Transport Phenomena In Porous Media Research Articles

Lattice Boltzmann Modelling of Fluid Flow through Porous Media: A Comparison between Pore-Structure and Representative Elementary Volume Methods

In this study, we present a novel comparison between pore-structure (PS) and representative elementary volume (REV) methods for modelling fluid flow through porous media using a second-order lattice Boltzmann method (LBM). We employ the LBM to demonstrate the importance of the configuration of square obstacles in the PS method and compare the PS and the REV methods. This research provides new insights into fluid flow through porous media as a novel study. The behaviour of fluid flow through porous media has important applications in various engineering structures. The aim of this study is to compare two methods for simulating porous media: the PS method, which resolves the details of the solid matrix, and the REV method, which treats the porous medium as a continuum. Our research methodology involves using different arrangements of square obstacles in a channel including in-line, staggered and random for the PS method and a porosity factor and permeability value for the REV method. We found that the porosity and obstacle arrangement have significant effects on the pressure drop, permeability and flow patterns in the porous region. While the REV method cannot simulate the details of fluid flow through pore structures compared to the PS method, it is able to provide a better understanding of the flow field details around obstacles (Tortuosity). This study has important applications in improving our understanding of transport phenomena in porous media. Our results can be useful for designing and optimizing various engineering systems involving porous media.

A novel equation to calculate primary drainage capillary pressure based on a porous plate model: Theory and application

This study aims to develop an equation for primary drainage capillary pressure as a function of water saturation based on the porous plate model. Several empirical and semiempirical equations are available to calculate Pc-Sw. The results of the previous equations are not ideal, so this is an attempt to present an accurate equation to calculate Pc-Sw based on governing theoretical physical analysis to describe two-phase immiscible displacement flow in porous media. Volumetric flow rates through the core plug and porous plate are applied to calculate the transport phenomena in porous media. The equation is derived from mass and momentum transfer through a core plug, and Darcy’s law is applied to water flow through a porous plate. Finally, the modified Bessel function is obtained to calculate Pc as a function of Sw. The findings of this study help provide a better understanding of two-phase immiscible displacement flow in porous media. The novelty of this work lies in the ability of the new Pc-Sw equation to accurately fit the primary drainage capillary pressure experimental data obtained from a porous plate, centrifugal, and mercury injection apparatus without restriction. The new equation can be used to calculate the relative permeability and initial fluid distribution in the reservoir. The accuracy of the new equation is a significant advantage compared to Brooks-Corey's Pc-Sw equation; therefore, the research results lead to an incremental advance in the field. This study fills the gap between analytical and empirical models to find the Pc-Sw equation.

Impact of thermodynamic hypotheses on the calculation of the quantity of CO2 stored in a saline aquifer

The aim of this paper is to study the impact of thermodynamics models on the CO2 storage capacity of an aquifer, by using modelling and simulation of transport phenomena in porous media. The aquifer is represented here by a simplified three phase isothermal non-reacting medium composed by an inert solid phase and two binary (CO2 and H2O) fluid phases. The mathematical description is classically developed by the volume averaging method. For each phase, the conservation equations of mass, momentum and energy alongside thermodynamic laws and boundary conditions are first written. They are then integrated over a representative elementary volume in order to establish the description at the local scale. In a thermodynamic point of view, two kinds of models have been implemented and compared. The first one assumes that the gas and liquid phases are ideal. On the contrary, in the second approach, non-ideal thermodynamics is taken into account by calculating an activity coefficient (γ-φ approach) for the liquid phase and a fugacity coefficient (PengRobinson approach) for the gas phase. Results show, among other things, that the amount of CO2 dissolved in the liquid phase is significantly reduced with the non-ideal approach compared to the ideal case. These results highlight the interest of considering non-ideal phases in more complex models.

