Porous Media Model Research Articles

Numerical Investigations on Wake Effects of Fish Cages

Abstract A typical fish farm in Norway usually consists of 6 to 12 fish cages, and these fish cages are moored together in a grid shape. Due to wake effects, individual fish cages may experience different flow velocities depending on their positions in the fish farm. Hereby, the drag forces on individual fish cages can be different. The drag forces on the downstream fish cages are difficult to be estimated without knowing the exact flow velocity, which will lead to challenges with the mooring system design. In this study, the computational fluid dynamic (CFD) method combined with a porous media model is employed to investigate the wake effects on the fish farm. The flow field through the fish cages and the drag forces on the downstream fish cages are investigated and discussed.

Application of the fast 3D simplified simulation method for the large CAP1400 nuclear island evaporator based on the coupled source term method

As for the evaporator of the large CAP1400 nuclear power plant, it has a large volume with numerous tubes along with the complex flow heat transfer phenomenon. The traditional direct simulation method usually takes a lot of time and computing resources to obtain the flow heat transfer data. To solve the problem, a fast simulation method established on the porous medium source term was herein proposed. In this simplified simulation method, the complex evaporator model is replaced with the porous medium model, where the derived heat and momentum source terms are added into the governing equation to control the heat flows. Five kinds of simplified evaporator models with different numbers of pipes were set to be the research objects, the internal flows inside the evaporator were studied with the traditional direct simulation method and the newly proposed simplified simulation method. Via comparative analysis, it can be found that: 1) The newly proposed simplified simulation method accurately captures the distribution characteristics of pressure, temperature, and entropy production in the evaporator, serving as a viable alternative to traditional direct simulation methods. Specifically, the average simulation errors for inlet-outlet pressure difference and temperature difference are both less than 5 % and 7 %, respectively. 2) The newly proposed simplified simulation method can capture the mutual interference effects between the evaporator and the nuclear main pump. When the evaporator is connected in series with the main nuclear pump, the average head of the main pump increases by 0.34 m, while the efficiency decreases by an average of 0.34 %. The average simulation errors of the simplified simulation method are 0.06 m and 0.13 %, respectively. 3) The application of the simplified simulation method leads to a significant 85 % decrease in the average computational cost for evaporator calculations and a notable 36 % decrease for combined calculations of the evaporator and main pump. The study here is expected to provide technique support for the simulation and evaluation of the large nuclear island.

Deriving an unsaturated hydraulic conductivity function based on ergun equation

Computational Fluid Dynamics (CFD) is a widely-used numerical technique for simulating flow phenomena, particularly unsaturated flow, which involves two-phase flow. This type of flow can be effectively modeled using the Volume of Fluid (VOF) method. The key to accurately depicting unsaturated flow is the unsaturated hydraulic function (K-function), which connects flow velocity to the hydraulic gradient. However, employing the VOF method alongside the commonly used Ergun equation for modeling porous media can result in an unrealistic K-function. This, in turn, often leads to unrepresentative models of unsaturated flow. This study focuses on determining the equivalent particle diameter, an essential factor in the Ergun equation, and uses this to derive an improved K-function. The modified K-function exhibits promising results, closely matching experimental data and outperforming other empirical methods. This improved function could enhance the description and simulation of unsaturated flows.

Evaporation in the presence of particles in a model porous medium: impact of corner liquid films

Evaporation in the presence of particles in a model porous medium: impact of corner liquid films

Sensitivity analysis of velocity field influence on condensers’ performance and parallel circuit design based on actual air velocity distribution

