## Publications

453 results found

Akai T, Lin Q, Bijeljic B,
et al., 2020, Using energy balance to determine pore-scale wettability, *Journal of Colloid and Interface Science*, Vol: 576, Pages: 486-495, ISSN: 0021-9797

HypothesisBased on energy balance during two-phase displacement in porous media, it has recently been shown that a thermodynamically consistent contact angle can be determined from micro-tomography images. However, the impact of viscous dissipation on the energy balance has not been fully understood. Furthermore, it is of great importance to determine the spatial distribution of wettability. We use direct numerical simulation to validate the determination of the thermodynamic contact angle both in an entire domain and on a pore-by-pore basis.SimulationsTwo-phase direct numerical simulations are performed on complex 3D porous media with three wettability states: uniformly water-wet, uniformly oil-wet, and non-uniform mixed-wet. Using the simulated fluid configurations, the thermodynamic contact angle is computed, then compared with the input contact angles.FindingsThe impact of viscous dissipation on the energy balance is quantified; it is insignificant for water flooding in water-wet and mixed-wet media, resulting in an accurate estimation of a representative contact angle for the entire domain even if viscous effects are ignored. An increasing trend in the computed thermodynamic contact angle during water injection is shown to be a manifestation of the displacement sequence. Furthermore, the spatial distribution of wettability can be represented by the thermodynamic contact angle computed on a pore-by-pore basis.

Blunt MJ, Akai T, Bijeljic B, 2020, Evaluation of methods using topology and integral geometry to assess wettability., *J Colloid Interface Sci*, Vol: 576, Pages: 99-108

HYPOTHESIS: The development of high-resolution in situ imaging has allowed contact angles to be measured directly inside porous materials. We evaluate the use of concepts in integral geometry to determine contact angle. Specifically, we test the hypothesis that it is possible to determine an average contact angle from measurements of the Gaussian curvature of the fluid/fluid meniscus using the Gauss-Bonnet theorem. THEORY AND SIMULATION: We show that it is not possible to unambiguously determine an average contact angle from the Gauss-Bonnet theorem. We instead present an approximate relationship: 2πn(1-cosθ)=4π-∫κG12dS12, where n is the number of closed loops of the three-phase contact line where phases 1 and 2 contact the surface, θ is the average contact angle, while κG12 is the Gaussian curvature of the fluid meniscus which is integrated over its surface S12. We then use the results of pore-scale lattice Boltzmann simulations to assess the accuracy of this approach to determine a representative contact angle for two-phase flow in porous media. FINDINGS: We show that in simple cases with a flat solid surface, the approximate expression works well. When applied to simulations on pore space images, the equation provides a robust estimate of contact angle, accurate to within 3°, when averaged over many fluid clusters, although individual values can have significant errors because of the approximations used in the calculation.

Scanziani A, Lin Q, Alhosani A,
et al., Dynamics of fluid displacement in mixed-wet porous media, *Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, ISSN: 1364-5021

We identify a distinct two-phase flow invasion patternin a mixed-wet porous medium. Time-resolved highresolutionsynchrotron X–ray imaging is used to studythe invasion of water through a small rock samplefilled with oil, characterized by a wide non-uniformdistribution of local contact angles both above andbelow 90 . The water advances in a connected front,but throats are not invaded in decreasing order ofsize, as predicted by invasion percolation theory foruniformly hydrophobic systems. Instead, we observepinning of the three-phase contact between the fluidsand the solid, manifested as contact angle hysteresis,which prevents snap-off and interface retraction. Inthe absence of viscous dissipation, we use an energybalance to find an effective, thermodynamic, contactangle for displacement and show that this angleincreases during the displacement. Displacementoccurs when the local contact angles overcome theadvancing contact angles at a pinned interface: itis wettability which controls the filling sequence.The product of the principal interfacial curvatures,the Gaussian curvature, is negative, implying wellconnectedphases which is consistent with pinningat the contact line while providing a topologicalexplanation for the high displacement efficiencies inmixed-wet media.

