1. Dispersion in Porous Media from Pore-scale Network Simulation
Branko Bijeljic
Ann Muggeridge
Martin Blunt
Dept. of Earth Science and Engineering,
Imperial College,
London

2. OVERVIEW Dispersion in Porous Media (Motivation) Network Model
Asymptotic Dispersion: Model vs. Experiments
Pre-asymptotic Dispersion: Model vs. CTRW
Conclusions

3. MIXING of FLOWING FLUIDS in POROUS MEDIA
Pore scale mixing processes are COMPLEX:
What is the correct macroscopic description?

4. MOTIVATION
Describe macroscopic dispersion using a Lagrangian-based pore network model over a wide range of Peclet numbers (0<Pe<105)
Aquifers
Contaminant transport
Oil reservoirs:
Tracers
Development of gas/oil miscibility

5. METHOD

6. Pore network representation
Process-based reconstruction
LARGE SCALE

7. Algorithm 1. Calculate mean velocity in each pore throat
by invoking volume balance at each pore 2.
Use analytic solution to determine velocity
profile in each pore throat 3.
In each time step particles move by a.
Advection b.
Diffusion 4.
Impose rules for mixing at junctions 5.
Obtain asymptotic dispersion coefficient

8. MIXING RULES at JUNCTIONS
Pe >>1
Pe<<1
- flowrate weighted rule ~ Fi /  Fi ;
- assign a new site at random &
move by udt;
- only forwards
- area weighted rule ~ Ai /  Ai ;
- assign a new site at random;
- forwards and backwards

9. Simulation (DL , Pe=0.1)

10. Comparison with experiments asymptotic DL (0<Pe<105)
Bijeljic et al. WRR, Nov 2004
- network model, reconstructed Berea sandstone
- Dullien, 1992, various sandstones
- Gist and Thompson, 1990, various sandstones
- Legatski and Katz, 1967, various sandstones
- Frosch et al., 2000, various sandstones 
- Pfannkuch, 1963, unconsolidated bead packs
- Seymour and Callaghan, 1997, bead packs
- Khrapitchev and Callaghan, 2003, bead packs

11. Comparison with experiments: DL - Boundary-layer dispersion
1 - Bijeljic et al network model, reconstructed Berea sandstone
2 - Brigham et al., 1961, Berea sandstone
3 - Salter and Mohanty, 1982, Berea sandstone
4 - Yao et al., 1997, Vosges sandstone
5 - Kinzel and Hill, 1989, Berea sandstone
6 - Sorbie et al., 1987, Clashach sandstone
7 - Gist and Thompson, 1990, various sandstones
8 - Gist and Thompson, 1990, Berea sandstone
9 - Kwok et al., 1995, Berea sandstone, liquid radial flow
10 - Legatski and Katz, 1967, various sandstones, gas flow
10<Pe<400; dL = 1.19
11 - Legatski and Katz, 1967, Berea sandstone, gas flow
12 - Pfannkuch, 1963, unconsolidated bead packs

12. Comparison with experiments asymptotic DT (0<Pe<105)
10<Pe<400; dT = 0.94
Pe>400; dT = 0.89
- network model, reconstructed Berea sandstone
- Dullien, 1992, various sandstones
- Gist and Thompson, 1990, various sandstones
- Legatski and Katz, 1967, various sandstones
- Frosch et al., 2000, various sandstones
- Harleman and Rumer, 1963 (+); (-);
- Gunn and Pryce, 1969 (□);
- Han et al (○)
- Seymour and Callaghan, 1997 ()
- Khrapitchev and Callaghan, 2003 (∆,◊).

13. Pre-asymptotic regime

14. Probability density distributions
Scher and Lax, 1973; Berkowitz and Scher, 1995

15. Comparison with CTRW theory
b= 1.80

16. Comparison with CTRW theoryB)
Dentz et al., 2004

17. CONCLUSIONS - Unique network simulation model able to predict
variation of D
,T/ D
vs Peclet
over the range
0< Pe
<10 5 . L m
- The boundary-layer dispersion regime is related to
the CTRW exponent b 1.80 where d = 3-b.
- The cross-over to a linear regime for Pe>400 is due to
a transition from a diffusion-controlled late-time cut-off,
to one governed by a minimum typical flow speed umin.

18. THANKS!

19. Structure-flow relationship
maximum velocities are in the throats of
intermediate radii