Transport In Porous Media Research Articles

Flow in temporally and spatially varying porous media: a model for transport of interstitial fluid in the brain.

Flow in a porous medium can be driven by the deformations of the boundaries of the porous domain. Such boundary deformations locally change the volume fraction accessible by the fluid, creating non-uniform porosity and permeability throughout the medium. In this work, we construct a deformation-driven porous medium transport model with spatially and temporally varying porosity and permeability that are dependent on the boundary deformations imposed on the medium. We use this model to study the transport of interstitial fluid along the basement membranes in the arterial walls of the brain. The basement membrane is modeled as a deforming annular porous channel with the compressible pore space filled with an incompressible, Newtonian fluid. The role of a forward propagating peristaltic heart pulse wave and a reverse smooth muscle contraction wave on the flow within the basement membranes is investigated. Our results identify combinations of wave amplitudes that can induce either forward or reverse transport along these transport pathways in the brain. The magnitude and direction of fluid transport predicted by our model can help in understanding the clearance of fluids and solutes along the Intramural Periarterial Drainage route and the pathology of cerebral amyloid angiopathy.

Geo-guided deep learning for spatial downscaling of solute transport in heterogeneous porous media

Resolving solute transport in heterogeneous porous media is a complex task, because of the sparse experimental data and the high computational cost of numerical simulations. This work proposes a unique two-stage deep learning architecture comprising a dual-branch autoencoder and a geo-guided super-resolution generative adversarial network (Gg-SRGAN) to address this dual challenge. The dual-branch autoencoder addresses the issue of sparsity by constructing a continuous, but coarse representation of concentration and pressure profiles from a sparse, discontinuous profile with up to 85% missing data points. The Gg-SRGAN is then employed to generate a finer representation of field variables from the outputs generated by the dual-branch autoencoder (i.e., downscaling). We train and test our framework using six solute transport cases with varying levels of heterogeneity and compare the results with standalone methods, namely the vanilla autoencoder and vanilla SRGAN, in addition to ground truth profiles generated by the finite element method (FEM). The comparisons are performed based on several statistical metrics, such as absolute point error (APE), mean squared error (MSE), peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and learned perceptual image patch similarity (LPIPS). The first four cases are used for training, evaluation, and testing. The last two cases are utilized for blind testing to determine the generalizability of the framework. Our results show that the dual-branch autoencoder outperforms the vanilla autoencoder, and the Gg-SRGAN outperforms the SRGAN during both the training and evaluation phases. Moreover, the proposed framework can successfully construct the fine representation of concentration profiles, compared to FEM, using the coarse representation of the pressure, concentration, and domain permeability fields. When tested using the two blind test cases, the proposed dual-branch autoencoder and Gg-SRGAN exhibit superior performance compared to their counterparts in terms of all evaluation metrics.

Shannon entropy of transport self-organization due to dissolution–precipitation reaction at varying Peclet numbers in initially homogeneous porous media

