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Simulation of reactive transport on pore-scale images. Zaki Al Nahari, Branko Bijeljic, Martin Blunt. Motivation. Contaminant transport: Industrial waste remedy Biodegradation of landfills Carbon capture and storage: Acidic brine. Over time, potential dissolution and/or mineral trapping.

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simulation of reactive transport on pore scale images

Simulation of reactive transport on pore-scale images

Zaki Al Nahari, Branko Bijeljic, Martin Blunt

motivation
Motivation
  • Contaminant transport:
    • Industrial waste remedy
    • Biodegradation of landfills
  • Carbon capture and storage:
    • Acidic brine.
    • Over time, potential dissolution and/or mineral trapping.
  • However….
    • Uncertainty in reaction rates
      • The field <<in the lab.
    • No fundamental basis to integrate flow, transport and reaction in porous media.
physical description of reactive transport model
Physical description of reactive transport model

Micro-CT scanner uses X-rays to produce a sequence of cross-sectional tomography images of rocks in high resolution (µm)

  • Place particles on the image
  • B injected in the first layer
  • A is placed in the rest of the image

Advection along streamlines using a novel formulation accounting for zero flow at solid boundaries. It is based on a semi-analytical approach: no further numerical errors once the flow is computed at cell faces

  • Geometry
  • Flow Field
  • Reactants Injection
  • Reaction
  • Transport by Advection
  • Transport by Diffusion

For incompressible laminar flow, Stokes equations

Diffusion using random walk. It is a series of spatial random displacements that define the particle transitions by diffusion.

geometry flow particle tracking
Geometry, Flow , Particle Tracking

Particle tracking:

Volume placement and front injection

Pore space

Velocity field

Pressure field

Particle tracking:

Transport and fluid/fluid reaction

reaction rate
Reaction Rate
  • Bimolecular reaction
  • A + B → C
  • The reaction occurs if two conditions are met:
    • Distance between reactant is less than or equal the diffusive step ( )
      • If there is more than one possible reactant, the reaction will be with the nearest reactant.
  • The probability of reaction (Pr) as a function of reaction rate constant (k) and diffusive step ( ) :
fluid fluid reactive transport benchmark experiment by gramling et al 2002
Fluid/fluid reactive transport benchmark experiment by Gramling et al (2002)
  • Description:
  • The experiment was conducted by Gramling et al. (2002)
  • Irreversible Bimolecular reaction
  • Na2EDTA2- + CuSO4(aq) → CuEDTA2- + 2Na+ + SO42-
  • A + B → C
  • The column is filled with grains of cryolite (Na3AlF6)
  • Reactant A was filled in the column and displaced by B
  • The change in the colour of solution records the progression of reaction

Gramling et al. (2002)

validation of the model with benchmark experiment by gramling et al 2002
Validation of the Model with benchmark experiment by Gramling et al (2002)

Gramling et al. (2002)

beadpack image used in simulation
Beadpack image used in simulation

Pore space

Pressure field

Velocity field

Used beadpack with grain size 100 microns:

To have the grain size of 1.3mm as in Gramling et al. need to multiply by 13

comparison of pdfs of voxel velocities for different beadpack image sizes and resolution
Comparison of PDFs of voxel velocities for different beadpack image sizes and resolution

3003beadpack with 26micron resolution can be used

size of the system in which particles a are initially placed
Size of the system in which particles A are initially placed

1

1

1

Image

Image 2

Image

Image 1

299x(n-1)

300

300

600

598

894

300

299xn

299

Image

1

Image

n

0 μm

0 μm

0 μm

0 μm

7774x(n-1)μm

7774xn μm

15548 μm

23244 μm

15600 μm

7774 μm

7800 μm

7800 μm

7800 μm

Image

2

Image

3

Image

n-1

conclusions
Conclusions
  • Developed a new particle tracking-based simulator for fluid/fluid reactive transport directly on the pore space of micro-CT images
  • The simulator is validated by comparison with the bechmark fluid/fluid reactive transport experiments by Gramling et al.(2002)
  • Capability to study the impact of heterogeneity in pore structure, velocity field, transport and reaction on the physicochemical processes in the subsurface
thank you
Acknowledgements:

Dr. Branko Bijeljic and Prof. Martin Blunt

Emirates Foundation for funding this project

Thank you
validation for bulk reaction
Validation for bulk reaction
  • Reaction in a bulk system against the analytical solution:
    • no porous medium
    • no flow
  • Analytical solution for concentration in bulk with no flow.
  • Number of Voxels:
    • Case 1: 10×10×10
    • Case 2: 20×20×20
    • Case 3: 50×50×50
  • Number of particles:
    • A= 100,000  density= 0.8 Np/voxel
    • B= 50,000  density= 0.4 Np/voxel
  • Parameters:
    • Dm= 7.02x10-11 m2/s
    • k= 2.3x109 M-1.s-1
    • Time step sizes:
      • Δt= 10-3 s  P= 3.335×10-3
      • Δt= 10-4 s  P= 1.055×10-2
      • Δt= 10-5 s  P= 3.335×10-2
case 1 number of voxels 10 1 0 1 0
Case 1: Number of Voxels= 10×10×10

Δt= 10-3 s

Δt= 10-4 s

Δt= 10-5 s

case 2 number of voxels 2 0 2 0 2 0
Case 2: Number of Voxels= 20×20×20

Δt= 10-3 s

Δt= 10-4 s

Δt= 10-5 s