Random Packing Research Articles

Efficient estimation of crystal filterability using the discrete element method and the Kozeny-Carman equation

A new method is proposed for efficiently predicting filter cake resistance as a function of crystal size distribution. The method is useful for the preliminary design of processes where an economic tradeoff is encountered between a crystallization step and a filtration step. In that case it is necessary to estimate the filter cake resistance repeatedly as a function of crystal size distribution for the process design and optimization. The method is faster than CFD-DEM and more precise than the random packing assumption. The proposed method is validated using published experimental data. To demonstrate the proposed method, an integrated crystallization-filtration process of ammonium alum is simulated and analyzed. The results show that by increasing the residence time of ammonium alum crystals in the crystallizer from 15 min to 60 min, the crystal cake resistance can be reduced by 42% and the filter area can be reduced by 23%.

ITZ volume fraction and thermal conductivity of concrete: A unified random packing model for gravels and crushed rocks

This work proposes a mesostructure-guided computational framework to evaluate the effective thermal conductivity (ETC) of concrete affected by aggregate and interfacial transition zone (ITZ) configurations at a mesoscopic scale. An unified aggregate shape descriptor for gravels and crushed rocks is characterized by superellipsoid covering from convexity to non-convexity, as well as random static and dynamic packings of superellipsoidal aggregates (SAs) are carried out to generate tri-phase concrete mesostructures consisting of homogeneous mortar, densely packed aggregates and their surrounding ITZs. A closed-form expression for the ITZ volume fraction is theoretically developed in the present concrete mesostructure, which is also validated using the one-point probability function simulation. Moreover, an optimized Browanian motion numerical strategy is developed to estimate the ETC of tri-phase concrete. This strategy is confirmed to be an accurate numerical technique by comparing against the Mori-Tanaka model. The present framework reveals the quantitative responses of various configurations on the ETC, which manifest rigorous “constituent-mesostructure-ETC” relations. The results are available for tailoring components to optimize ITZ structures for the improvement of thermal efficiency and durability of buildings.

Shear flow of non-Brownian rod-sphere mixtures near jamming.

We use the discrete element method, taking particle contact and hydrodynamic lubrication into account, to unveil the shear rheology of suspensions of frictionless non-Brownian rods in the dense packing fraction regime. We find that, analogously to the random close packing volume fraction, the shear-driven jamming point of this system varies in a nonmonotonic fashion as a function of the rod aspect ratio. The latter strongly influences how the addition of rodlike particles affects the rheological response of a suspension of frictionless non-Brownian spheres to an external shear flow. At fixed values of the total (rods plus spheres) packing fraction, the viscosity of the suspension is reduced by the addition of "short"(≤2) rods but is instead increased by the addition of "long"(≥2) rods. A mechanistic interpretation is provided in terms of packing and excluded-volume arguments.

Experimental investigation and modeling of the impact of random packings on mass transfer in fluidized beds

This study investigates the impact of two novel settings of bubbling fluidized beds equipped with random metal packings on the mass transfer. To do this, a comprehensive approach is applied that integrates experiments and modeling and explores the relevance of the different underlying mechanisms involved in interphase mass transfer in fluidized beds. Firstly, the mass transfer of water from moisturized silica gel particles to dry air is studied in both a packed-fluidized bed and a freely bubbling bed with no packing. The experimental set-up consists of a cylindrical bubbling fluidized-bed column with an inner diameter of 22 cm. Silica-gel particles with a mean particle diameter of 797 μm are used as bed material. The total bed amount ranges from 4 to 8 kg, while the fluidization number (F) varies between 1.7 and 2.3. Two types of packing, RMSR (stainless steel thread saddle rings) and Hiflow (stainless steel pall rings) are examined and compared to the reference case of a bubbling bed with no packing. The height of the packed section is maintained at 60 cm. The results show that, at all operating conditions, the use of packings enhances the amount of desorbed water in the fluidized bed. The increase is up to 17%, as compared to the bed without packing. The effect is believed to be inhibition of bubble growth in the packed-fluidized bed. To study this further, a mass-transfer model is introduced to analyze the different mass-transfer steps (intra-particle, particle surface to emulsion gas, and emulsion gas to bubble gas) in packed-fluidized beds compared to beds with no packing. TGA experiments are applied to describe the intra-particle mass transfer through a desorption kinetic model. Model analysis shows that the main resistance for mass transfer occurs across the bubble-emulsion boundary. The calculated value of the mass transfer coefficient for this, Kb, at reference conditions (6 kg of silica gel and F = 2.3) is 7.6e-5 s−1 with packings (in average) and 6.2e-5 s−1 without packings, i.e. a 23% improvement in the governing mass-transfer coefficient.

