Showing papers in "Transport in Porous Media in 2021"

An MHD of Nanofluid Flow Over a Porous Stretching/Shrinking Plate with Mass Transpiration and Brinkman Ratio

Abstract: An investigation of 2D laminar magnetohydrodynamics couple stress hybrid nanofluid is performed with inclined magnetic field over the stretching/-shrinking surface embedded in porous media. The quiescent water-based nanofluid is subjected to the external force by pulling the two ends of the sheet with equal magnitude and opposite forces. The governing nonlinear partial differential equations (PDEs) are converted into nonlinear ordinary differential equation (ODE) by adopting the suitable similarity transformation and obtains the analytical solution for velocity. The hydrodynamic characteristics are investigated in the presence of different physical parameters such as couple stress parameter, magnetic parameter, mass transpiration, stretching/shrinking parameter, porosity and magnetic parameter with the help of graphs. The thermal properties are enhanced by adding the copper and alumina nanoparticles to the base fluid. The result of this study has important applications in industrial and scientific are such as polymer extrusion process, liquid crystal solidification, cement artificial foams production, ceramics, metal spinning, and roofing shingles and also have possible technological applications in fluid-based systems involving stretchable/shrinkable materials.

Multiscale Characterization of Wettability in Porous Media

Abstract: Wettability is one of the key controlling parameters for multiphase flow in porous media, and paramount for various geoscience applications. While a general awareness of the importance of wettability was established decades ago, our fundamental understanding of how wettability influences transport and of how to characterize wettability has improved tremendously in recent years through breakthroughs in imaging technology and modeling techniques. Numerical modeling studies clearly show not only that macroscopic two-phase flow is influenced by the average wettability, but also that the spatial distribution of wetting significantly impacts the macroscopic parameters. Herein, we explore the thermodynamics for porous multiphase systems, and recent breakthroughs in wettability characterization. Our view is that bridging the multiscale characterization of wetting must consider two fundamental perspectives: geometry and energy. Advancing the overall description requires an improved understanding of the operative mechanisms that dominate at various scales, and the development of quantitative approaches to capture these effects. We take a multistage approach, looking at these fundamental perspectives from the sub-pore-to-pore length scales, followed by the pore-to-core length scales using various analytical techniques and numerical simulations. Within this context, there remain many open-ended questions, and we therefore highlight these issues to provide guidance on future research directions. Our overall aim is to provide comprehensive guidance on the multiscale characterization of wettability in porous media, in order to facilitate novel research.

Computationally Efficient Multiscale Neural Networks Applied to Fluid Flow in Complex 3D Porous Media

Abstract: The permeability of complex porous materials is of interest to many engineering disciplines. This quantity can be obtained via direct flow simulation, which provides the most accurate results, but is very computationally expensive. In particular, the simulation convergence time scales poorly as the simulation domains become less porous or more heterogeneous. Semi-analytical models that rely on averaged structural properties (i.e., porosity and tortuosity) have been proposed, but these features only partly summarize the domain, resulting in limited applicability. On the other hand, data-driven machine learning approaches have shown great promise for building more general models by virtue of accounting for the spatial arrangement of the domains’ solid boundaries. However, prior approaches building on the convolutional neural network (ConvNet) literature concerning 2D image recognition problems do not scale well to the large 3D domains required to obtain a representative elementary volume (REV). As such, most prior work focused on homogeneous samples, where a small REV entails that the global nature of fluid flow could be mostly neglected, and accordingly, the memory bottleneck of addressing 3D domains with ConvNets was side-stepped. Therefore, important geometries such as fractures and vuggy domains could not be modeled properly. In this work, we address this limitation with a general multiscale deep learning model that is able to learn from porous media simulation data. By using a coupled set of neural networks that view the domain on different scales, we enable the evaluation of large ( $$>512^3$$ ) images in approximately one second on a single graphics processing unit. This model architecture opens up the possibility of modeling domain sizes that would not be feasible using traditional direct simulation tools on a desktop computer. We validate our method with a laminar fluid flow case using vuggy samples and fractures. As a result of viewing the entire domain at once, our model is able to perform accurate prediction on domains exhibiting a large degree of heterogeneity. We expect the methodology to be applicable to many other transport problems where complex geometries play a central role.

Multiscale Digital Rock Analysis for Complex Rocks

Abstract: Many properties of complex porous media such as reservoir rocks are strongly affected by heterogeneity at different scales. Complex depositional and diagenetic processes have a strong control on the pore structures, leading to systems with a wide range of pore sizes covering many orders of magnitude in length scales. This poses a significant challenge for digital rock analysis since a single resolution image and associated simulation model cannot capture all the relevant length scales in sufficient detail due to limitations in computer memory and speed. The scale-transgressive effects of heterogeneity must therefore be accounted for through a multiscale digital rock workflow. We introduce a generalized multiscale imaging and pore-scale modelling workflow to derive transport properties of complex rocks having broad pore size distributions. A dry/wet micro-CT imaging sequence is used to spatially map the porosity and the connectivity of resolved and unresolved porous regions. The unresolved porosity regions are classified into different porosity classes or rock types. The resulting 3D rock-type map and the porosity map are combined and transformed into a multiscale pore network model. Resolved pores are treated in a conventional pore network manner while unresolved network elements are treated as a continuum Darcy-type porous medium. Similar to conventional continuum models, each Darcy pore is populated with single and multiphase flow properties. These properties are derived from high-resolution rock-type models constructed from backscatter SEM images and/or high-resolution micro-CT images of sub-samples. The multiscale digital rock workflow is applied to two heterogeneous rock samples: a mixed wet thinly laminated reservoir sandstone and an oil wet reservoir carbonate. Experimentally measured mercury–air primary drainage and oil–water imbibition capillary pressure curves (after ageing to restore wettability) are used to anchor the multiscale pore network model. Waterflood relative permeability is calculated in a blind test and compared with high-quality experimental data. A very encouraging agreement between computed and measured properties is found.

