Imperial College Consortium on Pore-Scale Modelling

From pore-space images to multiphase transport predictions

Anwar Al-Kharusi, Hassan Behbahani, Branko Bijeljic, Hu Dong, Hiroshi Okabe, Mohammad Piri, Sander Suicmez,

Per Valvatne and Martin Blunt

Department of Earth Science and EngineeringImperial College London

Major achievements and where next?• Predictive two- and three-phase pore-scale modelling• Analysis of effects of wettability and trapping in two and

three-phase flow – benchmark experiments• Generation of statistical images and networks• Direct simulation on pore-space images: Stokes solver,

lattice Boltzmann, level set, smoothed particle hydrodynamics

• Statistical analysis of granular packs• Focus on carbonates and carbon storage and links to our

own experiments• Fundamentals of wettability• We helped develop pore-to-prediction workflow – now

leave to the commercial domain

Contact angles in three-phase flow

owowwsos cos

Solid

OilWaterow

ow

Solid

Solid

gwgwwsgs cos

gogoosgs cos

owowgogogwgw coscoscos

Oil Gas

Water Gas

go

gw

go

gw

Bartell-Osterhoff (1927)

Young’s equation

3 Contact angles (O/W,G/W,G/O)

1 Constraint between them

2 Independent values of contact angle

Wettability alteration

Oil and water in a triangular pore after primary drainage (oil migration into the reservoir). The areas directly contacted by oil (shown by the bold line) have an altered wettability, while the corners that are water-filled remain water-wet. b is the length of the water-wet surface.

Water

Oil

b

Why ducks don’t get wet

Wettability in a three-phase system is defined by the spreading coefficient Cso and the oil/water contact angle ow. If the surface is oil-wet, then Bartell-Osterhoff implies:

This means that in a strongly oil-wet system, gas is wetting to water. This is obvious – hydrophobic surfaces are oil-wet.

0coscos

cos

gw

owowgogogw

WaterAir

Oily surface

Multiple phases in a porous medium

We have defined wettability and contact angles.

There is a pressure difference between two phases at a curved interface – the non-wetting phase is at a higher pressure. Young-Laplace equation:

where r1 and r2 are the principal radii of curvature.

21

11

rrPPP wnwc

From rock to network to predictions

• Starting point is a voxel image of the rock– Obtained from micro-CT, object-based or statistical methods

• From this a representative network of pores and throats is constructed

3 mm

Micro-CT scanning

• Direct 3D imaging of a small rock sample– Resolution from 4 – 10 microns

• Issues with carbonates over sufficient resolution and heterogeneity

• Other groups – ANU, Penn State etc and synchrotron sources (Trieste and Diamond)

Finding a network

• Direct simulation on the image works for absolute permeability and drainage capillary pressure. – Network model better

for multiphase flow properties

• Use maximal ball algorithm (Silin and Patzek)

• Other methods – erosion/dilation (ANU, Heriot-Watt, Lindquist)

3D images and extracted pores

3 mm

Oil invasion

Non-wetting phase trapping

Dong, 2007

Rock

Water

Residual phase

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

Throat radius (microns)

No

rmaliz

ed

fre

qu

en

cy

0%

5%

10%

15%

20%

25%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 26 34 36

Coordination number

No

rma

lize

d fr

equ

en

cy

Size: 0.0718mm, image resolution 1.2 μm 3D image

Extracted network

Coordination number distribution

Carbonates

Multiple point statistics

Pore network extraction

Throat size distribution

Berea network Equivalent Berea network – can be of arbitrary size

Statistical generation of random networks

Network building blocks

• Network topology is the same as voxel representation– Irregular pore shapes captured through shape factor, G

– Both pore bodies and throats are assigned shapes with volumes recorded from voxel image

2P

AG

36

3,0G

16

1G

4

1G

Simulating displacement - primary drainage

• Primary oil migration. Invade accessible elements in order of increasing capillary entry pressure– Invasion through piston-like displacement

– Part of elements in contact with oil alters its wettability

rP owrow

cow cos2

Altered wettability

Waterflooding

• Elements filled in order of reducing capillary entry pressure– Piston-like advance in throats – as in drainage, but

advancing contact angles and higher entry pressure due to movement of water onto water layers. Also snap-off.

Three-phase displacements

• A generalization of the two-phase displacement events– Assume that a single event only involves two phases

• Track target saturation path– Increase gas saturation – choose most favored of gas/oil or

gas/water displacement

• Double displacement. One phase displaces another, trapped phase, that displaces the third. Most common displacement is gas/oil/water. This mechanism reconnects oil during gas injection after waterflooding.

Example displacement sequence

Configuration CConfiguration A Configuration B

Configuration EConfiguration G

Primary Drainage

Water Flooding

Gas Injection

Configuration I

Layer Collapse

gw

go Gas Injection

GasWaterOil

Predictive modelling

• Single-phase dispersion and NMR response• Two-phase flow predictions – imbibition vs. waterflooding• Three-phase flow predictions

• Only a selection of results shown – many more predictions made for non-Newtonian flow, mixed-wet rocks and WAG flooding than we can show here.

Mean flow direction

Dispersion

Model advective movement in semi-analytic flow field combined with random motion to represent diffusion.

Predict amount of dispersion as a function of Peclet number = uL/D

Dispersion

II III IV I

PeDL ~PeDL ~1/(F)

= 1.2

Points are experiments and line is prediction.

Can physically interpret all the dispersion regimes.

2 = 2Dt.

NMR response – theory, simulation and experiment

Sand packs imaged using micro-CT scanning and extracted networks.

