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We report the results of modelling the transport of n-octane and n-hexadecane and their mixtures through carbonaceous nanopores at high-pressure conditions. Pores are modelled as smooth slit sheets with perturbations added as ridges and steps and a version of the Statistical Associating Fluid Theory (SAFT-γ Mie) is used both as equation of state and as a coarse-grained force field to account for fluid-fluid and fluid-solid molecular interactions. Molecular simulation allowed the description of transport diffusivities in terms of molecular flow, using boundary driven non-equilibrium molecular dynamics (BD-NEMD). Transport diffusivities are also independently calculated using equilibrium and external force non-equilibrium molecular dynamics (EF-NEMD) simulations, after accounting for the adsorption on the pores. We show consistency between the approaches for quantifying transport in terms of permeabilities (Darcy flows) and transport diffusivities. We find that smooth slit carbon pore models, which are commonly employed in literature as surrogates for kerogen regions in shale, are an inadequate representation of ultra-confined natural pores. For slit pores, the flow patterns are characterized by a fully-mutualized plug-like flow and fast transport. However, by incorporating even a small amount of rugosity (roughness) to the solid walls, the diffusion coefficients decrease dramatically with surface roughness significantly affecting the characteristic transport and velocity profiles inside the pores. In all cases, it is seen that there are important cross-correlation effects, influencing the way components of the mixture flow together. Calculated self-diffusivities are orders of magnitude smaller than the observed transport diffusivities for liquid mixtures. This work has a direct impact on the understanding and modelling of unconventional hydrocarbon recovery and flow in organic shale rocks.

A popular equation that is often employed to represent the relationship between the pressure loss and the fluid flow in fluidized or packed granular beds is the Ergun equation, which is an extension of Darcy’s law. In this paper, the method of Smoothed Particle Hydrodynamics (SPH) is used to numerically study the flow field across a rectangular channel partially filled with a porous layer both at the Representative Elementary Volume (REV) scale using the Ergun equation and at the pore scale. Since the flow field can be estimated at the REV scale with a much lower cost compared to the pore scale, it is important to evaluate how accurately the pore-scale results can be reproduced at the REV scale. The comparison between both scales is made in terms of the velocity profiles at the outlet of the rectangular channel and the pressure losses across the clear and porous zones for three different arrays of solid grains at the pore scale. The results show that minimum differences in the flow structure and velocity profiles between the REV and the pore scale always occur at intermediate values of the porosity (ϕ=0.44 and 0.55). As the porosity increases, the differences between the REV and the pore scale also increase. The details of the pressure losses are affected by the geometry of the porous medium. In particular, we find that the pressure profiles at the REV scale match those at the pore scale almost independently of the porosity only when the grains are uniformly distributed in a non-staggered square array.

Water injection with an oscillatory pressure boundary is a promising technology, which can achieve a more economical and environment-friendly EOR (enhanced oil recovery). However, due to the unclear critical injection frequency, its oil production performance has been unstable and is far from reaching the optimal level. Here, a numerical model is established for oil recovery by the water injection with the oscillatory boundary condition to find out the critical frequency for the optimal EOR. The correlations between the water injection frequency and the EOR level at diverse oil–water surface tensions and oil viscosities are integrated into the model. Our numerical model reveals that an optimal EOR of roughly 10% is achieved at the critical water injection frequency compared with water injection without an oscillatory boundary. The EOR mechanism is revealed showing that upon water injection with the optimum frequency, the formation of the preferential pathways is inhibited and the pressure transmits to the wall sides to displace the oil. Moreover, it is indicated that the required critical frequency increases with higher surface tension and larger oil viscosity. In addition, the difference between the residual oil saturation at the optimal frequency increases with the increase in surface tension compared with water injection without an oscillatory boundary. Last but not least, it is elucidated that at a constant injection frequency, a higher EOR is achieved when the water–oil surface tension is lower but the oil viscosity is larger. Our work promises economic, eco-friendly and controllable enhanced oil recovery.

