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Rapid implementation of large-scale carbon capture and storage is necessary to limit global warming this century. Amongst various CO2 storage sites, depleted oilfields provide an immediate option since injection infrastructure is in place and there is an economic benefit from enhanced oil recovery. To design secure carbon storage in oilfields, we need to understand how the three fluid phases - CO2, oil, and water - flow simultaneously in the microscopic pore spaces of the reservoir. In this PhD thesis, we present a novel methodology to study three-phase flow in porous media, at various wettability and gas-oil miscibility conditions, using X-ray microtomography. The use of X-ray imaging allows for a complete investigation of the pore-scale properties that control flow and trapping in three-phase flow, i.e., wettability order, spreading and wetting layers, and double/multiple displacement events. In addition, our advanced experimental and image analysis techniques permit access to key petrophysical properties including fluid saturations, capillary pressures, three-phase relative permeabilities and pore occupancy maps. The three-phase experiments we perform include unsteady-state and steady-state flow conditions and employ both laboratory-based and synchrotron X-ray sources. While laboratory-based scanners image the fluid configurations at the end of displacement or at steady-state equilibrium, synchrotron scanners allow us to capture the pore-scale dynamics during displacement. First, we investigate unsteady-state three-phase flow under near-miscible gas-oil conditions - where the gas-oil interfacial tension is ≤ 1 mN/m - and show that fluids display a unique behavior compared to that seen at immiscible conditions where the interfacial tension is larger by one order of magnitude. In a water-wet system, at near-miscible conditions, gas and oil appear to become neutrally wetting to the surface. This prevents oil from spreading in layers sandwiched between gas and water; the strict wettability order - water-oil-gas, from most to least wetting - seen at immiscible conditions breaks down. This facilitates the flow of oil and gas along the same path in the pore space occupying the centre of the larger pores, while water remains connected in wetting layers in the corners. While this behaviour is desirable for oil recovery, it can impact the storage security as oil can no longer trap CO2. In a weakly oil-wet system, the wettability order shifts from oil-water-gas to oil-gas-water as we move from immiscible to near-miscible conditions. As CO2 becomes the intermediate-wet phase, at near-miscible conditions, it forms spreading layers in the corners of the pore space. The existence of CO2 in spreading layers has huge implications on the storage design since its flow conductance is naturally restricted which implies that subsequent water injection is not necessary to prevent CO2 migration and escape. Next, we show that reservoir rocks can undergo severe wettability alterations rendering them strongly oil-wet. Under unsteady-state flow at immiscible conditions, we observe the predicted, but hitherto unreported, three-phase wettability order in strongly oil-wet rocks, where water occupies the largest pores, oil the smallest, while CO2 occupies pores of intermediate size. Although this wettability order is the same as that seen in a weakly oil-wet rock at near-miscible conditions, the pore-scale fluid configurations are different. While CO2, the intermediate-wet phase, spreads in layers at near-miscible conditions, at immiscible conditions, it exists in the pore space as disconnected ganglia. The existence of CO2 in disconnected clusters, at immiscible conditions, allows for the capillary trapping of gas by oil in the centre of the pores which is not possible when CO2 forms layers. However, capillary trapping of gas by water is still impossible at both miscibility conditions since gas is more wetting to the surface than water. This implies that water re-injection to disconnect the CO2 in the reservoir is unnecessary in both cases. Using a synchrotron X-ray source, we then investigate the invasion pattern during unsteady-state two- and three-phase flow - water injection followed by gas - in a strongly oil-wet reservoir rock at immiscible conditions. During water injection, we observe that the displacement of oil by water is a drainage-like process, where water advances as a connected front displacing oil in the centre of the pores, confining the oil to wetting layers. The displacement is an invasion percolation process, where throats, the restrictions between pores, fill in order of size, with the largest available throats filled first. Moreover, we observe drainage associated pore-filling dynamics including Haines jumps and snap-off events. Subsequently, during gas injection, a distinct invasion pattern is observed for three-phase flow, where gas progresses through the pore space in the form of disconnected clusters mediated by double and multiple displacement events. Gas advances in a process we name three-phase Haines jumps, during which gas re-arranges its configuration in the pore space, retracting from some regions to enable the rapid filling of multiple pores. The gas retraction leads to a permanent disconnection of gas ganglia, which do not reconnect as gas injection proceeds. Lastly, we develop a novel experimental approach to investigate steady-state three-phase flow using pore-scale X-ray imaging. Our newly designed flow cell allows for the differential pressure across the system to be measured, enabling for the simultaneous determination of three-phase relative permeability and capillary pressure. We first investigate steady-state three-phase flow in a water-wet system at immiscible conditions, where the wettability order is water-oil-gas, from most to least wetting. We discover a unique flow dynamics where gas is disconnected across the system despite its continuous injection; gas flows by periodically opening critical flow pathways in intermediate-sized pores. We observe intermittent gas-oil and oil-water behaviour even under capillary-dominated conditions in three-phase flow. At steady-state conditions, it was impossible to displace the trapped gas in our water-wet system since it is double capillary trapped by spreading, oil, and wetting, water, layers. Gas has the lowest relative permeability in the pore space, while oil the highest. Next, we study steady-state three-phase flow in a mixed-wet system at immiscible conditions with an oil-water-gas wettability order. We observe that the gas flow is disconnected, similar to the water-wet system. However, intermittency was more pronounced in the mixed-wet system. The oil relative permeability was the highest in the pore space followed by water, then gas like the water-wet system. The impact of saturation history on gas and water relative permeabilities was larger than its impact on the oil relative permeability. Surprisingly, there was no gas trapping in the system due to its mixed-wet nature which prevents oil and water from completely surrounding the gas phase. This thesis presents an effective and universal methodology to study three-phase flow in porous media at the pore-scale using X-ray microtomography. While the results were strictly discussed in the context of subsurface storage and recovery, it can have implications for many other engineering applications including microfluidic devices, packed bed chemical reactors and catalysis. The findings of this thesis can be used to advise on the design of the optimal conditions to store as much CO2 as possible while maximizing oil production in CO2-enhanced oil recovery projects.

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.

