Radial Dispersion Coefficient Research Articles

On the Role of Radial Dispersion in the Behavior of a Cooled Fixed‐Bed Reactor: Numerical Investigation of Fischer–Tropsch Synthesis with a Cobalt‐Based Catalyst

AbstractThe impact of radial dispersion of both heat and mass on the behavior of cooled fixed‐bed reactors was explored using a two‐dimensional reactor model. This study accounted for dispersion through an effective radial thermal conductivity (λrad) and a radial dispersion coefficient of mass (Drad), with Fischer–Tropsch synthesis serving as an illustrative process example. Under moderate reaction conditions and hence still rather gentle radial temperature profiles, the effect of mass dispersion on reactor performance was found to be minimal, even if disregarded (Drad = 0), whereas dispersion of heat (λrad) always significantly impacts reactor behavior. Nevertheless, for precise thermal runaway predictions by a reactor model, incorporating mass dispersion by a realistic Drad value is essential.

Investigating hydrodynamics and gas diffusion coefficient in CFB of binary particles with significant differences in particle properties

A composite fluidized bed (SCFB), which integrated the bubbling fluidization and circulating fluidization into one bed, was developed in this work. Wavelet transform was employed to analyze time-series signals of the pressure fluctuations and the steady-state tracer injection technique was used to study the gas diffusion coefficient in SCFB. The energy contribution in BFB and CFB mainly concentrated on the macrostructures, while that in SCFB was caused principally by the mesostructures as gas velocity was high. The circulating particles could effectively reduce particle aggregates and promoted a uniform distribution of heavy particles in the bottom region. Radial dispersion coefficients in SCFB were greater than that in BFB and CFB, demonstrating that the circulating particles enhanced gas mixing in SCFB. The ratio of Da/Dr in SCFB was less than that in BFB, indicating that gas-solid flow in SCFB was more closely to the mixed-type flow compared to the BFB.

Numerical investigation on the influence of immersed tube bundles on biomass gasification in industrial-scale dual fluidized bed gasifier

Immersed tubes play a pivotal role in enhancing fluidization quality within fluidized beds by effectively disrupting bubbles. However, the effect of such internals within a large-scale gasification apparatus remains unclear. Consequently, this study focuses on numerically simulating biomass steam gasification within an industrial-scale dual fluidized bed gasifier that features immersed tube bundles using the multiphase particle-in-cell method. In this method, particles with identical properties are grouped, and the interparticle collisions are model via the solid stress to improve computational efficiency. The numerical model has been well verified with experiment in terms of bed pressure drop, solid recirculation and chemical reactions. Some main conclusions are shown as follows. Immersed tubes significantly alter the motion of gas and particles in the gasifier. The presence of immersed tubes can ameliorate solid entrainment and avoid excess particles escaping from the gasifier. The asymmetrical structure of the gasifier results in asymmetrical distribution of gas temperature and gas species. Increasing the number of immersed tubes slightly enhances particle temperature near the loop seal outlet. The radial biomass dispersion coefficient and axial sand dispersion coefficient decrease about 40.9 % and 28.9 % when increasing the immersed tube number from three to nine. The results provide enhanced understanding of the role of immersed tubes in altering gas-particle interactions and fluidization dynamics in industrial-scale fluidized bed gasifier.

Mixing effects on the gas flow and mass transfer in a vertical single helical ribbon agitated reactor for propylene polymerization

The gas–solid vertical single helical ribbon agitated reactor is widely used in the polypropylene industry. The gas flow and mass transfer determine the heat transfer capacity and product quality. In this work, the pressure drop was measured below and above minimum fluidization velocity (umf). Then, the axial and radial dispersion coefficients (DL and DR) were estimated below umf by measuring the step residence time distribution and the stationary radial tracer profiles, respectively. Pressure analysis show the agitation significantly reduces the bed pressure drop, changing the fixed bed below umf and bubbling bed above umf to an agitated bed with a periodic voidage. The DL was proportional to the gas velocity, with little influences of the stirring speed. The radial tracer profiles show the bed is divided by the inner diameter of the helical ribbon into the peripheral ascending region and the central descending region, without gas exchange between them. Furthermore. the tracer profiles in the descending region are classified into two types. For type I, the DR, calculated by the plug flow model with radial dispersion, is proportional to the gas velocity, with little effects of stirring speed. Type II shows uniform profiles due to the deflection of the gas flow toward the low pressure area at the inner diameter of helical ribbon. The causes of the two types are explained by the relative size of particle circulation and gas flux. These two flow regimes are quantitatively clarified with an empirical correlation of Re and Fr as flow regime transition boundary, namely dispersed plug flow and perfect mixing flow. With lower Re and higher Fr, it changes from dispersed plug flow to perfect mixing flow.