Water flooding technology is widely used to improve oil recovery efficiency in oilfields. The capillary barrier effect induced by the complex pore structures in the reservoir rocks is a crucial reason for the trapping of a great deal of residual oil in oil reservoirs after water flooding. However, the formation condition along with the effect on the recovery rate of the capillary barrier under different wettability conditions should be investigated further. To bridge the gap between the microscopic mechanism of the capillary barrier effect and the macroscopic mechanism of oil displacement efficiency, a simple conceptual capillary model is constructed to obtain the formation conditions of the capillary barrier using the analysis method, and its influence on macroscopic oil displacement efficiency in the porous media model with an opening angle of 45° is systematically investigated in this study using direct numerical simulations (DNS) coupled with the volume of fluid method. The results showed that the capillary barrier effect plays a significant role in the formation of the residual oil in the reservoir rock and the contact angle and the opening angle are the primary factors for the formation of the capillary barrier. The capillary force is the driving force when the oil–water interface advances in the throat channel under water-wet conditions, while the capillary force hinders the movement of oil–water movement when the liquid flows out of the throat channel and when θ + β > 90o. Furthermore, the highest oil displacement efficiency is achieved at the intermediate capillary number and in the case that the minimum conditions of occurrence of the capillary barrier phenomenon are satisfied. This is of great significance for controlling the optimized contact angle to further enhance the oil recovery rate of current oil reservoirs using waterflooding technology.

Porous media can be found in all areas of scientific life, such as medicine, civil engineering, material science, fluid dynamics. Computing has achieved high efficiency and computational capacity – so far. However, three-dimensional Computational Fluid Dynamics (CFD) simulations of microstructure remain significant challenges. Pore-scale simulations can help understand the physical processes and determine macroscopic parameters such as the high-frequency limit of dynamic tortuosity, viscous, and thermal characteristic lengths. Independent of whether the computational problem is two or three-dimensional, the geometry as input parameter must be prepared. For this reason, geometry representation methods play a crucial role in the analysis at the pore-scale, especially in numerical simulations. In this article, an insight into microstructures’ visualization capabilities is provided essentially for CFD simulations.

In the present study, the radiation properties of a high porosity fibrous medium which is used in catalytic heaters were estimated. The calculation process was based on an inverse method using pore scale simulation and two-flux model. The results showed a good agreement with available experimental results. The effects of geometrical parameters including the solid volume fraction, fibers orientation, and diameter on the radiation properties were investigated. By increasing the solid share in the fibrous porous medium, the extinction coefficient increased, in which the absorption growth rate was higher than the scattering growth rate. The effect of the fibers angle on the scattering was greater than its effect on the absorption. For each porosity, an extinction coefficient could be defined in which, by increasing the fibers diameter, the extinction coefficient would not be reduced any more. The solid volume fraction, fibers diameter, and orientation were found to be the most effective geometric parameters on the radiation properties, respectively.

A key finding in soil carbon studies over the past decade is that soil organic carbon (SOC) stabilization is not controlled by its molecular complexity and clay content but by its physicochemical protections including occlusion in aggregates and sorption/precipitation with organo-mineral associations. The organo-mineral complexes and the adsorbed SOC could be dissolved microbially under anoxic conditions, which is an important pathway in the carbon cycle but has been overlooked by most carbon models. As it is reported that organo-mineral associations are formed in aerobic conditions and could be lost under anaerobic conditions, there should be a positive correlation between SOC and ability of the aggregates to transport dissolved oxygen. We test this using two long-term experiments with a SOC gradient at Rothamsted Research in the UK: One experiment compares the effects of different fertilizations on yield of winter wheat and the other experiment aims to study the consequence of cropping system change for SOC dynamics. Aggregates in samples taken from plots under different treatments on the two experiments were scanned using X-ray computed tomography at 1.5 μm resolution; the ability of each aggregate to transport oxygen was calculated based on the pore-scale lattice Boltzmann simulation assuming that the aggregate is saturated as this is the most anaerobic scenario. We compared porosity and diffusion coefficient of all aggregates and link them to soil carbon measured from different treatments on the two experiments. The results showed that the agronomic practice changes occurring 67 and 172 years ago substantially reshaped the intra-aggregate structure, and that the accrual of SOC is positively correlated with diffusion coefficient of the aggregates to transport oxygen. However, the diffusion coefficient increases with SOC asymptotically, plateauing when SOC exceeds a threshold value. We also found that diffusion coefficient of the aggregates in cropped soils chemically fertilized trended with their porosity approximately in the same way, deviating from those for other non-cropped treatments or fertilized with farmyard manure.