Bultreys T, Singh K, Raeini AQ,
et al., 2020, Verifying pore network models of imbibition in rocks using time‐resolved synchrotron imaging, *Water Resources Research*, Vol: 56, Pages: 1-13, ISSN: 0043-1397

At the pore scale, slow invasion of a wetting fluid in porous materials is often modeled with quasi‐static approximations which only consider capillary forces in the form of simple pore‐filling rules. The appropriateness of this approximation, often applied in pore network models, is contested in the literature, reflecting the difficulty of predicting imbibition relative permeability with these models. However, validation by sole comparison to continuum‐scale experiments is prone to induce model overfitting. It has therefore remained unclear whether difficulties generalizing the model performance are caused by errors in the predicted filling sequence or by subsequent calculations. Here, we address this by examining whether such a model can predict the pore‐scale fluid distributions underlying the behavior at the continuum scale. To this end, we compare the fluid arrangement evolution measured in fast synchrotron micro‐CT experiments on two rock types to quasi‐static simulations which implement capillary‐dominated pore filling and snap‐off, including a sophisticated model for cooperative pore filling. The results indicate that such pore network models can, in principle, predict fluid distributions accurately enough to estimate upscaled flow properties of strongly wetted rocks at low capillary numbers.

Alhosani A, Scanziani A, Lin Q,
et al., 2020, Pore-scale mechanisms of CO2 storage in oilfields, *Scientific Reports*, Vol: 10, Pages: 1-9, ISSN: 2045-2322

Rapid implementation of global scale carbon capture and storage is required to limit temperature rises to 1.5 °C this century. Depleted oilfields provide an immediate option for storage, since injection infrastructure is in place and there is an economic benefit from enhanced oil recovery. To design secure storage, we need to understand how the fluids are configured in the microscopic pore spaces of the reservoir rock. We use high-resolution X-ray imaging to study the flow of oil, water and CO2 in an oil-wet rock at subsurface conditions of high temperature and pressure. We show that contrary to conventional understanding, CO2 does not reside in the largest pores, which would facilitate its escape, but instead occupies smaller pores or is present in layers in the corners of the pore space. The CO2 flow is restricted by a factor of ten, compared to if it occupied the larger pores. This shows that CO2 injection in oilfields provides secure storage with limited recycling of gas; the injection of large amounts of water to capillary trap the CO2 is unnecessary.

Mularczyk A, Lin Q, Blunt MJ,
et al., 2020, Droplet and percolation network interactions in a fuel cell gas diffusion layer, *Journal of The Electrochemical Society*, Vol: 167, ISSN: 0013-4651

Product water accumulations in polymer electrolyte fuel cells can cause performance losses and reactant starvation leading to cell degradation. Liquid water removal in the form of droplets, fed by percolation networks in the gas diffusion layer (GDL), is one of the main transport mechanisms by which the water is evacuated from the GDL. In this study, the effect of droplet detachment in the gas channel on the water cluster inside the GDL has been investigated using X-ray tomographic microscopy and X-ray radiography. The droplet growth is captured in varying stages over a sequence of consecutive droplet releases, during which an inflation and deflation of the gas-liquid interface menisci of the percolating water structure in the GDL has been observed and correlated to changes in pressure fluctuations in the water phase via gas-liquid curvature analysis.

Alhammadi AM, Gao Y, Akai T,
et al., 2020, Pore-scale X-ray imaging with measurement of relative permeability, capillary pressure and oil recovery in a mixed-wet micro-porous carbonate reservoir rock, *Fuel*, Vol: 268, Pages: 1-14, ISSN: 0016-2361

Differential imaging X-ray microtomography combined with a steady-state flow apparatus was used to elucidate the displacement processes during waterflooding. We simultaneously measured relative permeability and capillary pressure on a carbonate rock sample extracted from a 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, the image-measured saturation, and the pressure differential across the sample.The relative permeabilities indicated favourable oil recovery for the mixed-wettability conditions. The pore-scale images showed that brine started to flow through pinned wetting layers, micro-porosity and water-wet pores, and then filled the centre of the larger oil-wet 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 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 remarkable saddle-shaped interfaces 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 for improved oil recovery and, potentially, on carbon storage. In future, the measured relative permeability, capillary pressure and pore-scale fluid distribution could be used to benchmark and validate pore-scale models.

