Transport Processes In Porous Media Research Articles

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.

P3D-BRNS v1.0.0: a three-dimensional, multiphase, multicomponent, pore-scale reactive transport modelling package for simulating biogeochemical processes in subsurface environments

Abstract. The porous microenvironment of soil offers various environmental functions which are governed by physical and reactive processes. Understanding reactive transport processes in porous media is essential for many natural systems (soils, aquifers, aquatic sediments or subsurface reservoirs) or technological processes (water treatment or ceramic and fuel cell technologies). In particular, in the vadose zone of the terrestrial subsurface the spatially and temporally varying saturation of the aqueous and the gas phase leads to systems that involve complex flow and transport processes as well as reactive transformations of chemical compounds in the porous material. To describe these interacting processes and their dynamics at the pore scale requires a well-suited modelling framework accounting for the proper description of all relevant processes at a high spatial resolution. Here we present P3D-BRNS as a new open-source modelling toolbox harnessing the core libraries of OpenFOAM and coupled externally to the Biogeochemical Reaction Network Simulator (BRNS). The native OpenFOAM volume-of-fluid solver is extended to have an improved representation of the fluid–fluid interface. The solvers are further developed to couple the reaction module which can be tailored for a specific reactive transport simulation. P3D-RBNS is benchmarked against three different flow and reactive transport processes: (1) fluid–fluid configuration in a capillary corner, (2) mass transfer across the fluid–fluid interface and (3) microbial growth with a high degree of accuracy. Our model allows for simulation of the spatio-temporal distribution of all biochemical species in the porous structure (obtained from μ-CT images), for conditions that are commonly found in the laboratory and environmental systems. With our coupled computational model, we provide a reliable and efficient tool for simulating multiphase, reactive transport in porous media.

In Situ pH Measurement in Microfluidic Porous Media Indicated by Surfaces Functionalized with Polyaniline (PAni)

Aqueous phase pH is a critical metric with significant importance in understanding reactive transport processes in porous media. At the microscale, however, traditional pH detection methods face challenges in capturing dynamic pH due to limited sample volume and sensing time. To overcome these limitations, we leveraged micro/nanofabrication techniques to create a microfluidic porous medium coated with polyaniline (PAni) on its surface. Using this innovative microfluidic design, we achieved colorimetric delineation of pH spatial distribution with fast response and robustness in porous media. By conducting coinjection tests with hydrochloric acid (pH = 2) and DI water (pH ≈ 5.8, equilibrated with air) at various flow rates and relative flow rate ratios in a sandstone-patterned microfluidic device, we observed dynamic pH changes in porous media and obtained a comprehensive understanding of the acid advection-diffusion dynamics. The results highlighted the capability of PAni to enable microscale pH sensing. This research contributes to the development of advanced porous media microfluidics and applications, particularly in mass transfer limits during reactive transport of carbon dioxide sequestration and geological hydrogen storage.

Numerical study of gas–solid transport characteristics within vortex region induced by porous media using lattice-Boltzmann based discrete particle simulation

Porous media, as delivery carriers, holds great potential application in various fields particular in drug delivery. A comprehensive understanding of gas–solid transport characteristics within porous media is significant and regulating retention and release of drug particles. A combined approach of lattice Boltzmann method and time-driven hard-sphere model (LBM-TDHS) was used to investigate particle transport process in porous media. The vortex induced by porous structures was observed. Particle trajectories with different connectivity of the vortex region and inlet flow angles was conducted. This study revealed that fluid velocity between connected regions significantly affects the gas streamlines’ shape and particle trajectories. Different inlet flow angles lead to five modes of particle trajectories in vortex regions. Finally, some modifications were performed in general irregular porous structure to control particle trajectories. LBM-TDHS successfully investigated particle dynamics in vortex regions within porous media, demonstrating potential applicationin optimizing the structure of drug delivery carriers.

