Solid Particle Size Distribution Research Articles

Comparison of Mathematical Models for the layout of Granulometric Curves of Brazilian Soils

The particle size distribution of solid particles (PSD) is critical in determining the potential for compaction, the availability and the redistribution of water in the soil, especially in the areas of building material and soil mechanics, among others. However, many banks of soil data does not contain detailed PSD data, but only some fractions. A mathematical accurate representation of the PSD is required to estimate soil hydraulic properties and texture comparing measurements of different classification systems. The objective of this study was to compare the performance of 12 models, with 2 and 3 tuning parameters proposed in the literature to represent the PSD, and, predict the water retention curve in the soil, from a wide range of Brazilian soils textures. The statistical parameters (NDEs, RD, MS CRM) showed three models tuning parameters proposed by Lima & Silva, Weibull and Fredlund got the best performance, with lower NDE, RD, MS very close to one and CRM values very low. The models Lima & Silva, Weibul, Fredlund and Skaggs, with three tuning parameters, and the models Skaggs end Lima & Silva, with two parameters, proved to be suitable for estimate the water retention curve in the soil, for soils with coarse and fine texture. Keywords: Granulometry; Soil texture; Curve Adjustments.

Effect of Particle Polydispersity on Flow and Reaction Behaviors of Methanol-to-Olefins Fluidized Bed Reactors

A reactor model has been first developed with the objective to fundamentally comprehend the qualitative influence of the solid polydispersity on the features of a methanol-to-olefins (MTO) fluidized bed reactor. Since coke deposition on the MTO catalyst significantly affects the reaction rate, with its formation usually taking dozens of minutes to achieve the desired coke content, the optimum average coke content was first obtained based on a filtered computational fluid dynamic (CFD) model. Furthermore, comparison of predictions through a CFD method and a reaction engineering approach was conducted. Predictions basically match the experimental data. Subsequently, the influence of the solid particle size distribution on reactor characteristics was comprehensively explored through a filtered CFD method coupled with the population balance model. Results suggested that the particle breakage performed a significant function in MTO fluidized bed reactors, causing particle size to evidently decrease.

Floating faeces: Effects on solid removal and particle size distribution in RAS

The removal of solid wastes originating from faecal matter is one of the decisive challenges for future fish farming, in particular given the current emphasis on water reuse in aquaculture. This study compared solid waste removal performance in replicate recirculating systems in which the only difference was the removal concept being deployed. Rainbow trout (Oncorhynchus mykiss) of the test group were fed an innovative diet supplemented with 2.5% cork granules (0.5–1mm) resulting in buoyant faecal casts (density values below 1.00gcm−3). These were removed directly from the tank by a low cost slotted pipe at the water surface. The control group was fed a conventional diet, identical to the experimental feed except that it lacked the cork additive. The resulting solids in both systems were removed by sedimentation in a classic manure pit, which was drained to the drum filter twice a day. Wastewater from both treatments was mechanically cleaned by a drum filter and biologically treated by a moving bed bioreactor before being returned to the tanks.The cork treatment led to a substantially higher solid load being delivered to the drum filter via the wastewater outflow than in the control system. The average removal efficiency of cork-treated wastes was more than twice that achieved in the control system (59% vs. 25%). Total suspended solid (TSS) in the backwash stream of the drum filter was about five times greater in the cork diet treatment. There was no significant difference in the particle size distribution or TSS load of water passing the 100μm gauze of the drum filter in the two systems. Cork supplementation did not affect growth or mortality of rainbow trout. The present study shows that the application of floating faeces is an exciting prospect in recirculating aquaculture systems, offering significant improvements in solid removal efficiency.

