Phenomena In Porous Media Research Articles

Microfluidic Study on the Effect of Single Pore-Throat Geometry on Spontaneous Imbibition.

Spontaneous imbibition is a naturally occurring phenomenon in porous media that plays an important role in various processes. Particularly during the oil recovery process, imbibition efficiency could be significantly affected by the physical properties of the reservoir rock, such as pore-throat structure. However, the effect of the pore-throat structure on the imbibition process has rarely been investigated quantitatively. Therefore, in this study, spontaneous imbibition was examined quantitatively using microfluidic devices with different single pore-throat geometries. Three key geometric parameters were examined, namely, pore-throat ratio, coordination number, and tortuosity. The pore-to-throat ratio of a single pore-to-throat structure under investigation ranges from 3 to 50. Designated coordination numbers range from 2 to 6. Tortuosity values for meandering channels range from 1 to 2. Imbibition process was mimicked using microfluidic devices with varying pore-throat geometries. The results showed that average imbibition velocity exhibited an initial increase followed by a subsequent decline with the increase in the pore-throat ratio. As the coordination number increased, imbibition velocity decreased as the coordination number increased, and the influence of the pore-throat ratio diminished as the coordination number increased. Imbibition velocity decreased as the tortuosity increased. Meniscus movements were investigated for different pore-throat structures. Statistical analysis was also conducted to determine the dominant factor governing the imbibition behavior. It was found that pore-throat ratio, tortuosity, and coordination number exerted a decreasing impact on the imbibition velocity. Wetting phase saturation was examined over time using a single pore-throat geometry device with varying pore-throat ratios. Four distinct types of imbibition behaviors were identified and characterized. In conclusion, this work examined the imbibition behaviors within specified pore-throat geometries, which could contribute to a comprehensive understanding of the imbibition behavior in realistic porous media.

Porous-DeepONet: Learning the Solution Operators of Parametric Reactive Transport Equations in Porous Media

Reactive transport equations in porous media are critical in various scientific and engineering disciplines, but solving these equations can be computationally expensive when exploring different scenarios, such as varying porous structures and initial or boundary conditions. The deep operator network (DeepONet) has emerged as a popular deep learning framework for solving parametric partial differential equations. However, applying the DeepONet to porous media presents significant challenges due to its limited capability to extract representative features from intricate structures. To address this issue, we propose the Porous-DeepONet, a simple yet highly effective extension of the DeepONet framework that leverages convolutional neural networks (CNNs) to learn the solution operators of parametric reactive transport equations in porous media. By incorporating CNNs, we can effectively capture the intricate features of porous media, enabling accurate and efficient learning of the solution operators. We demonstrate the effectiveness of the Porous-DeepONet in accurately and rapidly learning the solution operators of parametric reactive transport equations with various boundary conditions, multiple phases, and multi-physical fields through five examples. This approach offers significant computational savings, potentially reducing the computation time by 50–1000 times compared with the finite-element method. Our work may provide a robust alternative for solving parametric reactive transport equations in porous media, paving the way for exploring complex phenomena in porous media.

A Mini Review on Electroosmotic Phenomena in Porous Media

Electroosmosis phenomenon in porous media finds widespread applications in various fields such as microfluidic systems, polymer electrolyte membrane fuel cells, oil and gas engineering, wastewater sludge dewatering and groundwater dynamics etc. Therefore, the electroosmotic flow mechanism in porous media have attracted broad interests from multiple disciplines. This paper provides an overview on the physical mechanisms and mathematical models for electroosmosis in porous media. The background of electric double layer theory and state-of-art research progress on pore-scale models for electroosmotic flow through porous media are reviewed. Two typical and significant research topics, electroosmosis under pressure coupling effect and nanoscale electroosmotic phenomena, are then focused on. The advances in theoretical analysis, numerical simulation and experimental measurements are summarized. Finally, the potential research directions for the electroosmotic flow in porous media are addressed out.

Convective Drying of Porous Media: Comparison of Phase-Field Simulations with Microfluidic Experiments

Convective drying of porous media is central to many engineering applications, ranging from spray drying over water management in fuel cells to food drying. To improve these processes, a deep understanding of drying phenomena in porous media is crucial. Therefore, detailed simulation of multiphase flows with phase change is of great importance to investigate the complex processes involved in drying porous media. While many studies aim to access the phenomena solely by simulations, here we succeed to compare comprehensively simulations with an experimental methodology based on microfluidic multiphase flow studies in engineered porous media. In this contribution, we propose a Navier–Stokes Cahn–Hilliard model coupled with balance equations for heat and moisture to simulate the two-phase flow with phase change. The phase distribution of the two fluids air and water is modeled by the Phase-Field equation. Comparisons with experiments are rare in the literature and usually involve very simple cases. We compare our simulation with convective drying experiments of porous media. Experimentally, the interface propagation of the water–air interface was visualized in detail during drying in a structured microfluidic cell made from PDMS. The drying pattern and the drying time in the experiment are very well reproduced by our simulation. This validation will enable the application for the presented Navier–Stokes Cahn–Hilliard model in more complex cases focused more on applications, e.g., in the field of fibrous materials.

