Prediction Of Particle Size Distribution Research Articles

Predicting biomass comminution: Physical experiment, population balance model, and deep learning

An extended population balance model (PBM) and a deep learning-based enhanced deep neural operator (DNO+) model are introduced for predicting particle size distribution (PSD) of comminuted biomass through a large knife mill. Experimental tests using corn stalks with varied moisture contents, mill blade speeds, and discharge screen sizes are conducted to support model development. A novel mechanism in the extended PBM allows for including additional input parameters such as moisture content, which is not possible in the original PBM. The DNO+ model can include influencing factors of different data types such as moisture content and discharge screen size, which significantly extends the engineering applicability of the standard DNO model that only admits feed PSD and outcome PSD. Test results show that both models are remarkably accurate in the calibration or training parameter space and can be used as surrogate models to provide effective guidance for biomass preprocessing design.

Industrial application and numerical simulation on discrete dynamics of fine particulate matters: Condensational growth, deposition and agglomeration

The removal effects of multiple discrete dynamic mechanisms on particulate matters (PMs) are of great significance for industrial application and basic research. In this work, a wet phase transition agglomerator (WPTA) is installed between a wet electrostatic precipitator (WESP) and a stack at a 280 t/h coal-fired power plant. The removal effects of the WPTA are compared with those of the WESP by field measurement. Meanwhile, a numerical model for predicting particle size distributions is developed and verified through the experimental data. The results indicate that the WPTA reduces the emission concentrations of PM1 and PM2.5 to 0.64 mg/Nm3 and 0.89 mg/Nm3, respectively. The PM1 removal efficiencies for the independent WPTA, the independent WESP and the combined method are 33.07 %, 40.31 % and 58.36 %, respectively. The microscopic morphologies of the fine PMs in the particle size range of 0.98–1.64 μm exhibit blocky, spherical and crystal structure. The simulated errors of PM1, PM2.5 and PM10 are 7.81 %, 7.87 % and 12.27 %, respectively. The boundary layers of the tube bundle are conducive to strengthening thermophoretic force and supersaturation. Consequently, the WPTA can effectively replace the WESP to achieve the emission control of fine PMs in industrial applications. The developed numerical model can accurately predict the particle size distributions in the WPTA.

Implementation of near-infrared spectroscopy and convolutional neural networks for predicting particle size distribution in fluidized bed granulation

Monitoring the particle size distribution (PSD) is crucial for controlling product quality during fluidized bed granulation. This paper proposed a rapid analytical method that quantifies the D10, D50, and D90 values using a Convolutional Block Attention Module-Convolutional Neural Network (CBAM-CNN) framework tailored for deep learning with near-infrared (NIR) spectroscopy. This innovative framework, which fuses CBAM with CNN, excels at extracting intricate features while prioritizing crucial ones, thereby facilitating the creation of a robust multi-output regression model. To expand the training dataset, we incorporated the C-Mixup algorithm, ensuring that the deep learning model was trained comprehensively. Additionally, the Bayesian optimization algorithm was introduced to optimize the hyperparameters, improving the prediction performance of the deep learning model. Compared with the commonly used Partial Least Squares (PLS), Support Vector Machine (SVM), and Artificial Neural Network (ANN) models, the CBAM-CNN model yielded higher prediction accuracy. Furthermore, the CBAM-CNN model avoided spectral preprocessing, preserved the spectral information to the maximum extent, and returned multiple predicted values at one time without degrading the prediction accuracy. Therefore, the CBAM-CNN model showed better prediction performance and modeling convenience for analyzing PSD values in fluidized bed granulation.

Population Mass Balance Model for Precipitation with Turbidity Measurements.

The discretized population balance theory has been proven to be a useful method to simulate systems in which solid particles are present. In this work, we introduce a new approach to model precipitation reactions based on the temporal evolution of product concentration, from which particle size distribution, its dynamics, and the specific interfacial energies can be obtained. For a reference study, the previously investigated calcium oxalate precipitation was selected, where the reaction was followed via turbidity measurement. From the obtained particle size distribution, we can show that at low supersaturation, growth is the dominant process, while at higher supersaturation, nucleation is the dominant process. Moreover, the temporal change of the distribution curve has allowed us to split the precipitation into a nucleation, a growth-driven intermediate, and a saturation regime. Furthermore, the comparison between the experimental and calculated results has proved that the method is suitable for predicting particle size distributions and specific interfacial energies.

