What Determines Transport
Behaviour in Different Porous Media?
Science
What is the signature of flow / transport in porous media?
What is impact of structural/flow heterogeneity?
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
Distributions vs. Average Values?
Networks
Images
Transport – Dispersion
Sandpack
Bijeljic , Muggeridge and Blunt,
Water Resour. Res. (2004)
Sandstone
Flow - Permeability
Relative Permeability
1
0.8
Valvatne and Blunt,
Water Resour. Res.
(2004)
0.6
0.4
0.2
0
0
0.2
0.4
0.6
Water Saturation
0.8
1
Carbonate
Physically Describe Heterogeneity:
PDF of Transit Times in Image Voxels
y ( t) ~ t –(1+b)
b = 0.7
Portland limestone
Pe = uav L / Dm
DL/Dm ~ t2b; 0 < b < 1
Bijeljic, Mostaghimi and Blunt, Phys. Rev. Lett., 2011
tb = t / t1b
t1b = R /uav
Truncated power-law with wide range of transit times across image voxels
NMR Flow Propagators :
Displacement in non-Fickian Transport
t=0.106s; 0.2s;0.45s;1s;2s
Beadpack
P()
Bentheimer
sandstone
Probability of
displacement
<>0 =uavt
Portland
carbonate
Scheven et al.(2005)
average
displacement
Pore scale:
Direct Simulation on
micro-CT images
structure
X ray
microtomography
flow
diffusion
Stokes equation Random walk
p = m2u
FVM , Open Foam
r(x, t + dt) = r(x0 , t ) +
X adv + X diff
(Raeini, Blunt & Bijeljic,
J. Comp. Phys., 2012)
(Mostaghimi, Bijeljic & Blunt,
SPE Journal, 2012)
In each time step move particles by advection & diffusion
Beadpack
Sandstone Carbonate
Pore Space
Pressure field
Velocity field
Difference in:
connectivity
tortuosity &
distribution
.
Variograms:
Porosity and Velocity
porosity
Beadpack
Sandstone
velocity
Carbonate
L = p V/S
PDF Velocity
magnitude of u
(at the voxel centers)
uav
average flow speed
narrowest spread - single tube
widest spread - carbonate
Plume Evolution:
Beadpack
initial
uav=0.91mm/s
t=0.106s
t=0.2s
t=0.45s
t=1s
t=2s
Distance travelled (mm)
- few high u
- no retardation
- Gaussian
Plume Evolution:
Bentheimer sandstone
initial
uav=1.03mm/s
t=0.106s
t=0.2s
t=0.45s
t=1s
t=2s
Distance travelled (mm)
- more high u
- stagnant
- structure
Plume Evolution:
Portland carbonate
initial
uav=1.3mm/s
t=0.106s
t=0.2s
t=0.45s
t=1s
t=2s
Distance travelled (mm)
- even higher u
- even more
stagnant
Model Results:
Transport and Flow
Spread in velocity distribution
defines transport,
Bijeljic et al., Phys. Rev. E, 2012
t=0.106s
Model
vs.
NMR data
t=0.2s
(a) beadpack
uav=0.91mm/s
t=0.45s
t=1s
t=2s
(b) sandstone
uav=1.03mm/s
(c) carbonate
uav=1.3mm/s
Bijeljic et al.,
Phys. Rev. E, 2012
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. 5-500 uav
Carbonates:
Image and Flow Properties
L = p V/S
.
Carbonates:
Variograms of Porosity and Velocity
porosity
velocity
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.
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
Carbonates:
Resolution vs. Image Size
PDF Velocity
P()
Probability of
displacement
<>0 =uavt
average
displacement
Impact of Pe
tadv = L /uav tdiff = L2 / Dm
Pe = tadv / tdiff
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
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