Local randomized neural networks with discontinuous Galerkin methods for diffusive-viscous wave equation

The diffusive-viscous wave equation is an advancement in wave equation theory, as it accounts for both diffusion and viscosity effects. This has a wide range of applications in geophysics, such as the attenuation of seismic waves in fluid-saturated solids and frequency-dependent phenomena in porous media. Therefore, the development of an efficient numerical method for the equation is of both theoretical and practical importance. Recently, local randomized neural networks with discontinuous Galerkin (LRNN-DG) methods have been introduced in [21] to solve elliptic and parabolic equations. Numerical examples suggest that LRNN-DG can achieve high accuracy, and can handle time-dependent problems naturally and efficiently by using a space-time framework. In this paper, we develop LRNN-DG methods for solving the diffusive-viscous wave equation and present numerical experiments with several cases. The numerical results show that the proposed methods can solve the diffusive-viscous wave equation more accurately with less computing costs than traditional methods.

Time scales of spontaneous imbibition into porous material: From classic models to papers applications

Flow and spontaneous imbibition phenomena in porous media are important for various industrial applications, including printing and medical lateral flow assays. Their quantitative characterization is important to better understand and select the appropriate raw materials. However, standard methods often require time-consuming tests, and/or expensive equipment. Different time scales must be considered, limiting the range of possible characterization tools. A novel experimental approach based on image analysis for characterizing spontaneous imbibition processes is presented. Hence, ultra-fast diffusion may be quantitatively characterized. Models are issued from the literature to consider physical phenomena at small (milliseconds) and medium range (seconds) of time scales. The obtained experimental data fit with theoretical results, providing valuable insights into the understanding of fluid flow behavior at different time scales. Furthermore, the identification of some physical properties for either the fluid, or the substrate, based on the theoretical models are possible, as the contact angle, which remains to be otherwise challenging. This study contributes to bridging the gap between spontaneous imbibition and capillary phenomena at different time scales, their modeling, and a characterization of material and/or fluid properties paving the way for enhanced understanding and control of fluid behavior in porous media. Different papers are considered to illustrate the method.

Pore-scale experimental investigation on the co-current spontaneous imbibition of gas–water two-phase with gravity force

Gravity and capillary forces play pivotal roles in the natural capillary-driven spontaneous imbibition process. The opacity of the medium and the intricate pore structure make it challenging to elucidate the influence of gravity force on co-current gas–water imbibition. A series of pore-scale visualization experiments were conducted using capillary tubes of five different diameters (100, 300, 400, 500, and 1000 μm). The vector concept, represented by the interaction angle with the horizontal direction, was employed to quantify the varying levels of gravity force in the imbibition process, and its impact on imbibition recovery was assessed quantitatively. The findings revealed that the primary influence of gravity on gas–water spontaneous imbibition recovery was predominantly observed in the early stage. Due to the water blocking effect, the gas–water spontaneous imbibition process temporarily halted and resumed when the capillary diameter was 300 μm (at an angle of 60°). For capillary diameters between 100 and 500 μm, the water blocking effect induced a wave-like variation in gas–water spontaneous imbibition recovery as the interaction angle increased. Conversely, for a capillary diameter of 1000 μm, imbibition recovery exponentially decreased with the interaction angle, and no water blocking effect was observed. Consequently, the critical range of pore sizes for the water blocking effect in the gas–water spontaneous imbibition process was determined to be between 500 and 1000 μm. This research offers valuable theoretical insights into understanding capillary-driven flow phenomena in porous media.

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.

Automated Symbolic Upscaling: 2. Model Generation for Extended Applicability Regimes

AbstractIn this second part of the two paper series, we detail an algorithmic procedure for systematically implementing the generalized closure form strategy presented in Part 1. This strategy extends the applicability of homogenized models with respect to classical homogenization theory, as demonstrated in Part 1 where upscaled models are rigorously derived in moderately reactive physical regimes. After encoding the algorithm into Symbolica, an automated upscaling framework, we upscale two reactive mass transport problems and numerically validate the resulting nonlinear homogenized models by showing the absolute error estimates predicted by homogenization theory are satisfied. In both problems, nontrivial closure forms and closure problems are automatically formulated using the encoded strategy with no human interaction, nor prior knowledge regarding the closure required for the systems. We hope these demonstrations spark further interest in automated analytical frameworks for multiscale modeling, as such capabilities are invaluable for generating rigorous multiscale models of complex phenomena in 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.

