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

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 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

∆Xdiff ∆Xadv

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

Pore-scale streamline tracing

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

Example: Pore with one solid boundary z x w1 w2 u2 v1 v2 Calculate exit times and minimize

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.

Streamlines in the Ketton carbonate 3.5mm FLOW

Carbonate dissolution

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 = 0.00069 mol*m-2*s-1 @ 10MPa & 50C (Peng et al., 2014) Dissolution happens when a solid voxel (calcite) is hit by solute particles (lack of 𝑪 𝒂 𝟐+ ).

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

Dynamic imaging experiment – Menke et al. 2014 17 33 67 50 83 100 116 133 149 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

Workflow

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

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

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

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 = 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 PeDa = 10-2 Pe 1 Pe 1000 Pe 100 Pe 10 Inlet Outlet

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 10 Inlet Pe 100 Pe 1000 Outlet

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.

Estaillades Péclet = 50 0.67 mm 1.3 mm

High velocity flow (Péclet 280)  Uniform dissolution 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

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