English

Changes to soil use can modify the soil’s physical and hydraulic properties, affecting its potential for productivity. This study aimed to characterize the physical and hydraulic properties of a clayey Dystroferric Red Latosol under the following land uses: conventional tillage (CT), direct drilling systems (DD), and native forest (NF). The study was conducted in Londrina (PR), Brazil, (23°23′ S, 50°11′ W and altitude of 585 m). Soil samples were collected at depths of 0 to 0.10, 0.10 to 0.20, 0.20 to 0.30, and 0.30 to 0.40 m. The following properties were evaluated: size distribution of solid particles, particle density, soil bulk density, total porosity, macroporosity, microporosity, water infiltration, and soil water retention curve. Conventional tillage and DD of this land modified soil physical and hydraulic properties from that under NF. The NF soil had greater organic matter content in its surface layer, a greater number of macropores, lower density, and less water retention capacity than soils from the CT and DD systems. At a precipitation rate of 70 mm h-1, only the CT system exhibited surface run-off. This was due to rupturing of the porous system and a lower infiltration rate. In contrast, plant residues in the DD system protected the soil structure against damage caused by direct impact due to raindrops, allowing for total infiltration of simulated rainfall events. The NF soil is important in extracting and replenishing groundwater stores. However, it does not retain more water than the other systems in the surface layers. Key words: Soil water retention, soil water infiltration, direct drilling system, Dystroferric Red Latosols, conventional tillage.

Experimental investigation on molten slag granulation for waste heat recovery from various metallurgical slags

Metallurgical slags, discharged at high temperature range, are produced as by-products in metallurgical processes. In order to reuse waste energy in molten metallurgical slags, the dry granulation and waste heat recovery technology is a popular technology, compared to water quenching granulation. In the study, the solid particle diameter and size distributions of metallurgical slags with different viscosity and surface tension by dry granulation were investigated. The results indicated that the length of molten slag ligament in granulation for ferroalloy slag, with high viscosity, was long. And there was small change in mean diameter of solid particles with an increase in rotating speed for metallurgy slag with low viscosity and surface tension. The semi-empirical relations, based on the experimental data, can be applied to calculate mean diameter of solid particles for different kinds of metallurgical slags. For blast furnace slag and ferroalloy slag granulation, the main mass fraction peak was located in the range of 2.44–3.14mm. For copper slag granulation, the main mass fraction peak moved to the range of small diameter with an increase in rotating speed.

Characterization of Real-Time Particle Emissions from a Gasoline Direct Injection Vehicle Equipped with a Catalyzed Gasoline Particulate Filter During Filter Regeneration

Real-time solid particle number (PN), size distributions, black carbon (BC), and particulate matter (PM) mass measurements were obtained from a gasoline direct injection (GDI) vehicle with and without a catalyzed gasoline particulate filter (GPF) over the US Federal Test Procedure 75 (FTP-75) and US06 Supplemental Federal Test Procedure (US06) drive cycles. The organic and elemental carbon fractions of the carbonaceous PM and transmission electron microscope (TEM) images for the exhaust particles were examined. Particles emitted from the GDI vehicle over various moderate driving conditions have similar morphology, size, and composition. These accumulation mode particles have diameters of 50 to 90 nm, have comparable fractal structures to diesel particles, and contain mostly BC with little organic materials. Under aggressive driving conditions, many nanoparticles (<20 nm in diameter) are emitted with the accumulation mode particles. Over the FTP-75 driving conditions, the optimized GPF reaches particle filtration efficiency of over 90 % from clean condition rapidly and filtration efficiency remains unchanged as filter regeneration was not observed. Over the US06 driving condition, filter regeneration was triggered by the high exhaust temperature during which many nanoparticles with diameters smaller than 30 nm are formed downstream of the GPF. TEM image analysis suggests that BC particles collected during the filter regeneration contain a layer of semi-volatile materials on the aggregate surface while the nanoparticles were semi-volatile in nature. During filter regeneration, moderate filtration of the accumulation mode BC particles was still observed.

On the Use of Particle-Size-Distribution Data for Permeability Prediction

SummaryParticle-size distribution (PSD) is a list of values that defines the relative amount of particles present according to the size in a sample. The PSD of the McMurray Formation sediments characterizes rock granulometry and is a fundamental indicator of the nature of the sediment. The size distribution of the component solid particles in the McMurray Formation sediments relates to their porosity; volume of water and bitumen contained within the pore space; and the depositional environment, including lithological association, stratigraphy, areal distribution, and associated physical processes.PSD is known to be a significant factor for evaluating bitumen recovery from an oil-sand mine. This is because presence of fines (evaluated by PSD analysis) affects the hot-water-separation process and processing-plant recovery prediction and provides grade control. Presence of more fines translates into lower recovery from commercial oil-sand processing. In this study, we investigate whether the PSD should be also considered a critical parameter for evaluation and estimation of permeability of an oil-sand reservoir.We show, by use of the data from Cenovus Energy's Telephone Lake lease, that there is a strong relationship between permeability and PSD data. We also show that the information provided by the PSDs for permeability prediction is more significant than that inferred from a simple porosity/permeability relationship. Subsequently, we comment on permeability modeling by use of PSD data and list the techniques available for cleaning and modeling of multivariate PSDs.We document a methodology for modeling of PSDs and provide a work flow for incorporating these data in improved understanding and modeling of permeability and its distribution.

