What Determines Transport Behaviour in Different Porous Media?

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## What Determines Transport Behaviour in Different Porous Media?

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**What is the signature of flow / transport in porous media?**• What is impact of structural/flow heterogeneity? Science What Determines Transport Behaviour in Different Porous Media? Applications Contaminant Transport Development of miscibility in CO2storage in aquifers Mixing in CO2injection in gas and light oil fields BrankoBijeljic, Ali Raeini, PeymanMostaghimi and Martin Blunt Dept. of Earth Science and Engineering, Imperial College, London**Networks**Images Transport – Dispersion Distributions vs. Average Values? 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 = uavL / 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)**X ray**Stokes equation Random walk microtomography + = + 2 Ñ = m Ñ r x r x t dt t ( , ) ( , ) u p 0 + X X adv diff Pore scale:Direct Simulation on micro-CT images 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 (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**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-Fickianbehaviour 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-Fickianbehaviour associated with impact of Pe • - A priori predictions of transport possible**THANKS!**Prof. MasaProdanovic, Dr. Hu Dong Elettra synchrotron: GiulianaTromba, Franco Zanini, OussamaGharbi , Alex Toth & Matthew Andrew Qatar Petroleum, Shell and the Qatar Science & Technology Park Imperial College Pore-scale Modelling Consortium