Porous Media Model Research Articles

CFD modeling of gas–solid flow in a two‐stage jetting fluidized bed with an overflow standpipe

AbstractThe two‐fluid model–kinetic theory of granular flow (TFM–KTGF) model and the sub‐grid‐scale (SGS) model are used to conduct a three‐dimensional numerical simulation study on the hydrodynamic characteristics of a two‐stage fluidized bed with an integrated overflow pipe. Using various drag models, the gas–solid flows, bed expansions, pressure drop distributions, and equilibrium conditions in the two‐stage bed are compared, and the conditions for the formation of a stable overflow in the two‐stage bed are thoroughly investigated. In addition, during the simulation of the secondary distribution in the bed, the porous media model simulates the momentum loss caused by the redistribution plate to avoid the direct simulation of the redistribution plate, which requires extensive grid division work and calculation costs. This work can provide technical direction for the industrialization of one‐step coal to multistage fluidized bed natural gas technology.

Axial Flow Fan Performance in a Forced Draught Air-Cooled Heat Exchanger for a Supercritical Carbon Dioxide Brayton Cycle

Abstract An axial flow cooling fan has been designed for use in a concentrated solar power plant. The plant is based on a supercritical carbon dioxide (sCO2) Brayton cycle, and uses a forced draft air-cooled heat exchanger (ACHE) for cooling. The fan performance has been investigated using both computational fluid dynamics (CFD) and scaled fan tests. This paper presents a CFD model that integrates the fan with the heat exchanger. The objective is to establish a foundation for similar models and to contribute to the development of efficient ACHE units designed for sCO2 power cycles. The finned-tube bundle is simplified, with a Porous Media Model representing the pressure drop through the bundle. Pressure inlet and -outlet boundary conditions are used, meaning the air flowrate is solved based on the fan and tube bundle interaction. The flowrate predicted by the CFD model is 0.5% higher than the analytical prediction, and 3.6% lower than the design value, demonstrating that the assumptions used in the design procedure are reasonable. The plenum height is also found to affect the flowrate, with shorter plenums resulting in higher flow rates and fan efficiencies, and longer plenums resulting in more uniform cooling air flow.

Analytical prediction of the formation factor for anisotropic mono-sized unconsolidated porous media

The rectangular Representative Unit Cell (RUC) models for mono-sized isotropic unconsolidated porous media have been extended to anisotropic media. Volume averaging was applied to Ohm's law in order to propose analytical expressions for the formation factor for electrical conduction in terms of the pore-scale linear dimensions. The formation factor, crucial for understanding electrical conduction in porous media, has significant applications in subsurface geophysics, petroleum reservoir characterization, and the durability assessment of construction materials. These analytical models provide valuable insights for optimizing the electrical properties of porous structures in various engineering fields, for example in mapping groundwater resources, differentiating oil-bearing zones in reservoirs, and predicting ion migration in concrete. Aspect ratios of the cell and solid dimensions have been introduced, and the formation factor expressed in terms thereof for five different arrays, i.e. a regular, a non-overlapping streamwisely fully staggered, an overlapping streamwisely fully staggered, a non-overlapping transversally fully staggered, and an overlapping transversally fully staggered array. The Laplace equation has furthermore been solved numerically for two-dimensional versions of the different arrays and the formation factor computed for several values of the aspect ratios. The proposed analytical models have been validated against the generated numerical data and compared to experimental and numerical data obtained from the literature. The proposed models have also been adapted to include a percolation threshold porosity in order to improve the model predictions for very low porosity media.