Zn Loss into ZnFe2O4 in an Open Type Electric Arc Furnace: An In-Process Separation Performance Model

In order to reduce the burden of electric arc furnace dust on steel recycling plants, a new technology called in-process separation (IPS) was proposed. By separating Zn vapor from the solid particles in the electric arc furnace off-gas, production of Zn-containing electric arc furnace dust may be prevented. However, the spinel formation reaction at high temperatures and its impact on the technology’s feasibility still require better understanding. This paper demonstrates a model that was developed to provide this insight, based on the results of our previous work on the kinetics of the spinel formation.This model evaluates the performance of IPS based on four key process parameters: the position of the separation unit, the time–temperature profile inside the off-gas duct, the solid particle size distribution, and the initial Zn and Fe content of the off-gas. The impact on the efficiency of each parameter was demonstrated using the results of the model for a specific off-gas treatment setup.

Experimental investigation of hydrodynamics of liquid–solid mini-fluidized beds

Expanded fluidization behavior in liquid–solid mini-fluidized beds (MFBs) was experimentally investigated using visual measurements. Wall effects in the liquid–solid MFBs were identified and explained. The measured incipient/minimum fluidization liquid velocity (umf) in the MFBs was 1.67 to 5.25 times higher than that calculated using the Ergun equation when the ratio of solid particle diameter to bed diameter varied from 0.017 to 0.091. The ratio of the Richardson–Zaki (R–Z) exponent obtained by fitting with experimental data to that calculated using the R–Z correlation varied from 0.92 to 0.55. A wider solid particle size distribution resulted in a smaller R–Z exponent. The influence of the solid particle material on umf and R–Z exponent was negligible.

Development of a SOFC Performance Model to Analyze the Powder to Power Performance of Electrode Microstructures

While the development of new solid oxide fuel cell (SOFC) electrodes must fundamentally occur within a lab setting, computational models which aid in the initial characterization and selection process can help reduce the overall financial cost and development time. A computational performance model, which both evaluates the structural properties and predicts the performance (current production) within electrode microstructures, generated from either experimental or numerical techniques, is presented. The application of the model to investigate the effects of different initial powder manufacturing parameters on the electrode performance is also demonstrated. The first part of this work presents the aforementioned performance model, which was developed in a modified version of OpenFOAM, MicroFOAM (1). The model begins by evaluating the total TPB length and the normalized effective species transport of all three phases within the electrode microstructure. The model then predicts the current production within the electrode by coupling the three percolating transport regions (electron, ion and pore) at the electrochemically active triple phase boundary (TPB), with a Butler-Volmer type expression. The identification of the microstructure properties and performance will enable relationships between these properties to be established. A particle-based numerical reconstruction model (2) is employed in this study to generate the synthetic electrode microstructures. The generated microstructures consist of a random distribution of overlapping spherical particles placed using a drop-and-roll algorithm. The packing algorithm allows for user specification of the initial starting parameters and is ideal for studying microstructure with a wide range of properties. Among the modifiable initial parameters include; the solid volume faction, porosity, and particle size distribution. In the second part of the study the performance model, developed in the first section, and the packing algorithm, mentioned above, are used to study the effects of different manufacturing parameters on the structural properties and performance of a cermet anode active layer. Initially the structural properties and performance of anodes generated with different initial electron-ion phase volume fractions (solid volume fraction) and porosities will individually be examined to identify the microstructure settings which maximizes the current production. Once identified, the two optimal individual settings will be combined and varied again to explore what optimal balance maximizes current production. Once identified, conclusions about the microstructure properties and manufacturing settings will be reviewed and discussed. Further manufacturing parameters including the particle size, particle size distribution, and thickness may also be explore in this work. References Choi, H.-W., Berson, A., Pharoah, J.G., Beale, S.B. Proc. IMechE. J. Power & Energy, 225(2): 183-197 (2011).Kenney, B., Vadmanis, M., Baker, C., Pharoah, J.G., Karen, K. J. Power Sources, 189: 1051-1059 (2009).

