Coupled Processes in Charged Porous Media: From Theory to Applications

Charged porous media are pervasive, and modeling such systems is mathematically and computationally challenging due to the highly coupled hydrodynamic and electrochemical interactions caused by the presence of charged solid surfaces, ions in the fluid, and chemical reactions between the ions in the fluid and the solid surface. In addition to the microscopic physics, applied external potentials, such as hydrodynamic, electrical, and chemical potential gradients, control the macroscopic dynamics of the system. This paper aims to give fresh overview of modeling pore-scale and Darcy-scale coupled processes for different applications. At the microscale, fundamental microscopic concepts and corresponding mass and momentum balance equations for charged porous media are presented. Given the highly coupled nonlinear physiochemical processes in charged porous media as well as the huge discrepancy in length scales of these physiochemical phenomena versus the application, numerical simulation of these processes at the Darcy scale is even more challenging than the direct pore-scale simulation of multiphase flow in porous media. Thus, upscaling the microscopic processes up to the Darcy scale is essential and highly required for large-scale applications. Hence, we provide and discuss Darcy-scale porous medium theories obtained using the hybrid mixture theory and homogenization along with their corresponding assumptions. Then, application of these theoretical developments in clays, batteries, enhanced oil recovery, and biological systems is discussed.

     

Mesoscopic Modeling of Capillarity-Induced Two-Phase Transport in a Microfluidic Porous Structure

Mesoscopic modeling at the pore scale offers great promise in exploring the underlying structure transport performance of flow through porous media. The present work studies the fluid flow subjected to capillarity-induced resonance in porous media characterized by different porous structure and wettability. The effects of porosity and wettability on the displacement behavior of the fluid flow through porous media are discussed. The results are presented in the form of temporal evolution of percentage saturation and displacement of the fluid front through porous media. The present study reveals that the vibration in the form of acoustic excitation could be significant in the mobilization of fluid through the porous media. The dependence of displacement of the fluid on physicochemical parameters like wettability of the surface, frequency along with the porosity is analyzed. It was observed that the mean displacement of the fluid is more in the case of invading fluid with wetting phase where the driving force strength is not so dominant.     

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.     

湿润性对孔隙介质两相渗流驱替效率的影响

孔隙介质中多相渗流的驱替效率对二氧化碳封存效率和石油采收率具有决定性影响,是实际工程调控中的一个关键指标.湿润性是影响多相渗流驱替模式及其效率的一个重要因素.本文通过微流体模型?显微镜?高速相机可视化实验平台,对基于真实砂岩孔隙结构的微流体模型进行湿润性修饰,开展了5种流量和2种湿润性的两相驱替可视化实验,研究了湿润性...     

Effect of Organosilicon-Acrylic Emulsion Treatment on Wettability of Porous Media

To investigate the influence of the organosilicon-acrylic on wetting properties of porous media, contact angle tests were performed on two different sandstones. In addition, the effectiveness of the emulsion on wettability alteration of porous media was validated by capillary rise and spontaneous imbibition tests. The results of wettability tests showed that the wettability of two sandstones was altered from water-wet to gas-wet after treatment with the emulsion. The principle that the critical radius of pore throats and wettability of porous media affect liquids flow was derived analytically and verified experimentally. Coreflood results demonstrated that the latex resulted in increasing the water permeability through altering the rock wettability to gas-wetting, then decreasing the friction drag between liquids and rocks surface. Thereby, the emulsion treatment could increase the flowback rate of trapped liquids. Experimental results were in good agreement with the theoretical analysis. In conclusion, all results indicated that the emulsion could alter the wettability from water-wet to intermediate gas-wet and enhance water permeability in porous media. It was extrapolated that the emulsion had the tremendous potential to be applied in field conditions, enhancing gas productivity through the cleanup of trapped water in the vicinity of the wellbore.     

Evaluation of the Darcy's law performance for two-fluid flow hydrodynamics in a particle debris bed using a lattice-Boltzmann model

In the present paper, multiphase flow dynamics in a porous medium are analyzed by employing the lattice-Boltzmann modeling approach. A two-dimensional formulation of a lattice-Boltzmann model, using a D2Q9 scheme, is used. Results of the FlowLab code simulation for single phase flow in porous media and for two-phase flow in a channel are compared with analytical solutions. Excellent agreement is obtained. Additionally, fluid-fluid interaction and fluid-solid interaction (wettability) are modeled and examined. Calculations are performed to simulate two-fluid dynamics in porous media, in a wide range of physical parameters of porous media and flowing fluids. It is shown that the model is capable of determining the minimum body force needed for the nonwetting fluid to percolate through the porous medium. Dependence of the force on the pore size, and geometry, as well as on the saturation of the nonwetting fluid is predicted by the model. In these simulations, the results obtained for the relative permeability coefficients indicate the validity of the reciprocity for the two coupling terms in the modified Darcy's law equations. Implication of the simulation results on two-fluid flow hydrodynamics in a decay-heated particle debris bed is discussed. Received on 1 December 1999     