Subsurface fluid flow is ubiquitous in nature, and understanding the interaction of multiple fluids as they flow within a porous medium is central to many geological, environmental, and industrial processes. It is assumed that the flow pathways of each phase are invariant when modelling subsurface flow using Darcy's law extended to multiphase flow; a condition that is assumed to be valid during steady-state flow. However, it has been observed that intermittent flow pathways exist at steady-state, even at the low capillary numbers typically encountered in the subsurface. In this thesis we use both laboratory-based and synchrotron-based micro-CT imaging to capture the pore-scale flow dynamics that arise when multiple fluids flow simultaneously through the pore space of a rock. Using laboratory-based micro-CT we observed that intermittent flow pathways occur in intermediate sized pores due to the competition between both flowing fluids. This competition moves to smaller pores when the flow rate of the non-wetting phase increases. Intermittency occurs in regions where the non-wetting phase is poorly connected. Intermittency leads to the interrupted transport of the fluids; the impact on flow properties is significant because it occurs at key locations, whereby the non-wetting phase is otherwise disconnected. The amount of intermittency expected during flow is dependent on the capillary number and the viscosity ratio of the fluids. Using fast synchrotron X-ray tomography, with 1~s time resolution, we imaged the pore-scale fluid dynamics as the macroscopic flow transitioned to steady-state, and then during steady-state. We observed distinct behaviour during transient flow, with the intermittent fluid occupancy largest and most frequent during the initial invasion into the rock. Our observations suggest that transient flows require separate modelling parameters. We observed that, during steady-state flow, intermittent fluid transport allows the non-wetting phase to flow through a more ramified network of pores. While a more ramified flow network favours lowered relative permeability, intermittency is more dissipative than laminar flow through connected pathways, and the relative permeability remains unchanged for low capillary numbers, where the pore geometry controls the location of intermittency. As the capillary number increases further, the role of pore structure in controlling intermittency decreases, resulting in an increase in relative permeability. These observations can serve as the basis of a model for the causal links between intermittent fluid flow, fluid distribution throughout the pore space, and its upscaled manifestation in relative permeability.

This thesis is concerned with multiphase flow in porous media, focusing primarily on applications to oil recovery from subsurface rocks. The wettability of crude oil-brine-rock systems in petroleum reservoirs often exhibits mixed-wet states where effective contact angle varies locally, because surface active components such as asphaltenes in the crude oil can alter the wettability from its original water-wet to more oil-wet states. Furthermore, when a lower salinity brine than that of formation brine is injected to displace oil, which is known as low salinity water flooding, wettability alteration from a mixed-wet state to more water-wet condition can occur, resulting in an improvement of oil recovery. We use direct numerical simulation to study the impact of wettability and its alteration on multiphase flow in porous media at the pore-scale. A numerical model is constructed based on the lattice Boltzmann method with two newly developed numerical methods: a wetting boundary condition which precisely models contact angle, and a model to capture wettability alteration which changes contact angle depending on the computed local salinity. The numerical model is validated using several test cases where analytical solutions are available. In particular, the new wetting boundary condition is extensively validated using the static test cases of a flat, curved and staircase solid surfaces, and a dynamic test case of capillary rise. Water flooding in mixed-wet media is studied using the numerical model. Water flooding experiments imaged with a micro-CT by Alhammadi et al. are used in which hundreds of thousands of geometrically measured in situ contact angles are available using the method of AlRatrout et al. We show that a good agreement in both the fluid configurations and effective water permeability is obtained when we model the spatial distribution of contact angle on a pore-by-pore basis, but using higher contact angles than those measured in oil-wet regions of the pore space. This physically makes sense because the contact angle to use in simulations is the locally largest value that determines the threshold capillary pressure, whereas the geometrically measured angle may represent a hinging value on pores where displacement has not occurred. Using the matched simulation model to the water flooding experiments of Alhammadi et al., we study three enhanced oil recovery (EOR) methods -- low salinity water flooding, surfactant flooding, and polymer flooding -- through a parametric study changing fluid and/or rock properties of the simulation. This illustrates the use of a simulation model, namely to predict the behavior outside the range studied experimentally. We show the impact of these enhanced oil recovery methods on the microscopic displacement efficiency of the rock. Although this study does not consider the mixing between brine originally in the pore space and injected EOR fluids, this mixing is modeled for low salinity water flooding in the next study, using the two-phase lattice Boltzmann model coupled with mass transport of ions in water. We study wettability alteration caused by exposure to low salinity water using the new wettability alteration model. The numerical model is validated using two experiments performed at the pore-scale: detachment of oil droplets exposed to low salinity water by Mahani et al., and low salinity water flooding on a sinusoidal micro-model by Bartels et al. The phenomena observed in the experiments, including wettability alteration, detachment of oil droplets and recovery of trapped oil, are successfully simulated using a progressive wettability alteration driven by the slow development of thin water films implemented in the numerical model. The numerical model is, then, applied to micro-CT images of a Bentheimer sandstone. Higher oil recovery is observed in secondary mode injection compared to that of tertiary mode, whose mechanism is explained based on the simulation results, where a more stable displacement front is seen for secondary flooding. Lastly, we use the numerical model to validate recently developed pore-scale image analysis methods. A method to measure the interfacial curvature to obtain capillary pressure is studied. Through a comparison between measured curvature and curvature obtained from the simulated capillary pressure, the validation of the method and the assessment of its uncertainty is presented. We, then, validate a method to measure a thermodynamic contact angle by Blunt et al., through a comparison between the input contact angle of the simulations and the thermodynamic contact angle found from the simulated fluid configurations. Furthermore, we demonstrate how to use this method on a pore-by-pore basis to obtain the spatial distribution of wettability. We show that in mixed-wet media we can accurately capture the variation in local contact angle. Significant discrepancies are only seen in less consolidated media where the invading meniscus straddles several pores. Overall the thesis provides an improved method for direct simulation of flow in porous media which have undergone a wettability alteration. The work has been used to interpret experimental work and make predictions for local displacement efficiency for enhanced oil recovery processes. It has also been used to suggest methodologies to measure curvature and wettability from pore-scale imaging experiments.