Experimental Quantification of the Radial Mixing of Binary Mixtures in Annular Fluidized Beds Using the Capacitance Probe Method

A novel measurement system for radial particle mixing in annular fluidized beds is designed on the basis of the capacitance probe method. Mixing parameters at different radial positions are acquired. The effects of the convection/diffusion mechanism on radial mixing are analyzed individually. It is found that the governing mechanism of mixing at the axial line is convection; meanwhile, diffusion is the governing mechanism of mixing near the wall. The effect of convection on radial mixing at the upper part is more important than that at the lower part. The radial dispersion coefficient ranges from 0.006 to 0.072 m2/s. At the upper part, the radial dispersion coefficient at half-radius is between 0.016 and 0.072 m2/s and that near the wall is 0.006 and 0.028 m2/s, which is four times and twice that at the same radial position and at the lower part, respectively. The radial dispersion coefficient is about 1.5 times that in two-dimensional fluidized beds.

Detailed computational fluid dynamics study of the parameters contributing to the viscous heating band broadening in liquid chromatography at pressures up to 2500 bar in 2.1 mm columns

Over the past years viscous heating band broadening occurring in high pressure liquid chromatography has been studied extensively. In the present numerical study, we investigate the fine details of this band broadening contribution under extreme high-pressure conditions (2500 bar). To analyze the results, we first show that viscous heating leads to two clearly distinguishable band broadening effects, one originating from the radial differences in the species migration velocity and the other from the axial variations. It was found that the radial contribution is independent of the intrinsic band broadening of the bed (i.e. band broadening in absence of viscous heating) while it strongly depends on the radial dispersion coefficient and the retention enthalpy of the analytes. On the other hand, the axial contribution is strongly dependent on the bed intrinsic band broadening and it is found to be 4 to 5 times lower than the radial contribution. We also show the strong effect of the endfittings on the temperature gradients inside the column thus on the resulting viscous heating band broadening.

Mixing of nanoparticle agglomerates in fluidization using CFD-DEM at ABF and APF regimes

Mixing of nanoparticle agglomerates in a fluidized bed was investigated by CFD-DEM. A parallel program was used that simultaneously uses the computational resources of GPU and CPU on a single computer. The bed expansion obtained from simulation was compared with experimental and good agreement was observed. Bed expansion in agglomerate particulate fluidization (APF) was 2 to 5 times the initial bed height and final bed expansion in agglomerate bubbling fluidization (ABF) was 1 to 2 times the initial bed height by changing the gas velocity from 2 to 4 and 4 to 8cm/s for APF and ABF regimes respectively. Gas volume fraction distribution was investigated for both APF and ABF regimes, which showed a more uniform distribution in APF. Increasing the gas velocity led to a more homogenous in the APF bed but it did not change the homogeneity of the ABF bed. Besides, the axial and radial dispersion coefficients in ABF were greater than those in APF. Axial dispersion coefficient varied from 2×10−6 to 4×10−5m2/s. Lacey mixing index was investigated in both APF and ABF regimes and it showed that the quality of mixing in ABF was better than APF.