Abstract. Dissolution and precipitation processes in reactive transport in porous media are ubiquitous in a multitude of contexts within the field of Earth sciences. In particular, the dynamic interaction between the reactive dissolution and precipitation processes and the solute transport is of interest as it is capable of giving rise to the emergence of preferential flow paths in the porous host matrix. It has been shown that the emergence of preferential flow paths can be considered to be a manifestation of transport self-organization in porous media as these create spatial gradients that distance the system from the state of perfect mixing and allow for a faster and more efficient fluid transport through the host matrix. To investigate the dynamic feedback between the transport and the reactive processes in the field and its influence on the emergence of transport self-organization, we consider a two-dimensional Darcy-scale formulation of a reactive-transport setup, where the precipitation and dissolution of the host matrix are driven by the injection of an acid compound, establishing local equilibrium with the resident fluid and an initially homogeneous porous matrix, composed of a calcite mineral. The coupled reactive process is simulated in a series of computational analyses employing the Lagrangian particle-tracking (LPT) approach, capable of capturing the subtleties of the multiple-scale heterogeneity phenomena. We employ the Shannon entropy to quantify the emergence of self-organization in the field, which we define as a relative reduction in entropy compared to its maximum value. Scalability of the parameters, which characterize the evolution of the reactive process, with the Peclet number in an initially homogeneous field is derived using a simple one-dimensional ADRE model with a linear adsorption reaction term and is then confirmed through numerical simulations, with the global reaction rate, the mean value, and the variance of the hydraulic-conductivity distribution in the field all exhibiting dependency on the reciprocal of the Peclet number. Our findings show that transport self-organization in an initially homogeneous field increases with time, along with the emergence of the field heterogeneity due to the interaction between the transport and reactive processes. By studying the influence of the Peclet number on the reactive process, we arrive at a conclusion that self-organization is more pronounced in diffusion-dominated flows, characterized by small Peclet values. The self-organization of the breakthrough curve exhibits the opposite tendencies, which are observed from the perspective of a thermodynamic analogy. The hydraulic power, required to maintain the driving head pressure difference between the inlet and outlet of the field, was shown to increase with the increasing variance, as well as with the increasing mean value of the hydraulic-conductivity distribution in the field, using a simple analytic model. This was confirmed by numerical experiments. This increase in power, supplied to the flow in the field, results in an increase in the level of transport self-organization. Employing a thermodynamic framework to investigate the dynamic reaction–transport interaction in porous media may prove to be beneficial whenever the need exists to establish relations between the intensification of the preferential flow path phenomenon, represented by a decline in the Shannon entropy of the transport, with the amount of reaction that occurred in the porous medium and the change in its heterogeneity.

BioReactPy: An open-source software for simulation of microbial-mediated reactive processes in porous media

This paper provides a new open-source software, named BioReactPy, for simulation of microbial-mediated coupled processes of flow and reactive transport in porous media. The software is based on the micro-continuum approach, and geochemistry is handled in a fully coupled manner with biomass-nutrient growth treated with Monod equation in a single integrated framework, without dependencies on third party packages. The distinguishing features of the software, its design principles, and formulation of multiphysics problems and discretizations are discussed. Validation of the Python implementation using several established benchmarks for flow, reactive transport, and biomass growth is presented. The flexibility of the framework is then illustrated by simulations of highly non-linearly coupled flow and microbial reactive transport at conditions relevant to carbon mineralization for CO2 storage. All results can be reproduced by openly available simulation scripts.

Probabilistic assessment of scalar transport under hydrodynamically unstable flows in heterogeneous porous media

Quantitative predictions of scalar transport in natural porous media is a nontrivial task given the presence of multi-scale spatial heterogeneity in the permeability field. Due to data scarcity, the structural map of the permeability field is subject to uncertainty and therefore, model predictions are uncertain. For such reasons, probabilistic models of flow and transport in natural porous media are required in risk assessment and to provide reliable decision making under uncertainty. Further complexities arise when the viscosity of the injected solute differs from that of the ambient fluid. Under the presence of viscosity contrast, hydrodynamic instabilities give rise to viscous fingering, which induces additional disorder in both velocity and solute concentration fields. This work examines the combined role of viscous fingering and permeability heterogeneity in the probabilistic description of transport predictions. In particular, we focus on metrics that are important for risk analysis, such as the solute plume’s early arrival times and the maximum concentration observed at a given location. We propose to use the Projection Pursuit Adaptation (PPA) method in the Polynomial Chaos Expansion (PCE) framework to quantify uncertainty in transport model predictions. The PPA method is a data-driven approach that optimally represents a given quantity of interest in a low-dimensional manifold. Unlike other dimension reduction techniques in uncertainty quantification, the PPA method utilizes non-linear information of the quantity of interest to identify the low-dimensional manifold, thereby increasing the likelihood of finding a more accurate lower-dimensional space. Moreover, the PPA model converges to the physical solution in a mean squared sense with respect to the polynomial order, enabling the construction of a converged model even with limited available data. Then, the PPA results are compared to Monte Carlo simulations using the same amount of data. This comparison illustrates that while Monte Carlo simulations are able to capture low-order statistics, they struggle to represent more detailed probability density functions. Our results show how the combined effect of permeability heterogeneity and viscosity contrast can enhance the mobility of the solute plume.