Electrical conductivity model for reactive porous media under partially saturated conditions with hysteresis effects

The electrical conductivity of a porous medium is strongly controlled by the structure of the medium at the microscale as the pore configuration governs the distribution of the conductive fluid. The pore structure thus plays a key role since different geometries translate in variations of the fluid distribution, causing different behaviors measurable at the macroscale. In this study, we present a new physically-based analytical model derived under the assumption that the pore structure can be represented by a bundle of tortuous capillary tubes with periodic variations of their radius and a fractal distribution of pore sizes. By upscaling the microscale properties of the porous medium, we obtain expressions to estimate the total and relative electrical conductivity. The proposed pore geometry allows us to include the hysteresis phenomenon in the electrical conductivity estimates. The variations on these estimates caused by pore structure changes due to reactive processes are accounted by assuming a uniform dissolution of the pores. Under this hypothesis, we describe the evolution of the electrical conductivity during reactive processes. The expressions of the proposed model have been tested with published data from different soil textures, showing a satisfactory agreement with the experimental data. Hysteretic behavior and mineral dissolution are also successfully addressed. By including hysteresis and mineral dissolution/precipitation in the estimates of the electrical conductivity, this new analytical model presents an improvement as it relates those macroscopic physical phenomena to its origins at the microscale. This opens up exciting possibilities for studies involving electrical conductivity measurements to monitor water movement, and hysteretic and reactive processes in porous media.

Stress sensitivity analysis of vuggy porous media based on two-scale fractal theory

Interparticle pore space and vugs are two different scales of pore space in vuggy porous media. Vuggy porous media widely exists in carbonate reservoirs, and the permeability of this porous media plays an important role in many engineering fields. It has been shown that the change of effective stress has important effects on the permeability of vuggy porous media. In this work, a fractal permeability model for vuggy porous media is developed based on the fractal theory and elastic mechanics. Besides, a Monte Carlo simulation is also implemented to obtain feasible values of permeability. The proposed model can predict the elastic deformation of the fractal vuggy porous media under loading stress, which plays a crucial role in the variations of permeability. The predicted permeability data based on the present fractal model are compared with experimental data, which verifies the validity of the present fractal permeability model for vuggy porous media. The parameter sensitivity analysis indicates that the permeability of stress-sensitivity vuggy porous media is related to the capillary fractal dimension, capillary fractal tortuosity dimension, Young’s modulus, and Poisson’s ratio.

Solutions for a flame propagation model in porous media based on Hamiltonian and regular perturbation methods

This article extends the exploration of solutions to the issue of flame propagation driven by pressure and temperature in porous media that we introduced in earlier papers. We continue to consider a p-Laplacian type operator as a mathematical formalism to model slow and fast diffusion effects, that can be given in the non-homogeneous propagation of flames. In addition, we introduce a forced convection to model any possible induced flow in the porous media. We depart from previously known models to further substantiate our driving equations. From a mathematical standpoint, our goal is to deepen in the understanding of the general behavior of solutions via analyzing their regularity, boundedness, and uniqueness. We explore stationary solutions through a Hamiltonian approach and employ a regular perturbation method. Subsequently, nonstationary solutions are derived using a singular exponential scaling and, once more, a regular perturbation approach.

Fractal permeability model for power-law fluids in embedded tree-like branching networks based on the fractional-derivative theory

The investigation of permeability in tree-like branching networks has attracted widespread attention. However, most studies about fractal models for predicting permeability in tree-like branching networks include empirical constants. This paper investigates the flow characteristics of power-law fluids in the dual porosity model of porous media in embedded tree-like branching networks. Considering the inherent properties of power-law fluids, non-Newtonian behavior effects, and fractal properties of porous media, a power-law fluids rheological equation is introduced based on the fractional-derivative theory and fractal theory. Then, an analytical formula for predicting the effective permeability of power-law fluids in dual porous media is derived. This analytical formula indicates the influences of fractal dimensions and structural parameters on permeability. With increasing length ratio, bifurcation series, and bifurcation angle, as well as decreasing power-law exponent and diameter ratio, the effective permeability decreases to varying degrees. The derived analytical model does not include empirical constants and is consistent with the non-Newtonian properties of power-law fluids, indicating that the model is an effective method for describing the flow process of complex non-Newtonian fluids in porous media in natural systems and engineering. Therefore, this study is of great significance to derive analytical solutions for the permeability of power-law fluids in embedded tree-like bifurcation networks.