Pore-Scale Imaging and Modelling of Reactive Flow in Evolving Porous Media: Tracking the Dynamics of the Fluid–Rock Interface

Abstract: Fluid–mineral and fluid–rock interfaces are key parameters controlling the reactivity and fate of fluids in reservoir rocks and aquifers. The interface dynamics through space and time results from complex processes involving a tight coupling between chemical reactions and transport of species as well as a strong dependence on the physical, chemical, mineralogical and structural properties of the reacting solid phases. In this article, we review the recent advances in pore-scale imaging and reactive flow modelling applied to interface dynamics. Digital rocks derived from time-lapse X-ray micro-tomography imaging gives unprecedented opportunity to track the interface evolution during reactive flow experiments in porous or fractured media, and evaluate locally mineral reactivity. The recent improvements in pore-scale reactive transport modelling allow for a fine description of flow and transport that integrates moving fluid–mineral interfaces inherent to chemical reactions. Combined with three-dimensional digital images, pore-scale reactive transport modelling complements and augments laboratory experiments. The most advanced multi-scale models integrate sub-voxel porosity and processes which relate to imaging instrument resolution and improve upscaling possibilities. Two example applications based on the solver porousMedia4Foam illustrate the dynamics of the interface for different transport regimes (i.e., diffusive- to advective-dominant) and rock matrix properties (i.e., permeable vs. impermeable, and homogeneous vs. polymineralic). These parameters affect both the interface roughness and its geometry evolution, from sharp front to smeared (i.e., diffuse) interface. The paper concludes by discussing the challenges associated with precipitation processes in porous media, rock texture and composition (i.e., physical and mineralogical heterogeneity), and upscaling to larger scales.

Pore-Scale Imaging and Analysis of Wettability Order, Trapping and Displacement in Three-Phase Flow in Porous Media with Various Wettabilities

Abstract: Three-phase flow in porous media is encountered in many applications including subsurface carbon dioxide storage, enhanced oil recovery, groundwater remediation and the design of microfluidic devices. However, the pore-scale physics that controls three-phase flow under capillary dominated conditions is still not fully understood. Recent advances in three-dimensional pore-scale imaging have provided new insights into three-phase flow. Based on these findings, this paper describes the key pore-scale processes that control flow and trapping in a three-phase system, namely wettability order, spreading and wetting layers, and double/multiple displacement events. We show that in a porous medium containing water, oil and gas, the behaviour is controlled by wettability, which can either be water-wet, weakly oil-wet or strongly oil-wet, and by gas–oil miscibility. We provide evidence that, for the same wettability state, the three-phase pore-scale events are different under near-miscible conditions—where the gas–oil interfacial tension is ≤ 1 mN/m—compared to immiscible conditions. In a water-wet system, at immiscible conditions, water is the most-wetting phase residing in the corners of the pore space, gas is the most non-wetting phase occupying the centres, while oil is the intermediate-wet phase spreading in layers sandwiched between water and gas. This fluid configuration allows for double capillary trapping, which can result in more gas trapping than for two-phase flow. At near-miscible conditions, oil and gas appear to become neutrally wetting to each other, preventing oil from spreading in layers; instead, gas and oil compete to occupy the centre of the larger pores, while water remains connected in wetting layers in the corners. This allows for the rapid production of oil since it is no longer confined to movement in thin layers. In a weakly oil-wet system, at immiscible conditions, the wettability order is oil–water–gas, from most to least wetting, promoting capillary trapping of gas in the pore centres by oil and water during water-alternating-gas injection. This wettability order is altered under near-miscible conditions as gas becomes the intermediate-wet phase, spreading in layers between water in the centres and oil in the corners. This fluid configuration allows for a high oil recovery factor while restricting gas flow in the reservoir. Moreover, we show evidence of the predicted, but hitherto not reported, wettability order in strongly oil-wet systems at immiscible conditions, oil–gas–water, from most to least wetting. At these conditions, gas progresses through the pore space in disconnected clusters by double and multiple displacements; therefore, the injection of large amounts of water to disconnect the gas phase is unnecessary. We place the analysis in a practical context by discussing implications for carbon dioxide storage combined with enhanced oil recovery before suggesting topics for future work.