Suitability of body force model for pressure-difference driven flow in porous media

Pore-scale direct numerical simulation is an important tool for studying the flow of porous media nowadays. This work validates the suitability of body force model for simulating pressure-difference-driven porous flows in pore-scale simulations. The multi-relaxation time lattice Boltzmann method (MRT-LBM) with the color-gradient continuum-surface-force (CG-CSF) model is employed to calculate the absolute and relative permeability of randomly generated porous media. Results show that for single-phase flows, the relative errors are below 5% for most homogeneous porous structures while as high as 80% for structures with preferential paths. This study also reveals the pore-scale flow mechanisms and proposes a new heterogeneity parameter quantified by the standard deviation of the pressure at the boundary. For multiphase flows, errors of the body force model are significant at low Ca due to irreversible phase distribution difference appearing at the early stages. The findings of this work could be applied to other transport processes in porous media. It is crucial to consider the structural heterogeneity and proper parameters when employing the body force model in pore-scale simulations.

Two-Dimensional Continuous Model in Bimolecular Reactive Transport

In this work, a continuum 2D model is proposed to study the interaction at the interface of reactive transport processes in porous media. The analysis of the segregation produced by poor reactant homogenization at the poral scale is addressed by a parametric heuristic model that considers the relative gradient of the reacting species involved in the process. The micro inhomogeneities are incorporated by means of longitudinal and transversal mechanical dispersion coefficients. A two-dimensional continuous model for the bimolecular reactive transport is considered where modelling parameters are estimated numerically from experimental data. A competitive effect between segregation and dispersion is observed that is analyzed by means of numerical experiments. The two-dimensional model reproduces properly both the total mass of the product as well as its increase with the velocity of flow and the inhomogeneity of the advanced front. The methodology used is simple and fast, and the numerical results presented here indicate its effectiveness.

Pore-scale study of three-phase reactive transport processes in porous media

Coupled three-phase flow and reactive transport processes are widely encountered in many scientific and engineering problems. In the present study, a pore-scale model based on the lattice Boltzmann method is developed to simulate coupled three-phase flow and reactive transport processes. The model is validated by contact angle test of droplets on a curved surface and confined reactive mass transport in a three-phase system. The pore-scale model validated is then employed to study the three-phase reactive transport in channels and porous media. The evolution of the three-phase distribution, the concentration field, and the contact line length are discussed in detail. For a two-channel structure, the result shows that as the viscosity ratio increases, the phase with higher viscosity is more difficult to be displaced. Moreover, as the surface tension force between two certain phases increases, the third phase tends to form a film between the two phases, thus suppressing the reactive transport between the two phases. Finally, pore-scale simulation results of three-phase flow in a two-dimensional porous medium show that as viscosity of the phase to be displaced increases, the recovery rate of the displaced phase decreases, and the displacing phase tends to follow the mechanism of viscous fingering. Finally, while the viscosity of the displaced phase can be reduced due to the existence of the species, the recovery rate does not necessarily increase and sometimes even reduces due to the combined bypass and lubrication effects.

Pore-scale modeling of multiphase flow in porous media using a conditional generative adversarial network (cGAN)

Multiphase flow in porous media is involved in various natural and industrial applications, including water infiltration into soils, carbon geosequestration, and underground hydrogen storage. Understanding the invasion morphology at the pore scale is critical for better prediction of flow properties at the continuum scale in partially saturated permeable media. The deep learning method, as a promising technique to estimate the flow transport processes in porous media, has gained significant attention. However, existing works have mainly focused on single-phase flow, whereas the capability of data-driven techniques has yet to be applied to the pore-scale modeling of fluid–fluid displacement in porous media. Here, the conditional generative adversarial network is applied for pore-scale modeling of multiphase flow in two-dimensional porous media. The network is trained based on a data set of porous media generated using a particle-deposition method, with the corresponding invasion morphologies after the displacement processes calculated using a recently developed interface tracking algorithm. The results demonstrate the capability of data-driven techniques in predicting both fluid saturation and spatial distribution. It is also shown that the method can be generalized to estimate fluid distribution under different wetting conditions and particle shapes. This work represents the first effort at the application of the deep learning method for pore-scale modeling of immiscible fluid displacement and highlights the strength of data-driven techniques for surrogate modeling of multiphase flow in porous media.