Building a physics-based virtual refrigerated container filled with fruit in ventilated packaging

We build a validated physics-based model of a refrigerated container filled with fruit in ventilated packaging. This model of a virtual container is the basis for simulations in an accompanying paper on citrus fruit shipped overseas from South Africa to Europe. The model is used to understand better how the cargo cools and when and where food quality is lost in these supply chains. We build a computational fluid dynamics model with a two-phase porous media approach that simulates the airflow in the container and the cooling process of every fruit. This container can be considered aerodynamically to be a slot-ventilated enclosure. We also model the fruit's thermally-driven quality loss. Using a two-phase porous media approach for the ventilated cargo and modeling temperature-driven fruit quality evolution are two steps forward compared to most existing physics-based refrigerated container models. We validate the porous media model implementation. We define and apply actionable metrics for every fruit inside the cargo, such as remaining shelf life upon arrival and seven-eighths cooling time.• This model can help reduce food loss and increase supply-chain resilience• This model is an essential building block of a refrigerated container's digital twin• This model can support stakeholders in improving cargo temperature control and resulting fruit quality preservation.

Machine-learning aided calibration and analysis of porous media CFD models used for rotating packed beds

The proposed research is an attempt to advance the state-of-the-art of the numerical modelling of RPB by combining Computational Fluid Dynamics and Machine Learning approaches. The latter creates an accurate framework that should help quantify the potential of Rotating Packed Beds (RPB) technology to intensify conventional CO2 capture processes. To this end, a direct sensitivity analysis is detailed to supplement a machine-learning (ML) algorithm built for calibrating resistance coefficients needed for porous media modelling. The algorithm is used to improve CFD predictions of dry pressure drop in rotating packed beds (RPBs) for a wide range of operating conditions. The sensitivity derivatives with respect to the packing resistance coefficients are demonstrated for the first time in RPBs, which is not available in the current CFD open source and commercial codes. In this regard, sensitivity differential equations are derived from three-dimensional Navier-Stokes equations for porous media in a rotating reference frame. These sensitivity equations are discretized using a finite volume scheme and solved to obtain the sensitivity pressure drop differences at the packing edges. The results are validated against the predictions of the analytical sensitivity analysis and the finite difference approximation. After, the Newton – Gauss method that employs the sensitivity pressure drop derivatives, is used to minimize the error (cost function) between the pressure drop obtained from CFD simulations and the available experimental data. This is achieved by tuning the packing resistance coefficients to the RBPs' operating conditions (gas flowrate and rotating speed) and correlate them using an artificial neural network (ANN). The results of the proposed approach show a significant improvement in porous media-based CFD predictions of RPBs' pressure drop across a wide range of operating conditions and this over conventional porous media-based CFD models. This is necessary for CFD models to be reliably used as a tool that can efficiently improve existing RPBs' designs and/or participate in RPBs' design innovation.

Numerical study and experimental validation of a porous biochar supported form stable composite for thermal energy storage

This study numerically investigates the performance of the melting process for a biochar-based phase change material latent heat energy storage system. The melting processes of a composite made from softwood biochar combined with paraffin RT28, were compared numerically using the equilibrium porous medium model in ANSYS Fluent. The set up was validated through results from previous literature and experimental work. The enhancement in melting was compared to the pure PCM melting scenario and the effects of different paraffins, boundary conditions and inclination angle were investigated for real world application. Softwood biochar composites significantly surpass the performance of paraffin alone, reducing the melting time by 79 %. Different paraffins within the softwood composite produced different melting times, ranging from 2565 s to 4790 s. In terms of inclination angle adjusting to 90° produced steadier heating and reduced the melting time by 63 % in the composite. These findings offer insights into optimising latent heat thermal energy storage systems for improved performance and reduced energy wastage, highlighting the potential of biochar composites in sustainable energy solutions.

Inhomogeneous Fluid Transport Modeling in Dual-Scale Porous Media Considering Fluid-Solid Interactions.

