1. What Determines Transport Behaviour in Different Porous Media?
What is the signature of flow / transport in porous media?
What is impact of structural/flow heterogeneity?
Science
Applications
Contaminant Transport
Development of miscibility in CO2 storage in aquifers
Mixing in CO2 injection in gas and light oil fields
Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt
Dept. of Earth Science and Engineering, Imperial College, London

2. Distributions vs. Average Values?
Networks
Images
Transport – Dispersion
Sandpack
Sandstone
Carbonate
Bijeljic , Muggeridge and Blunt,
Water Resour. Res. (2004)
Flow - Permeability
Valvatne and Blunt,
Water Resour. Res. (2004)

3. Physically Describe Heterogeneity: PDF of Transit Times in Image Voxels
y ( t) ~ t –(1+b)
b = 0.7
Portland limestone
Pe = uav L / Dm
tb = t / t1b
DL/Dm ~ t2b; 0 < b < 1
t1b = R /uav
Bijeljic, Mostaghimi and Blunt, Phys. Rev. Lett., 2011
Truncated power-law with wide range of transit times across image voxels

4. NMR Flow Propagators : Displacement in non-Fickian Transport
t=0.106s; 0.2s;0.45s;1s;2s
Beadpack
P()
Probability of
displacement
Bentheimer
sandstone
<>0 =uavt
average
displacement
Portland
carbonate
Scheven et al.(2005)

5. Pore scale: Direct Simulation on micro-CT images
X ray
microtomography
Stokes equation
Random walk
diff
adv X t dt + = ) , ( x r u 2 Ñ m p
FVM , Open Foam
(Raeini, Blunt & Bijeljic,
J. Comp. Phys., 2012)
(Mostaghimi, Bijeljic & Blunt,
SPE Journal, 2012)
In each time step move particles by advection & diffusion

6. Beadpack
Sandstone
Carbonate
Pore Space
Pressure field
Difference in:
connectivity
tortuosity &
distribution
Velocity field

7. Variograms: Porosity and Velocity.
porosity
Beadpack
Sandstone
velocity
Carbonate
L = p V/S

8. PDF Velocity magnitude of u (at the voxel centers) uav
average flow speed
narrowest spread - single tube
widest spread - carbonate

9. Plume Evolution: Beadpack
initial
uav=0.91mm/s
t=0.106s
t=0.2s
t=0.45s
t=1s
t=2s
- few high u
- no retardation
- Gaussian
Distance travelled (mm)

10. Plume Evolution: Bentheimer sandstone
initial
uav=1.03mm/s
t=0.106s
t=0.2s
t=0.45s
t=1s
t=2s
- more high u
- stagnant
- structure
Distance travelled (mm)

11. Plume Evolution: Portland carbonate
initial
uav=1.3mm/s
t=0.106s
t=0.2s
t=0.45s
t=1s
t=2s
- even higher u
even more
stagnant
Distance travelled (mm)

12. Model Results: Transport and Flow Spread in velocity distribution
defines transport,
Bijeljic et al., Phys. Rev. E, 2012

13. Model vs. NMR data t=0.106s t=0.2s t=0.45s t=1s t=2s (a) beadpack
uav=0.91mm/s
(b) sandstone
uav=1.03mm/s
(c) carbonate
uav=1.3mm/s
t=0.45s
t=1s
Bijeljic et al.,
Phys. Rev. E, 2012
t=2s

14. Carbonate types with distinct transport behaviour
ME1
ME2
Normalised velocities as the ratios of the magnitude of u at the voxel centers divided by the average flow speed uav uav

15. Carbonates: Image and Flow Properties
L = p V/S

16. Variograms of Porosity and Velocity
Carbonates:
Variograms of Porosity and Velocity .
porosity
velocity

17. Velocity distributions in the images of carbonate rock
Normalised velocities as the ratios of the magnitude of u at the voxel centers divided by the average flow speed uav.

18. Different type of transport in carbonates
Diffusion from stagnant to flowing regions.
In the heterogeneous samples, there is no typical, average velocity.
Sampling at later times, longer lengths, with more structure.
No representative transport speed.
Challenge for upscaling.
Implications for reactive transport?
td = t / tdiff

19. Plume Evolution: Mt Gambier, Pe =200
initial
t=0.1s
t=0.3s
t=1s
t=3s
t=10s
Distance travelled (mm)
Less stagnant

20. Plume Evolution: Mt Gambier, Pe =10
initial
t=0.1s
t=0.3s
t=1s
t=3s
t=10s
Less stagnant
and more diffusive
Distance travelled (mm)

21. Plume Evolution: Estaillades, Pe =200
initial
t=0.1s
t=0.3s
t=1s
t=3s
t=10s
Distance travelled (mm)
More stagnant

22. Carbonates: Resolution vs. Image Size
P()
<>0 =uavt
PDF Velocity
average
displacement
Probability of
displacement

23. Impact of Pe
tadv = L /uav
tdiff = L2 / Dm
Pe = tadv / tdiff

24. CONCLUSIONS
Different generic non-Fickian transport behaviour demonstrated in carbonates compared to sandstones and beadpacks
Different non-Fickian behaviour due to different spread in velocity distribution and connectivity
Agreement with NMR flow propagators experiments on rock cores in the pre-asymptotic regime
Different non-Fickian behaviour associated with impact of Pe
- A priori predictions of transport possible

25. THANKS! Prof. Masa Prodanovic, Dr. Hu Dong
Elettra synchrotron: Giuliana Tromba, Franco Zanini,
Oussama Gharbi , Alex Toth & Matthew Andrew
Qatar Petroleum, Shell and the Qatar Science & Technology Park
Imperial College Pore-scale Modelling Consortium