A pore network model for calculating pressure drop in packed beds of arbitrary-shaped particles

A pore network model is built to predict pressure drop in packed beds of arbitrary-shaped particles, using a method that consists of particle packing by the rigid body technique, pore network construction by the maximal sphere algorithm, and numerical calculation of fluid flow. The pore network model is firstly validated by comparing with experiments, Ergun-type equations, and particle-resolved computational fluid dynamics (CFD). The pore network model is as accurate as the particle-resolved CFD, and is remarkably two to three orders of magnitude less computationally intensive. Then, the pore network model is used to calculate the pressure drops in the beds packed with particles of different shapes and sizes, as well as using different flow media. These calculation results prove the versatility of the pore network model. This work provides an accurate yet efficient pore network model for predicting pressure drop, which should be a powerful tool for designing packed beds.     

Mass transfer between irregular particles and liquid in packed beds

Dissolution of irregular particles has been studied in packed beds for the systems of alabaster-water, marble-aqueous HCl solutions and mossy zinc-aqueous acidic I₂ solutions, where the sphericity of particles varied in a wide range. The observed values of the Sherwood number have been correlated well by

     

Experimental and numerical investigation of structure and hydrodynamics in packed beds of spherical particles

In chemical industry, flows often occur in nontransparent equipment, for example in steel pipelines and vessels. Magnetic resonance imaging is a suitable approach to visualize the flow, which cannot be performed with classical optical techniques, and obtain quantitative data in such cases. It is therefore a unique tool to noninvasively study whole‐field porosity and velocity distributions in opaque single‐phase porous media flow. In this article, experimental results obtained with this technique, applied to the study of structure and hydrodynamics in packed beds of spherical particles, are shown and compared with detailed computational fluid dynamics simulations performed with an in‐house numerical code based on an immersed boundary method‐direct numerical simulation approach. Pressure drop and the radial profiles of porosity and axial velocity of the fluid for three packed beds of spheres with different sizes were evaluated, both experimentally and numerically, in order to compare the two approaches. © 2018 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 64: 1896–1907, 2018     

Modeling of the pressure drop across polydisperse packed beds in cake filtration

Filtration is the separation of solid–liquid mixtures. In this study, we assess the predictive power of Kozeny–Carman model for systems operated at low Reynolds numbers and relatively high pressure drops. We find substantial agreement between the K-C model and experiment only for systems that exhibit tight void size distribution. Dramatic disagreement is observed for particle beds that exhibit wide void size distributions. We propose a modified modeling approach, based on a bimodal void distribution, by introducing two quantities: the fraction of expanded voids and the ratio of void sizes. The simulation results are found to be much more similar to the experimental flow rates than those calculated using the K-C model. The modified model is deemed reliable at predicting the flow behavior, provided that an accurate representation of the void size distribution is available.     

Deposition of Brownian particles in packed beds

An analysis is presented to describe the deposition of Brownian particles from suspensions flowing through granular media. The constricted tube porous media model recently proposed by Payatakes et al.[8] was used to characterize the media and the deposition process was assumed to be controlled by convective diffusion as well as the nature of the surface interaction between the media grains and the Brownian particles. Three different tube configurations were considered and the differences among the results were found to be relatively unimportant. Agreement between the analysis and available experimental data was found to be reasonably good for the limiting case when the surface effect is favorable.     

Modelling of pressure drop in packed columns

The correct choice of packing is of decisive importance for optimum process efficiency in the operation of two-phase countercurrent columns. An important criterion for this choice is the pressure drop in the gas flow. Theoretical relationships are derived for calculating the pressure drop in beds with dry and trickle packings. It has been demonstrated by comprehensive experiments that these relationships allow the pressure drop to be determined more accurately than by previous methods. The experiments were performed at the Department of Thermal Separation Processes of Bochum University on 54 different packed beds, using 24 different systems.     

Pressure drop across packed beds in the low Knudsen number regime

The solutions of Happel and Kuwabara describing flow through systems of multiple spheres have been compared with available pressure drop data to determine the applicability of cell models for analyzing flow in packed beds. The comparisons indicate that these solutions describe the flow with reasonable accuracy. Of the two solutions, the Kuwabara flow field has been found to give better agreement between predictions and experimental results. In order to describe flow in beds operating at low Knudsen numbers the Kuwabara solution has been extended by allowing for gas slippage at the collecting surfaces. The resulting solution is presented as a correction to the Basset-Millikan expression and accounts for the presence of neighboring spheres in low Knudsen number flows. Using this extended solution, the pressure drop across packed beds is predicted as a function of Knudsen number and packing density.     

Foam and drop penetration kinetics into loosely packed powder beds

Foam granulation is a new liquid delivery method for wet granulation, where the liquid binder is delivered as an aqueous foam, rather than as an atomised spray to the powder bed. This paper reports for the first time the similarities and differences between wet granulation via foamed and sprayed binder addition methods.The kinetics of single foam and single drop (of HPC and HPMC solutions) penetrations into loosely packed powder beds (of glass ballotini and lactose powders) were studied. Specific penetration time (defined as penetration time per unit of binder mass) and nucleation ratio (defined as the ratio of nuclei granule mass to liquid binder mass) were compared between foam and drop nucleation methods. The impact of particle size and binder concentration on both parameters was also studied.The results indicate that the foamed binder addition method allows a greater mass of binder fluid to be absorbed into the particle bed and uses less liquid binder to nucleate the same number of gram of powder, which indicates improved nucleation efficiency compared to the drop addition method.     

