1. From pore-space images to multiphase transport predictions
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 Engineering
Imperial College London

2. 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

3. Contact angles in three-phase flow
Bartell-Osterhoff (1927)
Solid
Water
Oil
Water
Gas
Solid
3 Contact angles (O/W,G/W,G/O)
1 Constraint between them
2 Independent values of contact angle
Oil
Gas
Solid
Young’s equation

4. Wettability alteration
Water
Oil b
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.

5. 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 qow. 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.
Air
Water
Oily surface

6. 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.

7. From rock to network to predictions
3 mm
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

8. 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)

9. 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)

10. 3D images and extracted pores
3 mm

11. Oil invasion

12. Non-wetting phase trapping
Dong, 2007
Rock
Water
Residual phase
So how far does the CO2 spread? Fortunately we know that it doesn’t keep on spreading forever. As the CO2 moves through the rocks it leaves behind a trail of tiny bubbles of CO2 that are effectively immobilized. This picture is a CT image of um sized bubbles of blue CO2 trapped in pores in the grey rocks in the presence of green water.

13. Carbonates Multiple point statistics Pore network extraction
Size: mm, image resolution 1.2 μm
Extracted network
3D image
Coordination number distribution
Throat size distribution

14. Statistical generation of random networks
Berea network
Equivalent Berea network –
can be of arbitrary size

15. 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

16. 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
Altered wettability

17. 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.

18. 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.

19. Example displacement sequence
Gas
Water
Oil
Configuration C
Configuration A
Configuration B
Configuration E
Configuration G
Primary Drainage
Water Flooding
Gas Injection
Configuration I
Layer Collapse

20. 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.

21. 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
Mean flow direction

22. Dispersion Points are experiments and line is prediction.
Can physically interpret all the dispersion regimes.
s2 = 2Dt. II
III IV I
1/(F)
d = 1.2

23. NMR response – theory, simulation and experiment
Sand packs imaged using micro-CT scanning and extracted networks.

24. 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°]
Primary drainage
Secondary waterflooding
Relative permeability
Relative permeability

25. 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

26. 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.

27. 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).

28. 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

29. 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.

30. At the field scale
Performed a field study on Maureen in the North Sea – wettability trend with initial water saturation.
Representative, fine-scale geological model.
3 km

31. 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).

32. 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 X
3200m Y
2280m
Trapped CO2 saturation

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

34. 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.

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

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

37. 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

38. 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
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