Current advances in capillarity: Theories and applications

As common physical phenomena in porous media, capillarity behaviors exist in many engineering applications and natural science fields. The experimental, theoretical and numerical research on capillarity in porous media has lasted for more than a century, and the research results have been widely used in various fields, such as the development of conventional and unconventional resources. However, although the research has made great progress, the complex imbibition mechanism poses new challenges to us. The 1st National Conference on Imbibition Theory and Application in Porous Media was held in Beijing from April 22 to 24, 2023, to gather researchers who are interested in imbibition research, exchange the latest progress and achievements in the field of imbibition in porous media, and discuss research hotspots and difficulties. Cited as: Cai, J., Sun, S., Wang, H. Current advances in capillarity: Theories and applications. Capillarity, 2023, 7(2): 25-31. https://doi.org/10.46690/capi.2023.05.01

Experimental study of viscous fingering in sand-pack model for heavy oil reservoir

Viscous fingering phenomenon in porous media has a great impact on industrial processes, such as enhanced oil recovery processes. The previous experimental works mainly used Hele-Shaw models and micromodels to investigate viscous fingering mechanisms. However, Hele-Shaw models simulate porous media flow in a narrow gap with no pore structure. Micromodels’ pore structures are simplified, and the material used to make micromodel generally has different wettability compared with real rocks. Therefore, a large-dimensions of 40 cm × 20 cm× 0.5 cm sand-pack model with a vertical well in the center is used in this study to mimic real reservoir in terms of pore structure, wettability conditions and real radial flow. To the best of our knowledge, there is no reported literature on viscous fingering experimental study for radial flow in real sand-pack models. Immiscible flooding processes with high viscosity ratios ranging from 853.9 to 32080 and different injection rates ranging from 0.01 to 0.5 ml·min−1 were conducted. The viscous fingering phenomena were captured and analyzed qualitatively and quantitatively. As capillary number increases, more unstable interfaces and complicated finger structures were visually observed and validated through fractal dimension analysis. These experimental results are in well agreement with previously reported results obtained from Hele-Shaw models and micromodels. The dimensionless number (Ca*µr2) analysis suggests viscosity has a greater effect on viscous fingering compared with injection rate, which was consistent with the conclusion of micromodel studies. Besides critical injection rate (0.01–0.05 ml∙min−1), increasing the viscosity ratio to a critical viscosity ratio (2946) leads to a significant decrease of breakthrough time, which was not reported in the literature. And different from linear displacement in which the viscous fingering followings two stages, additional pseudo-stable displacement could be generated after the rapid finger generation stage and combination stage for the radial displacement.

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.

Comparison of an Experimental Electrolyte Wetting of a Lithium-Ion Battery Anode and Separator by a Lattice Boltzmann Simulation

The filling with electrolyte and the subsequent wetting of the electrodes is a quality-critical and time-intensive process in the manufacturing of lithium-ion batteries. The exact processes involved in the wetting are still under investigation due to their poor accessibility. The accurate replication of the wetting phenomena in porous media can be demonstrated in other research fields by lattice Boltzmann simulations. Therefore, this paper deals with the comparison of experimental wetting and the simulative investigation of the wetting processes of lithium-ion battery materials by a lattice Boltzmann simulation. Particular attention is paid to the interfaces between the battery materials. These effects are relevant for a simulation of the wetting properties at the cell level. The experimental results show a 43% faster wetting of the interface between an anode and a separator than with only an anode. Overall, the simulation results show a qualitatively successful reproduction of the experimental wetting phenomena. In addition, the steps for a more precise simulation and the development of the Digital Twin are shown. This extension enables simulations of the electrolyte wetting phenomena in manufacturing lithium-ion batteries and the quantification of the wetting times.

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.

Stability analysis of MHD radiative mixed convective flow in vertical cylindrical annulus: Thermal nonequilibrium approach

AbstractIn the present study, the influence of the induced magnetic field on the MHD mixed convective electrically conducting fluid flow inside the vertical cylindrical annulus is analyzed numerically. The heat transfer is presumed to be due to a combination of mixed convection and radiation. The stability of the flow is examined when the solid and fluid phases are not in local thermal equilibrium. The governing equations are solved numerically by both finite difference and finite element methods. To control the flow formation rate more accurately the induced magnetic field is also considered in this study. As the magnetic Prandtl number (Pm) and Hartmann number (M) get enhanced, the velocity and induced magnetic fields get retarded in the annulus due to the presence of drag‐like force, namely, the Lorentz force. When there is an increase in the mixed convection parameter the induced magnetic field gets enhanced. An increase in radiation parameter tends to decline the fluid temperature and reverse the behavior of the solid temperature. Increment in Pm decreases the wall shear stress near the conducting cylinder. Increasing values of porous, magnetic, and radiation parameters lead to an unstable system with smaller heat transfer coefficient values but the system gets stabilized for larger values of heat transfer coefficient. The results could be used as first‐hand information for comprehending and developing the thermal flow phenomenon in porous media. The obtained numerical results are in good accordance with the existing results. Using an artificial neural network, heat transfer characteristics are analyzed through mean square error and regression analysis.