Electro-elastic instability in electroosmotic flows of viscoelastic fluids through a model porous system

Electrokinetic transport phenomena in porous media are encountered in many practical applications such as electro-chromatography, micro-pumping, chemical remediation of contaminated soil, etc. These applications often deal with various complex viscoelastic fluids (such as polymers, emulsions, suspensions, different kinds of biofluids, etc.) along with simple Newtonian ones. This study presents a detailed numerical investigation on this electrokinetic transport of both Newtonian and viscoelastic fluids in a model porous system consisting of a long micropore with step expansion and contraction. Over the whole range of conditions encompassed in this study, a steady and symmetric flow field is observed for a Newtonian fluid. However, for a viscoelastic fluid, we observe a transition in the flow field from steady and symmetric to unsteady and asymmetric once the Weissenberg number (ratio of the elastic to that of the viscous forces) exceeds a critical value. We show that this transition is caused due to the onset of an electro-elastic instability in the system. The critical value of this Weissenberg number (at which this transition occurs) depends on various factors. In particular, we find that this value increases with the polymer viscosity ratio and expansion and contraction lengths of the micropore. At fixed values of the electric field strength, polymer viscosity ratio, contraction and expansion lengths of the micropore, we observe the existence of different vortex dynamics within this model porous system as the Weissenberg number gradually increases, such as the emergence of the entrant and re-entrant lip vortices, oscillating lip vortices, multi vortices, etc. Therefore, the electrokinetic flow dynamics of viscoelastic fluids in a porous system is much more complex than that of simple Newtonian fluids. We hope this study for a model porous system would facilitate a better understanding of the electrokinetic transport phenomena of viscoelastic fluids in an actual porous media. Furthermore, we show how this model system of a long micropore with step expansion and contraction could also be successfully utilized for other practical applications such as mixing two viscoelastic fluids.

Development and quality assurance of computer programs for the review of long-term safety analysis

Abstract. During the site selection process, regulated by the Site Selection Act (Standortauswahlgesetz – StandAG), the implementer has to identify adequate siting regions and has to perform long-term safety analysis for these regions. The Federal Office for the Safety of Nuclear Waste Management (Bundesamt für die Sicherheit der nuklearen Entsorgung – BASE) as the responsible federal authority has to review the implementer's long-term safety analysis. To perform this duty in the required depth, it will be necessary to recalculate important aspects of the analysis by means of numerical computer programs. In addition, this will allow assessment of the underlying uncertainties of the implementer's long-term safety analysis from a regulatory point of view. Numerical modelling requires a high degree of quality assurance. Therefore, it is of vital importance that the same problem is modelled with different computer programs and – if possible – by different teams of modelers. This strategy is known as the diverse modelling approach. The goal of this approach is to perform a cross-check of the computer programs in use as well as of the correctness of data handling, data interpretation, and model implementation. Comparing outcomes of different modelling teams also integrates complementary views and approaches, which can be beneficial when dealing with complicated problems. The diverse modelling approach forms the basis of regulatory modelling. It can also be implemented within organizations if more than one code is used to tackle the same task. The diverse modelling approach has been carried out at GRS gGmbH over the past two decades by means of the computer programs, TOUGH2-GRS and MARNIE(2). Both (co-)developed programs are thermohydraulic codes that compute transport phenomena in porous media and can be coupled to geochemical codes, see Navarro (2018) and Navarro et al. (2021) for further details. TOUGH2-GRS and MARNIE(2) were applied in various projects, such as preliminary safety analysis Gorleben (VSG, Vorläufige Sicherheitsanalyse Gorleben), ZIESEL and EVEREST. A recent example for the diverse modelling approach was the use of TOUGH2-GRS and MARNIE for the development of indicators for the safe confinement of radionuclides in a deep geological repository (Navarro et al., 2019). A high degree of quality assurance is also achieved by involving computer programs in benchmarks to compare results among different codes for well-defined problems. For the calculation of THM (thermo-hydraulical-mechanical) processes TOUGH2-GRS has been coupled with the geomechanical computer program FLAC3D and this approach has been used in the benchmark BenVaSim (Seher et al., 2019). In this contribution selected works related to TOUGH2-GRS and MARNIE(2) are presented. From this starting-point, ideas and concepts for the continuation of development and quality assurance of the two computer programs at BASE in the near future are outlined. These works will contribute to strengthen the capabilities of BASE in the independent review process of implementer's long-term safety analysis within the site selection process.