The sequestration of carbon dioxide (CO2) into geologic formations is one of the long-term solutions proposed to mitigate atmospheric CO2 concentrations [1]. Potential storage sites include deep saline aquifers and depleted hydrocarbon reservoirs. In the case of carbonate reservoirs, the possibility of significant dissolution reaction taking place between CO2, in situ brines and rock is very real. Proposed in this thesis is a method to dynamically image reactive transport in carbonates at subsurface conditions, representing the movement of CO2 saturated brine in the reservoir. The work will focus on understanding reactive transport in carbonate reservoirs by imaging changes in the pore structure, porosity and permeability in representative rock samples induced by the simultaneous flow and reaction of CO2 saturated brine at reservoir conditions. X-ray micro-tomography will be the imaging tool of choice to investigate pore structure changes during reactive transport experiments. Effluent from the dissolution reactions will be collected for analysis via inductively coupled plasma mass spectrometry (ICP-MS) to monitor the preferential dissolution of different minerals in the rock. Direct simulation on 3D images from micro-tomography (μCT) and network modelling tools will be used for further analysis of the rock property evolution. In this thesis we study dissolution of carbonate minerals with an increasing level of complexity to observe the effect of chemical and physical heterogeneity. We start with a single mineral dolomite case where we investigate the impact of rock heterogeneity and flowrate on reaction rates and dissolution dynamics. Next we study dissolution in a chemically heterogeneous medium consisting of two minerals with contrasting initial structure and transport properties, but with uniform spatial distribution. Finally, we studied a heterogeneous reservoir sample consisting of dolomite and calcite (having the ratio 8 to 1) which had a non-uniform spatial distribution.

We present a new model to simulate multispecies reactive transport on pore space images. We solve the Navier-Stokes equations and the advection-diffusion equation for concentration fields on an unstructured grid using the finite volume method. We couple it with the chemical model Reaktoro, which we use to calculate the chemical equilibrium in each grid cell, considered as a completely mixed batch reactor. We validate the model against analytical solutions and experimental data, and investigate, for a range of Péclet numbers, the interplay between transport and reaction for multispecies reactive transport in a 3D bead pack where two streams of reactants at different pH are injected in parallel. We analyse the distribution of species and the rates of formation and consumption and find that, despite the relative homogeneity of the bead pack, the concentration fields of the products can be asymmetric because of the interplay between transport and chemical equilibrium. We observe that lower Péclet numbers give rise to higher relative yields because of increased transverse mixing by diffusion. However, higher absolute yields are obtained at higher injection velocities because of larger amount of matter available for reaction. Reaction is more favoured in the faster-flowing regions. However, this effect is more marked for species for which advection is the dominant mechanism of transport to reactive sites, as opposed to diffusion-mediated reactions where the full velocity distribution is sampled before reaction occurs. Furthermore, we study multispecies mixing and reaction in a more heterogeneous carbonate sample. We use a micro-CT image of Portland limestone containing both macroporosity resolved at the image resolution, and sub-resolution microporosity which is quantified using difference imaging. We extend our solver to accommodate transport and reaction in microporous regions. We demonstrate how the highly variable flow field in carbonate allows reactants and products to disperse more rapidly compared to the more homogeneous bead pack, resulting in a highly non-uniform reaction rate and concentration distribution. This is due to a complex interplay between advection-dominated flow and reaction in the connected fast-flowing macroporous regions, and diffusion-mediated transport and reaction in microporosity. Multispecies mixing and reaction in natural rocks are much more complex than hitherto observed, which needs to be considered in reactive transport studies at different length-scales. Finally, we test the applicability of our code to study dissolution. We first validate our code on multispecies dissolution of a single sphere and a semi-infinite solid. Then, we study dissolution on a micro-CT image composed of dolomite and calcite in ratio 10:1. We find that fast channels are strongly associated with dissolved dolomite, high concentrations of reactants, and low concentrations of products.

More than a trillion barrels of oil may be extracted from carbonate reservoirs in the Middle East. Oil recovery is known to be controlled by wettability (distribution of contact angles) that determines the pore-scale fluid configuration. However, these contact angles have not hitherto been measured in situ at reservoir conditions for reservoir rock that is saturated with crude oil. We use high resolution three-dimensional non-destructive imaging techniques (X-ray micro-tomography) combined with high-pressure high-temperature flow apparatus to study multiphase flow of crude oil and brine in complex mixed-wet carbonate reservoir rocks at subsurface conditions. The raw X-ray pore-scale images acquired were processed and used to measure oil and brine saturation and to study the in situ pore-scale properties controlling mulitphase flow in permeable media. The first part of this work used X-ray micro-tomography to image the in situ wettability, the distribution of contact angles, at the pore scale in carbonate cores from a producing hydrocarbon reservoir at subsurface conditions. The contact angle was measured at hundreds of thousands of points for three samples after twenty pore volumes of brine flooding. We found a wide range of contact angles with values both above and below 90°. The hypothesized cause of wettability alteration by an adsorbed organic layer on surfaces contacted by crude oil after primary drainage was observed with Scanning Electron Microscopy (SEM) and identified using Energy Dispersive X-ray (EDX) analysis. However, not all oil-filled pores were altered towards oil-wet conditions, which suggests that water in surface roughness, or in adjacent micro-porosity, can protect the surface from a strong wettability alteration. The lowest oil recovery was observed for the most oil-wet sample, where the oil remained connected in thin sheet-like layers in the narrower regions of the pore space. The highest recovery was seen for the sample with an average contact angle close to 90°, while an intermediate recovery was observed in a more water-wet system, where the oil was trapped in ganglia in the larger regions of the pore space. In the second part of this work, we have used differential X-ray imaging combined with a steady-state flow apparatus to elucidate the displacement processes during waterflooding. We simultaneously measured relative permeability and capillary pressure on another mixed-wet carbonate sample from the same giant producing oil field. We used the pore-scale images of crude oil and brine to measure the interfacial curvature from which the local capillary pressure was calculated; the relative permeability was found from the imposed fractional flow at eight points fw= 0, 0.15, 0.3, 0.5, 0.7, 0.85, 0.95, 1), the image-measured saturation, and the pressure differential measured across the sample. The measured relative permeabilities indicated favourable oil recovery with a cross-over saturation above 60%. Below this saturation water relative permeability is low, while above it oil still flows through thin layers resulting in additional recovery for the mixed-wettability conditions. The pore-scale images showed that brine started to flow through pinned wetting layers and micro-porosity and then filled the centre of the larger pores. Oil was drained to low saturation through connected oil layers. The brine relative permeability remained low until brine invaded a connected pathway of smaller throats, or restrictions in the pore space, at a high brine saturation. The interface between the oil and brine had a small average curvature, indicating a low capillary pressure, but we observed a remarkable saddle-type shape with nearly equal but opposite curvatures in orthogonal directions. This implies good oil phase connectivity, consistent with the favourable recovery and low residual oil saturation attained in the experiments. This work illuminated displacement processes from both macro-pores and micro-pores which have important implications on improved oil recovery and, potentially, on carbon storage. In future, the measured in situ contact angle, relative permeability, capillary pressure and pore-scale fluid distribution could be used to benchmark and validate pore-scale models.

