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

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)

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

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)

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

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

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 - few high u - no retardation - Gaussian Distance travelled (mm)

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)

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)

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

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

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

Variograms of Porosity and Velocity 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

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

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)

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

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