Akai T, Blunt MJ, Bijeljic B, 2020, Pore-scale numerical simulation of low salinity water flooding using the lattice Boltzmann method, *Journal of Colloid and Interface Science*, Vol: 566, Pages: 444-453, ISSN: 0021-9797

HYPOTHESIS: The change of wettability toward more water-wet by the injection of low salinity water can improve oil recovery from porous rocks, which is known as low salinity water flooding. To simulate this process at the pore-scale, we propose that the alteration in surface wettability mediated by thin water films which are below the resolution of simulation grid blocks has to be considered, as observed in experiments. This is modeled by a wettability alteration model based on rate-limited adsorption of ions onto the rock surface. SIMULATIONS: The wettability alteration model is developed and incorporated into a lattice Boltzmann simulator which solves both the Navier-Stokes equation for oil/water two-phase flow and the advection-diffusion equation for ion transport. The model is validated against two experiments in the literature, then applied to 3D micro-CT images of a rock. FINDINGS: Our model correctly simulated the experimental observations caused by the slow wettability alteration driven by the development of water films. In the simulations on the 3D rock pore structure, a distinct difference in the mixing of high and low salinity water is observed between secondary and tertiary low salinity flooding, resulting in different oil recoveries.

Rücker M, Bartels W-B, Bultreys T, et al., 2020, Workflow for upscaling wettability from the nano- to core-scales, International Symposium of the Society of Core Analysts

Shams R, Masihi M, Boozarjomehry RB,
et al., 2020, Coupled generative adversarial and auto-encoder neural networks to reconstruct three-dimensional multi-scale porous media, *JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING*, Vol: 186, ISSN: 0920-4105

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Akai T, Bijeljic B, Blunt M, 2020, Local Capillary Pressure Estimation Based on Curvature of the Fluid Interface-Validation with Two-Phase Direct Numerical Simulations, ISSN: 2555-0403

© The Authors, published by EDP Sciences, 2020. With the advancement of high-resolution three-dimensional X-ray imaging, it is now possible to directly calculate the curvature of the interface of two phases extracted from segmented CT images during two-phase flow experiments to derive capillary pressure. However, there is an inherent difficulty of this image-based curvature measurement: The use of voxelized image data for the calculation of curvature can cause significant errors. To address this, we first perform two-phase direct numerical simulations to obtain the oil and water phase distribution, the exact location of the interface, and local fluid pressure. We then investigate a method to compute curvature on the oil/water interface. The interface is defined in two ways. In one case the simulated interface which has a sub-resolution smoothness is used, while the other is a smoothed interface which is extracted from synthetic segmented data based on the simulated phase distribution. Computed mean curvature on these surfaces are compared with that obtained from the fluid pressure computed directly in the simulation. We discuss the accuracy of image-based curvature measurements for the calculation of capillary pressure and propose the best way to extract an accurate curvature measurement, quantifying the likely uncertainties.

Scanziani A, Singh K, Menke H,
et al., 2020, Dynamics of enhanced gas trapping applied to CO2 storage in the presence of oil using synchrotron X-ray micro tomography, *Applied Energy*, Vol: 259, ISSN: 0306-2619

During CO2 storage in depleted oil fields, under immiscible conditions, CO2 can be trapped in the pore space by capillary forces, providing safe storage over geological times - a phenomenon named capillary trapping. Synchrotron X-ray imaging was used to obtain dynamic three-dimensional images of the flow of the three phases involved in this process - brine, oil and gas (nitrogen) - at high pressure and temperature, inside the pore space of Ketton limestone. First, using continuous imaging of the porous medium during gas injection, performed after waterflooding, we observed chains of multiple displacements between the three phases, caused by the connectivity of the pore space. Then, brine was re-injected and double capillary trapping - gas trapping by oil and oil trapping by brine - was the dominant double displacement event. We computed pore occupancy, saturations, interfacial area, mean curvature and Euler characteristic to elucidate these double capillary trapping phenomena, which lead to a high residual gas saturation. Pore occupancy and saturation results show an enhancement of gas trapping in the presence of both oil and brine, which potentially makes CO2 storage in depleted oil reservoirs attractive, combining safe storage with enhanced oil recovery through immiscible gas injection. Mean curvature measurements were used to assess the capillary pressures between fluid pairs during double displacements and these confirmed the stability of the spreading oil layers observed, which facilitated double capillary trapping. Interfacial area and Euler characteristic increased, indicating lower oil and gas connectivity, due to the capillary trapping events.

