Simulation of 3D velocity and concentration profiles in a packed bed adsorber by lattice Boltzmann methods

Full 3D simulations of velocity and concentration profiles were carried out for the several ordered packing arrangements of spherical particles with small tube-to-particle diameter ratio (<10) using lattice Boltzmann methods. The effects of voids and diffusion coefficients on the adsorption concentration profiles in a packed bed of circular cross-section were investigated. In particular, the radial (r) and circumferential (θ) dependencies of the concentrations due to non-uniform velocity and particle voids across tube's cross-section, especially near the walls, were ascertained. The lattice Boltzmann technique allows simultaneous solution to velocity and concentration fields at all locations inside the packed tube without using any empirical correlations for certain transport parameters, for example, dispersion coefficient. Depending upon the packing arrangements and the magnitudes of diffusion coefficient, the concentration gradients in r- and θ-directions were found to be significant. The lattice model simulation results were also compared to the tomographic data obtained in a tubular adsorber packed with the zeolites coated glass beads and were found to be in reasonably good agreement.     

Visualization of water vapour flow in a packed bed adsorber by near-infrared diffused transmittance tomography

This work presents a procedure based on spatially-resolved near-infrared imaging, in order to observe temperature and composition maps in gas–solid packed beds subjected to effects of aspect ratio and non-isothermal conditions. The technique was applied to the water vapour flow in a packed bed adsorber of low aspect ratio, filled with silica gel, using a tuneable diode laser, focal planar array detector and tomographic reconstruction. The 2D projected images from parallel scanning permitted data to be retrieved from the packing and above the packing sections of 12.0×12.0×18.2 mm³ at a volume-resolution of 0.15×0.15×0.026 mm³ and a time-resolution of less than 3 min. The technique revealed uneven temperature and composition maps in the core packed bed and in the vicinity of the wall due to flow maldistribution. In addition, the heat uptake from the packed bed and local cross-mixing were experimentally ascertained by local profiles of the water vapour composition and temperature under various aspect ratios and feed flow rates. The relative deviations in temperature and compositions were 11.1% and 9.3%, respectively. The deviation in composition, which covers the packing and above the packing sections, was slightly higher than the deviation of 8% obtained up-to-date but was limited to the exit of a packed bed adsorber.     

The application of theoretical solutions to the differential mass balance equation for modeling of adsorptive desulfurization in a packed bed adsorber

Adsorptive removal of organosulfur compounds, lumped as total sulfur content, from a real diesel fuel was carried out in a packed bed adsorber. A novel approach was taken in the application of theoretical solutions to the differential mass balance equation using modern software tools, and one classic method as point of reference. Adsorptive desulfurization is a perspective downstream process to hydrodesulfurization for achieving sulfur concentration levels of less then 10 mg kg⁻¹. Compared to the conventional hydrodesulfurization process, the deep desulfurization can be accomplished without changing the physical properties of the product and at relatively low temperature and pressure. The adsorber apparatus comprised computer control, enabling completely automated operation. Adsorbent was activated carbon SOLCARB C from Chemviron Carbon, Belgium. The experimental results regarding the influence of flow rate and bed depth on the outlet sulfur concentration were evaluated as well as the models ability to describe the adsorption kinetics and to estimate the breakthrough curves. Ultra deep desulfurization of diesel fuel was achieved and it was determined that outlet sulfur concentration was being lowered by decreasing flow rate and increasing bed depth. The closest fit to the experimental data was achieved for the Bohart-Adams model.     

Simulation of micro- and macro-transport in a packed bed of porous adsorbents by lattice Boltzmann methods

In this study we report 3D simulation of concentration profiles in a fixed bed packed with spherical porous adsorbents using lattice Boltzmann methods (LBMs). The lattice models have been developed to investigate evolution of concentration profiles due to inter- and intra-particle mass transport in an adsorber having small tube-to-sphere diameter (d_t/d_p) ratios. The multi-scaling feature of LBMs permits full 3D simulation of concentration profiles both in the bed voids and within the pores of the adsorbents without using any empirical correlations or without making 1D or 2D approximations that are usually made in traditional numerical methods. The model simulation is carried out for varying packing arrangements and small to large pore diffusivities. The simulation results show significant concentration gradients for small pore diffusivities and large particle size, which must be considered in predicting breakthrough and adsorption times for a tubular adsorber having d_t/d_p<10. The model predicted breakthrough curves are validated with the experimental data obtained by tomography technique in a tubular adsorber packed with zeolite particles.     