NAGPKin: Nucleation-and-growth parameters from the kinetics of protein phase separation.

The assembly of biomolecular condensate in eukaryotic cells and the accumulation of amyloid deposits in neurons are processes involving the nucleation and growth (NAG) of new protein phases. To therapeutically target protein phase separation, drug candidates are tested in in vitro assays that monitor the increase in the mass or size of the new phase. Limited mechanistic insight is, however, provided if empirical or untestable kinetic models are fitted to these progress curves. Here we present the web server NAGPKin that quantifies NAG rates using mass-based or size-based progress curves as the input data. A report is generated containing the fitted NAG parameters and elucidating the phase separation mechanisms at play. The NAG parameters can be used to predict particle size distributions of, for example, protein droplets formed by liquid-liquid phase separation (LLPS) or amyloid fibrils formed by protein aggregation. Because minimal intervention is required from the user, NAGPKin is a good platform for standardized reporting of LLPS and protein self-assembly data. NAGPKin is useful for drug discovery as well as for fundamental studies on protein phase separation. NAGPKin is freely available (no login required) at https://nagpkin.i3s.up.pt.

Modelling Outer Ash Deposition Rates in Second Generation Atmospheric Pressure Oxy-Fuel Combustion Systems

ABSTRACT The particle size distribution (PSD) measurements of coarse fly-ash particles (diameter, dp >10 µm) near the depositing surface are often not available, creating challenges in formulating mechanistic models for ash deposition. This void may be partially alleviated if measurements of deposition rate and PSD of the ash deposits are available. This is demonstrated using well-resolved Computational Fluid Dynamic simulations in conjunction with a particle viscosity and particle kinetic energy based capture criterion to model the outer ash deposition processes for three different fuels (two types of coal and Rice Husk) during their combustion in AIR and O2/CO2 (70/30 vol %, OXY70; 50/50 vol %, OXY50) oxidizer compositions. First, deposition rate predictions for monodisperse fly-ash particles (10 µm < dp < 150 µm) encompassing the aforementioned scenarios were carried out. The PSD of the fly-ash particles were then inferred by mass-weighted averaging the monodisperse fly-ash diameters to match the measured deposition rates as well as the deposit ash PSD. While the methodology proved to be promising in the coal-firing scenarios, the deposit ash PSD predictions for Rice Husk were smaller than their corresponding measurements and may be attributed to irregular particle sizes or necessary modifications to surface capture characteristics.

Morphology and phase state of PM2.5 in urban and coastal-rural areas during summer

The morphology and phase state are critical physical properties of aerosol particles. However, studies related to the analysis of these properties primarily focus on laboratory experiments, and studies on real aerosol particles are limited. Herein, fine particulate matter (PM2.5) filter samples were obtained to investigate and compare the morphology and phase state of ambient aerosol particles in South Korea. The PM2.5 samples were collected in the summer of June 2021 from two different environments: Seoul (urban) and Seosan (coastal-rural). Optical microscopy was combined with the poke-and-flow technique to determine the morphology and phase state of the PM2.5 as a function of relative humidity (RH) at 293 ± 1 K. At both sites, the PM2.5 droplets, which were extracted in purified water, showed a multiphase nature that was dependent on the RH and chemical composition. Based on the results and ambient average RH in Seoul, most of the PM2.5 was observed in a liquid state on polluted days under an inorganic-dominant condition, but in a semisolid state on clean days under an organic carbon-rich condition. In Seosan, the PM2.5 predominantly existed in a liquid state, due to the high RH caused by proximity to the Yellow Sea. Our study provides fundamental physical properties of PM2.5 for both urban and coastal-rural environments. The results have strong applications for atmospheric chemistry and predicting particle size distributions.