Gao Y, Lin Q, Bijeljic B,
et al., 2020, Pore-scale dynamics and the multiphase Darcy law, *Physical Review Fluids*, Vol: 5, Pages: 1-12, ISSN: 2469-990X

Synchrotron x-ray microtomography combined with sensitive pressure differential measurements were used to study flow during steady-state injection of equal volume fractions of two immiscible fluids of similar viscosity through a 57-mm-long porous sandstone sample for a wide range of flow rates. We found three flow regimes. (1) At low capillary numbers, Ca, representing the balance of viscous to capillary forces, the pressure gradient, ∇P, across the sample was stable and proportional to the flow rate (total Darcy flux) qt (and hence capillary number), confirming the traditional conceptual picture of fixed multiphase flow pathways in porous media. (2) Beyond Ca∗≈10−6, pressure fluctuations were observed, while retaining a linear dependence between flow rate and pressure gradient for the same fractional flow. (3) Above a critical value Ca>Cai≈10−5 we observed a power-law dependence with ∇P∼qat with a≈0.6 associated with rapid fluctuations of the pressure differential of a magnitude equal to the capillary pressure. At the pore scale a transient or intermittent occupancy of portions of the pore space was captured, where locally flow paths were opened to increase the conductivity of the phases. We quantify the amount of this intermittent flow and identify the onset of rapid pore-space rearrangements as the point when the Darcy law becomes nonlinear. We suggest an empirical form of the multiphase Darcy law applicable for all flow rates, consistent with the experimental results.

Krevor S, Blunt MJ, Trusler JPM, et al., 2020, Chapter 8: An introduction to subsurface CO<inf>2</inf> storage, RSC Energy and Environment Series, Pages: 238-295, ISBN: 9781788014700

© The Royal Society of Chemistry 2020. The costs of carbon capture and storage are driven by the capture of CO2 from exhaust streams or the atmosphere. However, its role in climate change mitigation is underpinned by the potential of the vast capacity for storage in subsurface geologic formations. This storage potential is confined to sedimentary rocks, which have substantial porosity and high permeability in comparison to crystalline igneous and metamorphic rocks. These in turn occur in the sedimentary basins of the Earth's continents and near shore. However, the specific capacity for storage is not correlated simply to the existence of a basin. Consideration must also be made of reservoir permeability, caprock integrity, injectivity, fluid dynamics, and geomechanical properties of pressurisation and faulting. These are the topics addressed in this chapter. These processes and properties will combine in complex ways in a wide range of settings to govern the practicality of storing large volumes of CO2. There is clear potential for storage at the scale required to mitigate the worst impacts of global climate change, estimated to be in the order of 10 Gt CO2 per year by 2050. However, until at least dozens of commercial projects have been built in a range of geologic environments, the upper reaches of what can be achieved, and how quickly, will remain uncertain.

Mosser L, Dubrule O, Blunt MJ, 2020, Stochastic Seismic Waveform Inversion Using Generative Adversarial Networks as a Geological Prior, *MATHEMATICAL GEOSCIENCES*, Vol: 52, Pages: 53-79, ISSN: 1874-8961

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Ladipo L, Blunt MJ, King PR, 2020, A salinity cut-off method to control numerical dispersion in low-salinity waterflooding simulation, *JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING*, Vol: 184, ISSN: 0920-4105

Akai T, Alhammadi AM, Blunt MJ,
et al., 2019, Mechanisms of microscopic displacement during enhanced oil recovery in mixed-wet rocks revealed using direct numerical simulation, *Transport in Porous Media*, Vol: 130, Pages: 731-749, ISSN: 0169-3913

We demonstrate how to use numerical simulation models directly on micro-CT images to understand the impact of several enhanced oil recovery (EOR) methods on microscopic displacement efficiency. To describe the physics with high-fidelity, we calibrate the model to match a water-flooding experiment conducted on the same rock sample (Akai et al. in Transp Porous Media 127(2):393–414, 2019. https://doi.org/10.1007/s11242-018-1198-8). First we show comparisons of water-flooding processes between the experiment and simulation, focusing on the characteristics of remaining oil after water-flooding in a mixed-wet state. In both the experiment and simulation, oil is mainly present as thin oil layers confined to pore walls. Then, taking this calibrated simulation model as a base case, we examine the application of three EOR processes: low salinity water-flooding, surfactant flooding and polymer flooding. In low salinity water-flooding, the increase in oil recovery was caused by displacement of oil from the centers of pores without leaving oil layers behind. Surfactant flooding gave the best improvement in the recovery factor of 16% by reducing the amount of oil trapped by capillary forces. Polymer flooding indicated improvement in microscopic sweep efficiency at a higher capillary number, while it did not show an improvement at a low capillary number. Overall, this work quantifies the impact of different EOR processes on local displacement efficiency and establishes a workflow based on combining experiment and modeling to design optimal recovery processes.