The Effect of Surface Roughness on Immiscible Displacement Using Pore Scale Simulation

Abstract: Pore scale immiscible displacement is crucial in oil industry. The surface roughness of throat is an important factor affecting water–oil interface movement. In this paper, the Navier–Stokes (N-S) equation coupled with the phase-field method is adopted to analyze the oil–water flow and interface movement in single channel, considering different surface roughness, diverse wettability and various capillary numbers. The simulation results show that the resistance increases significantly due to the surface roughness. The velocity of interface movement in rough channels is slower than that in smooth channels. The existence of asperities strengthens the interface deformation and promotes the formation of fingering phenomenon. The water flooding process presents different flow patterns in the rough channel with diverse wettability, and the influence of wall roughness on oil–water interface movement is different under various wettability conditions. There is an approximate exponential relationship between the ratio of interface length to channel length and capillary number. When the capillary number exceeds 0.03574, the phenomenon of viscous fingering is obvious, and the influence of capillary number is amplified by roughness.

ML-LBM: Predicting and Accelerating Steady State Flow Simulation in Porous Media with Convolutional Neural Networks

Abstract: Fluid mechanics simulation of steady state flow in complex geometries has many applications, from the micro-scale (cell membranes, filters, rocks) to macro-scale (groundwater, hydrocarbon reservoirs, and geothermal) and beyond. Direct simulation of steady state flow in such porous media requires significant computational resources to solve within reasonable timeframes. This study outlines an integrated method combining predictions of fluid flow (fast, limited accuracy) with direct flow simulation (slow, high accuracy) is outlined that reduces computation time by an order of magnitude without loss of accuracy. A convolutional neural network (CNNs) is trained with various configurations on simulations in 2D and 3D porous media to estimate steady state velocity fields. Permeability estimation (as an average of the field) is accurate, but the velocity fields themselves are error prone, unsuitable for further transport studies. This estimate can either be used as an indicative prediction, or as initial conditions in direct simulation to reach a fully accurate result in a fraction of the compute time. Using Deep Learning predictions (or potentially any other approximation method) to accelerate flow simulation to steady state in complex structures shows promise as a technique to push the boundaries fluid flow modelling.

Direct Numerical Simulation of Pore-Scale Trapping Events During Capillary-Dominated Two-Phase Flow in Porous Media

Abstract: This study focuses on direct numerical simulation of imbibition, displacement of the non-wetting phase by the wetting phase, through water-wet carbonate rocks. We simulate multiphase flow in a limestone and compare our results with high-resolution synchrotron X-ray images of displacement previously published in the literature by Singh et al. (Sci Rep 7:5192, 2017). We use the results to interpret the observed displacement events that cannot be described using conventional metrics such as pore-to-throat aspect ratio. We show that the complex geometry of porous media can dictate a curvature balance that prevents snap-off from happening in spite of favourable large aspect ratios. We also show that pinned fluid-fluid-solid contact lines can lead to snap-off of small ganglia on pore walls; we propose that this pinning is caused by sub-resolution roughness on scales of less than a micron. Our numerical results show that even in water-wet porous media, we need to allow pinned contacts in place to reproduce experimental results.

Rock Porous Structure Characterization: A Critical Assessment of Various State-of-the-Art Techniques

Abstract: The porous structure of geomaterials is of utmost importance for various industrial and natural processes. In this study, various conventional porous structure characterization techniques such as mercury intrusion porosimetry (MIP), nuclear magnetic resonance (NMR), micro-X-ray computed tomography (μCT) imaging, as well as gas injection have been employed to perform a systematic and critical evaluation of all such techniques for characterization of a carbonate rock sample porous structure. The porosity obtained from μCT (5 μm/voxel) (21.5%) is closer than the overall porosity obtained by MIP (17.23%) to the gas porosimetry result (23%). The 5% difference could be due to inaccessible pores to mercury, which can be accessible to nitrogen with much smaller molecules. The porosity obtained from NMR is 21.4%. It is lower than porosity values by μCT (5 μm/voxel) and by gas injection and higher than the prediction of MIP. The porosity is obtained by μCT, but the much lower resolution (27.5 μm/voxel) results in 8.19% underestimating the porosity by around 50%. Regarding permeability, the results of the NMR technique are highly dependent on the cutoff range used and very different from other techniques, whereas the permeability obtained by MIP is around 18.42 mD, close to that obtained by gas permeameter (20 mD). The μCT imaging provides the opportunity to measure pore and throat size distribution directly, to achieve open and closed porosity, the coordination number of pores and surface and volume characteristics of the porous medium, which can hardly be performed through other techniques. The resolution of images, however, fully controls the obtained pore and throat size distribution in CT analysis. The Kolmogorov–Smirnov distribution analysis reveals that the resulting pore size distribution from MIP is rather a rough estimation of the throat size distribution obtained from μCT (5 μm/voxel), while NMR prediction can provide a rather good approximation of the pore size distribution obtained from μCT (5 μm/voxel). The NMR prediction is however dependent on the choice made for the surface relaxivity coefficient, and changing it would significantly affect the resulting distribution. The results of this study provide further insight and elucidate the differences of the quantities such as porosity, permeability, and pore and throat size distribution obtained from various techniques which are essential either as an input to numerical models of flow and transport in porous media or as a building block of the theoretical models.