Pore-scale imaging provides an effective way to understand multiphase flow in porous media at the pore scale and provides benchmark data for larger-scale modelling. In this thesis, an X-ray tomography-based experimental and image analysis method was devised for investigating the relative permeability and associated pore occupancy during steady-state two-phase flow in a sandstone and a complex carbonate, and to identify dynamic flow regimes from low to high capillary numbers. First, a two-phase flow experiment at different fractional flows at steady state was conducted on a Bentheimer sandstone sample at mm-scale using a laboratory micro-CT scanner at both low and high capillary numbers. An intermittent flow, defined as the regions occupied by oil and water alternately, was observed at high capillary number during the hour-long scan time. Differential imaging method was used to quantify the fraction of the intermittency in pore space. Imbibition relative permeabilities and fractional flow curves were obtained with precise differential pressure measurements which compared well with literature measurements on larger cm-scale cores. This method was then expanded and applied into a micro-porous Estaillades carbonate using X-ray micro-tomography. Differential imaging method was applied to (i) distinguish micro-pores and quantify micro-porosity; (ii) determine fluid pore occupancy in both microporous regions; and (iii) identify the intermittency in macro-pore space. The brine saturation and relative permeabilities were obtained, which were impacted by the presence of water-wet micro-porosity which provides additional connectivity to the phases. Pore and throat occupancy of oil, brine and intermittency were obtained from images at different fractional flows using the generalized pore network extracted from the image of macro-pores. The intermittent flow was observed at high capillary number and was predominantly located in the small and intermediate size pores and throats. As laboratory-based instruments take around 1 hour to acquire an image, meaning that intermittency can only be observed indirectly, fast synchrotron X-ray micro-CT was used to capture changes in occupancy over time scales of approximate 1 minute. Thus, fluid behaviours as a function of flow rate (capillary number) at a fixed fractional flow of 0.5 were studied during steady state multiphase flow through a Bentheimer sandstone using synchrotron X-ray micro-tomography. Combining the fluid rearrangements observed from the continual scans taken every 60s with the pressure differential provided by the sensitive differential measurements, three flow regimes were classified: capillary-dominated flow, onset of dynamics, and intermittent flow. The pressure differential has a linear relationship with flow rate during the first two flow regimes. However, there is a power-law scaling of flow rate with pressure drop across the system during the intermittent flow regime. We observed that when there is sufficient energy to allow the oil to short circuit some pores and throats at high capillary number, the overall flow resistance decreases, meaning that oil moves along pathways that intermittently disconnect and reconnect.

In many important processes, that control CO2 storage in aquifers, oil recovery, and gas exchange in leaves, for instance, flow is controlled by the interaction of immiscible fluids with a rough surface. In this thesis, we present new automated methods for measuring in situ contact angle (θ), fluid/fluid interface curvature, rock surface roughness and pore morphology, applied to segmented pore-scale X-ray images. We first identify and mesh the fluid/fluid and fluid/solid interfaces. A Gaussian smoothing is applied to this mesh to eliminate artefacts associated with the voxelized nature of the image, while preserving large-scale features of the rock surface. Then, for the fluid/fluid interface we apply an additional local uniform curvature smoothing and adjustment of the mesh. We then track the three-phase contact line, and the two vectors that have a direction perpendicular to both surfaces: the contact angle is found from the dot product of these vectors where they meet at the contact line. This calculation can be applied at every point on the mesh at the contact line. We automatically generate contact angle values representing each invaded pore-element in the image with high accuracy. We validate the developed approach using synthetic three-dimensional images of a spherical droplet of oil residing on a tilted flat solid surface surrounded by brine with different resolutions of known curvature and contact angle. We show that we are able to estimate contact angle to within 3 degrees and curvature with error less than 9% when the sphere is 2 or more voxels across, which indicates that with a 2 µm voxel size we can accurately capture curvatures as high as 0.5 µm^{-1} and contact angles on pores 4 µm across. We then apply the developed methods to study the in situ distributions of contact angle and oil/brine interface curvature measured within mm-size rock samples from a producing hydrocarbon carbonate reservoir imaged after wateflooding at elevated temperature 60-80 celcius degrees and reservoir pressure (10MPa) using X-ray micro-tomography [Alhammadi et al., 2017b]. We analyse their spatial correlation on a pore-by-pore basis using a novel approach combining the automated methods for measuring contact angles and oil/brine interfacial curvature, with a recently developed method for pore network extraction [Raeini et al.,2017]. Also, we studied the contact angle and interfacial curvature correlation on a ganglion-by-ganglion basis using a ganglia labelled images. The automated methods allow us to study image volumes of diameter approximately 1.92 mm and 1.2 mm long, obtaining hundreds of thousands of values from a dataset with 435 million voxels. We calculate the capillary pressure based on the mode oil/brine interface curvature value, and associate this value with a nearby throat in the pore space. Then, we quantify rock surface roughness and assess its impact on the wettability of the rock. Rougher surfaces are associated with a wider range of local contact angle. Finally, we establish a methodology to characterise pore morphology (wall curvature) in complex porous materials to determine their potential for developing fluid layer flow in mixed-wet systems. We apply this on mm-sized three-dimensional images of a beadpack, a sandpack, two sandstones (Doddington and Bentheimer) and six carbonates (Portland, Ketton, Estaillades and the aforementioned 3 reservoir samples from the Middle East [Alhammadi et al.,2017b]), representing porous media with an increasing degree of pore-scale complexity. In this thesis, we demonstrate the capability of our methods to distinguish different wettability states in the samples studied: water-wet, mixed-wet and oil-wet. The measured contact angle and oil/brine interface curvature in the Middle Eastern reservoir samples are spatially correlated over approximately the scale of an average pore. There is a wide distribution of contact angles within single pores. A range of local oil/brine interface curvature is found with both positive and negative values. There is a correlation between interfacial curvature and contact angle in trapped ganglia, with ganglia in water-wet patches tending to have a positive curvature, and oil-wet regions seeing negative curvature. We observed a weak correlation between average contact angle and pore size, with the larger pores tending to be more oil-wet. Also, we identify a distinct pore-morphology signature where unconsolidated media have a large majority of pores with positive curvature, while consolidated media tend to be composed of more pores with negative curvature. In unconsolidated media there is no impact of relative pore size on pore curvature, in contrast to consolidated media for which we observe a tendency for the small pores to have negative pore curvature, while the large pores have positive ones. Both pore morphology and wettability have a large impact on the potential for layer flow. The signature of consolidated media having a wide range of positive and negative curvatures promotes layer flow in mixed-wet systems. Importantly, this allows us to understand the tendency for the large pores in mixed-wet systems to have the positive fluid interfacial curvature, while small pores show a broader range of both positive and negative fluid interfacial curvature.