Alhosani A, Scanziani A, Lin Q,
et al., 2019, In situ pore-scale analysis of oil recovery during three-phase near-miscible CO2 injection in a water-wet carbonate rock, *Advances in Water Resources*, Vol: 134, ISSN: 0309-1708

We study in situ three-phase near-miscible CO2 injection in a water-wet carbonate rock at elevated temperature and pressure using X-ray microtomography. We examine the recovery mechanisms, presence or absence of oil layers, pore occupancy and interfacial areas during a secondary gas injection process. In contrast to an equivalent immiscible system, we did not observe layers of oil sandwiched between gas in the centre of the pore space and water in the corners. At near-miscible conditions, the measured contact angle between oil and gas was approximately 73°, indicating only weak oil wettability in the presence of gas. Oil flows in the centres of large pores, rather than in layers for immiscible injection, when displaced by gas. This allows for a rapid production of oil since it is no longer confined to movement in thin layers. A significant recovery factor of 80% was obtained and the residual oil saturation existed as disconnected blobs in the corners of the pore space. At equilibrium, gas occupied the biggest pores, while oil and water occupied pores of varying sizes (small, medium and large). Again, this was different from an immiscible system, where water occupied only the smallest pores. We suggest that a double displacement mechanism, where gas displaces water that displaces oil is responsible for shuffling water into larger pores than that seen after initial oil injection. This is only possible since, in the absence of oil layers, gas can contact water directly. The gas-oil and oil-water interfacial areas are lower than in the immiscible case, since there are no oil layers and even water layers in the macro-pore space become disconnected; in contrast, there is a larger direct contact of oil to the solid. These results could serve as benchmarks for developing near-miscible pore-scale modelling tools.

Raeini AQ, Yang J, Bondino I,
et al., 2019, Validating the generalized pore network model using micro-CT images of two-phase flow, *Transport in Porous Media*, Vol: 130, Pages: 405-424, ISSN: 0169-3913

A reliable prediction of two-phase flow through porous media requires the development and validation of models for flow across multiple length scales. The generalized network model is a step towards efficient and accurate upscaling of flow from the pore to the core scale. This paper presents a validation of the generalized network model using micro-CT images of two-phase flow experiments on a pore-by-pore basis. Three experimental secondary imbibition datasets are studied for both sandstone and carbonate rock samples. We first present a quantification of uncertainties in the experimental measurements. Then, we show that the model can reproduce the experimental fluid occupancies and saturations with a good accuracy, which in some cases is comparable with the similarity between repeat experiments. However, high-resolution images need to be acquired to characterize the pore geometry for modelling, while the results are sensitive to the initial condition at the end of primary drainage. The results provide a methodology for improving our physical models using large experimental datasets which, at the pore scale, can be generated using micro-CT imaging of multiphase flow.

Spurin C, Bultreys T, Bijeljic B,
et al., 2019, Mechanisms controlling fluid breakup and reconnection during two-phase flow in porous media, *Physical Review E*, Vol: 100, ISSN: 2470-0045

The use of Darcy's law to describe steady-state multiphase flow in porous media has been justified by the assumption that the fluids flow in continuously connected pathways. However, a range of complex interface dynamics have been observed during macroscopically steady-state flow, including intermittent pathway flow where flow pathways periodically disconnect and reconnect. The physical mechanisms controlling this behavior have remained unclear, leading to uncertainty concerning the occurrence of the different flow regimes. We observe that the fraction of intermittent flow pathways is dependent on the capillary number and viscosity ratio. We propose a phase diagram within this parameter space to quantify the degree of intermittent flow.