New method for monitoring of adsorption column saturation and regeneration II: on-line measurement

A new method suitable for the on-line monitoring of adsorption column saturation/regeneration cycles was developed based on the discovery that the electrical resistance of packed bed adsorbents changes dramatically upon adsorption and returns to its original value upon desorption. This change can be measured reliably and reproducibly. The two systems studied on-line in real time were methyl chloride (MeCl) adsorption on zeolite molecular sieve (HISIV 3000) and water vapour adsorption on basic alumina (RF-200). The sequential change in electrical readings at localized points within the column indicated the movement of the adsorption front, tracking the onset of breakthrough. The electrical readings returned to their original values upon desorption and the results were reproducible. Concurrently with the electrical measurements, the effluent gas of the MeCl/HISIV system was monitored for MeCl using an on-line gas chromatograph. An adsorption isotherm was created using the “length of unused bed” concept. The resistance change of the HISIV was found to be proportional to the square root of the amount of MeCl adsorbed, similarly to the C/CO₂ system discovered recently by our group. The universality of this correlation is being investigated. The simple measurement technique introduced here has the potential to improve the operating efficiency of industrial adsorption towers.     

The heat transfer coefficient between a particle and a bed (packed or fluidised) of much larger particles

The heat transfer coefficient has been measured for a heated phosphor-bronze sphere (diam. 2.0, 3.0 or 5.56 mm) added to a bed of larger particles, through which air at room temperature was passed. The bronze heat transfer sphere was attached to a very thin, flexible thermocouple and was heated in a flame to before being immersed in the bed. The cooling of the bronze sphere enabled the heat transfer coefficient, h, to be measured for a variety of U/U_mf, as well as diameters of both the particles in the bed and the heat transfer sphere. It was found that before the onset of fluidisation, h rose with U, but h reached a constant value for U?U_mf. These measurements indicate that in this situation (of a relatively small particle in a bed of larger particles) all the heat transfer is between the hot bronze sphere and the gas flowing over it. Consequently, a Nusselt number, based on the thermal conductivity of the gas, is easy to define and for U?U_mf (i.e. a packed bed), Nu is given by

     

Flow distribution and velocity measurement in a radial flow fixed bed reactor using electrical resistance tomography

Electrical resistance tomography is a relatively simple and inexpensive technique for imaging electrically conducting systems. It has been applied to visualise the flow pattern and distribution inside a radial flow packed bed of novel design for improving reactor performance with lower pressure drop. The density of information yielded by electrical tomography is suitable for validation of Computational fluid dynamics. Sets of tomographic images representing slices through a packed bed have been obtained for a 8-plane × 16-electrode sensor configuration which produces of the order 10³ conductivity measurements in three-dimensions. Pulse injections of high conductivity tracer, both uniformly in the feed and localised, can be imaged as multiple tomographic images or 3D solid-body images, revealing the internal flow pattern. Differentiation of the motion of the tracer peak conductivity within pixels in the sensing planes and between the planes allows the local flow velocities and directions to be determined. This quantifies the flow pattern for uniformity and radial distributive properties.     

Improved one-dimensional model of a tubular packed bed reactor

The major drawback of one-dimensional models of tubular fixed bed reactors, which are often used if the computational effort should be small, is the fact that the reaction rate is calculated using the average temperature over the cross-section of the reactor. The difference between this reaction rate and the average reaction rate over the cross-section becomes increasingly significant with increasing temperature difference over the radius of the reactor and with increasing activation energy of the reaction(s). Improved versions of the one-dimensional model, such as that of Hagan et al. [1988. A simple approach to highly sensitive tubular reactors. SIAM Journal of Applied Mathematics 48, 1083-1091] are available, which use an analytical approximation of the radial temperature profile to improve the prediction of the average reaction rate. However, application of these models involves solving of implicit equations. Here, a new model is proposed as an alternative to the existing one-dimensional models. It has the same form as the conventional one-dimensional model and contains only explicit functions. It is demonstrated that, at conditions not too close to runaway, the new model performs better than the well-known α-model.     