We present a numerical scheme to model two-phase flow in porous media where capillary forces dominate over viscous effects. The volume-of-fluid method is employed to capture the fluid-fluid interface whose dynamics are described based on a finite volume discretization of the Navier--Stokes equations. Interfacial forces are calculated directly on reconstructed interface elements such that the total curvature is preserved. The computed interfacial forces are explicitly added to the Navier--Stokes equations using a sharp formulation which effectively eliminates spurious currents. The numerical model is validated in terms of physics, robustness, and mesh convergence, using an extensive hierarchy of static and dynamic test cases including wetting effects at the solid interface in two and three space dimensions. Next we provide an extensive study of viscous coupling effects in porous media flows, where the flow of one phase in the centre of a pore affects the flow of phases in layers or corners and vice versa. We perform two-phase flow simulations for different fluid configurations in non-circular capillary tubes to investigate viscous coupling effects as a function of viscosity ratio, contact angle, wetting phase saturation and wettability. We demonstrate the accuracy of our code in determining fluid velocities and capillary pressures, even for slow flows, where previous approaches fail. We specifically show the dependence of velocity profile and consequently flow conductivities on viscosity ratio and interface boundary condition, by modelling immiscible two-phase flow through an equilateral triangular capillary tube with sandwiched layers. We also demonstrate that imposing no-flow or free-slip interface boundary conditions at a clean fluid-fluid interface with zero interfacial shear viscosity, may lead to under- or over-estimation of flow conductance in layers compared to the physically correct continuity boundary condition at the interface. We use two-phase direct numerical simulation results in conjunction with basic arguments from fluid mechanics to present parametric models that estimate fluid conductivities as a function of the geometry and viscosity ratio. These scaling models, which take into account the flow coupling, can then be incorporated into pore-to-Darcy-scale flow models, for example two-phase pore-network models, to study the effects of viscous coupling on macroscopic flow properties such as relative permeabilities. These network models provide a much more computationally efficient framework for the simulation of flows to the centimetre or larger scales. Furthermore, in future work our methods can be used to assess local recovery and displacement mechanisms in multiphase flow using pore-scale images of different rocks.

In recent years, oil shale has attracted renewed attention as an unconventional energy resource, with vast and largely untapped reserves. Oil shale is a fine-grained sedimentary rock containing a sufficiently high content of immature organic matter from which shale oil and combustible gas can be extracted through pyrolysis. Several complex physical and chemical changes occur during the pyrolysis of oil shale where macromolecular network structures of kerogen are thermally decomposed. The pyrolysis of oil shale leads to the formation of a microscopic pore network in which the oil and gas products flow. The pore structure and the connectivity are significant characteristics which determine fluid flow and ultimate hydrocarbon recovery. In this thesis, a state-of-the-art multi-scale multi-dimensional workflow was applied to image and quantify the Lacustrine Eocene Green River (Mahogany Zone) formation, the world’s largest oil shale deposit. Samples were imaged before, during and after pyrolysis using laboratory and synchrotron-based X-ray Micro-tomography (µCT), Optical Microscopy, Automated Ultra-High Resolution Scanning Electron Microscopy (SEM), MAPS Mineralogy (Modular Automated Processing System) and Focused Ion Beam Scanning Electron Microscopy (FIB-SEM). Results of image analysis using optical (2-D), SEM (2-D), and µCT (3-D) reveal a complex fine-grained microstructure dominated by organic-rich parallel laminations in a tightly bound heterogeneous mineral matrix. MAPS Mineralogy combined with ultrafast measurements highlighted mineralogic textures dominated by dolomite, calcite, K-feldspar, quartz, pyrite and illitic clays. From high resolution backscattered electron (BSE) images, intra-organic, inter-organic-mineral, intra and inter-mineral pores were characterised with varying sizes and geometries. A detailed X-ray µCT study with increasing pyrolysis temperature (300-500°C) at 12 µm, 2 µm and 0.8 µm voxel sizes illuminated the evolution of pore structure, which is shown to be a strong function of the spatial distribution of organic content. In addition, FIB-SEM 3-D visualisations showed an unconnected pore space of 0.5% with pores sizes between 15 nm and 22 nm for the un-pyrolysed sample and a well-connected pore space of 18.2% largely with pores of equivalent radius between 1.6 µm and 2.0 µm for the pyrolysed sample. Synchrotron 4-D results at a time resolution of 160 seconds and a voxel size of 2 µm revealed a dramatic change in porosity accompanying pyrolysis between 390-400°C with the formation of micron-scale heterogeneous pores followed by interconnected fracture networks predominantly along the organic-rich laminations. Combining these techniques provides a powerful tool for quantifying petrophysical properties before, during and after oil shale pyrolysis. Quantitative 2-D, 3-D and 4-D imaging datasets across nm-µm-mm length scales are of great value to better understand, predict and model dynamics of pore structure change and hydrocarbon transport and production during oil shale pyrolysis.

