what determines transport behaviour in different porous media?

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

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

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)

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

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)

Beadpack

Sandstone

Carbonate

Pore Space

Pressure field

Velocity field

Difference in:connectivitytortuosity &distribution

Beadpack

Sandstone

Carbonate

Variograms:Porosity and Velocity

.

porosity

velocity

L = p V/S

magnitude of u (at the voxel centers) uav

average flow speed

PDF Velocity

narrowest spread - single tube

widest spread - carbonate

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

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

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

Model Results: Transport and Flow

Spread in velocity distribution defines transport,

Bijeljic et al., Phys. Rev. E, 2012

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

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

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

Distance travelled (mm)

t=0.1s

t=0.3s

t=1s

t=3s

t=10s

Less stagnant

Plume Evolution:Mt Gambier, Pe =10

initial

Distance travelled (mm)

t=0.1s

t=0.3s

t=1s

t=3s

t=10s

Less stagnantand more diffusive

Plume Evolution:Estaillades, Pe =200

initial

Distance travelled (mm)

t=0.1s

t=0.3s

t=1s

t=3s

t=10s

More stagnant

Carbonates:Resolution vs. Image Size

PDF Velocity

P() Probability ofdisplacement

<>0 =uavt averagedisplacement

Impact of Pe

Pe = tadv / tdiff

tadv = L /uav tdiff = L2 / Dm

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