Flow of a gas-solid two-phase mixture through a packed bed

This paper is concerned with an upward co-current flow of a gas-solid two-phase mixture through a packed bed, a system employed in a number of industrial processes. Experimental work was carried out by using glass balls for packed bed, and both glass beads and FCC as suspended particles. The effects of solids loading and gas velocity on the pressure drop as well as the static and dynamic solid hold-ups within packed bed were examined. Experimental results showed different behaviour of the FCC from glass beads. At a given gas velocity, pressure drop increased approximately linearly with solids loading with a slope for FCC much higher than that for glass beads. The static hold-up of glass beads was much lower than corresponding dynamic hold-up at a given gas velocity, and it did not seem to change much with solids loading under the conditions of this work. At a given gas velocity, the static hold-up of FCC, however, was found to be comparable with the corresponding dynamic hold-up. An analysis was conducted on the pressure drop using a modified version of the Ergun equation by taking into account the effects of suspended particles on the viscosity and density, as well as the gravitational force. It was found that the modified Ergun equation agreed well with the experimental results of both this work and those reported in the literature. Effort was also made to develop relationships for the dynamic hold-up and the interaction coefficient between the suspended and the packed particles, the so-called solid-phase friction factor in the literature. The dynamic hold-up was found to increase with an increase in the product of velocity ratio of the solid to gas phases and the square root of the diameter ratio of the suspended to packed particles, whereas the interaction coefficient increased in general with increasing Froude number but with significant scattering.     

Investigation of fine granular material flow through a packed bed

Three different methods cut-off, time-of-flight, and Pulsed Field Gradient Nuclear Magnetic Resonance were used to study downstream flow of fine granular material through the fixed bed reactor. For describing the transport of solid particles within a fixed granular bed, a model has been developed. In time-of-flight and cut-off techniques the highest average velocity of filtration is observed at the lowest mass flow rate in all experimental traces, while upon the flow rate increase it tends to an asymptotic value. Experimental results obtained by pulsed field gradient nuclear magnetic resonance technique have revealed the bimodal character of particles velocities distribution. The average filtration velocity has a maximum at an intermediate mass flow rate close to the bed flooding, in contrast to the results obtained by cut-off and time-of-flight methods. The velocities measured using all three techniques were compared by converting them into dimensionless values. From the experimental results, the values of model parameters have been evaluated which allowed us to describe particle velocities within a bed.     

Interfacial stress in non-Newtonian flow through packed bed

This study investigates the pressure drop characteristics, shear stress in packed bed with shear thinning power law type non-Newtonian liquid. A mechanistic model has also been developed to analyze the pressure drop and interfacial stress in packed bed with non-Newtonian liquid by considering the loss of energy due to wettability. The Ergun's and Foscolo's equations were used for comparison with the experimental data. The Ergun equation was modified to account for the effect of flow behavior index of non-Newtonian fluid in the column. The intensity factor of shear stress and the friction factor were analyzed based on energy loss due to wettability effect of liquid on the solid surface.     

Simulation of temperature fields in a narrow tubular adsorber by thermal lattice Boltzmann methods

Significant temperature gradients may exist in packed bed adsorbers due to the exothermic heat of adsorption. In this study we investigate temperature fields in a narrow tubular packed bed adsorber having tube to particle size ratio <10. Theoretical calculations are carried out using lattice Boltzmann methods (LBM) to simulate three-dimensional concentration and temperature profiles in macro- as well as micro-pores of the adsorption bed. Model simulation results show non-uniform temperature gradients across the tube's cross-section. Zones of significantly high temperature are observed within macro-voids. Temperature gradient is found to be primarily dependent on the amount of heat released, internal BET surface area, and hydrodynamic conditions prevailing in the adsorber. Agreement between the model results and the experimental data obtained with the aid of the tomography technique for a tubular adsorber is observed to be reasonable. The study is important from the point of view of a realistic design of packed bed adsorbers.     