(a) (b)

(c) (d)

(a) (b)

(c) (d)

2mm

(a) (b)

(c) (d)

(a) (b)

(c) (d)

2mm

F42B

0

0.05

0.1

0.15

0.2

0.25

100 1000 10000T2 (ms)

Por

osity

(a.

u)

ExperimentalMCT SimulationNetwork Simulation

F42B

0.01

0.1

1

0 1000 2000 3000Time (ms)

Nor

mal

ized

Am

plitu

de

ExperimentalMCT SimulationNetwork Simulation

Water-wet two-phase predictions

• Experimental data from Berea sandstone cores (Oak ‘90)– No tuning of network necessary

– The fluids are water and oil

– Water-wet data – predictions made with θa = [50°, 80°]

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Water Saturation

Rel

ativ

e P

erm

eabi

lity

Primary drainage

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Water Saturation

Rel

ativ

e P

erm

eabi

lity

ExperimentalPredicted

Rel

a ti v

e pe

rmea

bili t

y

Rel

a ti v

e pe

rmea

bili t

y

pp

rpp P

Kkq

Secondary waterflooding

Two displacement processes

• Two key displacement processes in porous media:

Waterflooding (water injection to displace oil);

Counter-current imbibition (water injection in a fractured medium, where water imbibes from fractures and oil escapes).

fracture matrix

oil

water

A paradox?

• For a mixed-wet system with a wettability index close to zero:

• Waterflooding is very favorable – combination of low Sor and low krw.

• But for spontaneous imbibition recovery is poor and very slow – up to 10,000 times slower than a water-wet medium.

0.3

0.4

0.5

0.6

0.7

0 1 2 3 4 5

Brine Injected, pore volumes

Wat

erfl

ood

Oil

Rec

over

y, f

ract

ion

ta = 48 h

ta = 72 hta = 240 h

ta = 4 h

ta = 0 h

after Zhou et al 0

0.1

0.2

0.3

0.4

1 10 100 1000 10000 100000

Imbibition Time, min

Imbi

bitio

n O

il re

cove

ry -

frac

tion

ta= 48 h

ta= 72 h

ta= 240 h

ta= 4 hafter Zhou et al

ta= 0 h

A resolution

• The very slow imbibition is due to low krw – Sw is low and water is only connected in layers leading to very slow movement (SPE 90132).

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

Mobile Water Saturation

Rel

ati

ve P

erm

eab

ilit

y

0

20

40

60

80

100

0.1 1 10 100 1000 10000 100000 1000000

Dimensionless Time (t D )

Oil

Rec

over

y, %

Rec

over

able

Oil

Strongly water-wet ta = 0 hours

ta = 4 hours ta = 48 hours

ta = 72 hours ta = 240 hours

Water-wet three-phase data

• Water-wet experimental data on Berea cores (Oak ’90)– Gas injection into oil/water

– Incorporate double displacement

• Few experimental three-phase data sets

0.001

0.01

0.1

1

0 0.2 0.4 0.6 0.8 1

Gas Saturation

Gas

Rela

tive P

erm

eabili

ty .

0.0001

0.001

0.01

0 0.2 0.4 0.6 0.8 1

Water Saturation

Wa

ter R

ela

tive P

erm

eab

ility

.

0.001

0.01

0.1

1

0 0.2 0.4 0.6 0.8 1

Oil SaturationO

il R

elat

ive

Per

mea

bilit

y .

Why make predictions?

• Validate models.• Aid understanding of pore-scale physics.• Make predictions for cases that are difficult to measure –

three-phase flow, different displacement paths and wettability transitions.

• Small scale physics does have an impact at the large scale.

At the field scale

3 km

• Performed a field study on Maureen in the North Sea – wettability trend with initial water saturation.

• Representative, fine-scale geological model.

Recovery curves

Much higher recoveries than current state-of-the-art hysteresis models – combination of low residual saturation (mixed-wet and oil layer drainage) and low water relative permeability giving stable flooding (poorly connected water).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1PV water injected

PV

of o

il pr

oduc

ed

Network modelWater-wet; no hysteresis

Killough modelOil-wet; no hysteresis

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1PV water injected

Wat

ercu

t

And it matters for CO2 injection

Trapping of CO2 after initial injection period – groundwater flow, water injection or vertical flow (Qi et al., IJGGC, 2009).

Mobile CO2 saturation

Z

170m

X3200m

Y

2280m

Trapped CO2 saturation

X3200m

Y

2280m

Z

170m

Future directions

• Use pore-space images directly. Single-phase Stokes solver: streamlines plus random walk (Peyman) and extensions to reactive transport (Branko).

Future directions• Use pore-space images directly for multiphase flow. Picture below look is a lattice Boltzmann

simulation – other methods include level set and smoothed particle hydrodynamics (Edo and Ali). Combine with proper wettability characterization based on pore-scale physics.

Future directions

• And use direct imaging for pore-by-pore validation and testing of models (Stefan).

Future directions

• Entropic characterization of granular media – a more rigorous way to understand the pore space (Rafi).

Conclusions

• Have methods to image and reconstruct real rocks and extract networks

• Predictions of single phase flow are good – non-Newtonian flow, NMT response and dispersion

• Two-phase experimental data are well predicted for a wide range of rocks– Wettability characterisation is not sufficiently well understood

– More work is needed to assess impact of pore scale heterogeneity on flow response

• Back to basics approach for future work – look at the pore space directly

Thanks to….

• All my post-docs and students• Useful discussions with many colleagues• Sponsors of the research

– DTI– EPSRC– ENI– Saudi Aramco– BG– BHP– JOGMEC– Schlumberger– Shell– Statoil– Total