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

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.

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

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

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

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

Validation of with experiment at t = 619 s

Validation of with experiment at t = 916 s

Validation of with experiment at t = 1510 s

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

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

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

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

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