Currently, most integral simulations of condensers are based on the assumption of uniform intake air, which differs from real scenarios and leads to imprecise circuit designs. To obtain the actual air velocity distribution and reflect its impacts in the model, a comprehensive methodological system is established in this study. The implementation involves employing the porous media model to simulate air velocity distribution and utilizing the results as the air inlet condition of the distributed parameter model to achieve an integral simulation of condensers. The results indicate that the air velocity distribution is significantly non-uniform. The distribution of air velocity has a limited impact on the performance of single-row tube condenser, but has a significant effect on double-row tube condenser. Minimizing the discrepancy in the positioning of each sub-flow circuit and arranging tubes with large temperature differences in the high air velocity area can enhance heat transfer performance, the “z"-shaped double-tube parallel circuit designed by these theories can continue to improve the heat transfer performance by 2.8 % compared to the single-tube serial circuit with countercurrent arrangement within the accuracy limits of the simulations, and marking a 43.5 % improvement compared to the conventional zigzag-shaped single-tube serial circuit.

Upscaling reactive transport models from pore-scale to continuum-scale using deep learning method

Reactive transport modeling of subsurface environments plays an important role in addressing critical problems of geochemical processes, such as dissolution and precipitation of minerals. Current transport models for porous media span various scales, ranging from pore-scale to continuum-scale. In this study, we established an upscaling method connecting pore-scale and continuum-scale models by employing a deep learning methodology of Convolutional Neural Networks (CNNs). We applied Darcy-Brinkmann-Stokes (DBS) method to simulate the fluid flow and reactive transport in pore-scale models, which would act as constituents of a continuum-scale model. The datasets of spatial pore distribution of subvolume samples were used as the input for the deep learning model, and the continuum (Darcy)-scale parameters such as permeability, effective surface area, and effective diffusion coefficient were figured out as outputs (i.e., labels). By applying the trained models of the subvolumes in the entire sample volume, we generated the initial field of porosity, permeability, effective diffusion coefficient, and effective surface area for continuum-scale simulation of a mineral dissolution problem. We took an acid dissolution case as an example to utilize the outcomes of trained deep learning models as input data in the continuum-scale simulation. This work presents a comprehensive upscaling workflow, as bridging the findings of microscale simulations to the continuum-scale simulations of a reactive transport problem.

Numerical simulation of shelter effect assessment for single-row windbreaks on the periphery of oasis farmland

Dust storms, resulting from aeolian erosion, pose significant environmental hazards, while farmland is one of the main sources of dust storm release. An effective strategy to mitigate surface wind speed and curb dust emissions involves the establishment of windbreaks on the periphery of oasis farmland. This study conducts a series of numerical simulations using computational fluid dynamics (CFD) to explore the airflow fields around windbreaks with diverse systematic structural parameters, encompassing porosity, planting spacing, and fence effects. The main findings are as follows: (1) When the vegetation porosity is consistent (e.g., porosity α = 0.7, 0.8, and 0.9), exact geometry results can effectively reflect the distribution of wall shear stress, while the porous medium model overlooks these details. (2) The “Venturi effect” contributes to the acceleration of surface erosion and improper planting spacing results in an elevation of near-surface velocity. Planting spacing of 0.5 m demonstrates superior wind speed reduction performance, mitigating aeolian erosion and accumulation. (3) When the fence is positioned at l = 5h (h represents the height of the windbreaks), the flow field around the windbreaks is minimally influenced. The optimal placement distance for fences should be close to the windbreaks, featuring minimal porosity (l = 0 h, α = 0.1), extending the shelter distance from 3 to 4 h to 5–6 h. The research results can provide a theoretical basis for optimizing the plant configuration of biological desertification control and soil erosion control measures.

Numerical Study on Permeability of Reconstructed Porous Concrete Based on Lattice Boltzmann Method

The reconstruction of the porous media model is crucial for researching the mesoscopic seepage characteristics of porous concrete. Based on a self-compiled MATLAB program, a porous concrete model was modeled by controlling four parameters (distribution probability, growth probability, probability density, and porosity) with clear physical meanings using a quartet structure generation set (QSGS) along with the lattice Boltzmann method (LBM) to investigate permeability. The rationality of the numerical model was verified through Poiseuille flow theory. The results showed that the QSGS model exhibited varied pore shapes and disordered distributions, resembling real porous concrete. Seepage velocity distribution showed higher values in larger pores, with flow rates reaching up to 0.012 lattice point velocity. The permeability–porosity relationship demonstrated high linearity (the Pearson correlation coefficient is 0.92), consistent with real porous concrete behavior. The integration of QSGS-LBM represents a novel approach, and the research results can provide new ideas and new means for subsequent research on the permeability of porous concrete or similar porous medium materials.