Theoretical analysis of a method to measure size distributions of solid particles in water by aerosolization

Reliable measurement of the size-resolved number concentration (size distribution) of solid particles dispersed in water or melted ice is of critical importance in many geoscientific observational studies. Because physical and chemical properties of particles can be measured more unambiguously and accurately in rarefied media (air) than in condensed media (water), particle measurement after aerosolization using a nebulizer is a significant method for the observation of solid particles dispersed in water. We propose a mathematical theory for estimating the original size distribution of solid particles in water from the measured size distribution of aerosolized particles. We assume that the size distribution of water droplets produced by a nebulizer is given. The size distribution of solid particles in water can be estimated by solving a system of nonlinear equations. The complexity in solving the equations increases rapidly with the computational resolution of particle size and the assumed maximum number of particles within each droplet. For such a system of equations, we found rigorous error bounds of a true solution using INTLAB, an interval arithmetic package. Our theoretical framework will be useful in many fields in geoscience as a fundamental scheme to quantify solid particles in water. In particular, an application of the proposed theoretical method is shown to be useful for the quantitative observations of the size distribution of black carbon particles in rainwater.

Impact of selective catalytic reduction on exhaust particle formation over excess ammonia events.

The introduction of selective catalytic reduction (SCR) aftertreatment to meet stringent diesel NOx emission standards around the world increases exhaust ammonia. Further to the direct air quality and health implications of ammonia, this may also lead to particle formation in the exhaust. In this study, an ammonia SCR system was examined with respect to its impact on both solid and total exhaust particle number and size distribution, downstream of a diesel particulate filter (DPF). Fuel post-injection was conducted in some tests to investigate the effect of ammonia during active DPF regeneration. On average, the post-DPF solid >23 nm and total <23 nm particle number emissions were increased by 129% (range 80-193%) and by 67% (range 26-136%), respectively, when 100 ppm ammonia level was induced downstream of the SCR catalyst. This is a typical level during ammonia overdosing, often practiced for efficient NOx control. Ammonia did not have a significant additional effect on the high particle concentrations measured during DPF regeneration. Based on species availability and formation conditions, sulfate, nitrate, and chloride salts with ammonium are possible sources of the new particles formed. Ammonia-induced particle formation corresponds to an environmental problem which is not adequately addressed by current regulations.

Effect of cardanol diol on the synthesis, characterization, and film properties of aqueous polyurethane dispersions

This article reports on the effect of a diol prepared from a renewable resource, cardanol, on the synthesis, film formation and film properties of aqueous polyurethane dispersions. The PU dispersions were prepared by the acetone process from poly(tetramethylene ether)glycol (PTMEG) and isophorone diisocyanate (IPDI) prepolymer at constant NCO/OH ratio of 1:1.1. Dispersions with two different concentrations of cardanol diol (OH value 140 mg KOH/g) were prepared through chain extension and characterized for solid content, particle size, and particle-size distribution (PSD). Free films were prepared by casting and were studied for their thermal, mechanical, viscoelastic, and hydrophobic properties. Due to the broad PSD, the dispersions containing cardanol diol exhibit better film formation property in comparison to the butane diol chain-extended PU. Soft and flexible films were obtained using cardanol diol as chain extender, whereas brittle film was obtained with butane diol chain extender. Morphological characterization using atomic force microscopy (AFM) and scanning electron microscopy (SEM) suggests a heterogeneous and amorphous nature of the polyurethanes-containing cardanol diol. The thermomechanical and viscoelastic properties show that incorporation of cardanol diol decreases the glass transition temperature and modulus of the films but enhances the properties like thermal stability, hydrophobicity, elongation, etc., of the polyurethane films.