Dynamics of fluid transport in ultratight reservoirs such as organic-rich shales differ from those in high-permeable reservoirs due to the complex nature of fluid transport and fluid-solid interaction in nanopores. We present a multiphase multicomponent transport model for primary production and gas injection in shale, considering the dual-scale porosity and intricate fluid-solid interactions. The pore space in the shale matrix is divided into macropores and nanopores based on pore size distribution. We employ density functional theory (DFT) to account for fluid-solid interactions and to compute the inhomogeneous fluid density distribution and phase behavior within a dual-scale matrix. The calculated fluid thermodynamic properties and transmissibility values are then integrated into the multiphase multicomponent transport model grounded in Maxwell-Stefan theory to simulate primary oil production from and gas injection into organic-rich shales. Our findings highlight DFT's adeptness in detailing the complex fluid inhomogeneities within nanopores─a critical concept that a cubic equation of state does not capture. Fluids within pores are categorized into confined and bulk states, restricted by a threshold pore width of 30 nm. Different compositions of fluid mixtures are observed in macropores and nanopores: heavier hydrocarbon components preferentially accumulate in nanopores due to their strong fluid-solid interactions. We utilize the developed model to simulate hydrocarbon production from an organic-rich shale matrix as well as CO2 injection into the matrix. During primary hydrocarbon production, strong fluid-solid interactions in nanopores impede the mobility of heavy components in the near-wall region, leading to their confinement. Consequently, heavy components mostly remain within the nanopores in the shale matrix during primary hydrocarbon production. During the CO2 injection process, the injected CO2 alters fluid composition within macropores and nanopores, promoting fluid redistribution. Injected CO2 engages in competitive fluid-solid interactions against intermediate hydrocarbons, successfully displacing a considerable number of these hydrocarbons from the nanopores.

Numerical study on the flow characteristics of an integrated fish cage based on the monopile offshore wind turbine foundation

The integration of net cages and offshore wind turbines can effectively develop and utilize marine resources and is one of the important ways of intensive use of the sea. The numerical simulation of the hydrodynamics of an integrated fish cage based on the monopile offshore wind turbine foundation in currents is carried out. The realizable k-ε model is adopted and the porous media model is used to simulate the net. To verify the validity of the numerical model, the numerical result is compared with the data of the corresponding literature. The results show that the numerical method is effective. On this basis, the flow field distribution results of the integrated structure at different velocities are calculated. At the center of the downstream zone of the integrated structure, the time-average velocity is lower than 80 % of the initial velocity. The effects of the net solidity and the cage draught on the flow field characteristics of the integrated structure are analyzed. The results show that the increase of net solidity will significantly reduce the velocity inside the net cage and in the downstream zone of the cage. As the net solidity increases from 0.14 to 0.32, the average velocity attenuation inside the net cage increased by 13.9 %. The change of cage draught will affect the velocity distribution in the horizontal and vertical directions. When the cage draught increases, the velocity on both sides in the downstream zone of the integrated structure increases more than 5 %. It is expected that the results of this study can provide data support for the design of integrated structure of net cages and offshore wind turbines.

Numerical Study on Effects of Nanoparticles Concentration and Steam Flow Rate on Oil Recovery from a Model Porous Medium

AbstractEffects of nanoparticle and steam injection on the extraction of Iranian American Petroleum Institute (API) 14 heavy oil from a model porous medium at temperatures of 110, 150, and 200 °C were investigated. Nanoparticle content was 1 %, 3 %, and 5 %, and injection flow rates were 0.018, 0.036 and 0.072 mL h−1. In short‐term injection, increasing the injection temperature to 200 °C and the flow rate to 0.072 mL h−1 resulted in the highest recovery. In the mid‐term injection, the highest recovery factor was at a temperature of 150 °C and flow rate of 0.036 mL h−1, while the results of the long‐term injection predicted a non‐monotonic effect of flow rate. The effect of alumina content on the recovery factor is less than that of temperature and flow rate. Interestingly, alumina content also has non‐monotonic effects on the recovery factor.

