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**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

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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

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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

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**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

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∆Xdiff ∆Xadv

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**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

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**Pore-scale streamline tracing**

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**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

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**Example: Pore with one solid boundary**

z x w1 w2 u2 v1 v2 Calculate exit times and minimize

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**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.

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**Streamlines in the Ketton carbonate**

3.5mm FLOW

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**Carbonate dissolution**

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**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+ ).

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**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

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**Dynamic imaging experiment – Menke et al. 2014**

17 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

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Workflow

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**Experimental x Simulation**

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

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**Porosity and permeability after flow and reaction**

Very good agreement between simulation and experiment.

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**Time-lapse images- perpendicular to flow**

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**Time-lapse images – parallel to flow**

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**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

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**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.

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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

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**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

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**Flow rate vs. dissolution extension**

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

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**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

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Pe 1 Pe 10 Inlet Pe 100 Pe 1000 Outlet

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**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.

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Estaillades Péclet = 50 0.67 mm 1.3 mm

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**High velocity flow (Péclet 280) Uniform dissolution**

Estaillades High velocity flow (Péclet 280) Uniform dissolution

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**Acknowledgments Hannah Menke for sharing her experimental results**

Ali Raeini for providing the flow solver Petrobras for sponsoring this project

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