The Effect of Porous Media Grain Size on non-Darcy Flow Behavior using Pore Scale Simulation

The impact of grain size of the porous media of the 3D images of a beadpack on the permeability values and non-Darcy flow behaviour is analyzed using pore-scale flow modelling utilizing the finite volume method. In this study, the sample used was a 3D image from random tight packing of spheres (beadpack) with a size of 250×250×250 voxels and a porosity of 0.36. Variation in grain size is carried out by upscaling the 3D image sample, so that this treatment affects the specific surface area value but does not change the porosity and tortuosity of the sample. Several variations of grain diameter include 100 μm, 125 μm, 150 μm, 175 μm, and 200 μm. In this study, we adopted PIMPLE algorithm, which combines SIMPLE and PISO algorithms to accomplish the Navier-Stokes equations of fluid dynamics in such porous media. The simulation results show that the permeability value exhibits an inverse relationship with the specific surface area. This correlation is in accordance with the Kozeny-Carman equation. In addition, the initiation of non-Darcy flow occurs at the reference length-based Reynolds number of 2.06 and the permeability-based Reynolds number of 0.049.

Experimental and numerical investigation on agglomeration of aluminum during combustion process of aluminized composite propellant

The addition of aluminum particles can effectively improve the energy characteristics of solid composite propellants in propulsion systems. However, these aluminum particles affecting propellant mixture viscosity, ignition delay time, burning time and specific impulse could also lead to undesirable effects. Therefore, it is a general practice that in the early stage of propellant formulation design that the particle size of condensed phase products is optimized/minimized through formulation adjustment to reduce its negative impact on the engine. In practice, it means that a costly manpower and materials are needed to obtain the size distribution of condensed phase products during the combustion process of propellants via experimental tests. Thus, there is a strong industrial need for a reasonable and feasible simulation method of agglomeration process during the combustion process of propellants. In this work, we propose and examine the implementation of molecular dynamics and a random packing algorithm on creating numerically models of aluminized composite propellants. Considering the pyrolysis of ammonium perchlorate (AP) and the combustion process of aluminum, we develop a more accurate agglomeration model basing on the classical Jackson model. Our proposed methods and simulations models are validated by our experimental results. It confirms that the present work provides a prediction tool for simulating and improving the agglomeration process, thus aiming at optimizing solid propellant formula.

Properties of packings and dispersions of superellipse sector particles.

Superellipse sector particles (SeSPs) are segments of superelliptical curves that form a tunable set of hard-particle shapes for granular and colloidal systems. SeSPs allow for continuous parametrization of corner sharpness, aspect ratio, and particle curvature; rods, circles, rectangles, and staples are examples of shapes SeSPs can model. We compare three computational processes: pair-wise Monte Carlo simulations that explore particle-particle geometric constraints, Monte Carlo simulations that reveal how these geometric constraints play out over dispersions of many particles, and Molecular Dynamics simulations that form random loose and close packings. We investigate the dependence of critical random loose and close packing fractions on particle parameters, finding that both values increase with opening aperture and decrease with increasing corner sharpness. The identified packing fractions are compared with the mean-field prediction of the random contact model; we find deviations from the model's prediction due to correlations between particle orientations. The complex interaction of spatial proximity and orientational alignment is also explored with a generalized spatioorientational distribution area (SODA) plot, which shows how higher density packings are achieved through particles assuming a small number of preferred configurations that depend sensitively on particle shape and system preparation.