A unified modelling and simulation for coupled anomalous transport in porous media and its finite element implementation

This paper presents an unified mathematical and computational framework for mechanics-coupled “anomalous” transport phenomena in porous media. The anomalous diffusion is mainly due to variable fluid flow rates caused by spatially and temporally varying permeability. This type of behaviour is described by a fractional pore pressure diffusion equation. The diffusion transient phenomena is significantly affected by the order of the fractional operators. In order to solve 3D consolidation problems of large scale structures, the fractional pore pressure diffusion equation is implemented in a finite element framework adopting the discretised formulation of fractional derivatives given by Grunwald–Letnikov (GL). Here the fractional pore pressure diffusion equation is implemented in the commercial software Abaqus through an open-source UMATHT subroutine. The similarity between pore pressure, heat and hydrogen transport is also discussed in order to show that it is possible to use the coupled thermal-stress analysis to solve fractional consolidation problems.

Special Issue “Fluid Dynamics, Multi-Phase Flow, and Thermal Recovery Methods”

Intricate fluid flow and transport phenomena in porous media are ubiquitous in natural processes and engineering systems [...]

Exuding porous media: deviations from Darcy's law

Abstract

Advances in porous media science and engineering from InterPore2020 perspective

Natural, artificial, and biological porous media can be seen everywhere in our daily lives. Transport phenomena in porous media, such as flow, diffusion, reaction, adsorption and deformation, are encountered in a wide variety of practical applications and scientific interests over widely disparate length scales, from molecular, to pore, core, and field scales. However, determination of transport properties in porous media remains a challenging issue. During the 12th Annual Meeting of the International Society for Porous Media (InterPore), held online from August 31-September 4, 2020, advances on porous media science and engineering in very broad areas were presented. The meeting was attended by more than 750 participants from across the globe, and a significant milestone was achieved in the history of InterPore conferences due to its online interactive platform. Participants could access the pre-recorded talks, leave comments and questions, chat with each other, one week before the conference. Then, all the feedback related to a talk was discussed in the presence of the author during several Q&A sessions. Invited and Keynote talks were live, and were also recorded. Each Q&A session was moderated by two experts, who first reviewed the 8 contributions of their session and then summarized the questions for each talk. The author could further elaborate their work and answer the questions. Cited as : Cai, J., Hajibeygi, H., Yao, J., Hassanizadeh, S.M. Advances in porous media science and engineering from InterPore2020 perspective. Advances in Geo-Energy Research, 2020, 4(4): 352-355, doi: 10.46690/ager.2020.04.02

High-Resolution Inline Density Measurements: Insight on Multiphase Flow and Transport Phenomena in Porous Media