Pore-scale modeling of effects of multiphase reactive transport on solid dissolution in porous media with structural heterogeneity

Fundamental understanding of the multiphase reactive transport with solid dissolution is crucial for a wide range of scientific and engineering problems. In this study, a pore-scale model is improved to study coupled processes of multiphase flow, mass transport, chemical reaction and solid dissolution in porous media with increasing structural heterogeneity. The results show that with the existence of multiphase flow, under the reactive transport conditions studied (Pe = 5, Da = 10; and Pe = 5, Da = 1), more compact dissolution pattern is generated due to the negative feedback between reactant transport and solid dissolution, while the feedback is positive in single-phase condition leading to wormhole dissolution. Besides, while it is found that the structural heterogeneity amplifies the wormhole dissolution in single-phase reactive transport processes or promotes the formation of fingering for multiphase flow, such heterogeneity effect is homogenized in the multiphase case. Finally, based on the pore-scale results, a new correlation between porosity, saturation and interfacial length is proposed which can be upscaled into the continuum-scale models.

Effect of pH on Spontaneous Imbibition in Calcareous Rocks

AbstractReactive transport in porous media exhibits multifaceted interactions that are dependent on the matrix and fluid properties, and which ultimately alter these properties. A set of calcareous rock samples with unique mineralogy and varying petrophysical properties are selected for this study. A capillary rise experiment is performed in each sample, first with deionized water and then with a dilute, pH 2, HCl solution. Pre‐ and post‐acid petrophysical properties such as porosity, permeability, pore size distribution, and contact angle are measured for each sample along with the capillary rise profile. The latter is tracked by applying image analysis on video recording. The rock mineralogy significantly affects the acidic fluid intrusion into the rock samples. Calcite dissolution is the main reaction that results in the opening of the pore space. This is more prominent in all the carbonate samples where a higher proportion of calcite minerals is present. A higher capillary rise is consistently observed compared to the neutral fluid along with an increase in porosity and the mean pore size. The contact angle also undergoes changes making the carbonate matrix from oil‐wet to neutral‐wet. Coupling capillary interactions with fluid reactivity is often neglected in fluid transport phenomena. This study offers new insights into the relative importance of reactivity at the timescale of spontaneous imbibition. This is important in understanding dissolution and precipitation processes during capillary flow.

Transport and clogging of microplastic particles in porous media: Microscale experiments and statistical analysis

In recent years, the migration and distribution of microplastics (MPs) in the natural environment have garnered worldwide attention. However, little is known about the transport and intercept of MPs in infiltration systems. In infiltration systems, MPs could affect the flow through porous media, leading to complex flow and removal dynamics in various engineering applications. This will threaten the ecosystem and human health due to the characteristics of MPs. In this study, a two-dimensional porous media flow cell was developed to visualize the transport and intercept of microplastic particles in porous media. Statistical data on pore characteristics were gathered by tracking changes in pore clogging state under different particle concentrations and flow rates. It was found that the size ratio dt/dp was the critical factor influencing pore throat clogging probability. Pore throats were categorized into persistent-clogging, occasional-clogging, and non-clogging based on their clogging probability at different dt/dp. Additionally, the parameter dt/dpU that distinguished the occasional-clogging zone from the non-clogging zone decreased with increasing particle concentration. The clogging probability in the occasional-clogging zone was influenced by dt/dp, particle flux, and flow velocity in the pore throat. Furthermore, two distinct clogging mechanisms, independent and dependent clogging, were observed, determined by the states of neighboring pores. These findings have implications for assessing the interception performance of MPs in filtration systems. The results enhance our understanding of MPs transport and interception dynamics in porous media and contribute to the optimization of filtration system design and operation.

