Report

What Determines Transport Behaviour in Different Porous Media? Science What is the signature of flow / transport in porous media? What is impact of structural/flow heterogeneity? 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 Bijeljic , Muggeridge and Blunt, Water Resour. Res. (2004) Sandstone Flow - Permeability Relative Permeability 1 0.8 Valvatne and Blunt, Water Resour. Res. (2004) 0.6 0.4 0.2 0 0 0.2 0.4 0.6 Water Saturation 0.8 1 Carbonate Physically Describe Heterogeneity: PDF of Transit Times in Image Voxels y ( t) ~ t –(1+b) b = 0.7 Portland limestone Pe = uav L / Dm DL/Dm ~ t2b; 0 < b < 1 Bijeljic, Mostaghimi and Blunt, Phys. Rev. Lett., 2011 tb = t / t1b t1b = R /uav 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() Bentheimer sandstone Probability of displacement <>0 =uavt Portland carbonate Scheven et al.(2005) average displacement Pore scale: Direct Simulation on micro-CT images structure X ray microtomography flow diffusion Stokes equation Random walk p = m2u FVM , Open Foam r(x, t + dt) = r(x0 , t ) + X adv + X diff (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 Velocity field Difference in: connectivity tortuosity & distribution . 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 Distance travelled (mm) - few high u - no retardation - Gaussian Plume Evolution: Bentheimer sandstone initial uav=1.03mm/s t=0.106s t=0.2s t=0.45s t=1s t=2s Distance travelled (mm) - more high u - stagnant - structure Plume Evolution: Portland carbonate initial uav=1.3mm/s t=0.106s t=0.2s t=0.45s t=1s t=2s Distance travelled (mm) - even higher u - even more stagnant Model Results: Transport and Flow Spread in velocity distribution defines transport, Bijeljic et al., Phys. Rev. E, 2012 t=0.106s Model vs. NMR data t=0.2s (a) beadpack uav=0.91mm/s t=0.45s t=1s t=2s (b) sandstone uav=1.03mm/s (c) carbonate uav=1.3mm/s Bijeljic et al., Phys. Rev. E, 2012 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 Carbonates: Resolution vs. Image Size PDF Velocity P() Probability of displacement <>0 =uavt average 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