Pore-scale Simulation of Reactive Transport in Micro-CT Images

João Paulo Pereira NunesSupervisors: Martin J. BluntBranko Bijeljic

Pore-scale consortium meeting, January 2015

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

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

Reactive transport in four steps

1. Particle Advection – Modified Pollock Algorithm

2. Diffusion – Random Walk

3. Reaction – Flux of particles through solid interface

4. Velocity Field update – Finite volume with OpenFoam

All simulations directly on segmented micro-CT images

∆Xdiff

∆Xad

v∆Xdiff

∆Xdiff

∆X

adv

Data input:Image loading &

velocity

Particle advection using

streamlines

Particle diffusion:

random walk

Velocity Field Update:

OpenFoamParticle hit solid ?

Then reaction.

Flow weighted particle injection

Par

ticl

e lo

op

Calculate statistics,

reaction rate etc.

Time loop

𝜟𝜱> ε ?yes

Update statistics

Model setup

no

Algorithm

Pore-scale streamline tracing

• 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

w1

u2

v2

y

z x

w2

A pore with two solid boundaries:

Modified Pollock for Streamline tracing at the pore-scale

y

z x

w1

w2

u2

v1

v2

Example: Pore with one solid boundary

Calculate exit times and minimize

Standard and modified Pollock have very different outcomes. The standard Pollock fails to capture the non-Fickian behavior expected in heterogeneous rocks.

Voxel Time-of-flight distributions Breakthrough

New method captures the complexity of flow in heterogeneous rocks

Late arrival

Streamlines in the Ketton carbonate

FLOW

3.5mm

Carbonate dissolution

---

Calcite Dissolution

Dissolution happens when a solid voxel (calcite) is hit by solute particles (lack of ).

Three reactions occurring in parallel at the grain surface:

𝒌=𝒌𝟏𝜶𝑯+𝒌𝟐𝜶𝑯𝟐𝑪𝑶𝟑+𝒌𝟑With intrinsic rate -

k = 0.00069 mol*m-2*s-1 @ 10MPa & 50C (Peng et al., 2014)

Reaction rate in the particle approach

k – intrinsic reaction rate Taken from independent experiments Dm – diffusion coefficient∆t – time stepC(r) – particle concentrationNmol – moles of calcite in each solid voxel

A solid voxel dissolves when the cumulative flux of particles is > Nhits

Dynamic imaging experiment – Menke et al. 2014

-Ketton oolite core flooded with CO2-equilibrated brine @ 10MPa / 50C

-Porosity and permeability increasing

-Péclet ≈ 2300 Damköhler ≈ 10-5

-Transport controlled reaction – dissolution limited to regions of significant intake of solute

t0 17 33 6750

83 100 116 133 149

Workflow

Slice-averaged porosity

Flow

t0

50min.

Experimental x Simulation

Porosity and permeability after flow and reaction

Very good agreement between simulation and experiment.

Time-lapse images- perpendicular to flow

Time-lapse images – parallel to flow

• More dissolution in regions of higher flux

• Essentially no dissolution in stagnant regions

• Magnitude of the flow field perpendicular to flow direction

• Dissolution in black• Stagnant regions in white

(not shown)

Average dissolution rates

Time (min.) ∆ϕ keff

[10-4 mol.m-2.s-1]∆ϕ keff

[10-4 mol.m-2.s-1]

0-17 0.029 0.87 0.023 0.68

17-33 0.023 0.76 0.027 0.90

33-50 0.020 0.62 0.026 0.84

Experimental Simulation

Compare with the batch rate: k = 6.9 10-4mol.m-2.s-1 (Peng et al., 2014)

Average rates 10 times smaller due to transport limitations –no chemical/surface heterogeneity in the model.

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

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

Flow rate vs. dissolution extension

Pe 1000

Pe 100

Inlet Outlet

Pe 10

Pe 1

PeDa = 10-2

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

Pe 1

Pe 100 Pe 1000

Pe 10

Inlet

Outlet

Estaillades

Slow flow Péclet =1

1.3

mm

0.67 mm

•Small Pe regime only “face dissolution” - Whole grains are being dissolved • No significant impact in permeability.

Estaillades

Péclet = 50

1.3

mm

0.67 mm

Estaillades

High velocity flow (Péclet 280) Uniform dissolution

Acknowledgments

• Hannah Menke for sharing her experimental results

• Ali Raeini for providing the flow solver

• Petrobras for sponsoring this project

END