Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt
What Determines Transport Behaviour in Different Porous Media?
Dept. of Earth Science and Engineering, Imperial College, London
Applications
Science
What is the signature of flow / transport in porous media?
What is impact of structural/flow heterogeneity?
Contaminant TransportDevelopment of miscibility in CO2 storage in
aquifersMixing in CO2 injection in gas and light oil fields
Distributions vs. Average Values?
Flow - Permeability
Bijeljic , Muggeridge and Blunt, Water Resour. Res. (2004)
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
Water Saturation
Rel
ativ
e P
erm
eabi
lity
Valvatne and Blunt,Water Resour. Res. (2004)
Transport – Dispersion
Networks
Sandpack
Sandstone
Carbonate
Images
Physically Describe Heterogeneity:PDF of Transit Times in Image Voxels
Portland limestone
Truncated power-law with wide range of transit times across image voxels
b = 0.7
tb = t / t1b
t1b = R /uav
Pe = uav L / Dm
Bijeljic, Mostaghimi and Blunt, Phys. Rev. Lett., 2011
DL/Dm ~ t2b; 0 < b < 1
( y t) ~ t –
(1+ )b
NMR Flow Propagators : Displacement in non-Fickian
Transport
Scheven et al.(2005)
Bentheimersandstone
Beadpack
Portland carbonate
P()
Probability ofdisplacement
<>0 =uavt
averagedisplacement
t=0.106s; 0.2s;0.45s;1s;2s
Pore scale:Direct Simulation on
micro-CT imagesstructure flow diffusion
X raymicrotomography
Stokes equationRandom walk
diffadv XXtdtt++=+ ),(),( 0xrxru2Ñ=Ñ mp
In each time step move particles by advection & diffusion
FVM , Open Foam
(Raeini, Blunt & Bijeljic,J. Comp. Phys., 2012)
(Mostaghimi, Bijeljic & Blunt,SPE Journal, 2012)
Beadpack
Sandstone
Carbonate
Pore Space
Pressure field
Velocity field
Difference in:connectivitytortuosity &distribution
Beadpack
Sandstone
Carbonate
Variograms:Porosity and Velocity
.
porosity
velocity
L = p V/S
magnitude of u (at the voxel centers)
uav
average flow speed
PDF Velocity
narrowest spread - single tube
widest spread - carbonate
Plume Evolution:Beadpack
Distance travelled (mm)
initial
t=0.106s
t=0.2s
t=0.45s
t=1s
t=2s
- few high u- no retardation- Gaussian
uav=0.91mm/s
Plume Evolution:Bentheimer sandstone
initial
Distance travelled (mm)
t=0.106s
t=0.2s
t=0.45s
t=1s
t=2s
- more high u- stagnant- structure
uav=1.03mm/s
Plume Evolution:Portland carbonate
initial
Distance travelled (mm)
t=0.106s
t=0.2s
t=0.45s
t=1s
t=2s
- even higher u- even more stagnant
uav=1.3mm/s
Model Results: Transport and Flow
Spread in velocity distribution defines transport,
Bijeljic et al., Phys. Rev. E, 2012
Modelvs.NMR data
t=0.106s
t=0.2s
t=0.45s
t=1s
t=2s Bijeljic et al., Phys. Rev. E, 2012
(a) beadpackuav=0.91mm/s
(b) sandstone uav=1.03mm/s
(c) carbonateuav=1.3mm/s
Carbonate types with distinct transport
behaviour
Normalised velocities as the ratios of the magnitude of u at the voxel centers divided by the average flow speed uav. 5-500 uav
ME1 ME2
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 ofdisplacement
<>0 =uavt
averagedisplacement
Impact of Pe
Pe = tadv / tdiff
tadv = L /uav tdiff = L2 / Dm
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