Modelling of reactive transport in porous media using continuous time random walks
File(s)
Author(s)
Oliveira, Rodolfo
Type
Thesis
Abstract
Reactive transport in porous media is commonly encountered in chemical engineering (e.g. packed beds), contaminant hydrology, reactive flow in batteries and fuel cells, and nuclear waste disposal. Some of those applications are centred in carbonate rocks, which hold over 60% of hydrocarbon reserves and are considered as potential sinks for carbon storage in aquifers and reservoirs.
We start with the description of the Continuous Time Random Walk (CTRW) particle transport model which is validated against experimental results in the literature. We then show that our model is capable of reproducing Fickian and non-Fickian transport signatures by carefully choosing a combination of the characteristic advective and diffusive times t1 and t2 , and the transport heterogeneity parameter β. The combination of parameters showed the ability to model sub- and super-diffusive systems. Furthermore the model also captures hydrodynamic dispersion over 6 orders of magnitude, and the model sensitivity to the β parameter demonstrates how it can be used to represent samples with different physical heterogeneity.
Having the transport component of our model defined, we proceed and extend it to a reactive transport model by including a first-order kinetics model to account for chemical reaction. Our model is validated with a dataset for a Ketton carbonate rock sample undergoing dissolution on injection of an acid, monitored using Nuclear Magnetic Resonance (NMR). The experimental data includes the 3D porosity distribution at the beginning and end of the experiment, 1D porosity profiles along the direction of flow during dissolution, as well as the molecular fluid displacement probability distributions (propagators). We also demonstrate that heterogeneity in the flow field leads to an effective reaction rate, limited by transport of reactants, that is almost three orders of magnitude lower than measured under batch reaction conditions. This study establishes a workflow to calibrate and validate the CTRW reactive transport model with NMR experiments.
After validating the transport and reactive model, we systematically demonstrate the impact of physical heterogeneity on transport and reactive flow signatures. We study this by creating three porous media of increasing heterogeneity,subjected to three advective dominated transport regimes each, and examine the emergent effective reaction rates. The different Pe numbers were capable of reproducing the appearance of two distinct dissolution patterns – a compact or face dissolution pattern and a channelized dissolution pattern. The distribution of propagators of each sample showed the imprint of heterogeneity on its asymmetrical shape, as well as the contrast between slow and fast regions that increased with the dissolution process. Later we extended the models to examine the impact of β in the average porosity evolution and effective reaction rates. The change in concentration is slower with a decrease of β which is in
line with the behaviour of transport only descriptions.
Finally, we study the impact of coupled flow and chemical heterogeneity on effective reaction rates. We start by modelling a multi-species fluid/fluid reactive system with the injection of sodium carbonate Na2CO3 and calcium chloride CaCl2 solutions through different halves of a porous domain and observe the production of sodium chloride NaCl and calcium carbonate CaCO3. The increase of heterogeneity leads to an increase in the production of NaCl and CaCO3 by increasing the mixing of the injected solutions. Then we use the same heterogeneous reactive transport solver to model porous media consisting mostly of calcite with dolomite near the fast flowing channels. The dependence of the effective reaction rates of the different minerals is related to their distance from fast-flowing channels. These results are supported by the results found in the literature where the pore-scale pattern of dissolution was measured on chemically heterogeneous samples.
We conclude our work suggesting additional work and experimental acquisitions to improve the predictability of our model, the addition of adsorption, precipitation and bio-chemical alterations of the porous media and a multi-scale integration using direct simulations at under-resolved scales.
We start with the description of the Continuous Time Random Walk (CTRW) particle transport model which is validated against experimental results in the literature. We then show that our model is capable of reproducing Fickian and non-Fickian transport signatures by carefully choosing a combination of the characteristic advective and diffusive times t1 and t2 , and the transport heterogeneity parameter β. The combination of parameters showed the ability to model sub- and super-diffusive systems. Furthermore the model also captures hydrodynamic dispersion over 6 orders of magnitude, and the model sensitivity to the β parameter demonstrates how it can be used to represent samples with different physical heterogeneity.
Having the transport component of our model defined, we proceed and extend it to a reactive transport model by including a first-order kinetics model to account for chemical reaction. Our model is validated with a dataset for a Ketton carbonate rock sample undergoing dissolution on injection of an acid, monitored using Nuclear Magnetic Resonance (NMR). The experimental data includes the 3D porosity distribution at the beginning and end of the experiment, 1D porosity profiles along the direction of flow during dissolution, as well as the molecular fluid displacement probability distributions (propagators). We also demonstrate that heterogeneity in the flow field leads to an effective reaction rate, limited by transport of reactants, that is almost three orders of magnitude lower than measured under batch reaction conditions. This study establishes a workflow to calibrate and validate the CTRW reactive transport model with NMR experiments.
After validating the transport and reactive model, we systematically demonstrate the impact of physical heterogeneity on transport and reactive flow signatures. We study this by creating three porous media of increasing heterogeneity,subjected to three advective dominated transport regimes each, and examine the emergent effective reaction rates. The different Pe numbers were capable of reproducing the appearance of two distinct dissolution patterns – a compact or face dissolution pattern and a channelized dissolution pattern. The distribution of propagators of each sample showed the imprint of heterogeneity on its asymmetrical shape, as well as the contrast between slow and fast regions that increased with the dissolution process. Later we extended the models to examine the impact of β in the average porosity evolution and effective reaction rates. The change in concentration is slower with a decrease of β which is in
line with the behaviour of transport only descriptions.
Finally, we study the impact of coupled flow and chemical heterogeneity on effective reaction rates. We start by modelling a multi-species fluid/fluid reactive system with the injection of sodium carbonate Na2CO3 and calcium chloride CaCl2 solutions through different halves of a porous domain and observe the production of sodium chloride NaCl and calcium carbonate CaCO3. The increase of heterogeneity leads to an increase in the production of NaCl and CaCO3 by increasing the mixing of the injected solutions. Then we use the same heterogeneous reactive transport solver to model porous media consisting mostly of calcite with dolomite near the fast flowing channels. The dependence of the effective reaction rates of the different minerals is related to their distance from fast-flowing channels. These results are supported by the results found in the literature where the pore-scale pattern of dissolution was measured on chemically heterogeneous samples.
We conclude our work suggesting additional work and experimental acquisitions to improve the predictability of our model, the addition of adsorption, precipitation and bio-chemical alterations of the porous media and a multi-scale integration using direct simulations at under-resolved scales.
Version
Open Access
Date Issued
2021-03
Date Awarded
2021-09
Copyright Statement
Creative Commons Attribution NonCommercial NoDerivatives Licence
Advisor
Blunt, Martin
Bijeljic, Branko
Publisher Department
Earth Science & Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)