Spurin C, Bultreys T, Bijeljic B,
et al., 2019, Intermittent fluid connectivity during two-phase flow in a heterogeneous carbonate rock, *Physical Review E*, Vol: 100, ISSN: 2470-0045

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 modeling 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. Little is known about the pore structure controls or the impact of intermittency on continuum scale flow properties. Here we investigate the impact of intermittent pathways on the connectivity of the fluids for a carbonate rock. Using laboratory-based micro computed tomography imaging we observe that intermittent pathway flow occurs in intermediate-sized pores due to the competition between both flowing fluids. This competition moves to smaller pores when the flow rate of the nonwetting phase increases. Intermittency occurs in poorly connected pores or in regions where the nonwetting phase itself is poorly connected. Intermittent pathways lead to the interrupted transport of the fluids; this means they are important in determining continuum scale flow properties, such as relative permeability. The impact of intermittency on flow properties is significant because it occurs at key locations, whereby the nonwetting phase is otherwise disconnected.

Blunt MJ, Lin Q, Akai T,
et al., 2019, A thermodynamically consistent characterization of wettability in porous media using high-resolution imaging., *J Colloid Interface Sci*, Vol: 552, Pages: 59-65

Conservation of energy is used to derive a thermodynamically-consistent contact angle, θt, when fluid phase 1 displaces phase 2 in a porous medium. Assuming no change in Helmholtz free energy between two local equilibrium states we find that Δa1scosθt=κϕΔS1+Δa12, where a is the interfacial area per unit volume, ϕ is the porosity, S is the saturation and κ the curvature of the fluid-fluid interface. The subscript s denotes the solid, and we consider changes, Δ, in saturation and area. With the advent of high-resolution time-resolved three-dimensional X-ray imaging, all the terms in this expression can be measured directly. We analyse imaging datasets for displacement of oil by water in a water-wet and a mixed-wet sandstone. For the water-wet sample, the curvature is positive and oil bulges into the brine with almost spherical interfaces. In the mixed-wet case, larger interfacial areas are found, as the oil resides in layers. The mean curvature is close to zero, but the interface tends to bulge into brine in one direction, while brine bulges into oil in the other. We compare θt with the values measured geometrically in situ on the pore-scale images, θg. The thermodynamic angle θt provides a robust and consistent characterization of wettability. For the water-wet case the calculated value of θt gives an accurate prediction of multiphase flow properties using pore-scale modelling.

Abd AS, Elhafyan E, Siddiqui AR,
et al., 2019, A review of the phenomenon of counter-current spontaneous imbibition: Analysis and data interpretation, *JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING*, Vol: 180, Pages: 456-470, ISSN: 0920-4105

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Akai T, Lin Q, Alhosani A,
et al., 2019, Quantification of uncertainty and best practice in computing interfacial curvature from complex pore space images., *Materials (Basel)*, Vol: 12, Pages: 1-21, ISSN: 1996-1944

Recent advances in high-resolution three-dimensional X-ray CT imaging have made it possible to visualize fluid configurations during multiphase displacement at the pore-scale. However, there is an inherited difficulty in image-based curvature measurements: the use of voxelized image data may introduce significant error, which has not-to date-been quantified. To find the best method to compute curvature from micro-CT images and quantify the likely error, we performed drainage and imbibition direct numerical simulations for an oil/water system on a bead pack and a Bentheimer sandstone. From the simulations, local fluid configurations and fluid pressures were obtained. We then investigated methods to compute curvature on the oil/water interface. The interface was defined in two ways; in one case the simulated interface with a sub-resolution smoothness was used, while the other was a smoothed interface extracted from synthetic segmented data based on the simulated phase distribution. The curvature computed on these surfaces was compared with that obtained from the simulated capillary pressure, which does not depend on the explicit consideration of the shape of the interface. As distinguished from previous studies which compared an average or peak curvature with the value derived from the measured macroscopic capillary pressure, our approach can also be used to study the pore-by-pore variation. This paper suggests the best method to compute curvature on images with a quantification of likely errors: local capillary pressures for each pore can be estimated to within 30% if the average radius of curvature is more than 6 times the image resolution, while the average capillary pressure can also be estimated to within 11% if the average radius of curvature is more than 10 times the image resolution.