Direct simulation at the pore-scale is crucial to unravel rarefaction effect on gas transport in tight porous media. To satisfy the dual demands on modeling accuracy and computation effort, an appropriate method must be chosen. This work, therefore, evaluates four numerical methods for pore-scale rarefied gas flows in a two-dimensional (2D) model porous media over a wide range of rarefaction. These methods are the incompressible Navier-Stokes equation with the first-order velocity-slip boundary condition, and three gas-kinetic solvers i.e. a finite-difference (FD) iterative solver for the linearized Bhatnagar, Gross and Crook (BGK) model kinetic equation, a finite-volume (FV) solver for the non-linear Shakhov model, and an open-source direct simulation Monte Carlos (DSMC) solver. The benchmark cases cover the characteristic Knudsen number ranging from 0.0231 to 4.62 while the characteristic Reynolds numbers are kept to be less than 1.0. All the solvers are developed in OpenFOAM, except the FD solver, allowing us to investigate the effect of local grid refinements using the automatic Cartesian grid generator in OpenFOAM. The flow fields and the apparent permeabilities predicted by all the solvers have been compared in detail. Besides, the computational time of these solvers is measured and analyzed to demonstrate the relative cost of the three kinetic solvers. It is found that the FD solver is the most efficient one and gives accurate results over the whole range of Knudsen number. Finally, this study also evaluates the feasibility of the recently developed discrete unified gas-kinetic scheme (DUGKS), the algorithm in the aforementioned non-linear Shakhov model equation solver, for pore-scale rarefied gas flow. It is found the results predicted by this solver agree well with the other two kinetic solvers.

Gaseous flow through ultra-tight porous media, e.g. shale and some high-performance insulation materials, is often rarefied, invalidating an analysis by the continuum flow theory. Such rarefied flows can be accurately described by the kinetic theory of gases which utilizes the Boltzmann equation and its simplified kinetic models. While discrete velocity methods (DVM) have been successful in directly solving these equations, the immense potential of a particle-based solution of the variance-reduced Boltzmann-BGK (Bhatnagar-Gross-Krook) equation for rarefied flows in porous media has not been exploited yet. Here, a parallel solver based on the low variance deviational simulation Monte Carlo (LVDSMC) method is developed for 3D flows, which enables pore-scale simulations using digital images of porous media samples. The unique advantage of this particle-based formulation is in providing additional insights regarding the multi-scale nature of the flow and surface/gas interactions via two new parameters, i.e. pore and surface activity respectively. Together, these two parameters can identify key flow properties of the porous media. The computational efficiency and accuracy of the current method has also been analysed, suggesting that this new solver is a powerful simulation tool to quantify flow properties of ultra-tight porous media.

Transport processes in porous media have been traditionally studied through the parameterization of macroscale properties, by means of volume-averaging or upscaling methods over a representative elementary volume. The possibility of upscaling results from pore-scale simulations, to obtain volume-averaging properties useful for practical purpose, can enhance the understanding of transport effects that manifest at larger scales. Several studies have been carried out to investigate the impact of the geometric properties of porous media on transport processes for solute species. However, the range of pore-scale geometric properties, which can be investigated, is usually limited to the number of samples acquired from microcomputed tomography images of real porous media. The present study takes advantage of synthetic porous medium generation to propose a systematic analysis of the relationships between geometric features of the porous media and transport processes through direct simulations of fluid flow and advection-diffusion of a non-reactive solute. Numerical simulations are performed with the lattice Boltzmann method on synthetic media generated with a geostatistically based approach. Our findings suggest that the advective transport is primarily affected by the specific surface area and the mean curvature of the porous medium, while the effective diffusion coefficient scales as the inverse of the tortuosity squared. Finally, the possibility of estimating the hydrodynamic dispersion coefficient knowing only the geometric properties of porous media and the applied pressure gradient has been tested, within the range of tested porous media, against advection-diffusion simulations at low Reynolds (, Geofluids, 11 (6), ISSN:1468-8115, ISSN:1468-8123