Modeling and Optimization of the Para-Xylene Continuous Suspension Crystallization Separation Process via a Morphology Technique and a Multi-Dimensional Population Balance Equation

In this study, we carried out a para-xylene crystallization experiment at constant temperature and concentration levels. Throughout the process, the kinetics of nucleation, growth, breakage, and aggregation of para-xylene particles were measured and built using a morphological approach. An additional a three-stage continuous suspension crystallization separation experiment was carried out, the process for which was simulated using the population balance model based on correlated kinetic equations. The population balance equation was solved using an extended moment of classes algorithm, and the solving process was implemented in MATLAB. In this case, the predicted particle size distribution of the products matched well with the experiment. In order to provide references for the optimization of the industrial para-xylene crystallization process, a three-stage suspension crystallization separation experiment was designed and conducted, in which each crystallizer had a distinct operating temperature and mean residence time. The effects of operating parameters on the final product were investigated further. The proposed models and algorithms can also be applied in other cases and provide an alternative approach for optimizing continuous crystallization processes.

Prediction of Particle Size Distribution of Mill Products Using Artificial Neural Networks

High energy consumption in size reduction operations is one of the most significant issues concerning the sustainability of raw material beneficiation. Thus, process optimization should be done to reduce energy consumption. This study aimed to investigate the applicability of artificial neural networks (ANNs) to predict the particle size distributions (PSDs) of mill products. PSD is one of the key sources of information after milling since it significantly affects the subsequent beneficiation processes. Thus, precise PSD prediction can contribute to process optimization and energy consumption reduction by avoiding over-grinding. In this study, coal particles (−2 mm) were ground with a rod mill under different conditions, and their PSDs were measured. The variables studied included volume% (vol.%) of feed (coal particle), vol.% rod load, and grinding time. Our supervised ANN models were developed to predict PSDs and trained by experimental data sets. The trained models were verified with the other experimental data sets. The results showed that the PSDs predicted by ANN fitted very well with the experimental data after the training. Root mean squared error (RMSE) was calculated for each milling condition, with results between 0.165 and 0.965. Also, the developed ANN models can predict the PSDs of ground products under different milling conditions (i.e., vol.% feed, vol.% rod load, and grinding time). The results confirmed the applicability of ANNs to predict PSD and, thus the potential contribution to reducing energy consumption by optimizing the grinding conditions.

Artificial neural network for mechanism identification and process prediction of the nanoclusters deagglomeration in the in-line HSM

A multiple-input multiple-output artificial neural network (ANN) for the mechanism identification of nanoclusters deagglomeration and the prediction of particle size distribution (PSD) evolution of nanocluster in deagglomeration process of in-line high shear mixer (HSM) was successfully established. It can successfully realize the description of nanoclusters deagglomeration process within single or multiple processing batches. Besides, this ANN model also can realize the accurate prediction of the d32 of fine and coarse agglomerates, and the fines fraction, at different operating conditions and structural parameters, within the relative error of 10 % and 20 % respectively. Meanwhile, 3D profiles of PSD versus different operating conditions and structural parameters were output by the established ANN model, which were useful for parameter selection of in-line HSM to realize efficient production of nanoparticles suspension. The successful establishment of this ANN model provides an effective, flexible, and advanced intelligent method for guiding the parameter selection of in-line HSM, for realizing the controllable and efficient production of the high-end nanoparticle products with specific particle characteristics.

Combining density functional theory and CFD-PBM model to predict TiO2 nanoparticle evolution during chemical vapor deposition