Effect of Wetting on the Dynamics of Drainage in Porous Media

We examine the consequences of the wettability properties on the dynamics of gravity drainage in porous media. The relation between the wetting properties at the pore scale and the macroscale hydrodynamics is studied. Model porous media consisting of hydrophilic and hydrophobic glass beads or sand with well defined wetting properties, are prepared for this study. Gravity drainage experiments with air displacing water (two-phase flow), are performed for different Bond numbers, and using different techniques such as gamma-ray densitometry, magnetic resonance imaging (MRI) and weight measurements. The dynamics of drainage is found to be different for hydrophilic and hydrophobic porous media in the transition zone (funicular regime). Moreover, for hydrophilic (water-wet) porous media, MRI experiments reveal the importance of drainage through the continuous water film, which leads to an increase of the residual quantity of water in the transition zone with time.     

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

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

     

Fractals — An overview of potential applications to transport in porous media

We present an overview of the potential applicability of fractal concepts to various aspects of transport phenomena in heterogeneous porous media. Three examples of phenomena where a fractal approach should prove illuminating are presented. In the first example we consider pore level heterogeneities as typified by pore surface roughness. We suggest that roughness may be usefully modelled by fractal curves and surfaces and also cite experimental evidence for regarding pores as fractals. In the second example we consider a fractal network approach to modelling large-scale heterogeneities. The presence of features on all length scales in simple fractal models should capture the essential role played by the presence of heterogeneities on many scales in natural reservoirs. Studies of transport phenomena in such models may yield valuable insights into the problems of macroscopic dispersion. The final example concerns dispersion in multiphase flow. Here the fractal character is attributed to the distribution of the fluid phases rather than the porous medium itself. Again studies of transport phenomena in simple fractal models should help to clarify various problems associated with the corresponding phenomena in real reservoirs.     

Gravitational forces in dual-porosity systems: I. Model derivation by homogenization

We consider the problem of modeling flow through naturally fractured porous media. In this type of media, various physical phenomena occur on disparate length scales, so it is difficult to properly average their effects. In particular, gravitational forces pose special problems. In this paper we develop a general understanding of how to incorporate gravitational forces into the dual-porosity concept. We accomplish this through the mathematical technique of formal two-scale homogenization. This technique enables us to average the single-porosity, Darcy equations that govern the flow on the finest (fracture thickness) scale. The resulting homogenized equations are of dual-porosity type. We consider three flow situations, the flow of a single component in a single phase, the flow of two fluid components in two completely immiscible phases, and the completely miscible flow of two components.This work was supported in part by the National Science Foundation and by the State of Texas Governor's Energy Office.     

Porous Media Characterization Using Minkowski Functionals: Theories,Applications and Future Directions

An elementary question in porous media research is in regard to the relationship between structure and function. In most fields, the porosity and permeability of porous media are properties of key interest. There is, however, no universal relationship between porosity and permeability since not only does the fraction of void space matter for permeability but also the connectivity of the void fraction. With the evolution of modern day X-ray microcomputed tomography (micro-CT) and advanced computing, it is now possible to visualize porous media at an unprecedented level of detail. Approaches in analyzing micro-CT data of porous structures vary in the literature from phenomenological characterization to network analysis to geometrical and/or topological measurements. This leads to a question about how to consistently characterize porous media in a way that facilitates theoretical developments. In this effort, the Minkowski functionals (MF) emerge from the field of statistical physics where it is evident that many physical processes depend on the geometry and topology of bodies or multiple bodies in 3D space. Herein we review the theoretical basis of the MF, mathematical theorems and methods necessary for porous media characterization, common measurement errors when using micro-CT data and recent findings relating the MF to macroscale porous media properties. This paper is written to provide the basics necessary for porous media characterization and theoretical developments. With the wealth of information generated from 3D imaging of porous media, it is necessary to develop an understanding of the limitations and opportunities in this exciting area of research.

     

Multiphase transfer model for intermittent microwave-convective drying of food: Considering shrinkage and pore evolution

Intermittent microwave convective (IMCD) drying is an advanced drying technology that improves both energy efficiency and food quality during drying. Although many experimental studies on IMCD have been conducted, there is no complete multiphase porous media model describing the physics of the process available in the literature. A multiphase porous media model considering liquid water, gases and the solid matrix of food during drying can provide in-depth understanding of IMCD process. Currently there is no IMCD model that have taken shrinkage and pore evolution during drying into consideration. In this study, first a multiphase porous media model with shrinkage (IMCD2) has been developed for IMCD. Then the model has been compared with IMCD model without shrinkage (IMCD1). Simulated temperature, moisture content, density, porosity from IMCD2 are then validated against experimental data. The profile of vapour pressures and evaporation during IMCD are also presented and discussed.     