In this thesis we have performed an experimental investigation on the impact of rock heterogeneity on solute spreading and mixing in porous rock using X-ray tomography. Furthermore, we have created a numerical model based on experimentally obtained statistical rock descriptions to investigate the impact of transport and chemical heterogeneity on reactive transport. We present a new core-flood test to characterize solute transport in 3-D natural-rock media. The test is carried out for three rocks with an increasing level of heterogeneity: Berea sandstone, Ketton carbonate and Indiana carbonate. The impact of heterogeneity on solute transport is analysed by: 1., quantifying spreading and mixing using metrics such as the transverse dispersion coefficient, the dilution index, and the scalar dissipation rate, and 2., visualizing and analysing flow structures such as meandering, flow-focusing and flow-splitting. The transverse dispersion coefficient, Dt, and the variation in Dt throughout the rock core, increases with Peclet number (Pe) and rock heterogeneity. The dilution index and scalar dissipation rate indicate that mixing is Fickian for the Berea sandstone and Ketton carbonate, but diverges for the Indiana carbonate. Heterogeneous rock features are observed to cause meandering, focusing or splitting of the plume depending on Pe. The impact of transport and chemical heterogeneity on reactive transport is investigated by modelling the injection of a HCl solution into the three rocks. The model shows that both transport and chemical heterogeneity are important and the dominating factor depends on the transport regime and reaction kinetics. The model is able to capture different dissolution regimes: compact dissolution is observed for low injection rates while the onset of wormholing and uniform dissolution is observed for the higher injection rates. The modelling results are a first indication that statistical descriptions of transport and chemical heterogeneity can improve continuum scale reactive transport modelling.

Reactive transport is an important field of study in the earth sciences. It captures both natural phenomena, and industrial and environmental applications, including transport of pollutants in the subsurface, nuclear waste storage, and carbon storage. The aim of this thesis is to provide a better understanding of coupled physico-chemical processes governing these phenomena as well as to be used as tools for better understanding these environmental applications. We introduce from first principles a novel pore-scale modelling approach capable of simulating single-phase fluid-fluid reactive transport directly on voxels of 3D images of porous media constructed from X-ray tomography. We use a streamline-based particle tracking method for simulating flow and transport, while for reaction to occur, both reactants must be within a diffusive distance. We assign a probability of reaction, as a function of the reaction rate constant and the diffusion length. The model for reaction is validated against analytical solutions in a free fluid as well as against experimental data on reactive transport in porous media. It takes into account the degree of incomplete mixing present at the sub-pore level. We demonstrate the nature of dynamic changes in the reaction rate, which is related to the degree of pore-scale mixing. Our model does not use any calibrating parameters to fit empirical data unlike other models published in the literature. The model is then extended to investigate the impact of pore structure heterogeneity, transport, and reaction conditions on the overall reaction rate in porous media by studying different classes of porous media. The overall reaction rate varies significantly according to the degree of heterogeneity and transport conditions. It is found that the rate of reaction is a subtle combination of the amount of mixing and spreading that cannot be predicted from the dispersion coefficient alone. At low Péclet number, the effective reaction rate is principally controlled by the amount of mixing due to diffusion. On the other hand, at high Péclet number the reaction rate is controlled by a combination of pore-scale mixing due to spreading and the degree of heterogeneity of the pore structure.

High resolution micro-CT images of porous rocks provide a very useful starting point to the development of pore-scale models of fluid flow and transport. Following a literature review covering recent results on the applicability of tomographic imaging to study reaction phenomena at the pore and core scales, this thesis presents a pore-scale streamline-based reactive transport model to simulate rock dissolution. The focus is on carbonate dissolution in CO2-saturated fluids. After injecting CO2-rich fluids into carbonate reservoirs, chemical reactions between the acidic fluid and the host rock are to be expected. Such reactions may cause significant variations in the flow and transport properties of the reservoir, with possible consequences for field development and monitoring. The interplay between flow and reaction exhibits a very rich behaviour that has not yet been fully understood, especially in the case of carbonate rocks, which possess a complex pore structure. The model is developed within a Lagrangian framework, where the advective displacement employs a novel streamline tracing method which respects the no-flow boundary condition at the pore walls. The method is implemented in the pore-space geometry reconstructed from micro-CT images of sedimentary rocks. Diffusion is incorporated with a random walk and fluid-solid reactions are defined in terms of the diffusive flux of reactants through the grain surfaces. To validate the model, simulation results are compared against a dynamic imaging experiment where a carbonate sample was flooded with CO2-saturated brine at reservoir conditions. The agreement is very good and a decrease of one order of magnitude in the average dissolution rate, compared to the rate measured in an ideal reactor, is explained in terms of transport limitations arising from the flow field heterogeneity. The impact of the flow heterogeneity in the reactive transport is illustrated in a series of simulations performed in rocks with different degrees of complexity. It is shown that more heterogeneous rocks, in the sense of flow heterogeneity, may exhibit a decrease of up to two orders of magnitude in the sample-averaged reaction rates, and that the flow rate is also an important factor when studying carbonate dissolution.

This thesis presents the first method for the imaging of multiple fluid phases at conditions representative of subsurface flow by the use of X-ray micro-CT, focussing on four principal applications: (1) Capillary Trapping; (2) Ganglion Snap-off and remobilization; (3) Contact angle measurement; and (4) Dynamic phenomena associated with CO2 drainage. Firstly the pore-scale arrangement of CO2 after drainage and imbibition was imaged in three carbonates and two sandstones. In each sample substantial amounts of CO2 were trapped, showing that residual trapping can be used to locally immobilise CO2. The size distributions of larger residual ganglia obey power law distributions with exponents broadly consistent with percolation theory, over two orders of magnitude. To examine snap-off in more detail residual CO2 was imaged at high resolution in a single carbonate. The capillary pressures of residual ganglia were found to be inversely proportional to the radius of the largest restriction surrounding each ganglion. The remobilization of residual ganglia was assessed using a reformulation of both the capillary and Bond numbers, finding the majority of ganglia in this system were remobilized at reformulated capillary numbers of around 1. Thirdly this thesis presents the first method for the measurement of in-situ contact angle at realistic conditions by the use of micro-CT, applied to a single carbonate sample at 50oC and 10 MPa. Contact angles ranging from 35o to 55o were observed, indicating that the CO2-brine-carbonate system is weakly water-wet. Finally, we use fast synchrotron-based X-ray micro-CT to examine drainage into a brine saturated carbonate. The equilibrium capillary pressure change associated with drainage events is not sufficient to explain the accompanying snap-off, showing that dynamic forces can have a persistent impact on the pattern and sequence of the drainage process.