Preparation of TiO2 nanoparticles by TiCl4 hydrolysis during chemical vapor deposition (CVD) is one of the effective techniques for producing TiO2 nanoparticles, while the mechanisms of TiO2 nanoparticle evolution are not well understood. This paper uses computational fluid dynamics (CFD) population balance model (PBM) to predict particle size distribution during CVD, and density functional theory (DFT) calculations to explore reaction mechanisms. DFT calculations reveal that the gas phase hydrolysis reaction can be simplified into two processes, the hydrolysis of TiCl4 to form TiO(OH)2 and the decomposition of TiO(OH)2 to TiO2. During the surface reactions, the energy barriers of TiO(OH)2 decomposition reactions on the surfaces of (TiO2)n nanoclusters (n = 1–8) are generally lower than those in the gas phase reactions, and the largest energy barrier of the surface reaction occurs on the surface of (TiO2)6 nanoclusters. Simulations using a perfect stirred reaction model indicate that Ti(OH)4 is the dominant hydrolysis products when the temperature is lower than 548 K, while TiO2 production starts at ∼610 K, indicating reaction temperature is a crucial factor that governs the products of TiCl4 hydrolysis. CFD-PBM model predict the evolution of Particle Size Distribution (PSD) of nanoparticles in a CVD reactor, which is agreed with experimental measurements in the literature. Increasing the reaction temperature results in an increase of the peak of the PSD of nanoparticles in the reactor. This study provides atomic insights into the nanoparticle evolution and a practical model to predict the nanoparticle evolution during the CVD process.

Simple Methods to Predict Particle Size for Growth-Only Systems Undergoing One or More Temperature Cycles

Three simple methods are presented for predicting particle size distribution (PSD) percentiles when subjecting a pharmaceutical crystallization wet-milled slurry to a single temperature cycle for two of Biogen’s drug substances. The methods are (I) a mathematical manipulation of the wet-milled PSD based on particle death during dissolution; (II) a linear empirical model fit of product PSD percentiles as a function of the wet-milled PSD percentiles and the amount of material dissolved; and (III) a nonlinear model fit to the change in PSD as a function of the amount of material dissolved and the particle surface area/volume ratio. The three methods were verified on production scale batches. Method II’s approach was also used for particle size control during manufacture by implementing a temperature solved from the model using the batch’s wet-milled particle size percentiles and a final target size. Method III was found to be the most accurate at prediction because it models particle surface area to volume ratio influencing crystal dissolution and growth rates. Method II was found to be not as accurate as method III; however, it was easily implementable during process control at the production scale. Method I provided the quickest estimate of final particle size using only the initial PSD and a solubility expression. Method III was recommended for best particle size prediction.

Numerical investigation of particle size distribution, particle transport and deposition in a modified chemical vapor deposition process

Modified chemical vapor deposition (MCVD) process in a rotating tube reactor is an important technology for manufacturing fiber optic preforms, whose performance strongly depends on the uniformity of the deposited particles on the tube wall. In this study, the Eulerian–Eulerian model with Population Balance Model (PBM) is applied to predict particle size distribution (PSD) of SiO2 particles in the reaction zone, and subsequently Discrete Particle Model (DPM) is used to represent typical particles and investigate trajectories and deposition locations of the SiO2 particles. The temperature, reaction components, and particle size distribution along the axial and radial directions within the tube are predicted reasonably. The deposition distances of the particles with size of 10 nm, 200 nm and 10 μm are mostly smaller than 120 mm for the condition with the peak wall temperature of 2000 K. The deposition distance and flight time of the particles increase with the increase of particle size. With increase of the wall temperature, the reaction zone and particle formation zone become larger, which promotes the growth of the SiO2 particles. The competing effects between the thermophoretic force and inertial force caused by the increase of the wall temperature lead to firstly an increase and then a decrease in the deposition distance and flight time of the particles.

Multiphase model to predict particle size distributions in close-coupled gas atomization

A novel two-stage multiphase model is developed for close-coupled gas atomization by combining formulations available in the literature. Primary atomization is simulated using an Eulerian atomization model, and the outputs are used as inputs of a Lagrangian particle tracking approach to predict the particle size distribution resulting from secondary atomization. The results given by the primary atomization model are validated with published Direct Numerical Simulations (DNS) values and by comparison with experimental images of the spray, while the particle size distributions obtained are accurately fitted to a log-normal distribution, and with powder mean diameters showing good agreement with experimental data. The variation of powder characteristic diameters d10, d50, and d90 as a function of the gas-to-melt mass flow rate ratio follows correct trends, and the values of powder mean diameters d50 are correctly predicted by the model.