4D Imaging of Two‐Phase Flow in Porous Media Using Laboratory‐Based Micro‐Computed Tomography

AbstractDynamic three‐dimensional computed tomography (CT) imaging of liquid transport in porous media has primarily been conducted at high brilliance synchrotrons thus allowing fast, sometimes sub‐second, temporal resolution to be obtained. University laboratory CT instruments lack the photon flux available at synchrotrons, limiting the obtainable spatiotemporal resolution. Here, we discuss our experiences with instrumentation and software methods to conduct time‐resolved micro‐computed tomography (4D‐CT) experiments of flow in porous media, based on a conventional CT instrument operated with a highly undersampled number of projections. An experimental stage outfitted with syringe pumps placed on a slip ring allowed two‐phase flow experiments to be carried out with continuous unidirectional rotation and without obstruction of the liquid supply lines. An iterative reconstruction algorithm based on a priori information was used to provide high image quality and ∼30 s time resolution despite the few and low‐exposed projections compared to standard protocols. The experimental technique was demonstrated with imbibition and drainage in glass bead‐pack and Bentheimer sandstone samples with sub‐minute temporal resolution, allowing the liquid configurations just before and after fast dynamic phenomena such as cooperative pore‐filling events and Haines jumps to be captured. Power law scaling exponents for burst volumes associated with imbibition and drainage were estimated and compared with the literature. That 4D‐CT experiments can be carried out using conventional CT instruments to challenge contemporary permeability models is of high importance for many geo‐, bio‐ and environmental physics challenges.

Effect of surfactant adsorption on the efficiency of drainage displacement at different viscosity ratios: A lattice Boltzmann study

Surfactant flooding is an effective method for enhanced oil recovery, accompanied by the adsorption of surfactant molecules during their transport in porous media. This paper studies the effects of surfactant adsorption on immiscible two-phase flows in porous media and focuses on two primary objectives. The first is to identify the influence of the water/oil viscosity ratio on the maximum adsorbed amount of surfactant. The second scope involves establishing a relationship between the viscosity ratio and the effect of surfactant adsorption on the displacement efficiency during drainage displacement. The novelty lies in the identification of new patterns characterizing the adsorption effect on the displacement efficiency depending on the viscosity ratio. The main results are based on statistical data collected from numerical simulations performed on various synthetic 2D micromodels. The lattice Boltzmann method was used as a mathematical model. It has been established that the adsorbed amount is influenced by the viscosity ratio as follows: the higher the oil viscosity, the less the adsorbed amount. However, the effect is not strong. An increase in oil viscosity leads to a decrease in the adsorption effect on displacement efficiency. This finding is determined by two factors: the maximum adsorbed amount and the adsorbed amount at the moment of surfactant breakthrough. It has been found that if surfactant adsorption is neglected, the viscosity ratio does not affect the increment in oil recovery compared to the injection of pure water. However, if adsorption is taken into account, an increase in oil viscosity enhances the effect of surfactant flooding on displacement efficiency. The dependence of the viscosity ratio on the adsorption effect on oil recovery obeys linear law. This trend was confirmed in a digital 3D model of natural sandstone obtained using X-ray computed tomography.

Visualization of phenanthrene effect on biochar colloids transport in porous media

Biochar colloids (BCs) can be used as adsorbent materials for remediation of phenanthrene due to their high specific surface area and other characteristics. Understanding the effects of phenanthrene on the transport of BCs contributes to facilitate the removal of phenanthrene in soil and water habitats. In this work, the influence of phenanthrene on the transport of BCs under different environmental factors (pH, ionic strength (IS), media size) in a one-dimensional sand column was firstly explored together with a real-time visualization system to explore the transport mechanism of BCs in two-dimensional sand tank. The results show that phenanthrene adsorbed on the surface of BCs, shielded its surface charge and reduced the mobility of BCs in porous media. Acidic conditions promoted the agglomeration of BCs and adsorption of phenanthrene, resulting in a 51.03 % decrease in the maximum breakthrough rate of BCs compared to alkaline conditions. The same was true for the high IS condition, where the maximum breakthrough rate of BCs was only 0.95 % at IS = 50. Additionally, there was a substantial and positive correlation between media particle size and BCs mobility. As the quartz sand particle size increased, the maximum breakthrough rates of BCs were 2.67 %, 33.28 %, and 52.27 % in the 1-D experiment, and 0, 13.88 %, and 13.10 % in the 2-D experiment, respectively. The contact area of BCs with the medium expands under the fine particle size condition, leading to a significant decrease in the mobility of BCs at low potentials influenced by phenanthrene. This finding is significant for biochar application in phenanthrene contaminated soil and groundwater remediation.

Research on the Flow Characteristics and Reaction Mechanisms of Lateral Flow Immunoassay under Non-Uniform Flow.