Gao Y, Qaseminejad Raeini A, Blunt MJ,
et al., 2019, Pore occupancy, relative permeability and flow intermittency measurements using X-ray micro-tomography in a complex carbonate, *Advances in Water Resources*, Vol: 129, Pages: 56-69, ISSN: 0309-1708

We imaged the steady-state flow of brine and decane (oil) at different fractional flows during dual injection in a micro-porous limestone, Estaillades, using X-ray micro-tomography. We applied differential imaging to: (a) distinguish micro-porous regions from macro-pores, and (b) determine fluid pore occupancy in both regions, and relative permeability at a capillary number, Ca = 7.3 × 10 −6 . The sample porosity was approximately 28%, with 7% in macro-pores and 21% in pores that could not be directly resolved (micro-porosity). Fluid occupancy in micro-porosity was classified into three sub-phases: micro-pore space with oil, micro-pore space with brine, and micro-pores partially filled with oil and brine. Our method indicated an initially higher oil recovery from micro-porosity, consistent with waterflooding in a water-wet rock. The fractional flow and relative permeabilities of the two fluids were obtained from measurements of the pressure differential across the sample and the saturation calculated from the images. The brine saturation and relative permeabilities are impacted by the presence of water-wet micro-porosity which provides additional connectivity to the phases. Furthermore, we find that in addition to brine and decane, a fraction of the macroscopic pore space contains an intermittent phase, which is occupied either by brine or decane during the hour-long scan time. Pore and throat occupancy of oil, brine and intermittent phase were obtained from images at different fractional flows using the generalized pore network extracted from the image of macro-pores. The intermittent phase, where the occupancy fluctuated between oil-filled and brine-filled, was predominantly located in the small and intermediate size pores and throats. Overall, we establish a new experimental methodology to: (i) quantify initial and recovered oil in micro-pores, (ii) characterise intermittent flow, and (iii) measure steady-state relative permeability in carbonates, whi

Lin Q, Bijeljic B, Berg S,
et al., 2019, Minimal surfaces in porous media: Pore-scale imaging of multiphase flow in an altered-wettability Bentheimer sandstone, *Physical Review E*, Vol: 99, Pages: 063105-1-063105-13, ISSN: 1539-3755

High-resolution x-ray imaging was used in combination with differential pressure measurements to measurerelative permeability and capillary pressure simultaneously during a steady-state waterflood experiment on asample of Bentheimer sandstone 51.6 mm long and 6.1 mm in diameter. After prolonged contact with crude oil toalter the surface wettability, a refined oil and formation brine were injected through the sample at a fixed total flowrate but in a sequence of increasing brine fractional flows. When the pressure across the system stabilized, x-raytomographic images were taken. The images were used to compute saturation, interfacial area, curvature, andcontact angle. From this information relative permeability and capillary pressure were determined as functionsof saturation. We compare our results with a previously published experiment under water-wet conditions. Theoil relative permeability was lower than in the water-wet case, although a smaller residual oil saturation, ofapproximately 0.11, was obtained, since the oil remained connected in layers in the altered wettability rock.The capillary pressure was slightly negative and 10 times smaller in magnitude than for the water-wet rock,and approximately constant over a wide range of intermediate saturation. The oil-brine interfacial area wasalso largely constant in this saturation range. The measured static contact angles had an average of 80◦ with astandard deviation of 17◦. We observed that the oil-brine interfaces were not flat, as may be expected for a verylow mean curvature, but had two approximately equal, but opposite, curvatures in orthogonal directions. Theseinterfaces were approximately minimal surfaces, which implies well-connected phases. Saddle-shaped menisciswept through the pore space at a constant capillary pressure and with an almost fixed area, removing most ofthe oil.

Mosser L, Dubrule O, Blunt M, 2019, Deep stochastic inversion

© 81st EAGE Conference and Exhibition 2019. All rights reserved. Numerous modelling tasks require the solution of ill-posed inverse problems where we seek to find a distribution of earth models that match observed data such as reflected acoustic waveforms or produced hydrocarbon volumes. We present a deep learning framework to create stochastic samples of posterior property distributions for ill-posed inverse problems using a gradient-based approach. The spatial distribution of petrophysical properties is created by a deep generative model and controlled by a set of latent variables. A generative adversarial network (GAN) is used to represent a prior distribution of geological models based on a training set of object-based models. Then we minimize the mismatch between observed ground-truth data and numerical forward-models of the generator output by first computing gradients of the objective function with respect to grid-block properties and then using neural network backpropagation to obtain gradients with respect to the latent variables. Synthetic test cases of acoustic waveform inversion and reservoir history matching are presented. In seismic inversion, we use a Metropolis adjusted Langevin algorithm (MALA) to obtain posterior samples. For both synthetic cases, we show that deep generative models such as GANs can be combined in an end-to-end framework to obtain stochastic solutions to geophysical inverse problems.

