Mass Transport In Porous Media Research Articles

Influence of Particle Shape on Tortuosity of Non-Spherical Particle Packed Beds

Tortuosity in packed beds or porous media is of significant interest in many fields, from geoscience to the chemical industry. Tortuosity plays a significant role in the mass transport in porous media, but also in their residual thermal or electric conductivity when the particles are not conducting. Several predictive models have been proposed to evaluate tortuosity, but there is still a gap when it comes to considering various particle shapes. The preponderance of tortuosity models substantiated in the literature are porosity-dependent while only a few include shape parameters. In this work, we propose a new model with sphericity and porosity to predict the tortuosity based on thermal simulations carried out with non-conducting particles for domains with no wall effect. The beds generated from rigid body simulations are compared and studied for different particle shapes with a sphericity range of 0.65–1. Sphericity showed a significant effect on the tortuosity compared with other 3D shape parameters (numbers of faces, edges, and vertices); therefore, only sphericity has been considered in the new model. The proposed new model is well suited for the porosity range of 0.3 to 0.4. In said ranges, it is an upgrade of the classical Zehner–Bauer–Schlünder (ZBS) model for the effective thermal conductivity of packed beds, with superior performance.

Water‐ and air‐filled pore networks and transport parameters under drying and wetting processes

AbstractThe connectivity and tortuosity of fluid‐filled pore networks in the water and air phases strongly influence the mass transport in porous media. Moisture conditions (water content and distribution) alter water‐ or air‐filled pore networks. In this study, using a sand column with variable saturated conditions, water‐ and air‐filled pore networks were analyzed using X‐ray computed tomography (CT). Water and air transport parameters, including hydraulic conductivity, gas diffusion coefficient, and air permeability, were measured. The objectives were (a) to identify the effects of entrapped air on the water‐filled pore network and hydraulic conductivity and (b) to understand the water‐ and air‐filled pore networks and relevant transport parameters in the sand column during the drying and wetting processes. Measurements of hydraulic conductivity using quasisaturated samples showed that hydraulic conductivity was drastically reduced when smaller in situ air bubbles were present inside the sand column. At the same air‐filled porosity, higher gas diffusivity and air permeability were obtained under wetting than those during drying. X‐ray CT image analysis revealed that the air‐filled pore network connectivity during wetting was higher than that during drying, resulting in enhanced gas transport parameters during the wetting process. The observed differences in water‐ and air‐filled pore networks during drying and wetting processes are highly promising for future multiphase mass transport models in soils.

Analysis of heat transfer and water flow with phase change in saturated porous media by bond-based peridynamics

A wide range of natural and industrial processes involve heat and mass transport in porous media. In some important cases the transported substance may undergo phase change, e.g. from liquid to solid and vice versa in the case of freezing and thawing of soils. The predictive modelling of such phenomena faces physical (multiple physical processes taking place) and mathematical (evolving interface with step change of properties) challenges. In this work, we develop and test a non-local approach based on bond-based peridynamics which addresses the challenges successfully. Our formulation allows for predicting the location of the interface between phases, and for calculating the temperature and pressure distributions within the saturated porous medium under the conditions of pressure driven water flow. The formulation is verified against existing analytical solutions for 1D problems, as well as finite element transient solutions for 2D problems. The agreement found by the verification exercise demonstrates the accuracy of the proposed methodology. The detailed coupled description of heat and hydraulic processes can be considered as a critical step towards a thermo-hydro-mechanical model, which will allow, for example, description of the hydrological behaviour of permafrost soils and the frost heave phenomenon.