Effect of Saturation and Image Resolution on Representative Elementary Volume and Topological Quantification: An Experimental Study on Bentheimer Sandstone Using Micro-CT

Abstract: The establishment of the representative elementary volume (REV) in studies of porous media is crucial for linking microscopic structure and pore-scale fluid configurations to macroscopic flow processes. We present analysis of the REV of porosity, specific interfacial area, and topological measures (Betti numbers and the Euler characteristic) for an air–water–Bentheimer sandstone system imaged using micro-CT at multiple wetting-phase saturation levels, acquired during primary imbibition (an unsteady-state displacement process). The original high-resolution tomographic data (1.66 μm voxel size) were downsampled to provide additional images at a range of voxel sizes, and REV analysis was also performed for these images. The results demonstrate that the REV is dependent on the image resolution: at large voxel size features are lost, resulting in unreliable parameter measurements. The wetting-phase saturation impacts the REV of the specific interfacial area, depending on the phase pair under consideration. Quantification of topological measures is especially sensitive to voxel size, as microporosity associated with clays in this sandstone sample significantly biases the results; treatment of microporosity is required to obtain connectivity results applicable to flow processes occurring within macropores. Additionally, the REV of the Euler characteristic is dependent on the heterogeneous structure of the air phase at intermediate saturations during the unsteady-state displacement processes. These results inform experimental design and 3D tomographic data acquisition parameter targets and provide insight into the microstructure of fluid phases during primary imbibition.

Adsorption Characteristics and Thermodynamic Analysis of CH 4 and CO 2 on Continental and Marine Shale

Abstract: To better understand the CO2 sequestration and enhanced shale gas recovery, it is of great significance to study the adsorption characteristics of CO2 and CH4 in different types of shale. In this study, the mineral composition, pore structure and CH4 and CO2 adsorption isothermals of marine and continental shale samples were determined, an adsorption model was proposed to describe the adsorption behaviors of CH4 and CO2, the thermodynamics parameter of adsorption was obtained, and then the influence of mineral composition and pore structure on the adsorption characteristics of CH4 and CO2 in shale was clarified. The results showed that the total organic carbon content (TOC), the specific surface area (SSA) and micropore volume of marine shale samples are larger than those of continental shale samples. Shale has a higher TOC and clay minerals contents corresponding to a higher adsorption capacity. Under the same conditions, the CO2 adsorption capacity of shale is significantly higher than that of CH4. The proposed adsorption model considered the different adsorption mechanisms in different pores and the temperature effect, which can well describe the CH4 and CO2 adsorption behaviors of shale in various temperatures. Based on the adsorption model, considering the real gas conditions, the variation of the calculated isosteric heat (ΔH) and entropy (ΔS) of CH4 and CO2 adsorption with the increasing adsorption amount experienced three stages: slow decline, rapid decline, and gradual flattening. For a certain adsorption amount, the ΔH and ΔS of CO2 adsorption in shale are higher than those of CH4, and with the increase in temperature, the ΔH and ΔS show a downward trend. Combining the proposed adsorption model with ideal adsorbed solution theory, the predicted selectivity factor ( $$\alpha_{{{\text{CO}}_{{2}} /{\text{CH}}_{{4}} }}$$ ) of CO2 over CH4 of all shale samples at the CH4 and CO2 mixed gas environment is greater than 1. Shale has a lower TOC corresponding to a higher $$\alpha_{{{\text{CO}}_{{2}} /{\text{CH}}_{{4}} }}$$ , and thus the $$\alpha_{{{\text{CO}}_{{2}} /{\text{CH}}_{{4}} }}$$ of continental shale samples is higher than that of marine shale samples. The $$\alpha_{{{\text{CO}}_{{2}} /{\text{CH}}_{{4}} }}$$ increased with the increase in fugacity and CO2 mole fraction, while decreased with the increase in temperature, and the variation of $$\alpha_{{{\text{CO}}_{{2}} /{\text{CH}}_{{4}} }}$$ can be well explained by thermodynamics analysis.

Spontaneous Imbibition Dynamics of Liquids in Partially-Wet Nanoporous Media: Experiment and Theory

Abstract: Nanoscale spontaneous imbibition is a common process in nanoporous soil and unconventional reservoirs Due to the complexity of these natural nanoporous media, the relevant spontaneous imbibition dynamics are still unclear Thus, this paper studies spontaneous imbibition dynamics of liquids into a nanoporous carbon scaffold (NCS, with controllable wettability and pore geometry) The effects of evaporation and surfactant on spontaneous imbibition are also examined For low-volatility liquids, a linear relationship between spontaneous imbibition height ( $$H$$ ) and square root of time ( $$\sqrt{t}$$ ) is observed A modified Lucas–Washburn (L–W) equation is developed to describe the corresponding dynamics and to predict the NCS effective radius and the advancing water contact angle A dimensionless time function is presented, which includes the properties of solid and liquid and their interactions, and can be used for upscaling spontaneous imbibition data in nanoporous media from laboratory to reservoir scales Both a larger NCS pore diameter and pore throat diameter cause faster imbibition The addition of surfactant into an aqueous solution increases the imbibition rate, although this influence is suppressed with pore size decrease In contrast, for high-volatility liquids, a significant deviation from the linear relationship between $$H$$ and $$\sqrt{t}$$ is found at late times The modified L–W equation is further developed to include evaporation effect This study thus provides fundamental understanding of spontaneous imbibition dynamics at nanoscales The developed theoretical models are expected to be applicable to important problems such as water infiltration into soil, fracturing fluid loss in unconventional reservoirs, and electrolyte migration in electrochemical devices