Data-driven discovery of interpretable water retention models for deformable porous media

The water retention behavior—a critical factor of unsaturated flow in porous media—can be strongly affected by deformation in the solid matrix. However, it remains challenging to model the water retention behavior with explicit consideration of its dependence on deformation. Here, we propose a data-driven approach that can automatically discover an interpretable model describing the water retention behavior of a deformable porous material, which can be as accurate as non-interpretable models obtained by other data-driven approaches. Specifically, we present a divide-and-conquer approach for discovering a mathematical expression that best fits a neural network trained with the data collected from a series of image-based drainage simulations at the pore-scale. We validate the predictive capability of the symbolically regressed counterpart of the trained neural network against unseen pore-scale simulations. Further, through incorporating the discovered symbolic function into a continuum-scale simulation, we showcase the inherent portability of the proposed approach: The discovered water retention model can provide results comparable to those from a hierarchical multi-scale model, while bypassing the need for sub-scale simulations at individual material points.

A novel micro-scale structure reconstruction approach for porous media and characterization analysis: An application in ceramics-based diesel particulate filter

Diesel particulate filter (DPF) made from cordierite with a porous filter media structure has become an essential component in diesel engines to meet the increasingly the strict emission standards. Hence, a more accurate and universal DPF porous filter media model is necessary to analyze the complex mechanism and optimize its performance. In this work, a new optimization method was proposed for the initial DPF model constructed by the quartet structure generation set (QSGS), and the fractal and spectral dimension were used to quantify the actual effects of the optimized DPF model. Results showed that the method could effectively repair dead zones and eliminate burr boundaries, thus decreasing the complexity of the pore structure and increasing the effective flow area of the DPF model. The increase in porosity decreased the fractal dimension and increased the spectral dimension in porous media. Additionally, simulation results showed that the proposed method was more effective on burr boundaries. This allows the optimization method to be adopted more effectively in porous media modeling and provides improved guidance for optimization. Not only DPF, the proposed method offers a new idea for the structure optimization of porous filter media.

Modeling of Chemical Tracers for Two-Phase Flow in Advective-Dominated Porous Media at Core Scale

Summary Chemical tracer modeling in porous media plays a key role in subsurface applications including oil recovery, aquifer remediation, and geothermal energy production. In oil reservoirs, chemical tracers are critical to quantifying the remaining oil saturation in porous media after displacing processes, enabling the correct evaluation of the sweep efficiency of recovery methods at the field scale. Even though the transport of solutes under single-phase flow has been modeled extensively with numerous solutions, there are no existing mathematical approaches to examine the displacement of solutes in two-phase flow conditions. Therefore, we present in this research work the first analytical solutions derived to model the transport of ideal and partitioning tracers in porous media with mobile water and oil phases. The models presented are derived from the classic study of fluid displacement by viscous forces and the analysis of dynamic phase distribution in porous media, where key transformation variables are introduced to simplify the nonlinear advection-dispersion equation (ADE) into a conventional partial differential expression. In our derivation process, it is recognized that the dispersion effect can be superimposed onto an ideal concentration front via a singular perturbation expansion, resulting in practical solutions that do not require complex numerical calculations or inversion methods. The solutions derived are verified with numerical simulations and validated with experimental data under different flow conditions for the transport of ideal and partitioning tracers, demonstrating that the complex mechanisms of hydrodynamic dispersion, partitioning, and adsorption are accurately modeled under two-phase flow. Thus, our solutions can be used to rapidly evaluate tracer transport under the existing flow conditions in porous media, significantly reducing the number of experiments and simulations to characterize and select the correct tracer to be used in field applications.

