1. João Paulo Pereira Nunes
Pore-scale Simulation of Reactive Transport in Micro-CT Images
João Paulo Pereira Nunes
Supervisors:
Martin J. Blunt
Branko Bijeljic
Pore-scale consortium meeting, January 2015

2. Objective
Develop a pore-scale particle tracking method capable of simulating rock-fluid reactions in carbonates – Predict how petrophysical properties evolve during reactive transport
Applications - CO2 injection (EOR or sequestration) and diagenesis modeling

3. Introduction
Already established that acidic fluids flowing through carbonates react with the rock matrix, changing petrophysical and elastic properties of the reservoir
Pore-scale is the natural scale to study rock-fluid interactions (and then upscale)
This work –
Lagrangian approach based on a pore-scale streamline method to simulate evolution of petrophysical properties at in situ conditions
Quantify the impact of flow heterogeneity on average reaction rates
Validate the model using 3D dynamic imaging data from a real carbonate

4. Reactive transport in four steps
Particle Advection – Modified Pollock Algorithm
Diffusion – Random Walk
Reaction – Flux of particles through solid interface
Velocity Field update – Finite volume with OpenFoam
All simulations directly on segmented micro-CT images

5. ∆Xdiff
∆Xadv

6. Algorithm Model setup Time loop 𝜟𝜱> ε ? Data input:
Image loading & velocity
Particle advection using streamlines
Particle diffusion: random walk
Velocity Field Update: OpenFoam
Particle hit solid ? Then reaction.
Flow weighted particle injection
Particle loop
Calculate statistics, reaction rate etc.
Time loop
𝜟𝜱> ε ?
yes
Update statistics
Model setup no

7. Pore-scale streamline tracing

8. Modified Pollock for Streamline tracing at the pore-scale
We improve Pollock’s algorithm, to trace streamlines semi-analytically, respecting the no-slip boundary conditions at pore-solid walls
No need to make the time-step small. More efficient than std. particle tracking methods. Very useful in high Pe flows.
In a cubic lattice there are 64 possible types of pores:
1 – no solid boundaries
6 – one solid boundary
15 – two solids
20 – three solids
15 – four solids
6 – five solids
1 – six solids
A pore with two solid boundaries: w1 u2 v2 y z x w2

9. Example: Pore with one solid boundaryz x w1 w2 u2 v1 v2
Calculate exit times and minimize

10. New method captures the complexity of flow in heterogeneous rocks
Voxel Time-of-flight distributions
Breakthrough
Late arrival
Standard and modified Pollock have very different outcomes. The standard Pollock fails to capture the non-Fickian behavior expected in heterogeneous rocks.

11. Streamlines in the Ketton carbonate
3.5mm
FLOW

12. Carbonate dissolution

13. k = 0.00069 mol*m-2*s-1 @ 10MPa & 50C (Peng et al., 2014)
Calcite Dissolution
Three reactions occurring in parallel at the grain surface:
- 𝑪𝒂𝑪 𝑶 𝟑 𝒔 + 𝑯 + 𝒌 𝟏 𝑪 𝒂 𝟐+ +𝑯𝑪 𝑶 𝟑 −
- 𝑪𝒂𝑪 𝑶 𝟑 𝒔 + 𝑯 𝟐 𝑪 𝑶 𝟑 𝒌 𝟐 𝑪 𝒂 𝟐+ +𝟐𝑯𝑪 𝑶 𝟑 −
- 𝑪𝒂𝑪 𝑶 𝟑 𝒔 𝒌 𝟑 𝑪 𝒂 𝟐+ +𝑪 𝑶 𝟑 𝟐−
With intrinsic rate -
𝒌= 𝒌 𝟏 𝜶 𝑯 + 𝒌 𝟐 𝜶 𝑯 𝟐 𝑪𝑶 𝟑 + 𝒌 𝟑
k = MPa & 50C (Peng et al., 2014)
Dissolution happens when a solid voxel (calcite) is hit by solute particles (lack of 𝑪 𝒂 𝟐+ ).

14. Reaction rate in the particle approach
A solid voxel dissolves when the cumulative flux of particles is > Nhits
k – intrinsic reaction rate  Taken from independent experiments
Dm – diffusion coefficient
∆t – time step
C(r) – particle concentration
Nmol – moles of calcite in each solid voxel

15. Dynamic imaging experiment – Menke et al. 201417 33 67 50 83
100
116
133
149
Ketton oolite core flooded with CO2-equilibrated 10MPa / 50C
Porosity and permeability increasing
Péclet ≈ 2300 Damköhler ≈ 10-5
Transport controlled reaction – dissolution limited to regions of significant intake of solute

16. Workflow

17. Experimental x Simulation
Slice-averaged porosity
Experimental x Simulation
50min. t0
Flow

18. Porosity and permeability after flow and reaction
Very good agreement between simulation and experiment.

19. Time-lapse images- perpendicular to flow

20. Time-lapse images – parallel to flow

21. Magnitude of the flow field perpendicular to flow direction
Dissolution in black
Stagnant regions in white (not shown)
More dissolution in regions of higher flux
Essentially no dissolution in stagnant regions

22. Average dissolution rates
Experimental
Simulation
Time (min.) ∆ϕ
keff
[10-4 mol.m-2.s-1]
0-17
0.029
0.87
0.023
0.68
17-33
0.76
0.027
0.90
33-50
0.020
0.62
0.026
0.84
Compare with the batch rate: k = mol.m-2.s-1 (Peng et al., 2014)
Average rates 10 times smaller due to transport limitations –
no chemical/surface heterogeneity in the model.

23. Conclusions
We have presented a particle tracking method to simulate carbonate dissolution at the pore-scale
The method was validated using dynamic image data – carbonate dissolution in CO2-rich brine - without any fitting parameters
Based on a very efficient streamline tracing method – Modified Pollock algorithm
We predict a decrease of one order of magnitude in the average dissolution rates due to transport limitations only
Easily modifiable to incorporate deposition and different flow regimes

24. Next steps: Impact of the flow rate on the average reaction rates
How to define the average rates for face dissolution ?
Run simulations on more complex rocks
Does the transition from face to uniform dissolution depends on the degree of heterogeneity?
Study different reaction rates  PeDa changing

25. Flow rate vs. dissolution extension
PeDa = 10-2
Pe 1
Pe 1000
Pe 100
Pe 10
Inlet
Outlet

26. Particle trajectories in the pore space
Particles travel longer distances when the Pe number is higher, thus moving the dissolution front away from the inlet face

27. Pe 1
Pe 10
Inlet
Pe 100
Pe 1000
Outlet

28. Estaillades Slow flow  Péclet =1 0.67 mm 1.3 mm
Small Pe regime only “face dissolution” - Whole grains are being dissolved
No significant impact in permeability.

29. Estaillades
Péclet = 50
0.67 mm
1.3 mm

30. High velocity flow (Péclet 280)  Uniform dissolution
Estaillades
High velocity flow (Péclet 280)  Uniform dissolution

31. Acknowledgments Hannah Menke for sharing her experimental results
Ali Raeini for providing the flow solver
Petrobras for sponsoring this project

32. END