Sensitivity and Uncertainty Analysis for Parameterization of Multiphase Flow Models

Abstract: The long-standing question on the adequate description of multiphase flow in porous media may be ultimately decided based on the ability to estimate model parameters with sufficient accuracy that make the models distinguishable. Since the most-common Darcy scale multiphase flow models all use a somewhat phenomenological relative permeability or resistance factor formulation, the key question is what the associated uncertainty really is when derived from flow experiments by inverse modeling. In this work, a recently developed workflow for systematic assessment of uncertainty was used to analyze the impact of the choice of relative permeability models and associated uncertainty. In an exemplary fashion, the Corey and LET relative permeability parameterizations were compared. The choice of Corey and LET models in the inverse modeling workflows showed differences in the derived relative permeability relations. The Corey parameterization is found to be more restrictive and imposed additional constraints on parameters. For example, varying the connate water saturation and residual oil saturation did not improve the match with experimental data. The pressure drop, saturation profiles and the capillary pressure–saturation relationship constrained the solution and imposing additional constraints on, e.g., residual oil saturation has very little impact on the result. In contrast, the LET function provided more degrees of freedom in order to accommodate the shape of the relative permeability curves. The findings also suggested that both Corey and LET models may not necessarily provide optimum parameterizations of the experimental data. The cross-correlations of fit parameters and non-Gaussian residuals indicated that we were still dealing with a phenomenological parameterization that is not yet the fully adequate description of the data. This may be the starting point for a comparison of different flow models beyond the uncertainty imposed by the choice of model parameterizations. Future work is aimed at assessing whether better choices in interpretation workflows and optimized experimental workflows can minimize these issues.

An Electrodiffusion Model Coupled with Fluid-Flow Effects for an On-Chip Electromembrane Extraction System

Abstract: This paper proposes the first computational modeling of a miniaturized version of an electromembrane extraction (EME) setup to a chip format, where the donor solution is delivered by a syringe pump to the sample reservoir. This system can be used for extraction of different analytes e.g., ionic drugs in wastewater. To design, analyze and optimize the entire process of extraction, a deep understanding of the mechanisms responsible for the analyte transport plays a key role. However, the interplay between the passive diffusion, fluid flow (convective diffusion), and electrokinetically driven SLM transfer may result in different mass transport patterns. A two-dimensional numerical model is developed to study the mass transport as well as the recovery in this on-chip EME. In order to simulate the mass transport of different analyte species, the electric field distribution, and the fluid flow, we made use of the Nernst–Planck, Poisson and Navier–Stokes equations, respectively. For all three mentioned fields (mass transport, electric field and fluid flow), appropriate boundary conditions are assigned to the setup borders to mathematically represent the real conditions of the device. The governing equations are solved by finite element method. It was revealed that at higher sample flow rates, a lower system recovery is predicted, e.g., from 80 to 60%, while higher voltages (smaller than a critical voltage) amplifies the recovery up to e.g., 75%. The presented model can predict the impact of different factors, e.g., sample flow rate, applied voltage, and extraction time on the system recovery, which are qualitatively in agreement with experimental results.

Lattice Boltzmann Modeling of Drying of Porous Media Considering Contact Angle Hysteresis

Abstract: Drying of porous media is governed by a combination of evaporation and movement of the liquid phase within the porous structure. Contact angle hysteresis induced by surface roughness is shown to influence multi-phase flows, such as contact line motion of droplet, phase distribution during drainage and coffee ring formed after droplet drying in constant contact radius mode. However, the influence of contact angle hysteresis on liquid drying in porous media is still an unanswered question. Lattice Boltzmann model (LBM) is an advanced numerical approach increasingly used to study phase change problems including drying. In this paper, based on a geometric formulation scheme to prescribe contact angle, we implement a contact angle hysteresis model within the framework of a two-phase pseudopotential LBM. The capability and accuracy of prescribing and automatically measuring contact angles over a large range are tested and validated by simulating droplets sitting on flat and curved surfaces. Afterward, the proposed contact angle hysteresis model is validated by modeling droplet drying on flat and curved surfaces. Then, drying of two connected capillary tubes is studied, considering the influence of different contact angle hysteresis ranges on drying dynamics. Finally, the model is applied to study drying of a dual-porosity porous medium, where phase distribution and drying rate are compared with and without contact angle hysteresis. The proposed model is shown to be capable of dealing with different contact angle hysteresis ranges accurately and of capturing the physical mechanisms during drying in different porous media including flat and curved geometries.

Physics-Driven Investigation of Wettability Effects on Two-Phase Flow in Natural Porous Media: Recent Advances, New Insights, and Future Perspectives

Abstract: Leveraging high-fidelity lattice Boltzmann simulations combined with analytical modeling, we establish a comprehensive micro-scale description of immiscible two-phase fluid displacement occurring during favorable and unfavorable displacement conditions in a heterogeneous porous medium under a wide range of wettability. The emergence of corner-flow events is found to promote a compact displacement pattern, leading to a maximum recovery efficiency of the defending fluid under the strong imbibition for both favorable and unfavorable displacement scenarios. Saturation of the invading fluid manifests the crossover in the displacement patterns from fingering to stable flow, as the wetting varies from drainage to strong imbibition. Quantifying the corner flow under both displacement conditions and strong imbibition reveals that corner-flow events are preferentially hosted by small-size pores and predominantly concentrated ahead of the primary fluid–fluid interface without perturbing the stability of the pore-body displacement. In addition to the numerical simulation, we developed an analytical model that can predict the saturation profile of invading fluid under given boundary conditions. Our study elucidates the fundamental control and interaction of wettability and heterogeneity on the dynamics of immiscible fluid displacement in porous media with implications in the description of subsurface flow and processes.