Wettability Alteration to Intermediate Gas-Wetting in Porous Media at Elevated Temperatures

Wettability alteration to intermediate gas-wetting in porous media by treatment with FC-759, a fluorochemical polymer has been studied experimentally. Berea sandstone was used as the main rock sample in our work, and its wettability before and after chemical treatment was studied at various temperatures from 25 to 93°C. We also studied recovery performance for both gas/oil and oil/water systems for Berea sandstone before and after wettability alteration by chemical treatment. Our experiment shows that chemical treatment with FC-759 can result in: (1) wettability alteration from strong liquid-wetting to stable intermediate gas-wetting at room temperature and at elevated temperatures; (2) neutral wetting for gas, oil, and water phases in two-phase flow; (3) significant increase in oil mobility for gas/oil system; and (4) improved recovery behavior for both gas/oil and oil/water systems. This work reveals a potential for field application for improved gas-well deliverability and well injectivity by altering the rock wettability around wellbore in gas condensate reservoirs from strong liquid-wetting to intermediate gas-wetting.     

Analysis of Multiphase Non-Darcy Flow in Porous Media

Recent laboratory studies and analyses (Lai et al. Presented at the 2009 Rocky Mountain Petroleum Technology Conference, 14–16 April, Denver, CO, 2009) have shown that the Barree and Conway model is able to describe the entire range of relationships between flow rate and potential gradient from low- to high-flow rates through porous media. A Buckley and Leverett type analytical solution is derived for non-Darcy displacement of immiscible fluids in porous media, in which non-Darcy flow is described using the Barree and Conway model. The comparison between Forchheimer and Barree and Conway non-Darcy models is discussed. We also present a general mathematical and numerical model for incorporating the Barree and Conway model in a general reservoir simulator to simulate multiphase non-Darcy flow in porous media. As an application example, we use the analytical solution to verify the numerical solution for and to obtain some insight into one-dimensional non-Darcy displacement of two immiscible fluids with the Barree and Conway model. The results show how non-Darcy displacement is controlled not only by relative permeability, but also by non-Darcy coefficients, characteristic length, and injection rates. Overall, this study provides an analysis approach for modeling multiphase non-Darcy flow in reservoirs according to the Barree and Conway model.     

The effective homogeneous behavior of heterogeneous porous media

The macroscopic equations that govern the processes of one- and two-phase flow through heterogeneous porous media are derived by using the method of multiple scales. The resulting equations are mathematically similar to the point equations, with the fundamental difference that the local permeabilities are replaced by effective parameters. The method allows the determination of these parameters from a knowledge of the geometrical structure of the medium and its heterogeneities. The technique is applied to determine the effective parameters for one- and two-phase flows through heterogeneous porous media made up of two homogeneous porous media.     

Mathematical modeling of multiphase seepage under near-critical conditions

A number of modern approaches to the modeling of multiphase flows in porous media are discussed. Some mathematical difficulties arising when modeling a seepage process numerically under near-critical thermodynamic conditions are analyzed. The usage of enthalpy instead of temperature as an independent variable is substantiated in the case of studying the seepage flows numerically under near-critical conditions.     

Preface on Physicochemical and Electromechanical Interactions in Porous Media

The focus of science and engineering shifts towards smaller length scales. Porous media mechanics has a vital role to play in the translation of microstructural data into macroscopic models of multicomponent systems. As the length scales shrink, more fundamental levels of understanding of natural laws, cause the boundaries between disciplines to blur. In particular, geosciences, polymer sciences and biosciences find a common ground of interest in high specific surface mixtures.     

An RVE-based multiscale modeling method for constitutive relations

This article reports an efficient method to characterize constitutive responses based on multiscale modeling for fluid flow in heterogeneous media based on the concept of representative volume element (RVE). Between different scales, it is considered as the basic principles for down-scaling information the conservation of velocity and of the strain rate tensor. Within this context, we formulate (i) the problem to be solved at the micro-scale, (ii) the up-scaling procedure which involves homogenization rules, and (iii) the generalized principle of multiscale virtual power. The complete theory for constitutive modeling is revisited and shown that when employing multiscale analysis among the suitable variational arguments we are able to obtain, in a straightforward manner, new constitutive behavior between kinematic motions and actions. Some examples of application of fluid flow in heterogeneous media with obstacles are presented to show the consequences of the proposed approach.