Understanding fluid flow in porous media is essential with complex and multiphase fluid flow. We demonstrate that high-resolution in-line density measurements are a valuable tool in this regard. An in-line densitometer is used in fluid flow in porous media applications to quantify fluid production and obtain quantitative and qualitative information such as breakthrough times, emulsion/foam generation, and steam condensation. In order to determine the potential applications for in-line densitometry for fluid flow in porous media, a series of sand pack floods were performed with a densitometer placed at the outlet of a sand pack. All fluids passed through the measurement cell at experiential temperatures and pressures. An algorithm was developed and applied to the density data to provide a quantitative determination of oil and water production. The second series of tests were performed at high temperature and pressure, with a densitometer placed at the inlet and outlet of a sand pack, for steam applications. In both series of experiments, data acquisition was collected at 1 hertz and the analyzed density data was compared to results from the conventional effluent analysis, including Dean-Stark, toluene separations, magnetic susceptibility measurement, and flash calculations where applicable. The high-resolution monitoring of effluent from a flow experiment through porous media in a system with two phases of known densities enables two-phase production to be accurately quantified in the case of both light and heavy oil. The frequency of measurements results in a high-resolution history of breakthrough times and fluid behavior. In the case of monitoring steam injection processes, reliable laboratory tests show that in-line density measurements enable the determination of steam quality at the inlet and outlet of a sand pack and qualitative determination of steam condensation monitoring The use of in-line densitometry provides insight on the monitoring of complex fluid flow in porous media, which typical bulk effluent analysis is not able to do. The ability to measure produced fluids at high resolution and extreme temperatures reduces mass balance error associated with the effluent collection and broadens our understanding of complex fluid flow in porous media.

Theory and Applications of Macroscale Models in Porous Media

Systems dominated by heterogeneity over a multiplicity of scales, like porous media, still challenge our modeling efforts. The presence of disparate length- and time-scales that control dynamical processes in porous media hinders not only models predictive capabilities, but also their computational efficiency. Macrosopic models, i.e., averaged representations of pore-scale processes, are computationally efficient alternatives to microscale models in the study of transport phenomena in porous media at the system, field or device scale (i.e., at a scale much larger than a characteristic pore size). We present an overview of common upscaling methods used to formally derive macroscale equations from pore-scale (mass, momentum and energy) conservation laws. This review includes the volume averaging method, mixture theory, thermodynamically constrained averaging, homogenization, and renormalization group techniques. We apply these methods to a number of specific problems ranging from food processing to human bronchial system, and from diffusion to multiphase flow, to demonstrate the methods generality and flexibility in handling different applications. The primary intent of such an overview is not to provide a thorough review of all currently available upscaling techniques, nor a complete mathematical treatment of the ones presented, but rather a primer on some of the tools available for upscaling, the basic principles they are based upon, and their specific advantages and drawbacks, so to guide the reader in the choice of the most appropriate method for particular applications and of the most relevant technical literature.

A comparative study between D2Q9 and D2Q5 lattice Boltzmann scheme for mass transport phenomena in porous media

Characterization of different transport phenomena through porous media represents a key factor to improve mechanical or electrical properties of materials. Porous materials have several applications in different fields such as geological sciences, energy sciences or biological applications. Considering the difficulty to carry out experimental studies in porous media, these transport phenomena are more feasible to describe with computational tools, i.e., to compute the involved parameters. In this scenario, the Lattice Boltzmann Method (LBM) appears as a powerful tool to solve different transport phenomena at micro- and meso-scale. The fluid flow behavior, analyzed with LBM, is commonly solved using the D2Q9 scheme. This scheme has shown a reliable solution for fluid flow problems. On the other hand, the mass transport phenomena are recommended to be solved using the D2Q5 scheme. However, there is not yet a comparative, detailed and complete study of the impact of using such schemes in porous media. The purpose of this study is to analyze the impact of using the D2Q5 and D2Q9 LBM scheme in the computation of mass concentration within porous media considering a constant particle size. Parameters such as porosity and tortuosity are also considered in this study.

Critical Review of Stabilized Nanoparticle Transport in Porous Media

Over the past few decades, due to the special features (i.e., easily produced, large-surface-area-to-volume ratio, and engineered particles with designed surface properties), nanoparticles have not only attracted great attentions from the oil and gas industry but also had various applications from drilling and completion, reservoir characterization, to enhanced oil recovery (EOR). As sensors or EOR agents, thus, fate and behavior of nanoparticles in porous media are essential and need to be investigated thoroughly. Nevertheless, most of the published review papers focus on particle transport in saturated porous media, and all of them are about steady-state flow conditions. So far, no attempts have been extended to systematically review current knowledge about nanoparticle transport in porous media with single-phase and two-phase flow systems under both steady-state and unsteady-state conditions. Accordingly, this review will discuss nanoparticle transport phenomena in porous media with its focus on the filtration mechanisms, the underlying interaction forces, and factors dominating nanoparticle transport behavior in porous media. Finally, mathematical models used to describe nanoparticle transport in porous media for both single-phase flow and two-phase flow under steady-state and transient flow conditions will be summarized, respectively.