Lateral flow immunoassay (LFIA) is extensively utilized for point-of-care testing due to its ease of operation, cost-effectiveness, and swift results. This study investigates the flow dynamics and reaction mechanisms in LFIA by developing a three-dimensional model using the Richards equation and porous media transport, and employing numerical simulations through the finite element method. The study delves into the transport and diffusion behaviors of each reaction component in both sandwich LFIA and competitive LFIA under non-uniform flow conditions. Additionally, the impact of various parameters (such as reporter particle concentration, initial capture probe concentrations for the T-line and C-line, and reaction rate constants) on LFIA performance is analyzed. The findings reveal that, in sandwich LFIA, optimizing parameters like increasing reporter particle concentration and initial capture probe concentration for the T-line, as well as adjusting reaction rate constants, can effectively enhance detection sensitivity and broaden the working range. Conversely, in competitive LFIA, the effects are inverse. This model offers valuable insights for the design and enhancement of LFIA assays.

Nonionic surfactant Tween 80-facilitated bacterial transport in porous media: A nonmonotonic concentration-dependent performance, mechanism, and machine learning prediction

The surfactant-enhanced bioremediation (SEBR) of organic-contaminated soil is a promising soil remediation technology, in which surfactants not only mobilize pollutants, but also alter the mobility of bacteria. However, the bacterial response and underlying mechanisms remain unclear. In this study, the effects and mechanisms of action of a selected nonionic surfactant (Tween 80) on Pseudomonas aeruginosa transport in soil and quartz sand were investigated. The results showed that bacterial migration in both quartz sand and soil was significantly enhanced with increasing Tween 80 concentration, and the greatest migration occurred at a critical micelle concentration (CMC) of 4 for quartz sand and 30 for soil, with increases of 185.2% and 27.3%, respectively. The experimental results and theoretical analysis indicated that Tween 80-facilitated bacterial migration could be mainly attributed to competition for soil/sand surface sorption sites between Tween 80 and bacteria. The prior sorption of Tween 80 onto sand/soil could diminish the available sorption sites for P. aeruginosa, resulting in significant decreases in deposition parameters (70.8% and 33.3% decrease in KD in sand and soil systems, respectively), thereby increasing bacterial transport. In the bacterial post-sorption scenario, the subsequent injection of Tween 80 washed out 69.8% of the bacteria retained in the quartz sand owing to the competition of Tween 80 with pre-sorbed bacteria, as compared with almost no bacteria being eluted by NaCl solution. Several machine learning models have been employed to predict Tween 80-faciliated bacterial transport. The results showed that back-propagation neural network (BPNN)-based machine learning could predict the transport of P. aeruginosa through quartz sand with Tween 80 in-sample (2 CMC) and out-of-sample (10 CMC) with errors of 0.79% and 3.77%, respectively. This study sheds light on the full understanding of SEBR from the viewpoint of degrader facilitation.

Influence of Concentration, Surface Charge, and Natural Water Components on the Transport and Adsorption of Polystyrene Nanoplastics in Sand Columns.

Information about the influence of surface charges on nanoplastics (NPLs) transport in porous media, the influence of NPL concentrations on porous media retention capacities, and changes in porous media adsorption capacities in the presence of natural water components are still scarce. In this study, laboratory column experiments are conducted to investigate the transport behavior of positively charged amidine polystyrene (PS) latex NPLs and negatively charged sulfate PS latex NPLs in quartz sand columns saturated with ultrapure water and Geneva Lake water, respectively. Results obtained for ultrapure water show that amidine PS latex NPLs have more affinity for negatively charged sand surfaces than sulfate PS latex NPLs because of the presence of attractive electrical forces. As for the Geneva Lake water, under natural conditions, both NPL types and sand are negatively charged. Therefore, the presence of repulsion forces reduces NPL's affinity for sand surfaces. The calculated adsorption capacities of sand grains for the removal of both types of NPLs from both types of water are oscillating around 0.008 and 0.004 mg g-1 for NPL concentrations of 100 and 500 mg L-1, respectively. SEM micrography shows individual NPLs or aggregates attached to the sand and confirms the limited role of the adsorption process in NPL retention. The important NPL retention, especially in the case of negatively charged NPLs, in Geneva Lake water-saturated columns is related to heteroaggregate formation and their further straining inside narrow pores. The presence of DOM and metal cations is then crucial to trigger the aggregation process and NPL retention.