Rheological behavior of coal bio-oil slurries

Coal bio-oil slurries (CBSs) were prepared by blending coal with bio-oil from the fast pyrolysis, and their apparent viscosities were measured by a rotary viscometer. The influences of coal rank, solid concentration, particle size distribution and temperature on the apparent viscosity and rheological properties of slurries were investigated. Additionally, the grey relational analysis was employed to determine the order of importance of factors affecting the apparent viscosity for different rank coals. Results show that, the CBS exhibits non-Newtonian fluid behavior and can be described by Herschel–Bulkley equation. The main factors for different rank coals affecting apparent viscosity of CBS are inherent moisture and carboxyl groups. The maximum solid concentration of CBS can reach 45–47 wt. % for Shenmu bituminous coal. Appropriate solid particle size distribution and preparation temperature can provide satisfied slurries with low viscosity.

New insights into intraparticle transfer, particle kinetics, and gas–solid two-phase flow in polydisperse fluid catalytic cracking riser reactors under reaction conditions using multi-scale modeling

This study provides new insights into fluid catalytic cracking (FCC) riser reactor from multi-scale viewpoint. The problem of simultaneous intraparticle molecule transfer and reaction, particle kinetics, and gas–solid flow in polydisperse FCC riser reactors was considered. A multi-scale CFD method was developed for constructing a multi-scale model to solve this problem. The multi-scale model consisted of a two-phase CFD model incorporating a single-particle model and a population balance model. The main flow field distribution parameters within the catalyst particles and reactors as well as the solid particle size distribution (PSD) could be calculated simultaneously based on intraparticle transfer and reaction using these models. The single-particle and multi-scale models were first verified and evaluated. Based on the validated models, intraparticle transfer limitations and/or flow fields in two size-scale FCC riser reactors were predicted. The simulations demonstrated three different reaction zones in FCC risers, and more elaborate mass, heat, and momentum transfer behaviors could be obtained. The simulations also demonstrated that particle kinetics (i.e., breakage and aggregation) have obvious influences on the FCC flow field in FCC risers; these effects have not been observed in conventional CFD models.

A model for predicting solid particle behavior in petroleum sludge during centrifugation

An efficient model is proposed for predicting the behavior of solid particles in petroleum sludge during centrifugation, from the particle size distribution and petroleum viscosity. Petroleum sewage sludge (PSS) and oil-tank bottom sludge (OBS), respectively collected from a sewage reservoir containing petroleum waste water and a petroleum oil storage tank, were studied. The solid particle removal and oil recovery rates were measured to assess the efficiency of the model. The model predicted that solid particles could be separated into three groups during centrifugation, with critical separation sizes of 69.2 and 80.3μm for the PSS and 91.2 and 110.3μm for the OBS, and that particles larger than the smaller critical separation size could be removed from each sludge efficiently at room temperature without pretreatment. The predicted cumulative particle removal rates using a three-stage centrifugation process were 50%, 61%, and 70%, for the three PSS-particle size ranges (in ascending order), which agreed well with experimental measurements (54%, 65%, and 75%, respectively). The experimental water/oil emulsion recovery rates were 86%, 81%, and 75%, respectively. Preheating enhanced the solid particle removal rate by 29% for PSS whose viscosity decreasing quickly with increasing temperature. Adding a solvent increased the solid particle removal rates to 90% for the PSS and 82% for the OBS, but caused the water/oil emulsion recovery rates to decrease to 69% for the PSS and 67% for the OBS. The model and experimental results suggest that the optimum centrifugation time should be determined after assessing the petroleum viscosity and the solid particle size distribution.

Simulation model of the mass balance in a supercritical circulating fluidized bed combustor

Abstract In the present work, a mass balance allows us to predict operating conditions of coal-fired circulating fluidized bed (CFB) combustor under full load operation. A mass balance model has been developed for the particle size distribution and solids mass fluxes of three granular materials supplied and led out in the 966MWth supercritical circulating fluidized bed boiler. This model emphasizes some important factors, such as feed rates, separator characteristics, drainage and recirculation rates of solids and internal processes. In the simulation model the internal processes such as the combustion process, particle shrinkage, fragmentation and attrition were taken into account, respectively. The model can theoretically predict the PSD and mass balance at different operating loads, ash content and points inside the supercritical CFB combustion system. The results of the simulation indicate that they are in accordance with the experimental data from large-scale supercritical CFB boiler. The results of modeling give an opportunity of studying the impact of changes on the solids particle size distribution (PSD) and solids mass fluxes in operating conditions.