Applications of nanofluids in porous medium

This investigation provides a review on the applications of nanofluids in porous media. The transport phenomena in porous media have been of continuing interest for the past decades. This is due to its wide applications in solar receiver devices, building thermal insulation, heat exchangers, energy storage units, ceramic processing, and catalytic reactors to name a few. Furthermore, nanofluids have been also used in porous media due to their superior thermal characteristics. This review is structured into two parts: The first part focuses on presenting the latest results for the thermal conductivity, viscosity, specific heat, and the thermal expansion coefficient of nanofluids reported in the literature. The second part of this review is allocated to the applications of nanofluids in thermal systems filled with porous medium and of different geometries, flow regimes, boundary conditions, and different types of nanofluids and thermophysical properties. Finally, future studies on the applications of nanofluids in porous media are recommended in this review.

Multiscale simulation of transport phenomena in porous media: from toy models to materials models

Multiscale modeling and simulation techniques are transforming the way we can address questions concerning design, characterization, and optimization of novel materials. This transformation is enabled by advanced computational models that incorporate realistic geometries of porous media and serve as tools to predict flow and transport phenomena. Recent developments in mesoscopic and pore-scale modeling include workflows that combine experimental information and direct modeling into an integrated multiscale approach. This review surveys the progress, challenges, and future directions in predictive modeling and simulation of multiphysics phenomena in porous media.

Global sensitivity analysis of multiscale properties of porous materials

Ubiquitous uncertainty about pore geometry inevitably undermines the veracity of pore- and multi-scale simulations of transport phenomena in porous media. It raises two fundamental issues: sensitivity of effective material properties to pore-scale parameters and statistical parameterization of Darcy-scale models that accounts for pore-scale uncertainty. Homogenization-based maps of pore-scale parameters onto their Darcy-scale counterparts facilitate both sensitivity analysis (SA) and uncertainty quantification. We treat uncertain geometric characteristics of a hierarchical porous medium as random variables to conduct global SA and to derive probabilistic descriptors of effective diffusion coefficients and effective sorption rate. Our analysis is formulated in terms of solute transport diffusing through a fluid-filled pore space, while sorbing to the solid matrix. Yet it is sufficiently general to be applied to other multiscale porous media phenomena that are amenable to homogenization.

Two-phase explicit CBS procedure for compressible viscous flow transport in porous materials

PurposeIn this work, a new two-phase version of the finite element-based Artificial Compressibility (AC) Characteristic-Based Split (CBS) algorithm is developed and applied for the first time to heat and mass transfer phenomena in porous media with associated phase change. The purpose of this study is to provide an alternative for the theoretical analysis and numerical simulation of multiphase transport phenomena in porous media. Traditionally, the more complex Separate Flow Model was used in which the vapour and liquid phases were considered as distinct fluids and mathematically described by the conservation laws for each phase separately, resulting in a large number of governing equations.Design/methodology/approachEven though the adopted mathematical model presents analogies with the conventional multicomponent mixture flow model, it is characterized by a considerable reduction in the number of the differential equations for the primary variables. The fixed-grid numerical formulation can be applied to the resolution of general problems that may simultaneously include a superheated vapour region, a two-phase zone and a sub-cooled liquid region in a single physical domain with irregular and moving phase interfaces in between. The local thermal non-equilibrium model is introduced to consider the heat exchange between fluid and solid within the porous matrix.FindingsThe numerical model is verified considering the transport phenomena in a homogenous and isotropic porous medium in which water is injected from one side and heated from the other side, where it leaves the computational domain in a superheated vapour state. Dominant forces are represented by capillary interactions and two-phase heat conduction. The obtained results have been compared with the numerical data available in the scientific literature.Social implicationsThe present algorithm provides a powerful routine tool for the numerical modelling of complex two-phase transport processes in porous media.Originality/valueFor the first time, the stabilized AC-CBS scheme is applied to the resolution of compressible viscous flow transport in porous materials with associated phase change. A properly stabilized matrix inversion-free procedure employs an adaptive local time step that allows acceleration of the solution process even in the presence of large source terms and low diffusion coefficients values (near the phase change point).