Direct numerical simulations of moisture transport in porous media by a multi-component/phase-change lattice Boltzmann method

In this paper, simultaneous heat and mass transport in porous media is studied numerically using a 2D multicomponent/multiphase phase-change lattice Boltzmann scheme. This newly developed LB model requires no correlation equations as inputs for physical properties of the porous medium (such as relative permeability, heat capacity, thermal conductivity and mass diffusivity) that is filled with a multi-component fluid of air/vapor mixture. Natural convection and condensation of humid air in an enclosure filled with and without a porous medium that is heated differentially by vertical walls are compared. The same numerical scheme is applied to simulate capillary rise of liquid in semi-infinite packed hydrophilic beds with different structures that are filled initially with a mixture of unsaturated vapor and air above a water reservoir. It is shown that evaporation in the packed hydrophilic bed plays an important role in capillary rise of liquid. Effects of contact angles as well as the influence of the directionality and heterogeneity of the packed bed are investigated. The directional and the heterogeneous packed beds are shown to be able to suck a larger amount of liquid in a shorter time period compared to homogeneous packed beds with the same porosity under the same condition.

A LOCAL THERMAL NONEQUILIBRIUM MODEL FOR COUPLED HEAT AND MASS TRANSFER WITH DISPERSION AND THERMAL DIFFUSION IN POROUS MEDIA

A theoretical model is proposed to predict Darcy-scale mass transport in porous media coupled with nonequilibrium heat transfer and taking into account the thermal diffusion process. A volume-averaging technique was used with approximations leading to a two-equation or two-temperature model for the macroscale energy balance equations. Because of the Soret effect, the concentration deviation with respect to the averaged value is a function of concentration and temperature gradients in the fluid phase, the temperature gradient in the solid phase, and the difference between the two averaged temperatures. The mapping between deviations and averages involves four closure problems for the mass transport equations: problems were solved numerically over a two-dimensional periodic-unit cell for evaluation purposes. The results show that the effective coefficients depend strongly on the thermophysical properties of the medium and the Peclet number. In particular, the effective-Soret coefficient in porous media changes with the Peclet number and the phases' thermal conductivity ratios.

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.

The Imaging Resolution and Knudsen Effect on the Mass Transport of Shale Gas Assisted by Multi-length Scale X-Ray Computed Tomography

The spatial resolution of 3D imaging techniques is often balanced by the achievable field of view. Since pore size in shales spans more than two orders of magnitude, a compromise between representativeness and accuracy of the 3D reconstructed shale microstructure is needed. In this study, we characterise the effect of imaging resolution on the microstructural and mass transport characteristics of shales using micro and nano-computed tomography. 3D mass transport simulation using continuum and numerical physics respectively is also compared to highlight the significance of the Knudsen effect on the reconstructed solid surface. The result shows that porosity measured by micro-CT is 25% lower than nano-CT, resulting in an overestimated pore size distribution and underestimated pore connectivity. This leads to a higher simulated intrinsic permeability. An overestimated diffusive flux and underestimated permeability are obtained from the continuum mass transport simulation compared to the numerical ones when the molecular-wall collision is accounted, evidenced by the large deviation of the measured Knudsen tortuosity factor and permeability correction factor. This study is believed to provide new knowledge in understanding the importance of imaging resolution and gas flow physics on mass transport in porous media.

Mass transport in porous media at the micro- and nanoscale: A novel method to model hindered diffusion

Abstract Mass transport in liquid-filled pores at the micro- and nanoscale can play an important role in applications such as membrane separations, chromatography, and catalytic processes. In this work, we use Brownian dynamics in order to describe the motion of spherical solute molecules at a pore-scale. The method can be used to calculate effective parameters intrinsically related to the porous medium such as the effective diffusivity and the hindrance factor for diffusion. The latter is calculated using a novel probabilistic model derived in the present study, which uses the Lennard-Jones potential to reproduce the hindering effect of the interaction between solute molecules and the wall atoms on the diffusivity. In addition, we introduce a fitting function that can be used to estimate the diffusive hindrance factor of a complex geometry when the pore size distribution of the porous network is known. Finally, a multiscale approach is presented and illustrated with an application example, whereby the hindrance factors of the micro- and nanoscale are used in the simulations of the mass transport at the larger scale.