A need for a reduction in energy intensity and greenhouse gas emissions of bitumen and heavy oil recovery processes has led to the invention of several methods where mass-transfer-based recovery processes in terms of cold or heated solvent injection are used to reduce bitumen viscosity rather than steam injection. Despite the extensive numerical and experimental investigations, the field results are not always aligned to what is predicted unless several history matches are done. These discrepancies can be explained by investigating the mechanisms involved in mass transfer and corresponding viscosity reduction at the pore level. A two-phase multicomponent pore-scale simulator is developed to be used for realistic porous media simulation. The simulator developed predicts the chamber front velocity and chamber propagation in agreement with 2D experimental data in the literature. The simulator is specifically used for vapor extraction (VAPEX) modelling in a 2D porous medium. It was found that the solvent cannot reach its equilibrium value everywhere in the oleic phase confirming the non-equilibrium phase behavior in VAPEX. The equilibrium assumption is found to be invalid for VAPEX processes even at a small scale. The model developed can be used for further investigation of mass transfer-based processes in porous media.

Miscible and near-miscible flooding are used to improve the performance of carbon-dioxide-enhanced oil recovery in heterogeneous porous media. However, knowledge of the effects of heterogeneous pore structure on CO2/oil flow behavior under these two flooding conditions is insufficient. In this study, we construct pore-scale CO2/oil flooding models for various flooding methods and comparatively analyze CO2/oil flow behavior and oil recovery efficiency in heterogeneous porous media. The simulation results indicate that compared to immiscible flooding, near-miscible flooding can increase the CO2 sweep area to some extent, but it is still inefficient to displace oil in small pore throats. For miscible flooding, although CO2 still preferentially displaces oil through big throats, it may subsequently invade small pore throats. In order to substantially increase oil recovery efficiency, miscible flooding is the priority choice; however, the increase of CO2 diffusivity has little effect on oil recovery enhancement. For immiscible and near-miscible flooding, CO2 injection velocity needs to be optimized. High CO2 injection velocity can speed up the oil recovery process while maintaining equivalent oil recovery efficiency for immiscible flooding, and low CO2 injection velocity may be beneficial to further enhancing oil recovery efficiency under near-miscible conditions.

Tortuosity is a parameter characterising the complexity of pore geometry in porous media for fluids and solutes to move through. It is loosely defined and has been calculated by different methods based on either the pore geometry or a special transport process. While it has been known that tortuosities calculated from different methods vary, it remains obscure if there is a one-to-one relationship between them, especially for soils which are not randomly structured but self-organised by a myriad of interactive biotic and abiotic processes. We studied this based on X-ray images of 30 soil aggregates taken from fields which have been under different land managements for more than 70 years and thus have contrasting structures. The tortuosity of every soil sample was calculated using three methods: viscous fluid flow, solute diffusion, and geometric structure of the pores, with the former two calculated from pore-scale simulations. The results showed that although the tortuosities calculated by all methods are correlated, their correlation is weak and there is no one-to-one relationship between them. On average, the tortuosity calculated from fluid flow is the highest and the geometrical tortuosity is the least, with that calculated from solute diffusion in between. The tortuosity calculated from all three methods decreases as porosity increases, but the coefficient of determination is low. We also found that the bulk diffusion coefficient cannot be predicted using geometrical tortuosity and porosity of the soils from the formulae suggested in the literature. These findings reveal that tortuosity is a process-dependent parameter rather than an intrinsic soil property, and that tortuosity calculated from different methods cannot be used interchangeably to estimate soil transport parameters.