Model of two-temperature convective transfer in porous media

In this paper, we study the asymptotic behaviour of the solution of a convective heat transfer boundary problem in an $$\varepsilon $$ -periodic domain which consists of two interwoven phases, solid and fluid, separated by an interface. The fluid flow and its dependence with respect to the temperature are governed by the Boussinesq approximation of the Stokes equations. The tensors of thermal diffusion of both phases are $$\varepsilon $$ -periodic, as well as the heat transfer coefficient which is used to describe the first-order jump condition on the interface. We find by homogenization that the two-scale limits of the solutions verify the most common system used to describe local thermal non-equilibrium phenomena in porous media (see Nield and Bejan in Convection in porous media, Springer, New York, 1999; Rees and Pop in Transport phenomena in porous media III, Elsevier, Oxford, 2005). Since now, this system was justified only by volume averaging arguments.

Effect of static porosity fluctuations on reactive transport in a porous medium

Reaction-diffusive transport phenomena in porous media are ubiquitous in engineering applications, biological and geochemical systems. The porosity field is usually random in space, but most models consider the porosity field as a well-defined deterministic function of space and time and ignore the porosity fluctuations. They use a reaction–diffusion equation written in terms of an average porosity and average concentration fields. In this contribution, we treat explicitly the effect of spatial porosity fluctuations on the dynamics of a concentration field for the case of a one-dimensional reaction-transport system with nonlinear kinetics. Three basic assumptions are considered. (i) The porosity fluctuations are assumed to have Gaussian properties and an arbitrary variance; (ii) we assume that the noise correlation length is small compared to the relevant macroscopic length scale; (iii) and we assume that the kinetics of the reactive term in the equations for the fluctuations is a self-consistently determined constant. Elimination of the fluctuating part of the concentration field from the dynamics leads to a renormalized equation involving the average concentration field. It is shown that the noise leads to a renormalized (generally smaller) diffusion coefficient and renormalized kinetics. Within the framework of the approximations used, numerical simulations are in agreement with our theory. We show that the porosity fluctuations may have a significant effect on the transport of a reactive species, even in the case of a homogeneous average porosity.

Investigation of intermittent microwave convective drying (IMCD) of food materials by a coupled 3D electromagnetics and multiphase model

ABSTRACTIntermittent microwave convective drying (IMCD) improves energy efficiency and the product quality during drying of agricultural products. However, the physical mechanism of heat and mass transfer involved in IMCD is poorly understood due to lack of a comprehensive and realistic mathematical model of this process. A multiphase porous media model considering coupled electromagnetics and multiphase transport phenomena in porous media can potentially provide fundamental details of underlying mechanisms of IMCD. The aim of this study is to develop a mathematical model for IMCD considering electromagnetics using Maxwell’s equations coupled with multiphase porous media in 3D and validate the model against experimental results. The results show that the temperature distribution is uneven in the material, which redistributes during the tempering period. The water and vapor fluxes showed asymmetric profile along the diameter of the sample due to the non-uniformity of microwave heating. A clear understanding of these transport mechanisms in IMCD will lead to the development of appropriate drying process for improved food quality, energy efficiency, and optimization of the IMCD process.