Hydraulic tortuosity of porous media: comparison of different modeling methods

Abstract Hydraulic tortuosity is a crucial parameter affecting the movement of fluid in porous media. Currently, researchers have used different methods to construct porous media models and studied the variation of hydraulic tortuosity with porosity. In this paper, we use Monte Carlo random particle, quartet structure generation set (QSGS), and CT-scan reconstruction to construct porous media models with different porosity. The finite element method is used to simulate the fluid passing through the models. The effectiveness of the QSGS algorithm in constructing porous media is verified. The hydraulic tortuosity of the three types of model is computed using the streamline length ratio method, and its variation law with porosity is explored. The results show that the change law of the three models is consistent. The law of power function change is satisfied between the two for all models, which means the increase in porosity causes a decrease in tortuosity. Different models are constructed to explore the effect of tortuosity on permeability. An increase in tortuosity results in a smaller permeability when other conditions are equal. This paper aims to provide effective methods for constructing porous media models and a reference for studying hydraulic tortuosity.

Shear Banding and Cracking in Unsaturated Porous Media through a Nonlocal THM Meshfree Paradigm

The mechanical behavior of unsaturated porous media under non-isothermal conditions plays a vital role in geo-hazards and geo-energy engineering (e.g., landslides triggered by fire and geothermal energy harvest and foundations). Temperature increase can trigger localized failure and cracking in unsaturated porous media. This article investigates the shear banding and cracking in unsaturated porous media under non-isothermal conditions through a thermo–hydro–mechanical (THM) periporomechanics (PPM) paradigm. PPM is a nonlocal formulation of classical poromechanics using integral equations, which is robust in simulating continuous and discontinuous deformation in porous media. As a new contribution, we formulate a nonlocal THM constitutive model for unsaturated porous media in the PPM paradigm in this study. The THM meshfree paradigm is implemented through an explicit Lagrangian meshfree algorithm. The return mapping algorithm is used to implement the nonlocal THM constitutive model numerically. Numerical examples are presented to assess the capability of the proposed THM mesh-free paradigm for modeling shear banding and cracking in unsaturated porous media under non-isothermal conditions. The numerical results are examined to study the effect of temperature variations on the formation of shear banding and cracking in unsaturated porous media.

Scour mechanism around a pipeline under different current-wave conditions using the CFD-DEM coupling model

Understanding the pipeline scour mechanism under different conditions is essential for protection measures. The computational fluid dynamics (CFD) and discrete element method (DEM) are coupled for the simulations. To reduce the computational effort, the coarse-grained method is applied, and the Darcy-Forchheimer porous model is used to replace the far field elements. Both of the porous medium and particles-fluid interaction model are validated by comparison between simulation results and theories. The scouring simulation results show a good agreement with the experiments conducted with single-diameter spherical particles under different current-wave conditions. Further, the flow around the pipeline, the seepage in the sediment bed and the force acting on the particles are analyzed. The vortex shedding exists downstream under current but the vortex moves around under waves. The seepage depends on the pressure, influenced by the pipeline and the water depth, and the variation of the seepage is discussed. The force acting on the particles is not uniform along bed and the distribution is analyzed.This paper provides an insight into scour mechanics from the aspects including seepage and flow-particle interaction. Different methods are used for modification, giving a reference for the usage of CFD-DEM model in the analysis of scour process.

