1. Direct simulation of multiphase flow on pore-space images
Mosayeb Shams
Supervised by
Prof. Martin Blunt
Dr. Branko Bijeljic
January 2016

2. Outlook Motivation Background Experimental analysis of snap-off
Direct simulation analysis of snap-off
Conclusion and future work

3. Motivation
Capillary trapping by imbibition happens in carbon-dioxide storage and oil recovery mechanisms.
Pore space geometry plays a key role in both quantity and distribution of residual fluids during imbibition.
A thorough understanding of the relationship between multiphase flow displacement mechanism and pore space structure is necessary
Direct two-phase flow simulation on micro-CT images to analyse snap-off events as a function of pore structure

4. Pore space extraction work flow
Big picture
Pore-network modelling:
Computational efficient
Significant loss of information
on the pore geometry
Direct modelling:
High simulation time
Capturing more detailed information
on the pore geometry
Pore space extraction work flow

5. Basic concept: Liquid-Liquid interactions
Young-Laplace equation:
𝑃 𝑐 =∆𝑃= 𝑃 𝐿2 − 𝑃 𝐿1 =𝜎𝐾=𝜎 1 𝑅 𝑡 𝑅 𝑠

6. Basic concept: Solid-Liquid interactions
Young’s equation:
𝜎 𝑆 𝐿 2 = 𝜎 𝑆 𝐿 1 + 𝜎 𝐿 1 𝐿 2 cos 𝜃 𝑐

7. Modeling: Mathematical
Navier-Stokes equations:
Continuum surface force (CSF):
Color function:

8. Modelling: Numerical
Discretization and solving the PDEs: Finite Volume Method
Capturing interface position: Volume of Fluid method
Surface tension forces: Filtered Surface Force (FSF) model (Raeini 2013)

9. Capillary trapping - Experimental measurments
Imaging fluid displacement and measuring residual non-wetting phase in carbonate samples are carried out by Andrew et all (2014)
Ketton rock sample is drained with supercritical CO2, and then imbibed by brine under in situ conditions (50C and 10 MPa)
Some statistical analysis of snap-off trapping has been carried out on the CO2 ganglia by Mohammed Al Geer.

10. Anomalous ganglia
Criterion: in a multi-pore ganglion all inner throats are mostly larger than adjacent throats
Multi-pore ganglion: A single ganglion that occupies more that one pore
Anomalous ganglion: a multi-pore ganglion that has at least one inner throat which is smaller than one of the adjacent throats
A rendered 3D realization of a multi-pore ganglion (By Mohammed Al Geer)

11. Statistics of pore-throat geometry
Throat size vs contraction ratio (By Mohammed Al Geer)

12. Studied ganglia Ganglia distribution at a 2×2×2 mm subset of the core
Multi-pore ganglia
Multi-pore ganglia with anomaly

13. Adjacent pore radius (µm)
Analysis of ganglion 72
Throat #
Throat radius
(µm)
Adjacent pore radius (µm)
Ratio
rp/rt
Remarks
214
31.60
72.40
2.29
Outer
259
20.90
102.03
4.88
262
19.99
57.73
2.89
315
22.63
71.19
3.15
365
35.51
61.90
1.74
393
27.14
52.52
1.94
467
29.13
2.45
554
29.35
48.05
1.64
360
17.67
57.37
3.27
Inner
481
39.18
1.82
A comparison between all inner (blue) and adjacent throats (red) at ganglion 72 (By Mohammed Al Geer)

14. Adjacent pore radius (µm)
Analysis of ganglion 15
Throat #
Throat radius
(µm)
Adjacent pore radius (µm)
Ratio
rp/rt
Remarks 92
24.73
83.38
3.37
Outer
326
20.90
64.38
3.07
327
20.29
51.07
2.52
Inner
A comparison between all inner (blue) and adjacent throats (red) at ganglion 15 (By Mohammed Al Geer)

15. Direct simulation of individual throats
In order to take into account the local pore topology on snap-off, images of the pore space around the anomalous adjacent throats are cropped and taken as input geometry
The criterion for snap-off phenomenon in direct simulation is snap-off Pc
Ganglion 15
Throat 326
Ganglion 15
Throat 327
Ganglion 15
Throat 92

16. Direct simulation analysis of ganglion 15
Example simulation - throat 327: indicator function showing water-layer growth

17. Capillary pressure vs time for individual throats
Snap-off Pc=366
Snap-off Pc=23
Snap-off Pc=162

18. Snap-off pressure of individual throats for 15
The outer throats (92,326), which are larger than the inner (327), are snapped off first , but 327 is not snapped off because of lower snap-off pressure

19. Snap-off pressure of individual throats for 72
Direct simulation shows that the inner throat, 360, does not snap off because of having a large negative snap-off pressure in comparison to the adjacent throats.

20. Snap-off pressure of individual throats for 72

21. Summary of simulations on individual throats
3 out of 7 ganglia with anomalous cases (15, 72 and 178) have already been resolved using direct simulation on individual throats.
For the 4 unresolved cases we have recently started to run simulations on whole ganglion to account for non-local effects.