A micromechanical model for estimating the shear modulus and damping ratio of loose sands under low stresses. Application to a Mars regolith simulant

The dynamic properties of loose sands under low stresses have been poorly investigated because of the higher order of magnitude of stress levels in terrestrial geotechnical structures. However, low densities and low stresses prevail in the sandy surface deposits of some other rocky planets, making low stress conditions relevant for extra-terrestrial soil mechanics. This is the case of Mars, on the surface of which a seismometer has been placed during the InSight mission. In this context, a dynamic shear rheometer was used to measure the shear modulus and damping ratio of a Martian regolith simulant under very low stresses to improve the interpretation of the InSight dataset on surface materials. This paper also revisits the grain contact stiffness and the overall modulus of a random packing of identical spheres, based on the Hertz-Mindlin contact theory. A micromechanical model accounting for the effects of both grain roughness and slipping in the soil degradation curve is proposed. The results of the model show a good agreement with experimental data, capturing the non-linear transition from low to high-shear strains. The model hence provides a new framework for a better understanding of the behaviour of granular materials in low gravity (extra-terrestrial) conditions.

Advances in design, scale and operability of the Rotating Liquid Sheet (RLS) contactor: Pressure drop, flood-point and mass transfer – Comparison to random packing

The Rotating Liquid Sheet (RLS) contactor is a novel packing-less gas-liquid contactor where multiple continuous liquid sheets form at the outlet of helical slots in a rotating central feed tube. Each liquid sheet is auger-shaped, and the rotation of the feed tube transfers momentum from the sheets to the gas. Multiple sheets travel in parallel to arrive unbroken at the column wall. The gas travels through the space between adjacent sheets providing close contact between the gas and liquid. Careful design ensures that liquid sheets travel in parallel arcs, enabling scale-up from 150–600 mm diameter column, a size suitable for the speciality chemical or pharmaceutical industries. Pressure drop and flooding measurements using an air/water system compared the RLS contactor with 25 mm Pall Rings. Results for the Pall Rings matched expected performance, while RLS contactor pressure drop was 10% of that measured for the Pall Rings. Mass transfer experiments using an air+CO2/NaOH solution system showed measured mass transfer coefficients using the RLS contactor were comparable to a packed bed (25 mm Pall Rings) of similar specific surface area, while foaming in the packed bed did not occur in the RLS contactor using the same liquid sample. The RLS contactor also displayed minimal entrainment.

Prediction of the aggregation rate of nanoparticles in porous media in the diffusion-controlled regime.

The fate and aggregation of nanoparticles (NPs) in the subsurface are important due to potentially harmful impacts on the environment and human health. This study aims to investigate the effects of flow velocity, particle size, and particle concentration on the aggregation rate of NPs in a diffusion-limited regime and build an equation to predict the aggregation rate when NPs move in the pore space between randomly packed spheres (including mono-disperse, bi-disperse, and tri-disperse spheres). The flow of 0.2M potassium chloride (KCl) through the random sphere packings was simulated by the lattice Boltzmann method (LBM). The movement and aggregation of cerium oxide (CeO2) particles were then examined by using a Lagrangian particle tracking method based on a force balance approach. This method relied on Newton's second law of motion and took the interaction forces among particles into account. The aggregation rate of NPs was found to depend linearly on time, and the slope of the line was a power function of the particle concentration, the Reynolds (Re) and Schmidt (Sc) numbers. The exponent for the Sc number was triple that of the Re number, which was evidence that the random movement of NPs has a much stronger effect on the rate of diffusion-controlled aggregation than the convection.

