscibility, hysteresis, etc.

– Improve the modeling capability and understanding the application of experimental data

• Better relationships between the parameters for multi-phase flow

31

The End

Thank you for listening

Questions?