PORE SIZE DISTRIBUTION IN SIMULATION OF MASS TRANSPORT IN POROUS MEDIA: A CASE STUDY IN RESERVOIR ANALYSIS

The modeling and numerical simulation of mass transport in porous media is discussed in this work by using the so-called pore size distribution for computing transport properties. The pore-size distribution is a property of the pore structure of a porous medium. This can be used to estimate the different transport properties, amongst other, the permeability. By starting with a formula for the absolute permeability, the simulation of water and oil transport in reservoirs is considered by solving mass conservation equations with the help of the control volume method. The influence of the pore size distribution on the transport behavior is discussed to demonstrate the adequacy of the use of pore size distribution in studying the behavior of reservoirs.

Implementation of salt transport modules in a solver framework for heat and mass transport in porous materials

The modeling framework and simulation program DELPHIN 6 for heat and mass transport in porous media is implemented as set of modules for balance equations, transport functions, sources and sinks, boundary and contact conditions. The article starts with an overview of the software architecture, modeling assumptions and numerical considerations. Then, the extension of the framework towards salt transport is presented from the perspective of a physical modeler without in-depth numerical programming experience. It will be shown, that the current modeling framework is sufficient to enable researchers and modelers to make extensions without investing excessive time on core solver and data structure development.

Lattice Boltzmann modeling of transport phenomena in fuel cells and flow batteries

Fuel cells and flow batteries are promising technologies to address climate change and air pollution problems. An understanding of the complex multiscale and multiphysics transport phenomena occurring in these electrochemical systems requires powerful numerical tools. Over the past decades, the lattice Boltzmann (LB) method has attracted broad interest in the computational fluid dynamics and the numerical heat transfer communities, primarily due to its kinetic nature making it appropriate for modeling complex multiphase transport phenomena. More importantly, the LB method fits well with parallel computing due to its locality feature, which is required for large-scale engineering applications. In this article, we review the LB method for gas–liquid two-phase flows, coupled fluid flow and mass transport in porous media, and particulate flows. Examples of applications are provided in fuel cells and flow batteries. Further developments of the LB method are also outlined.

Stochastic Nature of Salt Mass Transport in Porous Media Under Unstable Conditions

The two main transport mechanisms that occur simultaneously under unstable flow conditions are transport of saltwater from an overlying salt source to the porous media, and transport of salt through the porous media. These mechanisms were simultaneously studied through two fixed mass experiments conducted over 15 days. The transport through the porous media was also studied via three continuous injection experiments lasting between 5 to 29 days. There was no hydraulic gradient across the porous media in any of the experiments. Experiments were conducted in a 1 cm thick plexiglass rectangular sand column (1.70 m × 0.61 m × 0.61 m). The saline source concentration was 36 g/l, and the source heights were 4.5 cm. The sand porosity and hydraulic conductivity were 32% and 9.0 m/d, respectively. The rate of mass transport from the source to the porous media was observed by measuring the salt concentration within the source, while the salt transport through the porous media was documented by measuring breakthrough curves at five locations within the sand column. Fixed mass experiment results, using mass analysis, showed that the salt transport from the source to the porous media was deterministic since both experiments produced identical rates of mass transport from the source to the porous media, the salt transport through the porous media was stochastic since the observed breakthrough curves at the five locations were considerably different. The breakthrough curves measured in three identical continuous injection experiments were also very different supporting the results of the fixed mass experiments. The implications of these findings are that, under unstable conditions, one can predict the salt mass that would enter from a salt source into the underlying porous media with certainty, one cannot predict the rate or pattern of salt transport through the porous media itself.