Dense random packing of disks with a power-law size distribution in thermodynamic limit.

The correlation properties of a random system of densely packed disks, obeying a power-law size distribution, are analyzed in reciprocal space in the thermodynamic limit. This limit assumes that the total number of disks increases infinitely, while the mean density of the disk centers and the range of the size distribution are kept constant. We investigate the structure factor dependence on momentum transfer across various number of disks and extrapolate these findings to the thermodynamic limit. The fractal power-law decay of the structure factor is recovered in reciprocal space within the fractal range, which corresponds to the range of the size distribution in real space. The fractal exponent coincides with the exponent of the power-law size distribution as was shown previously by the authors of the work of Cherny et al. [J. Chem. Phys. 158(4), 044114 (2023)]. The dependence of the structure factor on density is examined. As is found, the power-law exponent remains unchanged but the fractal range shrinks when the packing fraction decreases. Additionally, the finite-size effects are studied at extremely low momenta of the order of the inverse system size. We show that the structure factor is parabolic in this region and calculate the prefactor analytically. The obtained results reveal fractal-like properties of the packing and can be used to analyze small-angle scattering from such systems.

Effect of Fly Ash on the Mass Transfer Performance of CO2 Removal Using MEA and DEA Solutions in a Packed Tower

The accumulation of uncollected fly ash from flue gas in post-combustion CO2 capture processes is a significant concern in current coal-fired power plants due to its potential impact on the performance of CO2 absorbent and absorption towers. In order to determine the effect of fly ash on the mass transfer performance of CO2 absorption into monoethanolamine (MEA) and diethanolamine (DEA) aqueous solutions, experimental studies were carried out using a small-sized packed tower equipped with θ-ring random packing. These studies were conducted under various operating parameters, including solution temperature, liquid/gas ratio (L/G), packing height, and fly ash concentration. The results show that the effect of fly ash on the outlet CO2 concentration was primarily observed during the initial stages of the experimental process. Moreover, the presence of fly ash leads to a reduction in the volumetric overall mass transfer coefficient (KGav) when using MEA and DEA solution, and increasing the fly ash concentration further exacerbates this negative impact. However, the effect of fly ash on the reduction in KGav is not significantly related to its chemical composition but rather depends on the operational parameters. With increasing solution temperature, liquid/gas ratio (L/G), and packing height, the KGav values for different solutions exhibit an upward trend. The negative effect of fly ash on KGav remains relatively stable for MEA as solution temperature and packing height increase. Compared to MEA, fly ash has a greater negative effect on DEA solution under the same experimental conditions. The analysis reveals that the detrimental effect of fly ash on KGav primarily stems from its ability to alter the distribution state of the absorption liquid within the packed tower.

Estimation of Effective Thermal Conductivity of Spherical and Ellipsoidal Shaped Randomly Packed Mono-Sized, Binary-Sized, and Poly-Dispersed Ceramic Pebble Beds

Estimation of Effective Thermal Conductivity of Spherical and Ellipsoidal Shaped Randomly Packed Mono-Sized, Binary-Sized, and Poly-Dispersed Ceramic Pebble Beds

Homogenisation method based on energy conservation and independent of boundary conditions

The foundation of homogenisation methods rests on the postulate of Hill–Mandel, describing energy consistency throughout the transition of scales. The consideration of this principle is therefore crucial in the discipline of Digital Rock Physics which focuses on the upscaling of rock properties. For this reason, numerous studies have developed numerical schemes for porous media to enforce the Hill–Mandel condition to be respected. The most common method is to impose specific boundary conditions, such as periodic ones. However, these boundary conditions influence both the effective property and the size of the REV. The recent study of Thovert and Mourzenko (2020) has shown that most boundary conditions still result in the same intrinsic effective physical property if the averaging is applied outside the range of the boundary layer. From this discovery, it becomes logical to question the status of Hill–Mandel postulate in porous media when homogenising away from the boundary. In this contribution, we simulate Stokes flow through random packings of spheres and a range of rock microstructures. For each, we plot the evolution of the ratio micro- vs macro-scale of the energy of the fluid transport outside the boundary layer, for a growing subsample size of porous media. Here, we prove that we naturally find energy consistency across scales when reaching the size of the Representative Elementary Volume (REV), which is a known condition for rigorous upscaling. Furthermore, we show that this index for the energy consistency is a more accurate indicator of REV convergence since the mean value is already known to be unitary.