Evaluation of mathematical models for predicting particle size distribution using digital soil mapping in semiarid agricultural lands

Soil Particle Size Distribution (PSD) is a fundamental physical property that can affect soil hydraulic properties, soil structure characterization, and available water. Many models have been applied to define the PSD curve, but predicting the spatial distribution information of PSD has been rarely investigated. Therefore, the main objective of the current study was to predict soil texture fractions using the most accurate PSD models. First, the performance of 16 mathematical PSD models was evaluated. Then, Random Forest (RF) was used to determine the relationship between covariates (i.e., remote sensing and the digital elevation model) and georeferenced measurements of the best PSD models’ parameters. Results indicated that a PSD model may be acceptable for some particle diameters or even whole particles, but not necessarily be suitable for other particles. For example, in the estimation of sand content, the best model was Simple Lognormal, while the Fred-4p was the best model in the estimation of the clay fraction. Importantly, the Jaky model with only one parameter of P did a great job in predicting soil particle fractions. Further, the spatial distribution of clay, silt, and sand contents was accurately derived from the predicted map of P (R2 for Sand = 0.86). Consequently, the current research indicated that the combination of PSD models and digital soil mapping techniques can be used to quantify the spatial distribution of the PSD curve in other similar agroclimatological regions.

Experimental and numerical investigation of the transition from non sooting to sooting premixed n-butane flames, encompassing the nucleation flame conditions

In a small range of rich equivalence ratios, premixed flat flames, so-called nucleation flames, were shown to produce very small-size (2–4 nm) soot particles, which undergo negligible growth with the residence time. In such flames, the contribution of the soot nucleation step with respect to the soot growth process is larger than in standard sooting flames, making nucleation flames ideal target flames to better understand the inception process. In order to scrutinize the transition from non sooting to sooting flames, three premixed atmospheric n-butane/oxygen/nitrogen flames surrounding the nucleation flame conditions were investigated: the flame at ϕ=1.6 is a fuel-rich non-sooting flame, the flame at ϕ=1.75 is a nucleation flame and the flame at ϕ=1.95 is a lightly sooting flame. The soot volume faction (SVF) profiles were previously measured by laser-induced incandescence as well as the soot size distributions. In the present study, mole fractions of stable species up to benzene were measured by gas chromatography while those of naphthalene and pyrene were obtained by jet-cooled laser-induced fluorescence. It is found that acetylene, propyne, benzene, naphthalene and pyrene species show the highest sensitivity with the equivalence ratio, while a two orders of magnitude increase of SVF is observed. The chemical flame structure of these flames was modeled using three kinetic mechanisms of the literature to which a recently developed soot code, based on a sectional approach, was coupled. The chosen model is representative of the current state-of-the-art of models describing all steps of soot formation and growth and fully coupled with the gas phase. The ability of such a model to predict soot volume fraction with reasonable predictions of gas-phase species is validated here based on the new experimental database presented in this work. It also highlights the improvement required on particle inception modeling to correctly predict particle size distributions.

Prediction of ball milling performance by a convolutional neural network model and transfer learning

This work proposed a three-phase modelling framework using the convolutional neural network (CNN) method to predict the performance a ball mill based on the externally measurable variables in the milling process. The data of the model were generated from the discrete element method under different conditions, including acoustic emission (AE) signals, power draw and grinding rate. In the pre-training and training phases, the CNN model was able to predict particle size distributions and grinding rates with R2 higher than 0.92. The model was then applied to the large mill system and the results showed that the model maintained its performance in the new system with limited training datasets. The transfer learning of the model was tested by comparing the model with an untrained model and the results showed the loss error (MSE) of transfer model converged to a lower level within 20 epochs while the untrained model could only converge to a larger error after 400 epochs, indicating with the pre-trained model required far less training time and data for better prediction. The potentials and limitations of the model were also discussed.