Partitioned analysis of acoustic fluid–solid-saturated porous medium interaction problems by a generalized saturated porous medium model and localized Lagrange multipliers

A partitioned formulation of acoustic fluid–solid-saturated porous medium interaction problems is presented based on a generalized saturated porous medium (GSPM) model and a new localized Lagrange multiplier (LLM) method. In this formula, all various media are modeled as the GSPM and a novel, powerful continuous condition is proposed for the interaction interfaces. This condition applies not only to interfaces of two partitions but also to intersections of simultaneous interactions of any number of media with different porosities. A (u, p) frame is introduced between partitions and the LLM fields are used to connect partitions with the frame. Furthermore, finite element spatial discretization and time integration strategies are provided for both matching meshes and nonmatching meshes. This partitioned formulation is validated numerically by computing the dynamic response of a horizontally layered seawater-seabed-bedrock model subjected to plane waves. The application scenarios for this method include, but are not limited to, the dynamic coupling analysis of marine engineering structures and hydraulic engineering structures. Future work will present and discuss a set of benchmarks and applications that involve the responses of existing dams to seismic excitation.

Sodium chloride crystallization in a model porous medium during drying with a receding sharp front

Visualization experiments in a model porous medium are presented in this work to study the interplay between salt precipitation and gas–liquid displacement during evaporation for the drying situation characterized by a receding sharp drying front. Various types of salt subflorescence are distinguished depending on the location of the subflorescence growth, namely, away from the drying front in the region predominantly occupied by gas or in the liquid-saturated region. A distinction is also made regarding the subflorescence that develops in the predominantly gaseous region depending on the degree of occupation of the pores by the subflorescence structure. The experiment confirms that the capillary liquid films can be a pathway for the dissolved salt transport. As a result of the capillary film effect, the evaporation front must be distinguished from the drying front and subflorescence structures can develop in the vicinity of the evaporation front away from the drying front. It is also shown that the pinning of the evaporation front leads to an anomalous drying front kinetics with a drying front position varying linearly with time and not according to the classical scaling with the square root of time.

Flow field analysis of cigarette filter through micro-CT-based geometries and CFD simulation

The cigarette filter is an essential component of modern cigarettes and studying the flow distribution within the cigarette filter is of great significance in reducing the harm of cigarettes and optimizing smoking sensations. As the object of numerical simulation research, a three-dimensional model of the cigarette was accurately constructed through micro-CT reverse engineering, achieving a scanning accuracy of 4.05 μm. An overall porous media model of the cigarette filter was established to characterize the pressure distribution inside the filter. Based on the three-dimensional reconstruction, a local simulation model of the cavity-filtered filter was created by extracting a 1/36 geometric model. The simulation results of the overall porous media model of the cigarette filter were used as the pressure boundary conditions for the local simulation model of the cavity-filtered filter, and the effects of the wrapped paper and cavity on the flow field were analyzed. The results show that the simulated pressure drop in the overall porous media model of the cigarette filter had a deviation of less than 3.5% compared to the experimental results. This suggests that the porous media model can effectively predict the changes in pressure drop within the filter. When both wrapped paper and cavity were present, the velocity at the interface between acetate fiber and wrapped paper increased by 141.54%, while the pressure approached 0 Pa. Similarly, at the interface between acetate fiber and cavity, the velocity increased by 130.77%. It indicates that both wrapped paper and cavity significantly influenced the flow field characteristics within the cigarette filter. Additionally, as the porosity of the wrapped paper gradually increased from 0.69 to 0.99 in the radial direction, the fluid velocity increased by 14.46%, while the fluid pressure decreased by 29.09%. These changes were particularly evident when the porosity was below 0.87.