Evaluating CO2 Capture Performance of Trisolvent MEA-BEA-AMP with Heterogeneous Catalysts in a Novel Bench-Scale Pilot Plant.

To reduce the huge energy cost of CO2 capture technology applicable in industry, the CO2 absorption-desorption performance was conducted in a novel bench-scale pilot plant with hot water as a heat source. The trisolvent MEA(monoethanol amine)-BEA(butylethanol amine)-AMP(2-amino-2-methyl-1-propanol) was prepared at a specific concentration to analyze the CO2 capture performance and compared with 5 M MEA as the benchmark. Meanwhile, several solid acid catalysts, blended H-ZSM-5/γ-Al2O3(1/2), or HND-8, were packed in the desorber, and the solid base catalyst, CaCO3 or CaMg(CO3)2, was packed in the absorber with random packing. The CO2 absorption efficiency (AE), cyclic capacity (CC), and heat duty (HD) were tested onto MEA-BEA-AMP and MEA under various operating conditions. Experimental results indicated that the performance of 4.3 mol/L MEA-BEA-AMP was significantly better than 5 M MEA under both catalytic and noncatalytic operation. The most energy efficient combination of this study was discovered as 0.3 + 2 + 2 mol/L MEA-BEA-AMP, with 50 g (CaCO3/CaMg(CO3)2) in the absorber and 150 g H-ZSM-5/γ-Al2O3(1/2) in the desorber. The heat duty reached as low as 2.4 GJ/tCO2 at a FG of 7.0 L/min and a FL of 70 mL/min. These results were highly applicable in an industrial amine scrubbing pilot plant for CO2 capture.

Dynamical Approach to the Jamming Problem.

A simple dynamical model, biased random organization (BRO), appears to produce configurations known as random close packing (RCP) as BRO's densest critical point in dimension d=3. We conjecture that BRO likewise produces RCP in any dimension; if so, then RCP does not exist in d=1-2 (where BRO dynamics lead to crystalline order). In d=3-5, BRO produces isostatic configurations and previously estimated RCP volume fractions 0.64, 0.46, and 0.30, respectively. For all investigated dimensions (d=2-5), we find that BRO belongs to the Manna universality class of dynamical phase transitions by measuring critical exponents associated with the steady-state activity and the long-range density fluctuations. Additionally, BRO's distribution of near contacts (gaps) displays behavior consistent with the infinite-dimensional theoretical treatment of RCP when d≥4. The association of BRO's densest critical configurations with random close packing implies that RCP's upper-critical dimension is consistent with the Manna class d_{uc}=4.

Development, verification and experimental validation of a 3D numerical model for tubular solar receivers equipped with Raschig Ring porous inserts