Pollution Source Identification in Groundwater Systems: Application of Regret Theory and Bayesian Networks

Pollution source identification in groundwater resources is a challenging task due to existing uncertainties in both pollutant source characteristics and mass transport in porous media. To obtain a robust and cost-effective groundwater monitoring configuration, this paper presents a new regret-based optimization model which minimizes the number of monitoring wells and average regret in estimating undetected polluted area. A Monte Carlo analysis is used to consider existing uncertainties in both pollution source characteristics and parameters of groundwater quality simulation model. MODFLOW and MT3D, groundwater quantity and quality simulation models, are used to simulate the spatial and temporal variations of a water quality indicator in groundwater. For each non-dominated solution provided by a bi-objective optimization model, the optimal positions of monitoring wells are also determined by minimizing the corresponding regret in undetected polluted area. Furthermore, a Bayesian network (BN) is trained and validated based on results of the Monte Carlo analysis. The trained BN is capable of accurately determining an unknown pollution source using monitoring data in real-time operation of monitoring system. To demonstrate the efficiency and applicability of the proposed methodology, it is applied to the Tehran Aquifer in the Tehran refinery region, which is highly polluted due to leakage from several tanks of petroleum products.

Mass and heat transport in the two-phase Buckley–Leverett model

In this article we study the initial boundary value problem for two-phase heat and mass transport in porous media described by the Buckley–Leverett model. We outline a method to construct asymptotic solutions of the initial boundary problem and show how to overcome singularities in solutions and shock waves.

Theoretical modeling of water vapor transport in cellulose-based materials

The theory of mass transport in porous media is of fundamental importance for different applications such as food, paper packaging, textiles, and wood for building materials. In this study, a theoretical water vapor transport model has been developed for cellulose-based materials, such as paper and regenerated cellulose film. Pore diffusivities were determined from the dynamic moisture breakthrough experiments comprising a stack of paper sheets and regenerated cellulose films in a configuration similar to a packed adsorption column. Other mass transfer parameters were determined from transient moisture uptake rate measurements. The model incorporates pore and surface diffusion as a lump parameter into a variable effective diffusion coefficient. The mass transport, involving both pore and surface diffusions, is evaluated independently. The theoretical water vapor transmission rates (WVTRs) obtained from the model were compared with experimentally determined WVTRs measured under steady-state conditions. The theoretical model, based on intrinsic diffusion, stipulates higher WVTR values compared to the experimental results. However, the theoretical water vapor transfer rates agree well with the experimental results when external mass transfer resistance is incorporated in the model.

Computational methods for reactive transport modeling: A Gibbs energy minimization approach for multiphase equilibrium calculations

We present a numerical method for multiphase chemical equilibrium calculations based on a Gibbs energy minimization approach. The method can accurately and efficiently determine the stable phase assemblage at equilibrium independently of the type of phases and species that constitute the chemical system. We have successfully applied our chemical equilibrium algorithm in reactive transport simulations to demonstrate its effective use in computationally intensive applications. We used FEniCS to solve the governing partial differential equations of mass transport in porous media using finite element methods in unstructured meshes. Our equilibrium calculations were benchmarked with GEMS3K, the numerical kernel of the geochemical package GEMS. This allowed us to compare our results with a well-established Gibbs energy minimization algorithm, as well as their performance on every mesh node, at every time step of the transport simulation. The benchmark shows that our novel chemical equilibrium algorithm is accurate, robust, and efficient for reactive transport applications, and it is an improvement over the Gibbs energy minimization algorithm used in GEMS3K. The proposed chemical equilibrium method has been implemented in Reaktoro, a unified framework for modeling chemically reactive systems, which is now used as an alternative numerical kernel of GEMS.

A synchronous cellular automaton model of mass transport in porous media

In this work we present a fully synchronous coarse grained cellular automaton model for large-scale simulations at molecular level. The model is based on Margolus partitioning scheme, which was generalized as to describe quantitatively diffusion, adsorption and directed flow in porous media. Our aim is to create conceptually simple and computationally efficient framework to model the mass transport in porous materials with large representative volume. This work focuses on the fundamental aspects of the generalized Margolus cellular automaton. We exemplify the model by solving several diffusion problems, studying the monolayer adsorption, chromatography on disordered porous structures and chemical transformation in a system with phase separation. The results indicate that the model reflects the essential features of these phenomena. Absence of round-off errors, fully synchronous way of implementation, autonomous physically meaningful time scale and ease-to-handle boundary conditions make this model a promising framework for study various transport phenomena in porous structures.

