1. Zaki Al Nahari, Branko Bijeljic, Martin Blunt
Pore-scale modelling of fluid/fluid reactive transport on micro-CT images
Zaki Al Nahari, Branko Bijeljic, Martin Blunt

2. Motivation However…. 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.

3. Physical description of reactive transport model
Geometry
Flow Field
Reactants
Injection
Reaction
Transport
Advection
Diffusion
Micro-CT scanner uses X-rays to produce a sequence of cross-sectional tomography images of rocks in high resolution (µm)
Pore space
Incompressible laminar flow, Stokes equations:
Velocity field
Pressure field
Place particles on the image
B injected in the first layer
A is placed in the rest of the image
Injection
Particle tracking
Advection along streamlines using a novel formulation accounting for zero flow at solid boundaries.
Diffusion using random walk

4. 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 nearest reactant.
The probability of reaction ( ) as a function of reaction rate constant ( ) and diffusive step ( ) :
: molecular diffusion coefficient
: conversion number of particles into moles
: time step size

5. Validation for bulk reaction
Reaction in a bulk system against the analytical solution:
no porous medium and no flow
Analytical solution for concentration in bulk with no flow.
constant
: initial concentration A C B
Model
Analytical
Parameters
Size of the System
70 x 70 x 70 voxels
Resolution (m)
2.6x10-6
(m2/s)
7.02x10-11
(s)
1.6
(moles/particles)
1.66x10-24
0.01
(m3/moles.s)
2.76x108
Injection (particles)
A= 12912
B= 6456
Density (particles/voxels)
A= 3.76X10-2
B= 1.88X10-2

6. Fluid/fluid reactive transport benchmark experiment
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)
Parameters
Grain Size (m)
1.3x10-3
(m2/s)
7.02x10-11
(m/s)
1.21x10-4
2240
(moles/m3) 20
Experiment
Model
Size of the System
0.36m x 0.055m x 0.018m
498 x 498 x 498 voxels
0.25m x 0.013m x 0.013m
Porosity (%) 36
36.23
1.75x10-7
1.69x10-7
Injection (particles)
A= 35x106, B= 1721
(moles/particles)
8.54x10-12
(m3/moles.s)
High

7. Validation of with experiment at t = 619 s

8. Validation of with experiment at t = 916 s

9. Validation of with experiment at t = 1510 s

10. Reaction Rate: ADRE vs Model
Early time
Late time
ADRE
Model

11. 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 analytical solution in bulk system as well as with the benchmark fluid/fluid reactive transport experiments by Gramling et al.(2002).
Unlike many reactive transport models, this model does not need any fitting parameters.
The model takes into account the degree of incomplete mixing at the sub-pore level, in contrast to ADRE that can over-predict pore-scale mixing.
Capability to study the impact of heterogeneity in pore structure, velocity field, transport and reaction on the physicochemical processes in the subsurface – will extend to other rocks, flow rates, and reaction rates

12. Thank you Acknowledgements: Dr. Branko Bijeljic and Prof. Martin Blunt
Emirates Foundation for funding this project
Thank you

13. Validation of the Model with benchmark experiment
619s
916s
1510s
500s
400s
300s
200s
100s
ADRE
Model
Early time
Late time
ADRE
Model

14. Size of the system in which particles A are initially placed
Image 1
300
0 μm
7800 μm
Image 1
300
0 μm
7800 μm
Image 1 1
300
0 μm
7800 μm
Image 2
600
15600 μm
Image 1
299
0 μm
7774 μm
598
15548 μm
894
23244 μm
299x(n-1)
7774x(n-1) μm
n-1 3 2 n
299xn
7774xn μm