It is well established that more than half of the world's hydrocarbon reserves are contained in carbonate reservoirs. In a global context, which is characterized by an increasing demand in energy, population growth and overall economic development, it is very important to unlock potential carbonate resources while mitigating the effects of climate change. Moreover, significant volumes of carbon dioxide - the major greenhouse gas contributor to global warming - can be stored in carbonate subsurface formations such as carbonate depleted reservoirs and deep saline aquifers. Therefore, better understanding of carbonate porous media has a wide range of major industrial and environmental applications. However, because of complex pore structures, including the presence of micro-porosity, heterogeneities at different scales, combined with high chemical reactivity, it remains very challenging to describe flow and transport in carbonates. In this thesis, we focus on carbonate porous media and aim to better describe flow, transport and reaction in them. The main application of this work is related to carbon storage in deep saline carbonate aquifers. More particularly, we address fluid-rock interactions e.g. wettability alterations and reactive transport, that occur in carbonate formations. First, we investigate the impact of wettability alteration on multi-phase flow properties. We use pore-network modelling to analyze the impact of wettability alteration by modelling water-flood relative permeability for six different carbonate samples with different connectivity. Pore-scale multi-phase flow physics is described in detail and the efficiency of water-flooding in mixed-wet carbonates is related to the wettability and pore connectivity. We study six carbonate samples. Four quarry samples - Indiana, Portland, Guiting and Mount Gambier - and two subsurface samples obtained from a deep saline Middle Eastern aquifer. The pore space is imaged in three dimensions using X-ray micro-tomography at a resolution of a few microns. The images are segmented into pore and void and a topologically representative network of pores and throats is extracted from these images. We then simulate quasi-static displacement in the networks. We represent mixed-wet behaviour by varying the oil-wet fraction of the pore space. The relative permeability is strongly dependent on both the wettability and the average coordination number of the network. We show that traditional measures of wettability based on the point where the relative permeability curves cross are not reliable. Good agreement is found between our calculations and measurements of relative permeability on carbonates in the literature. The work helps establish a library of benchmark samples for multi-phase flow and transport computations. The implications of the results for field-scale displacement mechanisms are discussed, and the efficiency of waterflooding as an oil recovery process in carbonate reservoirs is assessed depending on the wettability and pore space connectivity. Secondly, we investigate at the laboratory column scale (50 cm), fluid-rock interactions that occur through the injection of an acidic solution into carbonate porous media. Laboratory columns are packed with crushed and sieved porous Guiting carbonate grains. Therefore a homogenous porous medium at the Darcy scale is created and the effect of micro-heterogeneities on transport and reactive transport properties is highlighted. We first conduct a series of passive tracer experiments. Salinity is used as a non-reactive tracer as brine is injected at a constant flow rate into columns pre-saturated with equilibrated deionised water. Solute breakthrough curves are experimentally obtained by measuring the conductivity of collected effluent samples. Subsequently, by solving the advection-dispersion equations using PHREEQC geochemical software, we compare the experimental measurements with numerical predictions of breakthrough curves. A good match is obtained for a dual porosity model and a dispersion coefficient is estimated. We then investigate reactive transport by injecting at constant flow rate acidic brine (hydrochloric acid diluted in saline brine with an overall pH of 3) into columns pre-saturated with equilibrated brine. We measure the effluent concentrations using ICP-AES (inductively coupled plasma atomic emission spectroscopy) Moreover; scanning electron microscopy (SEM) is used to determine single grain-scale changes. We assess the impact of flow rate on the resident time distribution of solutes and reaction profiles along the columns. We discuss challenges encountered regarding the reproducibility of the results and we highlight the implications of such phenomenological studies on carbon storage in carbonates. Finally, we experimentally examine fluid-rock interactions that are induced by the injection of supercritical CO2 (sc-CO2) in carbonate formations at the pore scale. I designed and built a novel experimental apparatus that allows the injection of brine enriched with sc-CO2 at typical CO2 storage conditions. In our experiments the temperature is 500C and the injecting pressure is 9MPa. A novel methodology that combines pore-scale imaging, core flooding and pore-scale modelling is applied in the context of CO2-carbonate-brine interactions. We experimentally use a high pressure and temperature mixing vessel to generate brines enriched with sc-CO2.The mixture is then injected using high precision piston pumps at a constant flow rate (Q=0.1 ml/min) into carbonate micro samples (5 mm diameter and 20 mm length) saturated with pre-equilibrated high salinity brine. We measure the permeability changes in real time during the injection of reactive fluids, In addition, dry high-resolution micro-computed tomography scans are obtained prior to and after the experiments and the pore structure, connectivity and computed flow fields are compared using image analysis and pore-scale modelling techniques. We perform direct simulations of transport properties and velocity fields on the three-dimensional scans and we extract representative pore-throat networks to compute average coordination number and assess changes in pore and throat size distributions. Moreover, we assess the impact of reaction rate on reactive transport. We alter the reaction rate and hence the Damköhler number by under saturating the sc-CO2/brine mixture with crushed and sieved carbonate grains. Two regimes of dissolution are experimentally observed: dominant wormholing and a more uniform dissolution regime. High resolution 3D scans of the dissolution patterns confirm these observations. Permeability increases over several order of magnitude with wormholing whereas for the uniform dissolution, the increase in permeability is less pronounced. Overall, fewer pore and throats are present after dissolution while the average coordination number does not change significantly. Flow becomes concentrated in the wormhole regions after reactions although a very wide range of velocities is still observed. We then compare the observed results for single phase flow (wormholing induced by the injection of single phase brine saturated with sc-CO2) to two-phase flow reactive flow experiments (co injection of sc-CO2 and brine). Results show that wormholing is also seen in the two-phase experiments. Directions for future research in the area of fluid-rock interactions are then discussed.