Dispersion in Porous Media with Heterogeneous Nonlinear Reactions

The upscaling of mass transport in porous media with a heterogeneous reaction at the fluid–solid interface, typical of dissolution problems, is carried out with the method of volume averaging, starting from a pore-scale transport problem involving thermodynamic equilibrium or nonlinear reactive boundary conditions. A general expression to describe the macro-scale mass transport is obtained involving several effective parameters which are given by specific closure problems. For representative unit cell with a simple stratified geometry, the effective parameters are obtained analytically and numerically, while for those with complicated geometries, the effective parameters are only obtained numerically by solving the corresponding closure problems. The impact on the effective parameters of the fluid properties, in terms of pore-scale Peclet number Pe, and the process chemical properties, in terms of pore-scale Damkohler number Da and reaction order (n), is studied for periodic stratified and 3D unit cells. It is found that the tortuosity effects play an important role on the longitudinal dispersion coefficient in the 3D case, while it is negligible for the stratified geometry. When Da is very small, the effective reaction rate coefficient is nearly identical to the pore-scale one, while when Da is very large, the reactive condition turns out to be equivalent to pore-scale thermodynamic equilibrium, and the macro-scale mass exchange term is consequently given in a different form from the reactive case. An example of the application of the macro-scale model is presented with the emphasis on the potential impact of additional, non-traditional effective parameters appearing in the theoretical development on the improvement of the accuracy of the macro-scale model.

Mathematical Simulation of Mass Transport in Porous Media: An Innovative Method to Match Geometrical and Transport Parameters for Scale Transition

The scale-up and scale-down process is of great importance regarding modeling of mass transport phenomena in porous media. Three numerical simulations of porous media for three different scales were developed and validated in this study, analyzing the mass transport phenomena for each scale. More precisely, the first system is a spheres assemblage of various spatial distributions and sizes (mesoscopic), the second is a porous box (macroscopic), and the third is a sphere-in-cell model (microscopic). It was found that the porous structure—shape, size, and positioning—of the spheres at the mesoscopic scale have significant effects on the adsorption efficiency (up to 10%) of highly convective regimes. It was also concluded that a microscopic description at the pore scale is insufficient to adequately describe mass transport phenomena in porous media due to discontinuities of the structure and high local velocity. By comparing the results from the three scales, we obtained a method of matching all geometrical, flow, and transport parameters when a scale transition occurs. The qualitative description of transport phenomena through the three scales and their identical behavior demonstrates the method's effectiveness.

Measuring miscible fluid displacement in porous media with magnetic resonance imaging

AbstractThe development of new quantitative magnetic resonance imaging (MRI) technologies open new opportunities for measurements of mass transport in porous media. The current work examines a simple miscible displacement process of H2O and D2O in porous media samples. Laboratory measurements of dispersion in porous media traditionally monitor the effluent intensity of an injected tracer. We employ MRI to obtain quantitative water saturation profiles, and to measure dispersion in rock core plugs. The saturation profiles are modeled with PHREEQC, a fluid transport modeling program. We demonstrate how independent magnetic resonance measurements can be employed to estimate three important input parameters for PHREEQC, mobile porosity, immobile porosity, and dispersivity. Bulk Carr Purcell Meiboom Gill (CPMG) T2 distribution measurements were undertaken to estimate mobile and immobile porosity. Bulk alternating‐pulsed‐gradient‐stimulated‐echo (APGSTE) measurements were undertaken to measure dispersivity. The imaging method employed, T2 mapping Spin Echo Single Point Imaging (SE‐SPI), also provides information about the pore size distributions in the rock cores, and how the fluid occupancy of the pores changes during the displacement process.