Spontaneous ignition of wood, char and RDF in a lab scale packed bed

Many municipal waste combustors use preheated primary air in the first zone to dry the waste. In most cases the preheat temperature does not exceed 140 °C. In previous experiments it is found that at temperatures around 200 °C, in some circumstances, self- or spontaneous ignition can be achieved. Using preheated air can be a powerful tool to control the ignition and combustion processes in a waste combustion plant. To use this tool effectively, the influence of the preheated air on the fuel bed needs to be well understood. The present work is done to investigate in a systematically way the spontaneous ignition behaviour of a packed bed heated with a preheated air stream. Experiments on a lab scale packed bed reactor are carried out for various fuel types. Because MSW is an highly inhomogeneous fuel, wood and char are used as model fuels. To include the inhomogeneous character of MWS, also experiments are carried out with RDF. Parameters such as primary air flow velocity and temperature, addition of inert material, moisture content of the fuel (wood chips) and particle size (char) have been changed to see their effect on the spontaneous ignition temperature and on the minimum air temperature needed for ignition. The spontaneous ignition temperature is defined as the bed temperature at which a transition takes place from a negligible or slow fuel reaction rate to a rapid oxidation of either the volatiles or the solid fuel without an external source such as a spark or a flame. The minimum or critical air temperature is defined as the lowest air temperature at which ignition can be obtained. It is found that the type of fuel has influence on the ignition temperatures. Besides both the critical air temperature needed for the spontaneous ignition and the spontaneous ignition temperature increase with an increase in the primary air velocity (between 0.1 and 0.5  m/s) and increasing the added inert fraction (between 0 and 40 wt%), irrespective of the fuel type. The effect of air flow velocity and temperature and also the effect of inert on both the critical air temperature and the spontaneous ignition temperature can be explained qualitatively by using Semenov’s analysis of thermal explosions. Semenov’s theory is quantitatively applied to predict the spontaneous ignition and the critical air temperatures for wood.     

Heat transfer of gas-solid two-phase mixtures flowing through a packed bed

This paper reports an experimental study on both transient and steady-state heat transfer behavior of a gas-solid two-phase mixture flowing through a packed bed under constant wall temperature conditions. A logarithmic mean temperature difference (LMTD) method is used to process the temperature data to obtain the overall heat transfer coefficient. The influences of particle loading and gas flow Reynolds number are investigated. The results show that the introduction of suspended particles greatly enhances heat transfer between the flowing gas-solid two-phase mixture and the packed bed, and the enhancement increases approximately linearly with increasing particle loading. The heat transfer coefficient data are processed to give the Nusselt number, which is found to correlate well to the Reynolds number, the Archimedes number and the suspended particle loading ratio. A comparison of the data of this work with the published data reveals large discrepancy. Possible reasons for the discrepancy are discussed.     

Heat transfer of gas flow through a packed bed

This paper reports an experimental study of both the transient and steady-state heat transfer behaviour of a gas flowing through a packed bed under the constant wall temperature conditions. Effective thermal conductivities and convective heat transfer coefficient are derived based on the steady-state measurements and the two-dimensional axial dispersion plug flow (2DADPF) model. The results reveal a large temperature drop at the wall region and the temperature drop depends on the axial distance from the inlet. The 2DADPF model predicts the axial temperature distribution fairly well, but the prediction is poor for the radial temperature distribution. Length-dependent behaviour of the effective heat transfer parameters and non-uniform flow behaviour are proposed to be responsible. A comparison with previously published correlations and data in the literature shows that the relationships proposed by Bunnell et al. and Demirel et al. agree well with the measured effective radial thermal conductivity, whereas the wall-fluid heat transfer coefficient is better represented by the Li-Finlayson correlation.     