Pore-scale study of mineral dissolution in heterogeneous structures and deep learning prediction of permeability

Reactive transport processes in porous media with dissolution of solid structures are widely encountered in scientific and engineering problems. In the present work, the reactive transport processes in heterogeneous porous structures generated by Monte Carlo stochastic movement are simulated by using the lattice Boltzmann method. Six dissolution patterns are identified under different Peclet and Damkohler numbers, including uniform pattern, hybrid pattern, compact pattern, conical pattern, dominant pattern, and ramified pattern. Particularly, when Peclet and Damkohler numbers are larger than 1, the increase in the heterogeneity rises the chance of preferential channel flow in the porous medium and thus intensifies the wormhole phenomena, leading to higher permeability. The pore-scale results also show that compared with the specific surface area, the permeability is more sensitive to the alteration of the structural heterogeneity, and it is challenging to propose a general formula between permeability and porosity under different reactive transport conditions and structural heterogeneity. Thus, deep neural network is employed to predict the permeability–porosity relationship. The average value of mean absolute percentage error of prediction of 12 additional permeability–porosity curves is 6.89%, indicating the promising potential of using deep learning for predicting the complicated variations of permeability in heterogeneous porous media with dissolution of solid structures.

Numerical simulation on convective heat transfer characteristics in porous media based on the digital rock technology

Convective heat transfer in porous media has attracted great academic interests due to the complex geometry and the upscaling challenges. In this paper, the 3-D pore structures inside porous media is extracted with help of the digital rock technology, and the pore-scale convective heat transfer characteristics in the complex geometry domain is numerically investigated. A novel method is proposed on determination of the hydraulic characteristic sizes, including the equivalent diameter and heat transfer surface areas, of the transport process in porous media. After comprehensive validation of the numerical scheme, the convective heat transfer characteristics is thoroughly studied in the case of fluid with inlet temperature of 293 K flowing through the porous media with constant temperature of 353 K under different pressure drop conditions. Based on the obtained temperature field inside the core, the local convective heat transfer coefficient as well as the local Nusselt number (Nu) is obtained, which shows the obvious inlet behavior in the heat transfer process. Parameter investigations on the pore sizes and the fluid medium are also performed, and a correlation between Nu and Reynolds number (Re) and Prandtl number (Pr) is obtained. It is expected the reported work could help understanding the convective heat transfer process in porous media and therefore guiding the relevant industrial practices.

The Effects of Pore Geometry on Late Time Solute Transport with the Presence of Recirculation Zone

The solute transport process in porous media is central to understanding many geophysical processes and determines the success of engineered applications. However, fundamental understanding of solute transport in heterogeneous porous media remains challenging especially when inertial effects are significant. To address this challenge, we employed direct numerical simulations in a variety of intrapore geometries at a high Reynolds number (Re = 10) flow regime, where recirculation zones (RZs) are present with significant inertial effects. We find that the volume of RZs depends on pore geometries. Moreover, RZs serve as an immobile domain that can trap and release solutes that lead to non-Fickian transport, characterized by the early arrival and heavy tailing of breakthrough curves and bimodal residence time distributions (RTDs). Lastly, the late time portion of RTDs is fitted to the power law function with determined exponent n, where n depends on the pore geometries and consequently the volume of RZs. Our study sheds light on the mechanisms of an immobile zone on the solute transport, especially improving our understanding of late time transport tailing in pressurized heterogeneous porous media.

Linking mixing and flow topology in porous media: An experimental proof.