Effect of Wettability and Permeability on Pore-Scale of CH4–Water Two-Phase Displacement Behavior in the Phase Field Model

Hydraulic measures such as hydraulic slotting and hydraulic fracturing are commonly used in coal seam pressure relief and permeability enhancement. Two-phase flow patterns of CH4–water in pore-sized coal seams after hydraulic measures are critical to improve gas extraction efficiency. The phase field module in COMSOL Multiphysics™ 5.4 and the classical ordered porous media model were used in this paper. The characteristics of CH4–water two-phase immiscible displacement in coal seams under different capillary numbers (Ca) and viscosity ratios (M) were simulated and quantitatively analyzed. By changing the contact angle of the porous media, the flow patterns of CH4–water two-phase in coal with different wettability were simulated. Results show that wettability significantly affects the displacement efficiency of CH4. Additionally, by constructing a dual-permeability model to simulate the varying local permeability of the coal, the flow patterns of different Ca and M in dual-permeability media were further investigated. It is found that CH4 preferentially invades high-permeability regions, and the displacement efficiency in low-permeability regions increases with higher Ca and M, providing a reference for gas extraction from coal seams after hydraulic measures.

Atomistic-to-continuum modeling of carbon foam: A new approach to finite element simulation

Carbon foam materials exhibit useful characteristics for unique and diverse applications. However, accurately modeling three-dimensional carbon foam remains a significant challenge. This paper introduces a novel technique for transitioning atomistic-scale models of porous carbon, obtained via molecular dynamics simulation, to continuum-scale carbon foam models suited for finite element simulations. We present our method using the fractal properties of porous media, specifically carbon foams. The resulting models demonstrate testable properties consistent with those derived from computed tomography (CT) scans and experimental data. Stress–strain curves obtained from finite element analysis (FEA) calculations of our models correlate well with experimental measurements from dogbone testing samples of carbon foam sourced from CONSOL Innovations LLC, WV, USA, as well as CT scan models derived from the carbon foams. Our approach presents a computationally efficient alternative and encourages innovation in modeling porous media, particularly in extracting physical properties from an ensemble of models.

Research on drying characteristics of corn kernel based on COMSOL porous media model

AbstractDrying is an effective way to solve corn mildew. The heat and humidity flow interface in COMSOL Multiphysics heat transfer module was used to coupling fluid flow, water transport and heat transfer in multiple physical fields, and corn was used as a porous medium for simulation analysis, aiming to find the change rules of temperature field and humidity field. The research shows that the multi‐component model and method should be given priority in practice. The higher the hot air temperature is, the higher the average temperature of corn kernels is, and the faster the relative humidity decreases. The drying rate of corn is the highest at 348 K, and the hot air temperature should be appropriately increased at 333 K denaturation temperature. The higher the wind speed, the better the drying effect of corn kernels, but the improvement of drying effect will decrease with the increase of wind speed. Appropriately increase the wind speed between 2 and 4 m/s to improve the drying efficiency while avoiding excessive energy consumption. The mass transfer resistance of the pericarp cannot be ignored. The drying time of corn kernels closer to the hot air entrance is shorter, and the corn kernels close to the hot air exit are prone to humidity accumulation. Multiple hot air intakes should be set up to reduce the occurrence of uneven drying.Practical applicationsCorn is prone to mildew after harvest, resulting in resource waste and economic loss, so it is of great significance to dry corn efficiently. Corn is a typical porous medium, and the research on it can provide the basis for drying other porous medium grains. According to different components, the model of single granule and multi‐granule was established respectively. Use COMSOL Multiphysics simulation software to gain a deeper understanding of the complex physical processes involved in the drying process and provide valuable insights for industrial applications. COMSOL software was used to study the drying condition of corn under the synergic action of multiple physical fields, and effective drying strategies and measures to improve the structure of air drying silo were put forward.