Chemical Reaction Effect on Convection in Bidispersive Porous Medium

Abstract: The object of this study is to investigate the question of convective movement of a reacting solute in a viscous incompressible occupying a plane layer in a saturated bidisperse porous material. Among the characteristics of a bidisperse porous medium are pores, called macropores, but porosity in the solid skeleton, known as microporosity, arises where there are cracks or fissures in that skeleton. In this paper, a comparison is made between the thresholds for linear instability and those obtained from a global nonlinear energy stability analysis.

Double-Diffusive Convection in Bidispersive Porous Medium with Chemical Reaction and Magnetic Field Effects

Abstract: This study features a model for double-diffusive convection in a bidisperse porous medium where a vertical magnetic field chemical reaction’s effects are present. Double-diffusive convection is the convective motion of fluid resulting from temperature and salt gradient effects. A bidisperse porous medium is one in which there exist pores known as macropores. Furthermore, the solid skeleton has cracks or fissures which give rise to a porosity within the skeleton, called microporosity. The emphasis here is on the situation of a single temperature field where the layer is heated from below and simultaneously salted from above to below.

Transport of Turbulence Across Permeable Interface in a Turbulent Channel Flow: Interface-Resolved Direct Numerical Simulation

Abstract: Turbulence transportation across permeable interfaces is investigated using direct numerical simulation, and the connection between the turbulent surface flow and the pore flow is explored. The porous media domain is constructed with an in-line arranged circular cylinder array. The effects of Reynolds number and porosity are also investigated by comparing cases with two Reynolds numbers ( $$Re\approx 3000,6000$$ ) and two porosities ( $$\varphi =0.5,0.8$$ ). It was found that the change of porosity leads to the variation of flow motions near the interface region, which further affect turbulence transportation below the interface. The turbulent kinetic energy (TKE) budget shows that turbulent diffusion and pressure transportation work as energy sink and source alternatively, which suggests a possible route for turbulence transferring into porous region. Further analysis on the spectral TKE budget reveals the role of modes of different wavelengths. A major finding is that mean convection not only affects the distribution of TKE in spatial space, but also in scale space. The permeability of the wall also have an major impact on the occurrence ratio between blow and suction events as well as their corresponding flow structures, which can be related to the change of the Karman constant of the mean velocity profile.

Permeability Estimation of Regular Porous Structures: A Benchmark for Comparison of Methods

Abstract: The intrinsic permeability is a crucial parameter to characterise and quantify fluid flow through porous media. However, this parameter is typically uncertain, even if the geometry of the pore structure is available. In this paper, we perform a comparative study of experimental, semi-analytical and numerical methods to calculate the permeability of a regular porous structure. In particular, we use the Kozeny–Carman relation, different homogenisation approaches (3D, 2D, very thin porous media and pseudo 2D/3D), pore-scale simulations (lattice Boltzmann method, Smoothed Particle Hydrodynamics and finite-element method) and pore-scale experiments (microfluidics). A conceptual design of a periodic porous structure with regularly positioned solid cylinders is set up as a benchmark problem and treated with all considered methods. The results are discussed with regard to the individual strengths and limitations of the used methods. The applicable homogenisation approaches as well as all considered pore-scale models prove their ability to predict the permeability of the benchmark problem. The underestimation obtained by the microfluidic experiments is analysed in detail using the lattice Boltzmann method, which makes it possible to quantify the influence of experimental setup restrictions.

Estimating Fluid Saturations from Capillary Pressure and Relative Permeability Simulations Using Digital Rock

Abstract: Direct numerical simulations of fluid flow on three-dimensional pore-scale microstructures derived from images promise more, cheaper, and faster, special core analysis for estimating volumetric and transport properties of rocks. However, the micron-scale X-ray computer tomography images generated by the present imaging technology are limited in resolution, and thus, a significant portion of rock pore volume can remain unresolved. The missing pore volume is not accessible to direct numerical simulations which limits applicability of digital rock physics to infer true residual saturation of reservoir fluids. To derive meaningful results from direct simulations, at minimum, raw fluid saturation inferred from simulations on micron-scale images must be corrected for the missing pore volume. We use concepts of capillary physics in rocks to quantify the impact of image resolution on image-derived fluid saturation and develop novel transforms that compensate for this effect on estimates of fluid saturation from multiphase simulations without the need for higher-resolution imaging. We find that image resolution constraints provide quality indicators when comparing digital rock-derived fluid saturations (e.g., connate water saturation) with those measured in a laboratory.