Pore-scale studies of premixed gas combustion in a packed bed is conducted to study the flow and thermal non-equilibrium phenomenon in packed bed. The 3D random packed bed is generated using the EDEM software and solid surface radiation is computed using Discrete Ordinates (DO) model. The simulations are carried out using a commercial software package based on the finite volume method. It is shown that the local variation of species mass fraction, reaction rate et al. in pores near the flame front is significant, the radiation heat flux is transferred layer-by-layer. Cold flow simulation without reaction reveals that flow non-equilibrium is one of the essential characteristics of packing bed and increase in flow velocity leads to intensify non-equilibrium phenomenon. The distributions for content of axial velocity and gas temperature are wave-like shape in the burner and vary with time.

In this study, the spreading of a liquid droplet on the surface of a fibrous paper and its penetration into the paper is studied. The spreading of the droplet was visualized using confocal microscopy and the penetration depth was quantified using Automatic Scanning Absorptiometry (ASA) measurements. The three-dimensional structure of the paper was obtained through micro-tomography imaging with a resolution of 0.9 µm. The obtained images were used to reconstruct the pore space, which was in turn used in direct numerical simulations of penetration of a droplet into paper. Simulations were performed using open source code OpenFOAM, which solves equations of two-phase flow (in our case air and water) in pores based on the Volume of Fluid Method. Simulation results showed a good agreement with the experimental observations. In particular, the dimensions of spreading area of a droplet and the depth of penetration were simulated reasonably well. Then, we used the model to investigate effects of changes in various liquid properties on spreading and penetration of a droplet liquid. We made calculations for three different values of contact angle (CA): 0°, 60°, and 120°. We found the largest penetration depth for CA = 0. For CA = 60 and CA = 120, we found that the liquid droplet moved sideways from the jetted location, which is not favorable in inkjet printing. We also made simulations with larger values for viscosity and density, based on properties of an ink-based liquid used in inkjet printing. The results have shown a slower spreading and penetration compared with water. The model can be used to study effects of changes in either ink physical properties or paper layer microstructure on final spreading/penetration extent.

Quantitative modelling of the rheology of non-Newtonian fluids requires significant empirical input due to very complex behaviour of the bulk fluid as a result of particle-scale physics of fluids. The existing rheology models are mainly limited to certain fluid dynamics conditions such as shear rate, shear stress, etc. Adopting Doolittle's free volume theory approach, we have proposed an empirical equation to describe the relative free volume-dependent viscosity, the shear stress-dependent viscosity, the shear rate-dependent viscosity, and the dimensionless Peclet number-dependent relative viscosity of shear thickening fluids. The proposed formulae predict all rheologically different behaving Newtonian, intermediate shear thinning, shear thickening and extreme shear thinning regimes of shear-thickening fluids. The proposed formulae have been validated against the experimental rheological data of various shear thickening fluids over a range of pH, volume fraction, electrolyte concentration, temperature, and magnetic field. The results suggest that the predicted threshold material parameters of shear thickening fluids help to quantitatively evaluate the effect of varying physico-chemical conditions on the rheology of shear thickening fluids. We simulated the flow of a shear thickening fluid, modelled using proposed shear rate-dependent equation, in a 2D staggered porous medium. We observed bimodal distribution of pore-scale shear rate, shear viscosity and velocity in a porous medium.

In this work, we investigate particle deposition efficiency in porous media by way of pore-scale computational fluid dynamics simulations. First, we show how to employ a novel methodology of algorithmic generation of porous media to build the computational domain for our simulations, representing a realistic random packing of monodisperse spheres. Then, we focus on the effect of gravitational settling on particle deposition, comparing our results with the well-known simplified theoretical laws, showing how pore-scale numerical experiments can improve the prediction accuracy of these laws but, most of all, help gain fundamental insights in the physical mechanisms at work.