Pore-scale analysis of axial and radial dispersion coefficients of gas flow in macroporous foam monoliths using NMR-based displacement measurements

A micro-scale analysis of mass transport in ceramic foams that are used as catalyst supports in gas phase reactions is of high interest. Although the effects of flow rate and foam parameters on the radial and axial dispersion are known for liquid flows, no pore-scale experimental analysis has been yet reported to correlate the mechanical and diffusional dispersion of gas flows to the geometry of open-cell foams. Here, a spatially resolved Pulsed Field Gradient NMR method is applied to determine dispersion coefficients of thermally polarized gas along axial and transversal directions of open-cell foams. The comparative study of three commercial foam samples with different morphologies shows the effect of open porosity, window size, and flow rate on gas dispersion. Additionally, the influence of mechanical and diffusional dispersion at each flow rate is investigated for individual samples. By observing the transition from diffusional dispersion to mechanically driven dispersion of gas, it is found that diffusional dispersion plays an important role, even at higher flow rates after a transition from Darcy to Darcy-Forchheimer regime occurs. The measured values for dispersion coefficients of methane can be directly used in pseudo-heterogeneous models for the methanation reaction.

Alternative method to study the radial dispersion in liquid chromatography columns. Part I: Theory

We report on an alternative experimental method to determine the transversal or radial dispersion coefficient (Drad) in packed bed columns for liquid chromatography. The method uses a recently developed type of column end-fitting with an impermeable segmentation ring that splits the incoming flow in a central and peripheral part. Using this device and continuously sending a tracer-laden flow through the central inlet and a tracer-less flow through the peripheral inlet, a steady-state radial dispersion pattern is established which can be used to determine the degree of radial dispersion.The present part of the study lays the theoretical foundation for the method and shows the parameter sensitivity of the different possible data analysis variants. In addition, computational fluid dynamics simulations have been used to validate the established procedure (agreement between true and determined Drad-value better than 0.4%) as well as to study the effect of the most important error sources: the presence of the annular flow segmentation ring and the almost inevitable occurrence of mismatches between the central and the peripheral in- and outlet flows. In the latter case, a combined read-out method can be proposed that nearly perfectly compensates for the flow mismatch error (remaining error on the Drad-value smaller than 3%).

Computational tomography and CFD simulation of a biofilter treating a toluene, formaldehyde and benzo[α]pyrene vapor mixture

In this work, a 3D computational tomography (CT) of the packing material of a laboratory column biofilter is used to model airflow containing three contaminants. The degradation equations for toluene, formaldehyde and benzo[α]pyrene (BaP), were one-way coupled to the CFD model. Physical validation of the model was attained by comparing pressure drops with experimental measurement, while experimental elimination capacities for the pollutants were used to validate the biodegradation kinetics. The validated model was used to assess the existence of channeling and to predict the impact of the three-dimensional porous geometry on the mass transfer of the contaminants in the gas phase.Our results indicate that a physically meaningful simulation can be obtained using the techniques and approach presented in this work, without the need of performing experiments to obtain macroscopic parameters such as gas-phase axial and radial dispersion coefficients and porosities.

DEM simulation of cubical particle percolation in a packed bed

In this paper, percolation of cubical particles through a packed bed is studied using discrete element method (DEM). The influences of some key variables e.g. restitution coefficient, sliding coefficient, rolling coefficient and diameter ratio on cubical particles percolation behaviour were comprehensively analyzed. The results show that, compared with the sphere particles, cubical particles also have a constant vertical velocity during percolating in the packed bed, but it has a larger percolation velocity and a less off-center of radial distance. Restitution coefficient affects the cube percolation behaviour. With increasing the restitution coefficient, the percolation velocity decreases, but the radial dispersion coefficient increases. Effects of sliding friction coefficient and rolling friction coefficient show the same tendency. The percolation velocity and radial dispersion decrease with the increase of friction coefficient. The ratio of cubical particle diameter to packing particle diameter (diameter ratio) is another dominant variable that significantly affect the percolation behaviour. The percolation velocity and radial dispersion coefficient increases with decreasing the diameter ratio. The simulations are useful for understanding percolation and segregation of multi-scale cubical materials and optimization in cubical particles handling and mixing.

