Simulation of reactive transport on pore-scale images

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.

• 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

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

Geometry Flow Field Reactants Injection Reaction

Transport by

AdvectionTransport

by Diffusion

For incompressible laminar flow, Stokes equations

0u0uP- 2

g

Place particles on the image• B injected in the

first layer • A is placed in the

rest of the image

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

cos

sinsin

cossin

6

ttt

ttt

ttt

m

zz

yy

xx

tD

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

txx ttt u

Geometry, Flow , Particle Tracking

Pore space

Velocity field

Pressure field

Particle tracking:Volume placement and front injection

Particle tracking:Transport and fluid/fluid reaction

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.

d• The probability of reaction (Pr) as a

function of reaction rate constant (k) and diffusive step ( ) :

tDDkPV

Vtk

VCCtCkCPCkCr

VCCtrP

tVPVCN

tVMr

MM

r

BA

BArBA

BAr

rBAr

6,83

4 3

Fluid/fluid reactive transport benchmark experiment by Gramling et al (2002)

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

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

Gramling et al. (2002)

Parameters Experiment Model

Size of the System

0.36m x 0.055m x 0.018m

Beadpack: 300 x 300 x 300 grid blocks

Grain Size (m) 1.3x10-3

Porosity (%) 36 35.93

Diffusion Coefficient

(m2/s)7.02x10-11

Average Velocity (m/s) 1.21x10-4

Pe 2240

k (M-1 s-1) 2.3x10-9

Concentration of Reactant

A= 0.02 MB= 0.02 M

A= 3.5X106 NpB= 3.5X106 Np

Challenges Solutions

Size of the System

Exp= 0.36mModel= 7.8x10-3m

• Repeat the images as particles travel through pore space

• Place reactants in more than I image

Concentration of the reactants

0.02M ≈ 1.55x1021Np • Set Pr = 1 to max

the reaction• Estimates the

right concentrations

Rapid reactionReaction occurred

at a timescale several orders of magnitude faster

Beadpack image used in simulation

Pore space Velocity fieldPressure 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

3003 beadpack with 26micron resolution can be used

Size of the system in which particles A are initially placed

Image1 300

0 μm 7800 μm

Image1 300

0 μm 7800 μm

Image 11 300

0 μm 7800 μm

Image 2600

15600 μm

Image1

299

0 μm 7774 μm

598

15548 μm

894

23244 μm

299x(n-1)

7774x(n-1) μm

Imagen-1

Image3

Image2

Imagen

299xn

7774xn μm

Product concentration profile at t= 619s - Particle A placed in 5 images

0.0 7.8 15.5 23.3 31.1 38.9 46.6 54.4 62.2 70.0 77.7 85.5 93.3 101.1 108.8 116.6 124.4 132.2 139.9 147.7 155.5 163.3 171.00

0.05

0.1

0.15

0.2

0.25

0.3

0.35

ModelExp

Distance (mm)

C_C

/C0_

A

Product concentration profile at t= 619s - Particle A placed in 1 image

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 BluntEmirates Foundation for funding this project

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= 10×10×10

Δt= 10-5 s

Δt= 10-4 sΔt= 10-3 s


Δt= 10-5 s

Δt= 10-4 sΔt= 10-3 s


Δt= 10-4 s

Δt= 10-3 s

Simulation of reactive transport on pore-scale images

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