Study of gas cavity size hysteresis in a packed bed using DEM

When a high velocity gas jet is introduced into a packed bed a cavity is formed. The size of the cavity shows hysteresis on increasing and decreasing gas flow rates. This hysteresis leads to different cavity sizes at same gas flow rate depending on the bed history. The size of cavity affects the gas flow profiles in the packed bed. In this study the cavity size hysteresis phenomenon has been modeled using discrete element method along with turbulent gas flow. A reasonable agreement has been found between computed and experimental results on cavity size hysteresis. The effect of various parameters, such as nozzle height from the bed bottom and packing height, on the cavity size hysteresis has been studied. It is found that inter-particle interaction forces along with gas drag and bed porosity play an important role in describing the cavity size hysteresis. The injection of gas flow allows the particles to go to an unconstrained state than they were previously in, and their ability to remain in that state, even under decreased gas drag force, leads to the phenomenon of cavity size hysteresis.     

Simulation of packed bed reactors using lattice Boltzmann methods

Lattice Boltzmann (LB) methods are used to simulate hydrodynamics, reaction and subsequent mass transfer in a disordered packed bed of catalyst particles at sub-pore length-scales. In contrast to previous studies, a variety of modifications are introduced in the LB method enabling particle Pe numbers up to 10⁸, and hence realistic values of diffusivity, to be accessed. These include decoupling the hydrodynamics from mass transfer and the use of a rest fraction in the LB formulation of mass transfer. In addition the mass transfer simulations are modified to permit spatially varying values of diffusivity, essential to differentiate between intra- and inter-particle diffusivity (D_intra and D_inter, respectively). The simulation method is applied to both a disordered and ordered 2D packing for a range of Pe (15.6-1557.8) and Re (0.16-1.56) numbers, as well as various ratios of D_intra/D_inter (0-1), whilst simulating an esterfication reaction catalyzed by an ion-exchange resin. The value of D_intra is found to have limited effect, whilst reducing Pe number results in a considerable increase in overall conversion. The simulation method is then applied to a 3D lattice for which experimental conversion data is available. This experimental data is straddled by the simulation case of D_intra=0 and D_intra=D_inter, as expected.     

Liquid permeability of packed bed with binary mixture of particles

We investigate the effect of binary sized packing on the permeability of water flow through a column packed with binary mixture of spherical particles. The size ratios λ of large to small particles are chosen to be 1.4 and 2.5. Particle packing density for binary mixture of the particles is larger than that for equal sized particles and shows the maximum around the particle blending ratio at which large particles are densely packed and all the small particles fill the void among the large particles. This behavior is observed in both experimental results and theoretical estimation. The variation pattern of packing density with the blending ratio does not agree with that of permeability. The permeability increases with relative fraction of large particles at the maximum packing. Experimental results for the permeability are compared with three theoretical models. Variation pattern of the permeability with the blending ratio from these theoretical models agrees with that from the experiment. Theses theoretical models are in good agreement each other.     

穿透曲线法获取固定床吸附器的传质扩散系数

研究了煤质活性炭对不同浓度苯酚溶液的吸附，应用固定床吸附动力学模型、非线性回归固定床吸附流出曲线数据，获得了酚类在活性炭上的扩散传质系数。结果发现，酚类的表面扩散系数ＤＳ强烈地依赖于入口酚的浓度，随着酚浓度的升高，表面扩散系数增大。采用上述扩散系数理论预测了其他操作条件下的流出曲线，结果表明实验曲线与预测曲线相符甚好，穿透曲线法能可靠地获取液固吸附过程的吸附扩散系数，为吸附工程设计提供有益的帮助     

A one-dimensional transient model of down-flow through a swelling packed porous bed

A transient model of down-flow through an ion-exchange column in which the resin swells has been developed. The model is herein described and results are presented. Wall friction can lead to high bed stresses when the resin in columns with high length to diameter ratios swells. These stresses can lead to high and potentially excursive hydraulic pressure drops along a column. A non-dimensional grouping that effectively correlates the final steady-state hydraulic behavior of a column, with the resin compressibility and column geometric and flow parameters, has been determined.