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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 Transport Development of miscibility in CO 2 storage in aquifers Mixing in CO 2 injection in gas and light oil fields

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Distributions vs. Average Values? Flow - Permeability Bijeljic, Muggeridge and Blunt, Water Resour. Res. (2004) Valvatne and Blunt, Water Resour. Res. (2004) Transport – Dispersion Networks Sandpack Sandstone Carbonate Images

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Physically Describe Heterogeneity: PDF of Transit Times in Image Voxels Portland limestone Truncated power-law with wide range of transit times across image voxels = 0.7 b = t / t 1b t 1b = R /u av Pe = u av L / D m Bijeljic, Mostaghimi and Blunt, Phys. Rev. Lett., 2011 D L /D m ~ 2 ; 0 < t ~ t –(1+

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NMR Flow Propagators : Displacement in non-Fickian Transport Scheven et al.(2005) Bentheimer sandstone Beadpack Portland carbonate P( ) Probability of displacement 0 =u av t average displacement t=0.106s; 0.2s;0.45s;1s;2s

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Pore scale: Direct Simulation on micro-CT images X ray microtomography Stokes equationRandom walk diffadv XX tdtt ),(),( 0 xrxr u 2 p 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)

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BeadpackSandstoneCarbonate Pore Space Pressure field Velocity field Difference in: connectivity tortuosity & distribution

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Beadpack Sandstone Carbonate Variograms: Porosity and Velocity. porosity velocity L = V/S

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magnitude of u (at the voxel centers) u av average flow speed PDF Velocity narrowest spread - single tube widest spread - carbonate

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Plume Evolution: Beadpack Distance travelled ( m) initial t=0.106s t=0.2s t=0.45s t=1s t=2s - few high u - no retardation - Gaussian u av =0.91mm/s

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Plume Evolution: Bentheimer sandstone initial Distance travelled ( m) t=0.106s t=0.2s t=0.45s t=1s t=2s - more high u - stagnant - structure u av =1.03mm/s

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Plume Evolution: Portland carbonate initial Distance travelled ( m) t=0.106s t=0.2s t=0.45s t=1s t=2s - even higher u - even more stagnant u av =1.3mm/s

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

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Model vs. NMR data t=0.106s t=0.2s t=0.45s t=1s t=2s Bijeljic et al., Phys. Rev. E, 2012 (a) beadpack u av =0.91mm/s (b) sandstone u av =1.03mm/s (c) carbonate u av =1.3mm/s

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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 u av. 5-500 u av ME1ME2

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Carbonates: Image and Flow Properties L = V/S

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Carbonates: Variograms of Porosity and Velocity. porosity velocity

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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 u av.

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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? t d = t / t diff

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Carbonates: Resolution vs. Image Size PDF Velocity P( ) Probability of displacement 0 =u av t average displacement

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Impact of Pe Pe = t adv / t diff t adv = L /u av t diff = L 2 / D m

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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

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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

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