Transport processes in porous media are controlled by the characteristics of the flow field which are determined by the porous material properties and the boundary conditions of the system. This work provides experimental evidence of the relation between mixing and flow field topology in porous media at the continuum scale. The setup consists of a homogeneously packed quasi-two-dimensional flow-through chamber in which transient flow conditions, dynamically controlled by two external reservoirs, impact the transport of a dissolved tracer. The experiments were performed at two different flow velocities, corresponding to Péclet numbers of 191 and 565, respectively. The model-based interpretation of the experimental results shows that high values of the effective Okubo-Weiss parameter, driven by the changes of the boundary conditions, lead to high rates of increase of the Shannon entropy of the tracer distribution and, thus, to enhanced mixing. The comparison between a hydrodynamic dispersion model and an equivalent pore diffusion model demonstrates that despite the spatial and temporal variability in the hydrodynamic dispersion coefficients, the Shannon entropy remains almost unchanged because it is controlled by the Okubo-Weiss parameter. Overall, our work demonstrates that under highly transient boundary conditions, mixing dynamics in homogeneous porous media can also display complex patterns and is controlled by the flow topology.

The impact of pore-throat shape evolution during dissolution on carbonate rock permeability: Pore network modeling and experiments

Pore network model simulation (PNM) is an important method to simulate reactive transport processes in porous media and to investigate constitutive relationships between permeability and porosity that can be implemented in continuum-scale reactive-transport modeling. The existing reactive transport pore network models (rtPNMs) assume that the initially cylindrical pore throats maintain their shape and pore throat conductance is updated using a form of Hagen-Poiseuille relation. However, in the context of calcite dissolution, earlier studies have shown that during dissolution, pore throats can attain a spectrum of shapes, depending upon the imposed reactive-flow conditions (Agrawal et al., 2020). In the current study, we derived new constitutive relations for the calculation of conductance as a function of pore throat volume and shape evolution for a range of imposed flow and reaction conditions. These relations were used to build animproved new reactive pore network model (nrtPNM). Using the new model, the porosity-permeability changes were simulated and compared against the existing pore network models.In order to validate the reactive transport pore network model, we conducted two sets of flow-through experiments on two Ketton limestone samples. Acidic solutions (pH 3.0) were injected at two Darcy velocities i.e., 7.3 × 10−4 and 1.5 × 10−4 m.s − 1 while performing X-ray micro-CT scanning. Experimental values of the changes in sample permeability were estimated in two independent ways: through PNM flow simulation and through Direct Numerical Simulation. Both approaches used images of the samples from the beginning and the end of experiments. Extracted pore networks, obtained from the micro-CT images of the sample from the beginning of the experiment, were used for reactive transport PNMs (rtPNM and nrtPNM).We observed that for the experimental conditions, most of the pore throats maintained the initially prescribed cylindrical shape such that both rtPNM and nrtPNM showed a similar evolution of porosity and permeability. This was found to be in reasonable agreement with the porosity and permeability changes observed in the experiment. Next, we have applied a range of flow and reaction regimes to compare permeability evolutions between rtPNM and nrtPNM. We found that for certain dissolution regimes, neglecting the evolution of the pore throat shape in the pore network can lead to an overestimation of up to 27% in the predicted permeability values and an overestimation of over 50% in the fitted exponent for the porosity-permeability relations. In summary, this study showed that while under high flow rate conditions the rtPNM model is accurate enough, it overestimates permeability under lower flow rates.

Modeling of Flow and Transport in Saturated and Unsaturated Porous Media

Modeling fluid flow and transport processes in porous media is a relevant topic for a wide range of applications. In water resources problems, this topic presents specific challenges related to the multiphysical processes, large time and space scales, heterogeneity and anisotropy of natural porous media, and complex mathematical models characterized by coupled nonlinear equations. This Special Issue aims at collecting papers presenting new developments in the field of flow and transport in porous media. The 25 published papers deal with different aspects of physical processes and applications such as unsaturated and saturated flow, flow in fractured porous media, landslide, reactive transport, seawater intrusion, and transport within hyporheic zones. Based on their objectives, we classified these papers into four categories: (i) improved numerical methods for flow and mass transport simulation, (ii) looking for reliable models and parameters, (iii) laboratory scale experiments and simulations, and (iv) modeling and simulations for improved process understanding. Current trends on modeling fluid flow and transport processes in porous media are discussed in the conclusion.