Optimal Wetting Angles in Lattice Boltzmann Simulations of Viscous Fingering

Abstract: We conduct pore-scale simulations of two-phase flow using the 2D Rothman–Keller colour gradient lattice Boltzmann method to study the effect of wettability on saturation at breakthrough (sweep) when the injected fluid first passes through the right boundary of the model. We performed a suite of 189 simulations in which a “red” fluid is injected at the left side of a 2D porous model that is initially saturated with a “blue” fluid spanning viscosity ratios $$M = u _\mathrm{r}/ u _\mathrm{b} \in [0.001,100]$$ and wetting angles $$\theta _\mathrm{w} \in [ 0^\circ ,180^\circ ]$$ . As expected, at low-viscosity ratios $$M= u _\mathrm{r}/ u _\mathrm{b} \ll 1$$ we observe viscous fingering in which narrow tendrils of the red fluid span the model, and for high-viscosity ratios $$M \gg 1$$ , we observe stable displacement. The viscous finger morphology is affected by the wetting angle with a tendency for more rounded fingers when the injected fluid is wetting. However, rather than the expected result of increased saturation with increasing wettability, we observe a complex saturation landscape at breakthrough as a function of viscosity ratio and wetting angle that contains hills and valleys with specific wetting angles at given viscosity ratios that maximize sweep. This unexpected result that sweep does not necessarily increase with wettability has major implications to enhanced oil recovery and suggests that the dynamics of multiphase flow in porous media has a complex relationship with the geometry of the medium and the hydrodynamical parameters.

GeoChemFoam: Direct Modelling of Multiphase Reactive Transport in Real Pore Geometries with Equilibrium Reactions

Abstract: GeoChemFoam is an open-source OpenFOAM-based toolbox that includes a range of additional packages that solve various flow processes from multiphase transport with interface transfer, to single-phase flow in multiscale porous media, to reactive transport with mineral dissolution. In this paper, we present a novel multiphase reactive transport solver for simulations on complex pore geometries, including microfluidic devices and micro-CT images, and its implementation in GeoChemFoam. The geochemical model includes bulk and surface equilibrium reactions. Multiphase flow is solved using the Volume-Of-Fluid method, and the transport of species is solved using the continuous species transfer method. The reactive transport equations are solved using a sequential operator splitting method, with the transport step solved using GeoChemFoam, and the reaction step solved using Phreeqc, the US geological survey’s geochemical software. The model and its implementation are validated by comparison with analytical solutions in 1D and 2D geometries. We then simulate multiphase reactive transport in two test pore geometries: a 3D pore cavity and a 3D micro-CT image of Bentheimer sandstone. In each case, we show the pore-scale simulation results can be used to develop upscaled models that are significantly more accurate than standard macro-scale equilibrium models.

A Critical Review of Current Imaging Techniques to Investigate Water Transfers in Wood and Biosourced Materials

Abstract: This review paper proposes a critical overview of experimental techniques and innovative experimental methods to observe and deeply understand the migration of water inside wood and biosourced materials. The state of the art of the knowledge of water transfer phenomena are first presented, namely liquid and bound water migration, together with shrinkage/swelling. Then, the papers presenting the 3D imaging techniques at high resolution offered by recent technologies, such as magnetic resonance imaging, X-ray tomography, and in situ tomography-mechanical tests. They enable visualization and analysis of water transfer mechanisms in eco-responsible materials such as natural fiber-concretes, wood, and biobased insulating materials. The 2D and 3D images processed with specific software packages allow for an overview of the distribution and orientation of the material components, as well as the moisture-content field which affects most properties of the materials such as mechanical properties (compression and tensile strength), hygro-thermal performance, as well as durability. Finally, the Digital Volume Correlation method allows for the observation and evaluation of deformation, cracks and failure mechanisms resulting from either a mechanical or hydric loading. The paper intends to help the reader to acquire a deep understanding of water imbibition and drying mechanisms in such materials.

Experimental Investigation of CS2 Extraction to Enhance the Permeability of Coal

Abstract: To examine the permeability enhancement effect of the carbon disulfide (CS2) extraction on block coal samples, in this study, different cylindrical samples of anthracite coal were selected to conduct CS2 extraction experiments. Comprehensive measurement techniques, including Fourier transform infrared spectroscopy, X-ray diffraction, low-temperature nitrogen adsorption, industrial computed tomography, and permeability measurements, were employed to analyze the variations of in the chemical structure, microcrystalline structure, pore–fracture structure, and coal permeability before and after the CS2 extraction treatment. The results showed that CS2 extraction can improve the connectivity of multi-scale migration channels, with which the coal permeability can be enhanced. Also, it was found that the permeability enhancement performance by the CS2 extraction is related to the coal anisotropy, as the coal permeability in the vertical bedding direction is smaller than that in the parallel bedding direction before and after CS2 extraction. Also, the CS2 extraction had a time effect on enhancing the coal permeability, and the permeability enhancement was more significant after a longer period of CS2 treatment. It can be predicted that the permeability can be enhanced up to more than 1 mD when the extraction time exceeds 6 h. Also, we concluded that CS2 fracturing is worth exploring by the on-going studies to enhance the permeability and CBM recovery in low-permeability reservoirs.

Pore-Scale Transport and Two-Phase Fluid Structures in Fibrous Porous Layers: Application to Fuel Cells and Beyond.