Multiscale Porosity Microfluidics to Study Bacterial Transport in Heterogeneous Chemical Landscapes.

Microfluidic models are proving to be powerful systems to study fundamental processes in porous media, due to their ability to replicate topologically complex environments while allowing detailed, quantitative observations at the pore scale. Yet, while porous media such as living tissues, geological substrates, or industrial systems typically display a porosity that spans multiple scales, most microfluidic models to date are limited to a single porosity or a small range of pore sizes. Here, a novel microfluidic system with multiscale porosity is presented. By embedding polyacrylamide (PAAm) hydrogel structures through in-situ photopolymerization in a landscape of microfabricated polydimethylsiloxane (PDMS) pillars with varying spacing, micromodels with porosity spanning several orders of magnitude, from nanometers to millimeters are created. Experiments conducted at different porosity patterns demonstrate the potential of this approach to characterize fundamental and ubiquitous biological and geochemical transport processes in porous media. Accounting for multiscale porosity allows studies of the resulting heterogeneous fluid flow and concentration fields of transported chemicals, as well as the biological behaviors associated with this heterogeneity, such as bacterial chemotaxis. This approach brings laboratory studies of transport in porous media a step closer to their natural counterparts in the environment, industry, and medicine.

Mechanisms of Pore-Clogging Using a High-Resolution CFD-DEM Colloid Transport Model

Colloidal transport and clogging in porous media is a phenomenon of critical importance in many branches of applied sciences and engineering. It involves multiple types of interactions that span from the sub-colloid scale (electrochemical interactions) up to the pore-scale (bridging), thus challenging the development of representative modelling. So far published simulation results of colloidal or particulate transport are based on either reduced set of forces or spatial dimensions. Here we present an approach enabling to overcome both computational and physical limitations posed by a problem of 3D colloidal transport in porous media. An adaptive octree mesh is introduced to a coupled CFD and DEM method while enabling tracking of individual colloids. Flow fields are calculated at a coarser scale throughout the domain, and at fine-scale around colloids. The approach accounts for all major interactions in such a system: elastic, electrostatic, and hydrodynamic forces acting between colloids, as well as colloids and the collector surface. The method is demonstrated for a single throat model made of four spherical segments, and the impact of clogging is reported in terms of the evolution of the critical path diameter for percolation and permeability. We identified four stages of clogging development depending on position and time of individual colloid entrapment, which in turn correlates to a cluster evolution and local transport.

From tomographic imaging to numerical simulations: an open-source workflow for true morphology mesoscale FE meshes

Full-field techniques such as tomography are becoming progressively more central in the study of complex phenomena, in particular where spatiotemporal evolution is crucial, as in moisture transport or crack initiation in porous media. These techniques provide a unique insight in the local process whose quantification allows the improvement of our understanding and of the models describing them. Nevertheless, the model validation can be pushed further by attempting to explicitly represent the heterogeneities and simulate their role in the processes. Once validated, these models can be used to perform “virtual experiments”, and overcome the limitations of the experiments (e.g., sample size and number, fine control of the boundary and initial conditions). This study proposes a connection between tomography images and mesoscale models through a workflow that mainly employs open-source tools. This workflow is illustrated through the digitization of a Portland cement concrete sample, stemming from neutron tomographies and resulting in a numerical finite element mesh. The proposed workflow is flexible, allowing for the conversion of images from various sources, such as x-ray or neutron tomographies, to different numerical representations of the domain, such as finite element meshes or even a discrete domain required by discrete element methods, while preserving real morphologies with an accuracy proportionate to the specific need of the problem. Beside its generalizability, our method also offers automated labelling of the different domains and boundaries in both the volumetric and surface meshes, which is often necessary for assigning material properties and boundary conditions. Finally, the series of image, geometry and mesh processing steps described in this work are made available on a GitHub repository.