Experimental study of liquid renewal on the sheet of structured corrugation SiC foam packing and its dispersion coefficients

Developing efficient catalytic packing for reactive distillation can push its application greatly forward. Structured Corrugation SiC Foam Packing is considered an attractive candidate with the rapid development of the coating method. However, liquid flow behavior on the packing and its radial and axial dispersion coefficients remain unclear. We studied herein liquid renewal on the structured corrugation SiC foam packing sheet by photography. The images revealed that the liquid could be constantly refreshed on most of the wetted area and the process can be categorized into two stages by the renewal rate. Effects of liquid flow rate, viscosity, and surface tension on the renewal process were investigated. The renewal results highlight the applicability of the foam packing at low liquid load. Furthermore, axial and radial dispersion coefficients of two foam packing sheets with different pore sizes were characterized, and comparisons with KATAPAK-S showed that the foam packing has better liquid dispersion ability.

Hydrodynamics of descending gas-liquid flows in solid foams: Liquid holdup, multiphase pressure drop and radial dispersion

In this contribution we report on spatially resolved analysis of multiphase hydrodynamics in solid foam packed trickle bed reactors. For the investigation we used ultrafast X-ray computed tomography and fast response pressure transducers. The SiSiC foams’ pore density, the liquid distribution system as well as gas and liquid flow rates were varied. The transient behavior of the liquid holdup at trickle and pulse flow as well as after drainage were examined and correlations for static and dynamic holdups were derived. The correlations are based on Eötvös, Reynolds and Galileo number, using porosity and specific area for the definition of the hydraulic diameter. The correlations are applicable to a wide range of foam morphologies, pore densities and operating conditions reported in the literature. The axial pressure gradients in the solid foams showed significantly lower pressure drop compared to particle packings of similar specific surface area. The evolution of liquid spreading was analyzed qualitatively and quantitatively with various irrigation patterns. In addition, an approach for the determination of radial liquid dispersion coefficients in solid foams is presented.

CFD MODELING OF BINARY MIXTURE HYDRODYNAMICS IN GAS-SOLID PARTICLE FLUIDIZED BED REACTOR SYSTEM

The objective of this research was to compare the effect of a binary mixture between coal, including 500, 700 and 1000-micron size, and sand, 180-micron size, on the mixing behavior in a fluidized bed system. In addition, suitable computational fluid dynamics drag models were explored, including an EMMS model, Gidaspow model and Wen & Yu model. The simulation results were compared for correctness with real plant information. The EMMS model matched well with the obtained data, This is because the employed model considers the particle cluster effect. The EMMS drag model was then used for further computational fluid dynamics simulation. The levels of mixing between sand and coal were predicted by turbulent dispersion coefficient. These coefficients of coal particle were exhibited in axial and radial direction. The highest turbulent dispersion coefficients were found in the mixture with 500 and 1000 micron coal size for radial and axial directions, respectively. The low axial turbulent dispersion coefficient and high radial turbulent dispersion coefficient were preferred for good hydrodynamics behavior.

Experimental Investigation of Liquid Axial and Radial Dispersion in Winpak Modular Catalytic Structured Packing

The response technique was employed to investigate the axial and radial dispersion characteristics of the liquid phase in modular catalytic structured packing (MCSP) reaction elements. Residence time distribution (RTD) experiments were performed at ambient temperature and atmospheric pressure. A two-dimensional dispersion model was solved analytically to determine the axial and radial dispersion coefficients and the dynamic liquid holdup from the RTD curves. Three different reaction elements containing Winpak packing sheets, Mellapak packing sheets, or only catalytic particles were employed. The radial dispersion coefficient in these structures is approximately 1–2 orders of magnitude higher than the axial dispersion coefficient. The axial and radial dispersion coefficients in the Winpak elements are greater than those in the other structures. Thus, it can be concluded that the liquid dispersion characteristics in the Winpak elements are satisfactory. These measured dispersion coefficients enable the reli...

Heat transport in catalytic sponge packings in the presence of an exothermal reaction: Characterization by 2D modeling of experiments

Heat transfer in catalytically coated sponge packings (open-cell foams) was investigated by experiments in a tubular cooled-wall reactor while conducting an exothermal reaction. A two-dimensional (2D) reactor model was developed to analyze quantitatively the steady-state temperature distributions, which were measured at 108 different positions in the reaction zone at well-defined reaction conditions of varied severity. The heat transport inside the packings was described by correlations for the effective axial and radial two-phase thermal conductivities. The key model parameters are the effective static two-phase thermal conductivities and the axial and radial dispersion coefficients, which have been assessed for sponge supports made of mullite and of α-Al2O3 with different porosities. The resulting simulations of conversions and spatial temperature distributions were in very good agreement with the experimental data. The reactor model was also used as a predictive tool to evaluate other sponge types. The simulations indicate that packings made of well-conducting solids like SiC or Al-alloys are useful supports for reactions with high enthalpy change, when hot spot or catalyst bed temperatures need to be controlled.