Near-wall porosity characteristics of fixed beds packed with wood chips

Packed beds of fuel wood chips are commonly found in thermal conversion processes such as combustion or gasification. Wood chips in particular are mostly used as fuel for small-scale domestic heating boilers but also for commercial-scale combustion units. The characterization of spatial voidage distribution inside the wood chip beds is of great importance for flow and reactor modelling. This study focuses on the radial porosity variations of cylindrical beds of three different types of commercially available wood chips including chips classified as G30 size class. The conventional technique of consolidating packed beds with a resin was chosen as the experimental procedure. The radial voidage distribution in different cylindrical beds is determined by image analysis of sections of the solidified packings. Additionally, a packing of monosized spheres was investigated in order to assess the selected procedure in comparison with widely available literature data for spheres. The results are discussed and summarized in a mathematical expression correlating the radial voidage distribution depending on average wood chip size, packing core porosity and dimensionless distance from the tube wall.     

Effective thermal conductivity of packed beds of silicon-copper particles

The effective thermal conductivity of a bed of silicon-copper particles, as used in the technical synthesis of silicones was measured with a non-stationary method. The particles have an irregular shape and an average diameter of 0·111 mm.From the measured temperature profiles and from literature it was concluded that a mechanism, in which the energy transfer occurs through a series path consisting of an effective solid-path length and gas-path length, plays the main part in the model for heat transfer suggested by Masamune and Smith.The values for the effective thermal conductivity were in the region 0·192–0·440 kcal m^?1 h^?1 deg^?1.     

Analysis of flow in rotating packed beds via CFD simulations—Dry pressure drop and gas flow maldistribution

Three-dimensional unsteady-state turbulent rotating single-phase flows were simulated in rotating packed beds (RPB) and were validated using overall dry pressure drop measurements for three RPB designs [Liu, H.-S., Lin, C.-C., Wu, S.-C., Hsu, H.-W., 1996. Characteristics of a rotating packed bed. Industrial and Engineering Chemistry Research 35, 3590-3596; Sandilya, P., Rao, D.P., Sharma, A., Biswas, G., 2001b. Gas-phase mass transfer in a centrifugal contactor. Industrial and Engineering Chemistry Research 40, 384-392; Zheng, C., Guo, K., Feng, Y.D., Yung, C., 2000. Pressure drop of centripetal gas flow through rotating bed. Industrial and Engineering Chemistry Research 39, 829-834]. Analysis of the radial and tangential velocities highlighted the impact of gas feed entrance effects on the peripheral gas maldistribution in the rotating packing module. Recommendations were formulated for an optimum design with the aim to reduce gas flow maldistribution in RPBs. Breakdown of the overall pressure drop in its modular components for the housing, the rotating packing module, the free inner rotational zone, and the gas disengagement showed that the dissipation in the rotating packing could be a minor contributor to the overall pressure drop which may be undesirable in terms of RPB mass transfer and reaction efficiencies. Analysis of the simulated pressure drops allowed development of CFD-based Ergun-type semi-empirical relationships in which the gas-slip and radial acceleration effects, the laminar and inertial drag effects, and the centrifugal effect were aggregated additively to recompose the pressure drops in the rotating packing module.     

Correlations for critical fluidization velocity and maximum bed pressure drop for heterogeneous binary mixture of irregular particles in gas–solid tapered fluidized beds

The tapered fluidized bed is a remedial measure for certain drawbacks of the gas–solid system, by the fact that a velocity gradient exists along the axial direction of the bed with increase in cross-sectional area. To study the dynamic characteristics of heterogeneous binary mixture of irregular particles, several experiments have been carried out with varying tapered angles and composition of the mixtures with various particles. The tapered angle of the bed has been found to affect the characteristics of the bed. Models based on dimensional analysis have been proposed to predict the critical fluidization velocity and maximum bed pressure drop for gas–solid tapered fluidized beds. Experimental values of critical fluidization velocity and maximum bed pressure drop compare well with that predicted by the proposed models and the average absolute errors are well within 15%.     

Prediction of bed pressure drop and top packed bed formation in gas-liquid-solid semi-fluidized bed with irregular homogeneous binary mixtures

We studied the hydrodynamics of a gas-liquid-solid semi-fluidized bed relating to packed bed formation and bed pressure drop with irregular homogeneous binary mixtures in a 0.05 m internal diameter Perspex column, with water and air (secondary) as fluidizing medium at constant static bed height of 0.08 m. A homogeneous binary mixture has been taken for easy formation of a semi-fluidized bed. Air is supplied centrally below the bottom grid in radial direction with a special design air sparger after the bed is first fluidized by the liquid. Experimental parameters studied included superficial gas and liquid velocities, average particle size and density and the bed expansion ratio. Empirical and semi-empirical models were developed. The calculated values from predicted models were compared with the experimental values and fairly good agreement was obtained.     

Pressure drop and liquid holdup for two phase concurrent flow in packed beds

Pressure drop and liquid holdup for two-phase concurrent downward flow in packed beds were correlated for various types of packings by taking into account two hydrodynamic regimes: a poor and a high gas-liquid interaction regime.Foaming and non-foaming systems have been considered.In the poor interaction regime, the pressure drop was calculated as due to the gas flowing in a bed restricted by the presence of the liquid. A correlation valid for a free liquid trickling, modified in order to take into account the effect of the pressure drop, is proposed and used to correlate liquid holdup in the presence of a concurrent gas flow.In the high interaction regime, empirical correlations were proposed for both foaming and non-foaming systems.All the employed correlations fit experimental results from several authors better than those proposed in the literature.     

Wall effects for the pressure drop in fixed beds

A very simple model is presented for the effect of the container wall on the pressure drop in a fluid flowing through a bed of spheres. It is based on the application of the Ergun equation to the bulk region of the bed, unaffected by the wall. Pressure loss predictions are found to correspond well to the opposing trends reported in the literature for the viscous- and inertial-flow regimes.