Characterization of pore model and percolation simulation of bulk grain pile porous media

AbstractTo ensure the quality of grain storage, researchers have developed a variety of models for the morphological structure of bulk grain piles. However, traditional characterization methods suffer from issues such as inaccurate models, limited size ranges, and low precision. In this study, x‐ray computed tomography was employed for the first time to capture real three‐dimensional (3D) images, revealing the surface porosity distribution ranging from 30% to 38% along the slice direction and a fractal dimension primarily distributed between 1.45 and 1.47. Moreover, the box counting method was used to determine the representative elementary volume (REV) comprising 600 × 600 × 600 pixels, effectively characterizing pore structure using porosity as an index. Connectivity analysis of the REV was conducted by integrating the refined central axis method and the 3D watershed algorithm. Equivalent diameters of connected pores were mainly distributed between 0.5 and 3.5 mm, with an average pore diameter of 2.22 ± 0.02 mm, an average coordination number of 7.04 ± 0.07, and an average tortuosity of 1.58 ± 0.01. Based on the characteristic parameters of connected pores, an equivalent pore network model (EPNM) was reconstructed for numerical simulation of single‐phase percolation of bulk grain pile. In addition, the constructed experimental platform demonstrates that the constructed EPNM closely corresponds to the real pore structure of the seed body, accurately reflecting pore–throat size, connectivity, and morphological characteristics within the grain pile. Furthermore, this research model can be applied to the study of gas flow, heat transfer, and mass transfer within porous media.

Dual scale porous medium model of lung congestion caused by tuberculosis

Dual scale porous medium model of lung congestion caused by tuberculosis

Numerical study of the particle-scale heat transfer in the HTR-PM pebble bed based on GPU-DEM

An essential aspect of the design of a pebble bed high-temperature gas-cooled reactor (HTGR) is the consideration of heat transfer. A particle-scale heat transfer model was developed based on the previous GPU-DEM numerical model. This model includes the heat conduction of the particles in contact, the radiative heat transfer among particles, and unidirectional convection heat transfer in the flow field. The comparison of the predicted results with the results of the TF-PBEC experiment demonstrates the accuracy of the conduction and radiation modules within the current model. Based on the current model and the porous media model, a numerical study of the natural convection heat transfer in the High-Temperature gas-cooled Reactor-Pebble-bed Module (HTR-PM) after reactor shutdown is performed. This paper systematically introduces the model design, pebble bed generation, flow field calculation, and heat transfer simulation. The results indicate that natural convection contributes to removing residual heat in the reactor core, and a higher pressure leads to better convection heat transfer. At extremely low Reynolds numbers (Re < 10), convection heat transfer is comparable to conduction and radiation, while for pressurized pebble beds (Re = 50–500), convection heat transfer dominates. Furthermore, the influence of different models used to calculate the Nusselt number of the results is compared and analyzed. For most cases, the differences in the temperature distribution of the pebble bed obtained from the different correlations are minor. However, the impact of porosity on the local Nusselt number cannot be ignored in the extremely low Reynolds numbers flows. Overall, the particle-scale heat transfer model can provide more effective reference information for the design and construction of an HTGR.

Numerical investigation to predict the impact of pre-heated air on the tar formation of cocoa pod husk gasification in a fixed bed downdraft gasifier

Tar production is a critical aspect of gasification thermochemistry, and it hinders the widening of biofuel utilisation in several applications. Both the gasifier configuration and the operating conditions influence the quantity of tar in PG. Since temperature plays a major role, this study examines the performance parameters of a gasifier across a spectrum of input air temperatures, from 27 to 627 °C, utilising computational fluid dynamics with species transport and porous media models. Since the deviation of numerical predictions from experimental results is within 10 %, the model's validity is confirmed. CO and H2 gas production increased from 19.23 % to 27.12 % and 9.23 %–16.2 %, respectively, over the tested air temperature range; however, the variation in methane content was not significant. Furthermore, the higher heating values of PG and cold gas efficiency were found to be 5–6.8 MJ/Nm3 and 65–69 %, respectively. The study also investigates reaction rates for gasification, combustion, and volatiles' breakdown under various operating conditions. Among the tar species studied, benzene is the most concentrated at 1.6 g/Nm3, followed by toluene at 0.9 g/Nm3, with naphthalene and phenol present in comparatively smaller amounts. Furthermore, the research indicates that an appropriate temperature of gasifying medium can control tar in PG.