Architecture-Based Runtime Software Evolution Peyman Oreizy, Nenad Medvidovic & Richard N. Taylor.
Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour...
-
Upload
darby-peffer -
Category
Documents
-
view
217 -
download
0
Transcript of Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour...
![Page 1: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/1.jpg)
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
![Page 2: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/2.jpg)
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
![Page 3: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/3.jpg)
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
![Page 4: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/4.jpg)
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
![Page 5: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/5.jpg)
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)
![Page 6: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/6.jpg)
Beadpack
Sandstone
Carbonate
Pore Space
Pressure field
Velocity field
Difference in:connectivitytortuosity &distribution
![Page 7: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/7.jpg)
Beadpack
Sandstone
Carbonate
Variograms:Porosity and Velocity
.
porosity
velocity
L = p V/S
![Page 8: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/8.jpg)
magnitude of u (at the voxel centers)
uav
average flow speed
PDF Velocity
narrowest spread - single tube
widest spread - carbonate
![Page 9: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/9.jpg)
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
![Page 10: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/10.jpg)
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
![Page 11: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/11.jpg)
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
![Page 12: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/12.jpg)
Model Results: Transport and Flow
Spread in velocity distribution defines transport,
Bijeljic et al., Phys. Rev. E, 2012
![Page 13: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/13.jpg)
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
![Page 14: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/14.jpg)
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
![Page 15: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/15.jpg)
Carbonates: Image and Flow Properties
L = p V/S
![Page 16: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/16.jpg)
Carbonates: Variograms of Porosity and
Velocity.
porosity
velocity
![Page 17: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/17.jpg)
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.
![Page 18: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/18.jpg)
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
![Page 19: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/19.jpg)
Carbonates:Resolution vs. Image Size
PDF Velocity
P()
Probability ofdisplacement
<>0 =uavt
averagedisplacement
![Page 20: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/20.jpg)
Impact of Pe
Pe = tadv / tdiff
tadv = L /uav tdiff = L2 / Dm
![Page 21: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/21.jpg)
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
![Page 22: Branko Bijeljic, Ali Raeini, Peyman Mostaghimi and Martin Blunt What Determines Transport Behaviour in Different Porous Media? Dept. of Earth Science and.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649ca45503460f94964ae1/html5/thumbnails/22.jpg)
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