A hysteresis model for the unfrozen liquid content in freezing porous media

The description of the freezing characteristics of porous media is one of the most conspicuous ingredients in flow and heat transport models that involve freezing and thawing processes. Unfrozen liquid content (ULC) shows strong hysteresis during freezing and thawing cycles in different types of soils and other porous media. We discuss the possible mechanisms of hysteresis in porous media and develop a numerical model for the unfrozen liquid content that is capable of describing the hysteresis phenomenon in freezing and thawing cycles. We present a coupled finite element model as the framework for the numerical simulation of fluid flow and heat transport in partially frozen porous media. The implementation aspects of the ULC model as well as its integration into numerical codes are discussed in detail. We investigate the potential impact of the hysteresis phenomenon on the numerical simulation of transport processes in porous media through benchmark examples and validate the behavior of the model against available laboratory measurement data.

The feasibility of shortwave infrared imaging and inverse numerical modeling for rapid estimation of soil hydraulic properties

AbstractMeasurements of the soil water characteristic (SWC) and unsaturated hydraulic conductivity [K(h)] curves, which are at the core of modeling flow and transport processes in porous media, are laborious and prone to experimental errors. To overcome some of the current experimental limitations, we examined the potential feasibility of shortwave infrared (SWIR) imaging of water imbibition into dry soil during a controlled laboratory experiment in conjunction with inverse numerical modeling to determine the wetting SWC and the K(h) function. To generate time series of high‐resolution surface moisture maps, the imaged surface reflectance was converted to surface soil moisture via a recently developed physical radiative transfer model. The moisture time series were then used to parameterize the HYDRUS 2D/3D numerical code for forward simulations. The optimization was performed with simulated annealing in MATLAB that was linked to HYDRUS 2D/3D to automate the inversion process. The obtained SWC wetting curves were subsequently compared with Tempe cell and Dewpoint PotentiaMeter measurements. Although further research and refinements of the proposed method are needed, the results of this exploratory study obtained for a broad range of soil textures are promising and demonstrate the potential feasibility of the proposed approach for rapid estimation of soil hydraulic properties.

The Effect of Morphological and Topological Characteristics on Effective Diffusivity and Permeability of Dual-Structural-Scale Synthetic Porous Medium

Image-based simulations at pore scale provide direct insight into the impact of the microstructure on flow and transport processes in porous media. Diffusion is an important mechanism of mass transfer in gas or liquid phases, confined in porous media. Similar to fluid flow, the diffusive transport in porous media is a strong function of pore size and structure. Although the effect of porosity, pore connectivity and constrictivity of homogeneous porous media on macroscopic properties is clear, this is not well understood for heterogeneous porous media. This study uses a dual-structural-scale medium to analyze the effect of topological and morphological parameters on effective properties such as permeability and the effective diffusivity. A synthetic porous medium was created by two sizes of small and large glass beads, and 3D pore structure image of the sample was captured by X-ray computed tomography technique. The Stokes and diffusion equations were directly solved on the extracted pore geometry of sample, using a finite element method. The results show a strong nonlinear relationship between constrictivity, as a morphological parameter, with permeability and effective diffusivity. Based on the results obtained from pore-scale imaging and modeling, the connectivity of the pore space is increased by decreasing the Euler number and consequently the permeability and effective diffusivity is increased. Good agreement between image-based computed effective diffusivity with that estimated by van Brakel and Heertjes empirical relation confirms the reliability of this relation for heterogeneous porous medium, which includes constrictivity in addition to porosity and tortuosity, as three important morphological properties.