Mosser L, Dubrule O, Blunt M, 2019, Deep stochastic inversion

© 81st EAGE Conference and Exhibition 2019. All rights reserved. Numerous modelling tasks require the solution of ill-posed inverse problems where we seek to find a distribution of earth models that match observed data such as reflected acoustic waveforms or produced hydrocarbon volumes. We present a deep learning framework to create stochastic samples of posterior property distributions for ill-posed inverse problems using a gradient-based approach. The spatial distribution of petrophysical properties is created by a deep generative model and controlled by a set of latent variables. A generative adversarial network (GAN) is used to represent a prior distribution of geological models based on a training set of object-based models. Then we minimize the mismatch between observed ground-truth data and numerical forward-models of the generator output by first computing gradients of the objective function with respect to grid-block properties and then using neural network backpropagation to obtain gradients with respect to the latent variables. Synthetic test cases of acoustic waveform inversion and reservoir history matching are presented. In seismic inversion, we use a Metropolis adjusted Langevin algorithm (MALA) to obtain posterior samples. For both synthetic cases, we show that deep generative models such as GANs can be combined in an end-to-end framework to obtain stochastic solutions to geophysical inverse problems.

Oliveira TDS, Blunt MJ, Bijeljic B, 2019, Modelling of multispecies reactive transport on pore-space images, *Advances in Water Resources*, Vol: 127, Pages: 192-208, ISSN: 0309-1708

We present a new model, named poreReact, to simulate multispecies reactive transport on pore space images. We solve the Navier–Stokes equations and the advection-diffusion equation for concentration on an unstructured grid using the finite volume method implemented in OpenFOAM. We couple it with the chemical model Reaktoro, which we use to calculate the chemical equilibrium of homogeneous reactions 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 in the pore space and find that, despite the relative homogeneity of the bead pack and symmetry in injection conditions, the concentration fields of the products can be asymmetric because of the interplay between transport and chemical equilibrium. For different Péclet numbers, we calculate relative yields (the ratio between the observed change in concentration and the change that would be obtained if the reactants were completely mixed). 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 the larger amount of matter available for reaction in a given time. Reaction is more favoured in the faster-flowing regions of the pore space. 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.

Al-Khulaifi Y, Lin Q, Blunt MJ,
et al., 2019, Pore-scale dissolution by CO₂ saturated brine in a multimineral carbonate at reservoir conditions: impact of physical and chemical heterogeneity, *Water Resources Research*, Vol: 55, Pages: 3171-3193, ISSN: 0043-1397

We study the impact of physical and chemical heterogeneity on reaction rates in multimineral porous media. We selected two pairs of carbonate samples of different physical heterogeneity in accordance with their initial computed velocity distributions and then injected CO 2 saturated brine at reservoir conditions at two flow rates. We periodically imaged the samples using X-ray microtomography. The mineralogical composition was similar (a ratio of dolomite to calcite of 8:1), but the intrinsic reaction rates and mineral spatial distribution were profoundly different. Visualizations of velocity fields and reacted mineral distributions revealed that a dominant flow channel formed in all cases. The more physically homogeneous samples had a narrower velocity distribution and more preexisting fast channels, which promoted dominant channel formation in their proximity. In contrast, the heterogeneous samples exhibit a broader distribution of velocities and fewer fast channels, which accentuated nonuniform calcite distribution and favored calcite dissolution away from the initially fast pathways. We quantify the impact of physical and chemical heterogeneity by computing the proximity of reacted minerals to the fast flow pathways. The average reaction rates were an order of magnitude lower than the intrinsic ones due to mass transfer limitations. The effective reaction rate of calcite decreased by an order of magnitude, in both fast channels and slow regions. After channel formation calcite was shielded by dolomite whose effective rate in slow regions could even increase. Overall, the preferential channeling effect, as opposed to uniform dissolution, was promoted by a higher degree of physical and/or chemical heterogeneity.

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