Probabilistic Forecast of Multiphase Transport Under Viscous and Buoyancy Forces in Heterogeneous Porous Media

AbstractWe develop a probabilistic approach to map parametric uncertainty to output state uncertainty in first‐order hyperbolic conservation laws. We analyze this problem for nonlinear immiscible two‐phase transport in heterogeneous porous media in the presence of a stochastic velocity field. The uncertainty in the velocity field can arise from incomplete descriptions of either porosity field, injection flux, or both. This uncertainty leads to spatiotemporal uncertainty in the saturation field. Given information about spatial/temporal statistics of spatially correlated heterogeneity, we leverage the method of distributions to derive deterministic equations that govern the evolution of pointwise cumulative distribution functions (CDFs) of saturation for a vertical reservoir, while handling the manipulation of multiple shocks arising due to buoyancy forces. Unlike the Buckley‐Leverett equation, the equation describing the fine‐grained CDF is linear in space and time. Ensemble averaging of the fine‐grained CDF results in the CDF of saturation. Thus, we give routes to circumventing the computational cost of Monte Carlo simulations (MCS), while obtaining a pointwise description of the saturation field. We conduct a set of numerical experiments for one‐dimensional transport, and compare the obtained saturation CDFs, against those obtained using MCS as our reference solution, and the statistical moment equation method. This comparison demonstrates that the CDF equations remain accurate over a wide range of statistical properties, that is, standard deviation and correlation length of the underlying random fields, whereas the corresponding low‐order statistical moment equations significantly deviate from the MCS results, except for very small values of standard deviation and correlation length.

High‐order models for hydro‐mechanical coupling problems in multiscale porous media

AbstractAn accurate prediction of nonlinear hydro‐mechanical (HM) coupling in subsurface structures with pronounced heterogeneity at multiple spatial scales is still an open topic and crucial for numerous engineering applications, for example, hydraulic fracturing and enhanced geothermal systems. In this study, novel high‐order multi‐scale asymptotic solutions are developed to accurately capture the locally oscillating characteristics of gas flow and solid displacement fields at multiple scales. First, the formal macro‐meso two‐scale asymptotic expansion is performed to establish the homogenized solutions and macro‐meso high‐order models which can predict the HM coupling problems at the macroscale and mesoscale. By directly expanding the cell functions defined at the mesoscale to the microscopic levels, the high‐order two‐scale expansion for the mesoscopic cell functions is built, and the upscaled relations for the flow parameters and constitutive coefficients from the microscale to the mesoscale and macroscale are developed correspondingly. The multi‐scale low/high‐order models are established by combining the high‐order expansion of all cell functions at the mesoscale and the developed macro‐meso two‐scale models. The main contributions are that the present approaches follow the reverse thought processes of reiteration homogenization methods, and offer a very innovative and efficient way to establish high‐accuracy high‐order models for the nonlinear HM coupling problems in the heterogeneous porous medium with any number of spatial scales. The effectiveness and accuracy of the present solution are validated by several representative cases with different constitutive coefficient contrasts. The results demonstrate that the high‐order solutions provide an accurate prediction for gas transport and solid deformation of heterogeneous porous media with multi‐scale configurations.

SiO2 and microparticle transport in a saturated porous medium: effects of particle size and flow rate

SiO2 and polystyrene (PS) are carriers of microorganisms and metals in porous media, which can produce changes in groundwater quality and cause issues related to clogging of the porous medium. Although SiO2 and PS particle transport in porous media has been previously studied, what influences transport at various particle sizes and flow rates remains unclear. Here, we looked at how pH and ionic strength affected the surface zeta potentials as well as how particle size and flow rate affected the transport of suspended SiO2/PS particles in a porous media. The results indicate that increasing pH and decreasing ionic strength increased the negative surface charges on both the SiO2 and PS particles, thereby yielding greater electrostatic repulsion between particles. At the same flow rate, the retention rate of 10 μm PS particles in the porous medium was 46.1% better than that of 2 μm particles, whereas the retention rate of 10 μm SiO2 particles was 7.88% better than that of 2 μm particles. For the same particle size, increasing the flow rate decreased SiO2 and PS retention in the porous medium. Thus, particle size and flow rate substantially impact the transport of SiO2 and PS-suspended particles in a porous media.