Axial and Radial Dispersion in a Large‐Diameter Bubble Column Reactor at Low Height‐to‐Diameter Ratios

AbstractExperiments are conducted in a bubble column reactor with inner diameter of 970 mm at atmospheric pressure with an air/water system at height‐to‐diameter ratios of 1 and below. Axial and radial dispersion coefficients are measured using a tracer, which is detected by conductivity probes. An analytical mathematical model for the determination of the dispersion coefficients from the experiments is presented. The measurements show the determined axial dispersion coefficients to vary significantly over the height of the column while increasing linearly with the gas flow rate.

Determination of Radial Dispersion Coefficient in Beds of Sand from Measurements of the Rate of Dissolution of Buried Cylinders Aligned with the Flow

A method is presented for determining the coefficient of transverse dispersion in flow through packed beds, which is based on the measurement of the rate of dissolution of planar or cylindrical surfaces, buried in the bed and aligned with the flow direction. The underlying theory is initially explained and experiments are then described in which more than three hundred new data points were obtained. These data are for the flow of water, at interstitial velocities between 0.1 and 1.5 mm/s, through beds of silica sand with average particle sizes between 0.219 and 0.496 mm. The experiments were performed at a range of temperatures, between 20oC and 35oC, and this yielded dispersion data for values of the Schmidt number (Sc=μ/ρDm) between 1170 and 570. For all the data reported, the ratio between the coefficient of transverse dispersion and the coefficient of molecular diffusion was shown to correlate well with the Reynolds number (Re=udρ/μ), both for beds with narrow and with wide particle size distributions.

In-depth system parameters of transition flow pattern between turbulent and fast fluidization regimes in high solid particle density circulating fluidized bed reactor

The transition flow between turbulent and fast fluidization regimes in high solid particle density circulating fluidized bed reactor was successfully investigated in this study. In addition, the effects of computational cell and simulation time were compared. Then, the comprehensive explanation and in-depth system parameters were discussed. The results showed the unique system characteristics. For the transition flow between turbulent and fast fluidization regimes, lower range of energy spectrum than the turbulent and fast fluidization regimes was found. As the increasing of gas inlet velocity, the axial and radial solid particle dispersion coefficients increased and decreased, respectively. For the axial and radial gas dispersion coefficients, both of them were increased with the increasing of gas inlet velocity. At the near wall region, the transition flow had no obvious power spectrum peak except the one below 0.2Hz, while, at the center region, the maximum peak at 5.0Hz was found. All the velocities had no significant correlation with solid volume fraction. The solid particle–solid particle interaction or collision then governs the system characteristic. The transition flow between turbulent and fast fluidization regimes will be an alternative choice for applying with circulating fluidized bed reactor in other new physical and chemical processes.

On the near-wall accumulation of injectable particles in the microcirculation: smaller is not better.

Although most nanofabrication techniques can control nano/micro particle (NMP) size over a wide range, the majority of NMPs for biomedical applications exhibits a diameter of ~100 nm. Here, the vascular distribution of spherical particles, from 10 to 1,000 nm in diameter, is studied using intravital microscopy and computational modeling. Small NMPs (≤100 nm) are observed to move with Red Blood Cells (RBCs), presenting an uniform radial distribution and limited near-wall accumulation. Larger NMPs tend to preferentially accumulate next to the vessel walls, in a size-dependent manner (~70% for 1,000 nm NMPs). RBC-NMP geometrical interference only is responsible for this behavior. In a capillary flow, the effective radial dispersion coefficient of 1,000 nm particles is ~3-fold larger than Brownian diffusion. This suggests that sub-micron particles could deposit within diseased vascular districts more efficiently than conventional nanoparticles.