Hydrodynamic effects of air sparging on hollow fiber membranes in a bubble column reactor

Air sparging is now a standard approach to reduce concentration polarization and fouling of membrane modules in membrane bioreactors (MBRs). The hydrodynamic shear stresses, bubble-induced turbulence and cross flows scour the membrane surfaces and help reduce the deposit of foulants onto the membrane surface. However, the detailed quantitative knowledge on the effect of air sparging remains lacking in the literature due to the complex hydrodynamics generated by the gas–liquid flows. To date, there is no valid model that describes the relationship between the membrane fouling performance and the flow hydrodynamics. The present study aims to examine the impact of hydrodynamics induced by air sparging on the membrane fouling mitigation in a quantitative manner. A modelled hollow fiber module was placed in a cylindrical bubble column reactor at different axial heights with the trans-membrane pressure (TMP) monitored under constant flux conditions. The configuration of bubble column without the membrane module immersed was identical to that studied by Gan et al. (2011) using Phase Doppler Anemometry (PDA), to ensure a good quantitative understanding of turbulent flow conditions along the column height. The experimental results showed that the meandering flow regime which exhibits high flow instability at the 0.3 m is more beneficial to fouling alleviation compared with the steady flow circulation regime at the 0.6 m. The filtration tests also confirmed the existence of an optimal superficial air velocity beyond which a further increase is of no significant benefit on the membrane fouling reduction. In addition, the alternate aeration provided by two air stones mounted at the opposite end of the diameter of the bubble column was also studied to investigate the associated flow dynamics and its influence on the membrane filtration performance. It was found that with a proper switching interval and membrane module orientation, the membrane fouling can be effectively controlled with even smaller superficial air velocity than the optimal value provided by a single air stone. Finally, the testing results with both inorganic and organic feeds showed that the solid particle composition and particle size distribution all contribute to the cake formation in a membrane filtration system.

Granular suspension avalanches. I. Macro-viscous behavior

We experimentally studied the flow behavior of a fixed volume of granular suspension, initially contained in a reservoir and released down an inclined flume. Here “granular suspension” refers to a suspension of non-Brownian particles in a viscous fluid. Depending on the solids fraction, density mismatch, and particle size distribution, a wealth of behaviors can be observed. Here we report and interpret results obtained with granular suspensions, which consisted of neutrally buoyant particles with a solids fraction (ϕ = 0.575–0.595) close to the maximum random packing fraction (estimated at ϕm = 0.625). The particles had the same refractive index as the fluid, which made it possible to measure the velocity profiles inside the moving bulk and far from the sidewalls. Additional information such as the front position and the flow depth was also recorded. Three regimes were observed. At early times, the flow features were reminiscent of homogeneous Newtonian fluids (e.g., the same dependence of the front position on time). At later times, the free surface became more and more bumpy as fractures developed within the bulk. This fracture process ultimately gave rise to a stick-slip regime, in which the suspension moved intermittently. In this paper, we focus on the first regime referred to as the macro-viscous regime. Although the bulk flow properties looked like those of Newtonian fluids, the internal dynamics were much richer.

Particle Size Effects on Optimal Sizing and Lifetime of Pipelines Transporting Multi-sized Solid-Liquid Mixtures

A life-cycle cost analysis model is developed in this study, to examine the effects of particle size distribution of the solid particles to be transported on the optimal sizing and lifetime of the pipelines used for transportation of solid-liquid mixtures. The method determines the lifetime of the pipe corresponding to the least annual total cost per unit length of the pipe. The optimum diameter is obtained so that the total cost per unit pipe length per unit volume of the transported mixture throughout this lifetime is minimum. The total cost includes manufacturing and repair cost of pipe, cost of pumping power as well as the cost of power required for the crushing of particles from an initial size distribution to a desirable particle size distribution. The repair cost of pipe and cost of pumping power increase as the pipe becomes older due to more frequent pipe breaks and due to the pipe wear that makes wall roughness, and thereby pressure drop, greater. These costs together with the cost of power for crushing must be considered for through life costing of pipelines. Since the transportation of solid-liquid mixtures is maintained by several pumping stations in long pipelines, the spacing between two successive pumping stations must also be determined. The study shows interdependence of parameters such as the lifetime, the optimum diameter, the corresponding spacing for a given pumping power and the particle size distribution of solid particles transported in the pipeline. Furthermore, the method also provides the interrelation between the total length of pipeline when crushing is economical and the different particle size distributions.