We present a numerical method for modelling two-phase flow through porous media directly at the pore scale. The volume of fluid method is used to capture the interface motion. The volume of fluid equation and the incompressible Navier-Stokes equations are discretised by the finite volume method using a single fluid methodology, with a discontinuity in the phase properties. Capillary forces are calculated using a new semi-sharp formulation and filtered, to allow for simulations at low capillary numbers and avoid non-physical velocities. They are applied into the Navier-Stokes equations using a semi-implicit formulation, which allows larger time steps at low capillary numbers. The numerical method is verified on several test cases, demonstrating its efficiency, stability and accuracy in modelling multiphase flow through porous media with complex interface motion and irregular solid boundaries. We present two-phase flow simulations on simple pore geometries and study the mechanisms controlling two-phase flow at the pore scale. Particularly, we study the effect of geometry and flow rate on trapping and mobilization of the non-wetting-phase. We introduce a new concept to upscale the subpore-scale forces and find the relations between the flow and the pore-scale pressure drops. These information can be used as input to pore-network models. As an example, we applied this concept to predict the threshold capillary number to prevent trapping during imbibition. Furthermore, we present two-phase flow simulations on two micro-CT images of porous media and show the effect of capillary number on the flow pattern, the trapped non-wetting phase saturation and blob sizes. We present a rigorous approach to relate the pore-scale forces controlling the flow to the Darcy-scale parameters and use it to obtain relative permeability curves. Overall, this thesis provides a methodology for a detailed pore-scale analysis of multiphase flow, serving as a rigorous foundation for large-scale modelling and prediction.

CO2 storage in saline aquifers (sandstone/carbonate types) has been proposed as a promising solution to help reduce CO2 emissions to the atmosphere. CO2 will likely be stored as a dense, supercritical (sc.) phase. There are different mechanisms by which CO2 could be stored safely underground; structural and stratigraphic trapping, dissolution trapping, capillary trapping, and mineral trapping. I study capillary trapping. We assume that in the middle of a CO2 plume, many kilometres in extent, the CO2, brine and rock have been in mutual contact for several years. In these circumstances, the degree of capillary trapping is determined by a displacement of CO2 by brine under these equilibrated conditions. Reproducing such conditions in the laboratory poses a challenge. I have measured the first trapping curve, the relation between initial and residual CO2 saturation, for carbonates in the literature, as well as contributing to the first data on sandstones. For capillary trapping experiment, the porous plate method was used during primary drainage. Two sandstones (Berea and Doddington) and two types of carbonates (Ketton and Indiana) were studied. These experiments were conducted at temperatures of 33, 50, and 70 ˚C and 9 MPa pressure, which matches the conditions observed for several current and planned storage sites. Two displacement steps, primary drainage and water flooding were followed to reach residually trapped CO2 saturation. The isothermal de-pressurization method was used to measure the amount of scCO2 residually trapped. The drainage capillary pressure curve, the Leverett J-function and the trapping curve were measured. During capillary trapping experiments, the brine was equilibrated with CO2 to achieve immiscible displacement. We used a stirred reactor, to equilibrate CO2 with brine. The solubility of CO2 in brine was also measured using the isothermal depressurization method and compared with data in the literature.In Berea sandstone the trapping curves at 33, 50 and 70˚C were compared. We showed that temperature (density) variation has no effect on the saturation of scCO2 that is residually trapped. In Doddington sandstone our result was consistent with that from a micro-flow cell in which the trapped scCO2 was imaged using an X-ray source at the pore scale. We find that significant quantities of the CO2 can be trapped, with residual saturations up to 35%, but less than in analogue experiments where oil is displaced by brine. Hence, it is hypothesized that scCO2-brine systems in sandstones are weakly water-wet with less trapping than the more strongly wetting analogues. Capillary trapping in carbonates is very challenging. In carbonates, another step was required, where brine/CO2/carbonate will be equilibrated together before running the capillary trapping experiment. The apparatus used for sandstone rocks was modified so that the geochemical reaction between CO2/rock was accounted for. Samples are taken and analysed to ensure that the brine/CO2 mixture is saturated with carbonate minerals. In Indiana, the CO2 trapping curve for scCO2 at 50 ˚C and 9 MPa was compared with that of gaseous CO2 at 50 ˚C and 4.2 MPa. A scCO2 residual trapping endpoint of 23.7% was observed in Indiana for scCO2, with a smaller trapping end point in Ketton limestone. This indicates a slightly less trapping of scCO2 in carbonates than in sandstone. There is also less trapping for gaseous CO2 (endpoint of 18.8%). The system appears to be more water-wet under scCO2 conditions, which is different from the trend observed in Berea; the greater concentration of Ca2+ in brine at higher pressure was hypothesised to lead to more water-wet conditions. Our work indicates that capillary trapping could effectively store CO2 in carbonate aquifers.

Fluid flow and dispersion of solute particles are modelled directly on three-dimensional pore-space images of rock samples. To simulate flow, the finite-difference method combined with a standard predictor-corrector procedure to decouple pressure and velocity is applied. We study the permeability and the size of representative elementary volume (REV) of a range of consolidated and unconsolidated porous media. We demonstrate that the flow-based REV is larger than for geometry-based properties such as porosity and specific surface area, since it needs to account for the tortuosity and connectedness of the flow paths. For solute transport we apply a novel streamline-based algorithm that is similar to the Pollock algorithm common in field-scale reservoir simulation, but which employs a semi-analytic formulation near solid boundaries to capture, with sub-grid resolution, the variation in velocity near the grains. A random walk method is used to account for mixing by molecular diffusion. The algorithm is validated by comparison with published results for Taylor-Aris dispersion in a single capillary with a square cross-section. We then accurately predict experimental data available in the literature for longitudinal dispersion coefficient as a function of Peclet number. We study a number of sandpack, sandstone and carbonate samples for which we have good quality three-dimensional images. There is a power-law dependence of dispersion coefficient as a function of Peclet number, with an exponent that is a function of pore-space heterogeneity: the carbonates we study have a distinctly different behaviour than sandstones and sandpacks. This is related to the differences in transit time probabilities of solute particles travelling between two neighbouring voxels. We then study the non-Fickian behaviour of solute transport in porous media by modelling the NMR propagators and the time-dependent dispersion coefficients of different rock types. The behaviour is explained using Continuous Time Random Walk (CTRW) theory: transport is qualitatively different for the complex porous media such as carbonates compared to the sandstone or sandpack, with long tailing and an almost immobile peak concentration. We discuss extensions of the work to reactive transport and the simulation of transport in finely-resolved images with billions of voxels.