Singular limit for reactive transport through a thin heterogeneous layer including a nonlinear diffusion coefficient

<p style='text-indent:20px;'>Reactive transport processes in porous media including thin heterogeneous layers play an important role in many applications. In this paper, we investigate a reaction-diffusion problem with nonlinear diffusion in a domain consisting of two bulk domains which are separated by a thin layer with a periodic heterogeneous structure. The thickness of the layer, as well as the periodicity within the layer are of order <inline-formula><tex-math id="M1">\begin{document}$ \epsilon $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M2">\begin{document}$ \epsilon $\end{document}</tex-math></inline-formula> is much smaller than the size of the bulk domains. For the singular limit <inline-formula><tex-math id="M3">\begin{document}$ \epsilon \to 0 $\end{document}</tex-math></inline-formula>, when the thin layer reduces to an interface, we rigorously derive a macroscopic model with effective interface conditions between the two bulk domains. Due to the oscillations within the layer, we have the combine dimension reduction techniques with methods from the homogenization theory. To cope with these difficulties, we make use of the two-scale convergence in thin heterogeneous layers. However, in our case the diffusion in the thin layer is low and depends nonlinearly on the concentration itself. The low diffusion leads to a two-scale limit depending on a macroscopic and a microscopic variable. Hence, weak compactness results based on standard <i>a priori</i> estimates are not enough to pass to the limit <inline-formula><tex-math id="M4">\begin{document}$ \epsilon \to 0 $\end{document}</tex-math></inline-formula> in the nonlinear terms. Therefore, we derive strong two-scale compactness results based on a variational principle. Further, we establish uniqueness for the microscopic and the macroscopic model.</p>

Nanoparticle Tracking to Probe Transport in Porous Media.

From the granular and fractured subsurface environment to highly engineered polymer membranes used in pharmaceutical purification, porous materials are ubiquitous in nature and industrial applications. In particular, porous media are used extensively in processes including water treatment, pharmaceutical sterilization, food/beverage processing, and heterogeneous catalysis, where hindered mass transport is either essential to the process or a necessary but undesirable limitation. Unfortunately, there are currently no universal models capable of predicting mass transport based on a description of the porous material because real porous materials are complex and because many coupled dynamic mechanisms (e.g., adsorption, steric effects, hydrodynamic effects, electrostatic interactions, etc.) give rise to the observed macroscopic transport phenomena.While classical techniques, like nuclear magnetic resonance and dynamic light scattering, provide useful information about mass transport in porous media at the ensemble level, they provide limited insight into the microscopic mechanisms that give rise to complex phenomena such as anomalous diffusion, hindered pore-space accessibility, and unexpected retention under flow, among many others. To address this issue, we have developed refractive index matching imaging systems, combined with single-particle tracking methods, allowing the direct visualization of single-particle motion within a variety of porous materials.In this Account, we summarize our recent efforts to advance the understanding of nanoparticle transport in porous media using single-particle tracking methods in both fundamental and applied scenarios. First, we describe the basic principles for two-dimensional and three-dimensional single-particle tracking in porous materials. Then, we provide concrete examples of nanoparticle transport in porous materials from two perspectives: (1) understanding fundamental elementary particle transport processes in porous media, including pore accessibility and cavity escape, which limit transport in porous media, and (2) facilitating applications in industrial processes, e.g., by understanding the mechanisms of particle fouling and remobilization in filtration membranes. Finally, we provide an outlook of opportunities associated with investigating other types of mass transport in confined environments using single-particle tracking methods, including electrophoretic and self-propelled motion.

Bimolecular Reactive Transport Experiments and Simulations in Porous Media

For reactive transport process in porous media, limited mixing and non-Fickian behavior are difficult to understand and predict. To explore the effects of anomalous diffusion and limited mixing, the column-based experiments of bimolecular reactive migration were performed and simulated by the CTRW-FEM model (continuous time random walk-finite element method). Simulated parameters were calibrated and the correlation coefficients between modeled and observed BTCs (breakthrough curves) were greater than 0.9, indicating that CTRW-FEM can solve over-prediction and tailing problems effectively. Porous media with coarser particle size show enhanced mixing and the non-Fickian behavior is not affected by particle size. β (a parameter of CTRW-FEM) and Da (Damköhler number) of CTRW-FEM under different Pe (Péclet number) values showed logarithmic linear relationship. Model sensitivity analysis of the CTRW-FEM model show that the peak concentration is most sensitive to the average pore velocity and the arriving peak time of peak concentration is most sensitive to β. These findings provide a theoretical basis for handling mixing and non-Fickian behavior patterns under actual environmental conditions.