Digital predictions of complex cylinder packed columns

A digital computational approach has been developed to simulate realistic structures of packed beds. The underlying principle of the method is digitisation of the particles and packing space, enabling the generation of realistic structures. Previous publications [Caulkin, R., Fairweather, M., Jia, X., Gopinathan, N., & Williams, R.A. (2006). An investigation of packed columns using a digital packing algorithm. Computers & Chemical Engineering, 30, 1178–1188; Caulkin, R., Ahmad, A., Fairweather, M., Jia, X., & Williams, R. A. (2007). An investigation of sphere packed shell-side columns using a digital packing algorithm. Computers & Chemical Engineering, 31, 1715–1724] have demonstrated the ability of the code in predicting the packing of spheres. For cylindrical particles, however, the original, random walk-based code proved less effective at predicting bed structure. In response to this, the algorithm has been modified to make use of collisions to guide particle movement in a way which does not sacrifice the advantage of simulation speed. Results of both the original and modified code are presented, with bulk and local voidage values compared with data derived by experimental methods. The results demonstrate that collisions and their impact on packing structure cannot be disregarded if realistic packing structures are to be obtained

Packing items from a triangular distribution

We consider the problem of packing n items which are drawn according to a probability distribution whose density function is triangular in shape. For triangles which represent density functions whose expectation is 1/p for p = 3, 4, 5, ..., we give a packing strategy for which the ratio of the number of bins used in the packing to the expected total size of the items asymptotically approaches 1

Targeted optimization of chromatographic columns based on 3D analysis of packing microstructure

The preparation, structure, and performance of functional materials porous are strongly interrelated. Hence, a detailed analysis of the pore structure of a functional porous material in combination with a detailed characterisation of its performance can provide an understanding of the influence of individual parameters during preparation and thus identify structural limitations to an improved utilization. The obtained results can be used to tune the preparation towards a better pore structure suited for the targeted application. This work focuses on packings of silica-based particles for highly efficient chromatographic separations. The prepared packings combine an interparticle macropore space for fast flow-based transport with an intraparticle mesopore space providing high surface areas for molecule-surface interactions. Such packed columns have a wide field of application, not only in highly efficient separations, but also for catalysis, and (energy) storage However, the focus here is on separations in liquid chromatography. In Chapter 1, the influence of the slurry concentration on separation efficiency and bed structure was investigated for capillary columns (75 µm inner diameter, 30 cm length) packed with 1.3 µm bridged-ethyl hybrid (BEH) fully porous silica particles. The slurry concentration was varied from 5 to 50 mg/mL while every other packing parameter was kept constant. Chromatographic characterisation with hydroquinone as weakly retained analyte revealed highly efficient separations (reduced plate heights as low as 1.5) at an optimal intermediate slurry concentration of 20 mg/mL for this specific set of packing parameters. Confocal laser scanning microscopy (CLSM) was utilized to conduct a three-dimensional reconstruction and to carry out a detailed morphological analysis of the column with the best performance, a column packed with a slurry concentration below the optimum, and one packed above the optimum. Two counteracting effects were revealed: Radial heterogeneities limit the separation efficiency for columns packed at low slurry concentrations. With an increase in slurry concentration, these radial effects get supressed but the number and size of large voids with a diameter similar to the mean particle diameter increase significantly. Interestingly, the reconstructions also revealed high external bed porosities between 0.47 and 0.50 which are higher than expected with respect to the random loose packing limit reported for frictional, cohesionless particles. However, no signs of bed instability could be observed demonstrating the significant impact of interparticle forces for particles as small as 1.3 µm. In Chapter 2, the investigation of the optimal slurry concentration was expanded by analysing the effects for a different particle size to obtain a more general picture. A similar set of capillary columns (75 µm inner diameter, 45 cm length) was packed with 1.9 µm BEH particles at eleven different slurry concentrations between 5 and 200 mg/mL including additional tests for reproducibility at selected concentrations and the observation of bed formation using optical microscopy. While comparable reduced plate heights were achieved, the observed optimum of 140-160 mg/mL to pack highly efficient columns reproducibly differed significantly from the 20 mg/mL for the 1.3 µm particles identified in Chapter 1. This can be explained by the difference in the particle diameter as interparticle forces and particle aggregation become more dominant at still smaller diameters. CLSM-based reconstructions revealed similar trends in the bed structures as seen in Chapter 1. At low concentrations, pronounced ordered particle layers in the direct vicinity of the column wall, local bed densification near the column wall, and particle size-segregation limit the achieved separation efficiency. The peculiarity of the first effect is continuously decreasing with an increase in the slurry concentration even beyond the optimum while the latter two effects are already supressed at the optimal slurry concentration. On the other hand, the number and size of large voids increase with an increase in the utilized slurry concentration as already seen in Chapter 1. The videos acquired during column packing provided very helpful insights into bed formation mechanisms and thus delivered possible explanations for these structural features. At 10 mg/mL, particles arrive individually at the bed front allowing individual settlement and rearrangement on the arrival of following particles what allows a discrimination of particles according to their individual properties. The picture looks completely different for 100 mg/mL as example for higher concentrated slurries. Here, particles tend to aggregate during packing and arrive in large batches. This prevents discrimination of individual particles but significantly reduces the chances for rearrangement and is thus prone to the conservation of defects formed between the border of the arriving batches of particles and the front of the bed. Chapter 3 is based on the results obtained during the work presented in Chapters 1 and 2. The combination of high slurry concentration and ultrasound was already proposed there as chance to keep transcolumn heterogeneities as low as possible while preventing the formation of large voids. To test this hypothesis, two sets, each consisting of three capillary columns (75 µm inner diameter, 100 cm length) were packed with 1.9 µm BEH particles at a slurry concentration of 200 mg/mL; one set under application of ultrasound during packing, the other one without. All three columns, which underwent sonication, showed significantly better performance than each of the other columns. The obtained reduced minimum plate height for a weakly retained analyte was even lower than the already impressive value of 1.5 for columns packed at a slurry concentration optimal for packing without sonication and reached values close to unity over a length of 1 m for the best-performing column. The achieved theoretical plate counts of ~500,000 demonstrate a unique potential for highly efficient separations of extremely complex samples. In Chapter 4, the focus is shifted from capillary columns to the more common analytical format. CLSM could not be applied here as the steel columns are not transparent and extrusion of the bed is not possible without losing either stability or optical transparency. Thus, an imaging and reconstruction procedure based on focused ion beam scanning electron microscopy was developed using a commercial narrow-bore analytical column (2.1 mm inner diameter, 50 mm length) packed with 1.7 µm BEH particles. The packing was embedded with poly(divinylbenzene) prior to extrusion from the steel column in order to conserve the bed structure. Two image stacks were acquired and reconstructed at characteristic positions within the bed: one in the central section of the column along the flow direction to obtain the bulk properties of the bed and one from the column wall towards the column centre to investigate and quantify the influence of the geometrical wall effect and the second wall effect. To investigate the effect of the microstructure in the wall region on local flow through the bed, a radially resolved flow profile was obtained by lattice-Boltzmann simulations. For this column, the region affected by wall effects spanned over approximately 62 particle diameters showing a decrease in the local mean porosity by up to 10% and an increase in the local mean particle diameter by up to 3% with respect to the bulk region inducing a decrease of the local flow velocity by up to 23%. Furthermore, four more ordered layers of particles were formed directly at the hard column wall due to the geometrical wall effect leading to local velocity fluctuations by up to a factor of three. These quantified structural features are in excellent agreement with previous reports about macroscopic characterisations of the wall effects by optical or chromatographic measurements