Wettability is an important factor controlling the displacement of immiscible fluids in porous media and therefore affects the flow and transport of supercritical (sc) CO2 in geologic carbon sequestration. Because few studies have focused on the wettability effect in scCO2-brine flow systems, we experimentally and numerically tested influences of wettability on drainage at the pore network scale. Using a high-pressure micromodel-microscopy system, we performed experiments of scCO2 invasion into brine-saturated water-wet and intermediate-wet micromodels, and recorded the scCO2 invasion morphology under reservoir relevant conditions. We also performed pore-scale numerical simulations to infer 3D details of fluid–fluid displacement processes. During drainage under intermediate-wet conditions, we found higher scCO2 saturation, wider scCO2 fingering, and more compact displacement patterns. The simulation results are qualitatively consistent with the experiments. Through quantitative analyses of the experiments, we found that the reduced wettability decreases the displacement front velocity, promotes non-wetting phase pore-filling events in the longitudinal direction, delays the breakthrough time of invading fluid, and increases the displacement efficiency. Simulated results also show that the fluid–fluid interface area follows a unified power-law relation with scCO2 saturation, and show smaller interface area in intermediate-wet case which suppresses the mass transfer between the phases. These pore-scale results provide insights for the wettability effects on CO2–brine immiscible displacement in geologic carbon sequestration.

In this work several geometries, each representing a different porous medium, are considered to perform detailed computational fluid dynamics simulation for fluid flow, particle transport and deposition. Only Brownian motions and steric interception are accounted for as deposition mechanisms. Firstly pressure drop in each porous medium is analyzed in order to determine an effective grain size, by fitting the results with the Ergun law. Then grid independence is assessed. Lastly, particle transport in the system is investigated via Eulerian steady-state simulations, where particle concentration is solved for, not following explicitly particles’ trajectories, but solving the corresponding advection–diffusion equation. An assumption was made in considering favorable collector-particle interactions, resulting in a “perfect sink” boundary condition for the collectors. The gathered simulation data are used to calculate the deposition efficiency due to Brownian motions and steric interception. The original Levich law for one simple circular collector is verified; subsequently porous media constituted by a packing of collectors are scrutinized. Results show that the interactions between the different collectors result in behaviors which are not in line with the theory developed by Happel and co-workers, highlighting a different dependency of the deposition efficiency on the dimensionless groups involved in the relevant correlations.

A fast method with tunable accuracy is proposed to estimate errors and uncertainties in pore-scale and Digital Rock Physics (DRP) problems. The overall predictivity of these studies can be, in fact, hindered by many factors including sample heterogeneity, computational and imaging limitations, model inadequacy and not perfectly known physical parameters. The typical objective of pore-scale studies is the estimation of macroscopic effective parameters such as permeability, effective diffusivity and hydrodynamic dispersion. However, these are often non-deterministic quantities (i.e., results obtained for specific pore-scale sample and setup are not totally reproducible by another “equivalent” sample and setup). The stochastic nature can arise due to the multi-scale heterogeneity, the computational and experimental limitations in considering large samples, and the complexity of the physical models. These approximations, in fact, introduce an error that, being dependent on a large number of complex factors, can be modeled as random. We propose a general simulation tool, based on multilevel Monte Carlo, that can reduce drastically the computational cost needed for computing accurate statistics of effective parameters and other quantities of interest, under any of these random errors. This is, to our knowledge, the first attempt to include Uncertainty Quantification (UQ) in pore-scale physics and simulation. The method can also provide estimates of the discretization error and it is tested on three-dimensional transport problems in heterogeneous materials, where the sampling procedure is done by generation algorithms able to reproduce realistic consolidated and unconsolidated random sphere and ellipsoid packings and arrangements. A totally automatic workflow is developed in an open-source code [1], that include rigid body physics and random packing algorithms, unstructured mesh discretization, finite volume solvers, extrapolation and post-processing techniques. The proposed method can be efficiently used in many porous media applications for problems such as stochastic homogenization/upscaling, propagation of uncertainty from microscopic fluid and rock properties to macro-scale parameters, robust estimation of Representative Elementary Volume size for arbitrary physics.\ud \ud

At the high water cut stage, the residual oil in a reservoir becomes complex and dispersed. Moreover, it is challenging to achieve good predictions of the movement of oil and water in a reservoir according to the macroscopic models based on the statistic parameters of this scenario. However, pore-scale simulation technology based on directly tracking the interaction among different phases can make an accurate prediction of the fluid distribution in the pore space, which is highly important in the improvement of the recovery rate. In this work, pore-scale simulation methods, including the pore network model, lattice Boltzmann method, Navier–Stokes equation-based interface tracking methods, and smoothed particle hydrodynamics, and relevant technologies are summarized. The principles, advantages, and disadvantages, as well as the degree of difficulty in the implementation are analyzed and compared. Problems in the current simulation technologies, micro sub-models, and applications in physicochemical percolation are also discussed. Finally, potential developments and prospects in this field are summarized.