This study presents a numerical investigation of gaseous tubular absorbers used in a solar furnace and introduces a 3D model to simulate porous inserts with random packing of metallic Raschig Rings (RR) at pore-scale. A comprehensive verification and validation process was conducted based on the experimental data obtained at Plataforma Solar de Almeria (SF60). The evaluations were carried out on three samples, including a smooth pipe (SP) and two enhanced pipes (20RR and 40RR) with 20 mm and 40 mm RR inserts. The effects of several influential parameters, such as the fluid turbulence model, the effective thermal conductivity of the porous material, and the randomness of the RR in the porous structure, were studied to assess the accuracy and repeatability of the model in predicting thermal and fluidic characteristics of air inside the absorber pipes under different working conditions. A detailed thermo-hydraulic analysis revealed an irregular flow pattern inside the porous zone, while the air recirculation at the porous entrance and exit provides an uneven pressure drop distribution in the azimuthal direction. Moreover, fluid turbulence is enhanced downstream of the porous insert thanks to several stream jets formed by uneven flow discharge at the insert outlet face, which improves heat transfer in that area. The analyses demonstrated a significant improvement in heat transfer, with a maximum enhancement factor of 10–15 than the smooth tube. Additionally, in the evaluation of thermo-hydraulic performance, the enhanced absorbers exhibit Performance Evaluation Criteria up to 2, compared to the tube without RR inserts.

High-Yield Synthesis of Colloidal Carbon Rings and Their Applications in Self-Standing Electrodes of Li-O2 Batteries.

The use of carbon materials in porous electrodes has impressive advantages. However, precisely tailoring the multilevel pore structure of carbon electrodes remains an unsolved challenge. Here, we report a highly efficient site-selective growth strategy to synthesize colloidal carbon rings by templating patchy droplets. Carbon rings are used for the direct fabrication of self-standing porous electrodes with hierarchical pores for lithium-oxygen batteries (LOBs). In situ atomic force microscopy reveals that during discharge the discharge products densely nucleate and grow on carbon rings, demonstrating that such rings are a very potential electrode material in LOBs. The hollow carbon ring electrode (HCRE) possesses micrometer-scale channels formed by random packing of rings and nanochannels consisting of ring-shaped hollow cavities connected by nanosized pores in the wall. Both channels contribute to ion transportation and gas diffusion, but the storage of the discharge products mainly lies in micrometer-scale channels, leading to a high discharge capacity of LOBs (20 658 mAh/g). Our work paves a new way to construct hierarchically porous electrodes for application in electrocatalysis and electrochemical energy storage.

TEA of the CO2 capture process in pre-combustion applications using thirty-five physical solvents: Predictions with ANN

A Techno-Economic Analysis (TEA) of the CO2 capture process in a pre-combustion 543 MWe power plant was performed for thirty-five physical solvents employed to capture 90 % of CO2 from the sulfur-free fuel gas of the power plant. The process was built in Aspen-Plus v.11 and included one countercurrent fixed-bed CO2 absorber, containing structured (Mellapak 250Y) or random (IMTP50) packing, three flash-drums to regenerate the solvent, and multi-stage compressors to condition the captured CO2 for subsequent sequestration. The process operating expenditure (OPEX), capital expenditure (CAPEX), and levelized cost of CO2 captured (LCOC) were obtained.Aspen-Plus calculations revealed that Mellapak 250Y, having larger specific surface area than IMTP50, improved gas-liquid mass transfer and decreased LCOC; low-temperature operation enhanced CO2 solubility in the solvents and decreased solvent loss, lowering LCOC; high- temperature operation increased volatile solvent loss, increasing LCOC; and among the thirty-five solvents used, diethyl sebacate (DES) had the lowest LCOC ($7.14 per ton of CO2 captured).All Aspen-Plus TEA results were used to develop an Artificial-Neural-Network (ANN), consisting of one-input layer with 11 nodes, two-hidden layers with 10 nodes, and one-output layer with 3 nodes. The ANN was trained, then tested with 40 % and 60 % of the data, respectively; and it predicted the process CAPEX, OPEX, and LCOC with high accuracy. Thus, this ANN can perform TEA of numerous potential new solvents for CO2 capture in seconds compared to hours with Aspen-Plus, which is a significant timesaving, provided that plant capacity, solvent properties, and operating conditions are within its boundaries.

Коэффициент случайной упаковки бинарной системы подобных частиц: новый взгляд на модель исключённого объёма Онзагера

Коэффициент случайной упаковки бинарной системы подобных частиц: новый взгляд на модель исключённого объёма Онзагера