Pore-Scale Modeling of Pressure-Driven Flow and Spontaneous Imbibition in Fracturing-Shut-In-Flowback Process of Tight Oil Reservoirs

Tight oil reservoirs are characterized by multiple pore spaces where nano-micropores and multiscale fractures coexist, and each type of medium varies in scale, implying a tight coupling of multiscale fractures with matrix and giving rise to extremely complicated flow patterns. To further investigate its flow mechanism, we first construct three two-dimensional (2-D) fracture-pore geometry models based on microfocus computed tomography (CT) imaging of a typical tight rock. A pore-scale modeling workflow is thereafter developed using the Shan-Chen lattice Boltzmann model (SC-LBM) to simulate the pressure-driven flow and spontaneous imbibition. The influence of fracture-pore geometry on the pore-scale fluid exchange dynamics in the fracturing-shut-in-flowback process is clearly clarified. Results show that, for the porous medium model without fracture, the fracturing fluid can displace and replace some crude oil by spontaneous imbibition while a large amount of crude oil droplets remains unexploited away from the oil/water contact line, resulting in a low oil imbibition recovery. The injected fracturing fluid migrates into the deep position along the fractures, only a few entering the matrix pore space near the fractures. Small pores are the main channel for fracturing fluid to imbibe into the matrix pores, and the replaced crude oil droplets flow into fractures through large pores as intermittent or continuous pipe flow. The complexity of fracture network typically exerts a significant impact on the fluid exchange dynamics during pressure-driven flow and spontaneous imbibition. The more complex the fracture network, the larger the volume of fracturing fluid injected, the easier for oil droplets replaced from the matrix pores, and the more difficult for the flowback of fracturing fluid in the fracture-pore geometry model. Our understanding will provide a basis for explaining the underlying mechanisms of oil replacement by pressure-driven flow and spontaneous imbibition in the fracturing-shut-in-flowback process.

Experimental Study of Hydrogen Synthesis under Conditions of a Natural Gas Reservoir

This research discusses issues related to hydrogen production, a promising source of “green” energy. Various methods of hydrogen production are considered, along with a new technology for hydrogen synthesis in natural gas reservoirs that has never been implemented before. At the same time, existing published experimental studies indicate a high probability of hydrogen synthesis when steam is injected into oil reservoirs. However, considering that oil is the primary raw material for hydrogen generation, there is high uncertainty about the success of the process in natural gas fields in the absence of residual oil. The experimental study presented in this work aims to justify the possibility of hydrogen synthesis under conditions of a natural gas reservoir. Specially designed reactors filled with different models of porous media, including the rock of a real gas field, are used for the physical modeling of the process. The process simulates injecting steam into a preheated porous medium mixed with hydrocarbon gas, specifically methane, at a reservoir pressure of 80 atm. The main variable parameters, aside from the type of porous medium, are the temperature and the steam-to-methane ratio in the system. The article presents the results of a series of nine experiments. The gas products were analyzed using a gas chromatograph. At the same time, the properties of rock samples were investigated after each experiment. The results of the experiments reveal patterns of concentration of hydrogen produced depending on the parameters, indicating the high potential of hydrogen synthesis technology under reservoir conditions in natural gas fields.

Thermal Management for a Stadium Power Supply Container Using a Rack-Level Air Cooling Strategy

This study investigates the airflow and thermal management of a compact electric energy storage system by using computational fluid dynamic (CFD) simulation. A porous medium model for predicting the flow resistance performance of the battery modules in a battery cabinet is developed. By studying the influence of rack shapes, the effects of heat exchanger arrangements and other parameters on the airflow and battery thermal distribution are analyzed. When applying a larger bottom air channel, the inlet flow uniformity of each battery cabin in the cabinet increases by 5%. Meanwhile, temperature standard deviation decreases by 0.18 while raising the flow rate from 3 m/s to 8 m/s, indicating better temperature uniformity in the battery cabin. When the charge–discharge ratio reaches 0.5 C, the temperature deviation of the entire cabinet significantly increases, reaching 8 K. Furthermore, a rack-level thermal management scheme is proposed to effectively reduce the thermal deviation of the container electric energy storage system and improve the overall temperature uniformity. Results reveal that the rack-level thermal management of the wavy cabinet in the electric storage container can effectively improve the thermal uniformity of the distributed battery cabin, and the overall thermal deviation is controlled within 1.0 K.