Oil-water relative permeability and capillary pressure of a water-wet digital core are computed using the finite-volume/volume of fluid method and mimicking traditional laboratory steady-state experiments carried out on a water saturated sample. Commercial software is used for immiscible multiphase fluid flow simulations, carried out on a low-cost multicore workstation, and the porescale data are upscaled to derive relative permeability and capillary pressure curves as function of water saturation. The digital sample is obtained by high resolution X-ray computed tomography scanning. [Received: March 13, 2013; Accepted: June 25, 2013]

International audience; Underground hydrogen storage (UHS) as a means of energy storage is an efficient way of compensating for seasonal fluctuations in the availability of energy. One important factor which influences this technology is the activity of methanogenic microorganisms capable of utilising hydrogen and carbon dioxide for metabolism and leading to a change in the stored gas composition. A coupled, pore-scale model is presented which aids in the investigation of the mechanisms that govern the conversion of hydrogen to methane, i.e. advective hydrogen flow, its diffusion into microbial biofilms of multiple species, and its consumption within these biofilms. The model assumes that spherical grains are coated by a film of residual water and treats the biofilm development within each film in a quasi one-dimensional manner. A sample simulation using the presented model illustrates the biofilm growth process in these films as well as the competition between three different microbial species: methanogens, acetogens, and acetotrophs.

The experimental investigation of flow through porous media is inherently difficult due to the lack of optical access. The recent developments in the fields of X-ray micro-tomography (micro-CT hereafter), digital sample reconstruction by image-processing techniques and fluid-dynamics simulation, together with the increasing power of super-computers, allow to carry out pore-scale simulations through digitally-reconstructed porous samples. The scientific relevance of pore-scale simulations lies in the possibility of upscaling the pore-level data, yielding volume-averaged quantities useful for practical purposes. One of the best-known examples of upscaling is the calculation of absolute and relative permeability of reservoir rocks. This contribution presents a complete work-flow for setting up pore-scale simulations, starting from the micro-CT of a (in general small) porous sample. Relevant applications are discussed in order to reveal the potential of the proposed methodology.

We report finite-element simulations of gas–liquid two-phase flows through a model porous medium made of corrugated tubes. By resolving the pore-scale fluid dynamics and interfacial morphology, we compute the relative permeability of the porous medium by averaging over a pore-size-distribution of a real porous medium. A constant pressure gradient is applied on both fluids to simulate a pressure-driven creeping flow, and a diffuse-interface model is used to compute the interfacial evolution and the contact line motion. We observe a number of flow regimes in the micro-pores, depending on the pore size, imposed pressure gradient, and other geometric and physical parameters. The flow rates vary nonlinearly with the pressure gradient, and the extended Darcy’s law does not hold in general. The interaction between the two phases, known as viscous coupling, is a prominent feature of the process. As a result, the relative permeability depends not only on saturation, but also on the capillary number, viscosity ratio, wettability of the solid wall, pore geometry, and the initial configuration. The effects of these factors are explored systematically and compared with previous studies.

X-ray microtomography is routinely used to image the three-dimensional pore space of sedimentary rocks. Flow and transport properties can then be simulated directly in such images. Advective transport in porous media is frequently simulated using streamlines. We present a novel streamline tracing algorithm based on a substantial development of the most widely used method (the Pollock algorithm) employed for macroscale (Darcy) flow, making it consistent with solutions of the Navier-Stokes equation with no flow at solid boundaries. We use this new algorithm to calculate breakthrough curves and time-of-flight distributions for advection-dominated transport in two three-dimensional images of sedimentary rocks containing up to $$10^9$$ voxels: a sandstone and a carbonate. We show that our approach provides a more accurate description of flow, particularly when only a few image voxels span each pore. Therefore, it is better suited to capture anomalous (non-Fickian) transport behaviour than the standard Pollock method.