Active control of electro-visco-fingering in Hele-Shaw cells using Maxwell stress

SummaryViscous fingering is an extensively observed phenomenon in porous media or Hele-Shaw cells. In general, this instability is particularly difficult to control for given fluids and geometries. Therefore, investigating a control method of viscous fingering is quite attractive. Here, we present that electro-visco-fingering (EVF) in fluids with different relative permittivity shows a controllable performance under electric fields. The theoretical model is established from the perspective of force analysis to indicate that active control of EVF is achieved by the competition between the Maxwell stress jump and hydrostatic pressure gradient. In addition, an Electric Control number (EC) is adopted to characterize the electric effect on EVF and experimentally confirmed for broad ranges of flow rates and voltages. Unlike the electro-osmotic flow, this method shows a considerable achievement in energy efficiency. Our work provides a new way to actively control viscous fingering and opens new routes for applications of interfacial instabilities.

Study of the Imbibition Phenomenon in Porous Media by the Smoothed Particle Hydrodynamic (SPH) Method.

Over recent decades, studies in porous media have focused on many fields, typically in the development of oil and gas reservoirs. The imbibition phenomenon, a common mechanism affecting multi-phase flows in porous media, has shown more significant impacts on unconventional reservoir development, where the effect of the pore space increases with decreased pore sizes. In this paper, a comprehensive SPH method is applied, considering the binary interactions among the particles to study the imbibition phenomenon in porous media. The model is validated with physically meaningful results showing the effects of surface tension, contact angle, and pore structures. A heterogeneous porous medium is also constructed to study the effect of heterogeneity on the imbibition phenomenon; it can be referred from the results that the smaller pore throats and wetting surfaces are more preferred for the imbibition. The results show that the SPH method can be applied to solve the imbibition problems, but the unstable problem is still a sore point for the SPH method.

An analytical model for wicking in porous media based on statistical geometry theory

Abstract In this work, an analytical model describing liquid wicking phenomenon in porous media was constructed, based on the statistical geometry theory and the fractal theory. In the model, a new structure-property relationship, depicted by specific surface, porosity, tortuosity, pore fractal dimension, maximum pore size of the porous media, was introduced into the energy conservation equation. According to the theoretical model, the accumulated imbibition weight in porous media was achieved, and the predictions were verified by available experimental data published in different literatures. Besides, structure parameters influencing the imbibition process upon approaching equilibrium height were discussed. The model and results in this work are useful for the application of porous media in scientific research and industry.

A high-order finite-difference scheme for time-domain modeling of time-varying seismoelectric waves

Simulation of the seismoelectric effect serves as a useful tool to capture the observed seismoelectric conversion phenomenon in porous media, thus offering promising potential in underground exploration activities to detect pore fluids such as water, oil, and gas. The static electromagnetic (EM) approximation is among the most widely used methods for numerical simulation of the seismoelectric responses. However, the static approximation ignores the accompanying electric field generated by the shear wave, resulting in considerable errors when compared to analytical results, particularly under high-salinity conditions. To mitigate this problem, we have adopted a spatial high-order finite-difference time-domain method based on Maxwell’s full equations of time-varying EM fields to simulate the seismoelectric response in 2D mode. To improve the computational efficiency influenced by the velocity differences between seismic and EM waves, different time steps are set according to the stability conditions, and the seismic feedback values of EM time nodes are obtained by linear approximation within the seismic unit time step. To improve the simulation accuracy of the seismoelectric response with the time-varying EM calculation method, finite-difference coefficients are obtained by solving the spatial high-order difference approximation based on the Taylor expansion. Our method yields consistent simulation results compared to those obtained from the analytical method under different salinity conditions, thus indicating its validity for simulating seismoelectric responses in porous media. We further apply our method to layered and anomalous body models and extend our algorithm to three dimensions. Results indicate that the time-varying EM calculation method can effectively capture the reflection and transmission phenomena of the seismic and EM wavefields at the interfaces of contrasting media. This may allow for the identification of abnormal locations, thus highlighting the capability of seismoelectric response simulation to detect subsurface properties.