Abstract: We present pore-scale simulations of two-phase flows in a reconstructed fibrous porous layer. The three-dimensional microstructure of the material, a fuel cell gas diffusion layer, is acquired via X-ray computed tomography and used as input for lattice Boltzmann simulations. We perform a quantitative analysis of the multiphase pore-scale dynamics, and we identify the dominant fluid structures governing mass transport. The results show the existence of three different regimes of transport: a fast inertial dynamics at short times, characterised by a compact uniform front, a viscous-capillary regime at intermediate times, where liquid is transported along a gradually increasing number of preferential flow paths of the size of one-two pores, and a third regime at longer times, where liquid, after having reached the outlet, is exclusively flowing along such flow paths and the two-phase fluid structures are stabilised. We observe that the fibrous layer presents significant variations in its microscopic morphology, which have an important effect on the pore invasion dynamics, and counteract the stabilising viscous force. Liquid transport is indeed affected by the presence of microstructure-induced capillary pressures acting adversely to the flow, leading to capillary fingering transport mechanism and unstable front displacement, even in the absence of hydrophobic treatments of the porous material. We propose a macroscopic model based on an effective contact angle that mimics the effects of the such a dynamic capillary pressure. Finally, we underline the significance of the results for the optimal design of face masks in an effort to mitigate the current COVID-19 pandemic.

The Effect of Wettability on Waterflood Oil Recovery in Carbonate Rock Samples: A Systematic Multi-scale Experimental Investigation

Abstract: The effect of wettability on waterflooding oil recovery and the associated pore-scale displacement mechanisms are systematically investigated during flow processes in limestone core samples with a broad spectrum of wettability. Using a miniature core-flooding setup integrated with micro-computed tomography (CT) imaging apparatus, we, for the first time, characterize in situ equilibrium wettability states and demonstrate capillary interactions of the flowing phases in strongly water-wet (SWW), intermediate-wet (IW), weakly oil-wet (WOW), and strongly oil-wet (SOW) systems. The microscale observations were then employed to explain the recovery results obtained from replicate, macroscale experiments. The waterflooding parameters, such as experimental temperature, brine composition, defending and invading phase properties, and the initial water saturation, were maintained nearly identical in all of the waterflooding tests, thereby ensuring that the wettability state was the only factor that controlled the variations in waterflood oil recoveries. We provide pore-scale evidences of various pore-scale displacement mechanisms and the consequent fluid configurations in systems with different wettability states. These findings are then linked to the recovery trends of macroscale experiments. The production from IW, WOW, and SOW cases portrayed a prolonged oil recovery owing to the gradual invasion of brine into small and intermediate-sized oil-wet pores. The IW case showed the highest oil recovery among all cases. Moreover, when the injection flow rate was increased, the oil recovery was gradually increased for the IW, WOW, and SOW systems, whereas no significant additional production was observed in the case of SWW.

Hygrothermally Induced Vibration Analysis of Bidirectional Functionally Graded Porous Beams

Abstract: In this article, the nonlinear hygrothermally induced vibrational behavior of bidirectional functionally graded porous beams is studied through a numerical approach. Two-dimensional material and temperature distributions, even and uneven porosity distributions, temperature-dependent nature of material properties, and hygroscopic effects are all taken into account in studying beam’s lateral deflection. All material properties are assumed to vary along both thickness and axial directions of beam following a modified power-law distribution in terms of volume fractions of the material constituents, which are considered temperature dependent using Touloukian experiments. Beam's upper surface is subjected to a sudden temperature rise, while its lower surface is kept at reference temperature or is thermally adiabatic; meanwhile, left and right boundaries are thermally insulated. Two-dimensional transient heat conduction equation is solved using generalized differential quadrature (GDQ) method for discretizing spatial derivatives, while time derivatives are approximated using Newmark-beta integration method. Nonlinear sinusoidal moisture concentration is assumed through the thickness direction. Governing equations of motion are derived based on Timoshenko beam theory (TBT) and with the assumption of Von-Karman geometrical nonlinearity, which is solved afterward using an iterative scheme in conjunction with GDQ and Newmark's method. Finally, the effects of porosity volume fractions, porosity cases, thermal boundary conditions, moisture concentration, FG indexes, slenderness ratio, and temperature rise on maximum non-dimensional lateral deflection are investigated considering various boundary conditions.

Lattice Boltzmann Modeling of the Apparent Viscosity of Thinning–Elastic Fluids in Porous Media

Abstract: Many non-Newtonian fluids, including polymers, exhibit both shear-thinning and viscoelastic rheological properties. A lattice Boltzmann (LB) model is developed for simulation of the flow of thinning–elastic fluids through porous media. This model applies the Oldroyd-B constitutive equation and the Carreau model, respectively, to account for the viscoelastic and shear-thinning behaviors of the thinning–elastic fluid in porous media. Both rheological features are captured well by this model and are verified against analytical solutions. The thinning-then-thickening viscosity curve of the thinning–elastic fluid observed in experiments is reproduced by the present pore-scale simulations. In addition to the traditional extensional theory, we propose other important mechanisms for the increase in apparent viscosity of viscoelastic fluids at higher shear rates. The mechanisms proposed include the reduction in conductivity due to stagnant fluid, the compressed effective flow region, and larger energy dissipations caused by the viscoelastic instability. We find that the viscoelastic thickening effect is more prominent in porous geometries with a large pore–throat ratio.