A New Framework for Modelling Fine Sediment Transport in Rivers Includes Flocculation to Inform Reservoir Management in Wildfire Impacted Watersheds

Fine-grained cohesive sediment is the primary vector for nutrient and contaminant redistribution through aquatic systems and is a critical indicator of land disturbance. A critical limitation of most existing sediment transport models is that they assume that the transport characteristics of fine sediment can be described using the same approaches that are used for coarse-grained non-cohesive sediment, thereby ignoring the tendency of fine sediment to flocculate. Here, a modelling framework to simulate flow and fine sediment transport in the Crowsnest River, the Castle River, the Oldman River and the Oldman Reservoir after the 2003 Lost Creek wildfire in Alberta, Canada was developed and validated. It is the first to include explicit description of fine sediment deposition/erosion processes as a function of bed shear stress and the flocculation process. This framework integrates four existing numerical models: MOBED, RIVFLOC, RMA2 and RMA4 using river geometry, flow, fine suspended sediment characteristics and bathymetry data. Sediment concentration and particle size distributions computed by RIVFLOC were used as the upstream boundary condition for the reservoir dispersion model RMA4. The predicted particle size distributions and mass of fine river sediment deposited within various sections of the reservoir indicate that most of the fine sediment generated by the upstream disturbance deposits in the reservoir. Deposition patterns of sediment from wildfire-impacted landscapes were different than those from unburned landscapes because of differences in settling behaviour. These differences may lead to zones of relatively increased internal loading of phosphorus to reservoir water columns, thereby increasing the potential for algae proliferation. In light of the growing threats to water resources globally from wildfire, the generic framework described herein can be used to model propagation of fine river sediment and associated nutrients or contaminants to reservoirs under different flow conditions and land use scenarios. The framework is thereby a valuable tool to support decision making for water resources management and catchment planning.

Offshore Online Measurements of Total Suspended Solids Using Microscopy Analyzers.

Accurate online water quality measurements have gained attention during the last decades in the oil and gas industry for improving operational performance and protecting the surrounding environment. One potential solution to extend the reservoirs’ economic life and put less strain on the environment is by re-injecting the produced water, but the injected water quality must be high and consistent to prevent injectivity reduction. This paper evaluates two different online microscopy analyzers that utilize a high-resolution video camera for capturing images of the particles passing their view cell. The calibration procedure for both online microscopy analyzers has been thoroughly validated for steady-state and real-time measurements. The real-time measurements were achieved by post-processing the data captured by the microscopes and applying a trailing moving average window. The performance of measuring the oil-in-water concentration was compared with an online fluorescence-based monitor. The paper addresses the statistical considerations when defining the level of accuracy of the predicted particle size distribution within a defined confidence interval. Both microscopes showed promising results for measuring known particle sizes and oil-in-water concentrations, both in steady-state and real-time.

An evaluation of size-resolved cloud microphysics scheme numerics for use with radar observations Part II: Condensation and evaporation

AbstractAccurate numerical modeling of clouds and precipitation is essential for weather forecasting and climate change research. While size-resolved (bin) cloud microphysics models predict particle size distributions without imposing shapes, results are subject to artificial size distribution broadening owing to numerical diffusion associated with various processes. Whereas Part 1 addressed collision-coalescence, here we investigate numerical diffusion that occurs in solving condensation and evaporation. In a parcel model framework, all of the numerical schemes examined converge to one solution of condensation and evaporation as the mass grid is refined, and the advection-based schemes are recommended over the reassigning schemes. Including Eulerian vertical advection in a column limits the convergence to some extent, but that limitation occurs at a sufficiently fine mass grid, and the number of iterations in solving vertical advection should be minimized to reduce numerical diffusion. Insubstantial numerical diffusion in solving condensation can be amplified if collision-coalescence is also active, which in turn can be substantially diminished if turbulence effects on collision are incorporated. Large-eddy simulations of a drizzling stratocumulus field reveal that changes in moments of Doppler spectra obtained using different mass grids are consistent with those obtained from the simplified framework, and that spectral moments obtained using a mass grid designed to effectively reduce numerical diffusion are generally closer to observations. Notable differences between the simulations and observations still exist, and our results suggest a need to consider whether factors other than numerical diffusion in the fundamental process schemes employed can cause such differences.