Impact of shape representation schemes used in discrete element modelling of particle packing

In different computer models, shape is represented using different methodologies, to varying degrees of precision. This paper examines two approaches to shape representation, and their effects on accuracy in the context of cylindrical particle packing. Two discrete element method (DEM) based software packages are used. A X-ray CT scan of a packed bed provides the experimental measurements for comparison. Eight sphere-composite representations of the same cylindrical pellet were tested. Two of these gave results that quantitatively follow experimental measurements. A range of factors that in theory could affect accuracy of the simulation results are examined, including edge roundedness, surface roughness and restitutional behaviour as a function of sphere-composite representations. The conclusion is that, for packing at least, matching the object's overall shape and dimensions is not enough. Only when a high enough resolution is applied to corners and edges, could the sphere-composite approach possibly match the experimental data quantitatively

Validation of a stochastic digital packing algorithm for porosity prediction in fluvial gravel deposits

Porosity as one of the key properties of sediment mixtures is poorly understood. Most of the existing porosity predictors based upon grain size characteristics have been unable to produce satisfying results for fluvial sediment porosity, due to the lack of consideration of other porosity-controlling factors like grain shape and depositional condition. Considering this, a stochastic digital packing algorithm was applied in this work, which provides an innovative way to pack particles of arbitrary shapes and sizes based on digitization of both particles and packing space. The purpose was to test the applicability of this packing algorithm in predicting fluvial sediment porosity by comparing its predictions with outcomes obtained from laboratory measurements. Laboratory samples examined were two natural fluvial sediments from the Rhine River and Kall River (Germany), and commercial glass beads (spheres). All samples were artificially combined into seven grain size distributions: four unimodal distributions and three bimodal distributions. Our study demonstrates that apart from grain size, grain shape also has a clear impact on porosity. The stochastic digital packing algorithm successfully reproduced the measured variations in porosity for the three different particle sources. However, the packing algorithm systematically overpredicted the porosity measured in random dense packing conditions, mainly because the random motion of particles during settling introduced unwanted kinematic sorting and shape effects. The results suggest that the packing algorithm produces loose packing structures, and is useful for trend analysis of packing porosity

Computational analysis of transitional airflow through packed columns of spheres using the finite volume technique

Copyright © 2010 Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Computers and Chemical Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computers and Chemical Engineering, Volume 34 Issue 6 (2010), DOI: 10.1016/j.compchemeng.2009.10.013We compare computational simulations of the flow of air through a packed column containing spherical particles with experimental and theoretical results for equivalent beds. The column contained 160 spherical particles at an aspect ratio N=7.14N=7.14, and the experiments and simulations were carried out at particle Reynolds numbers of (RedP=700−5000)(RedP=700−5000). Experimental measurements were taken of the pressure drop across the column and compared with the correlation of Reichelt (1972) using the fitted coefficients of Eisfeld and Schnitzlein (2001). An equivalent computational domain was prepared using Monte Carlo packing, from which computational meshes were generated and analysed in detail. Computational fluid dynamics calculations of the air flow through the simulated bed was then performed using the finite volume technique. Results for pressure drop across the column were found to correlate strongly with the experimental data and the literature correlation. The flow structure through the bed was also analysed in detail