Measurements and particle resolved modelling of the thermo- and fluid dynamics of a packed bed

The objective of this study is to investigate experimentally and numerically into heat-up, drying and pyrolysis of a packed bed consisting of large single particles. The novelty of the current approach is that the numerical model contrary to continuum mechanic approaches considers a packed bed as an ensemble of a finite number of particles, which may have different material properties or sizes. The heat-up, drying and pyrolysis process of each particle is described sufficiently accurate by a set of one-dimensional and transient differential conservation equations for mass and energy. Applying this model to all particles, including interactions between them, of a packed bed forms the entire backed bed process as a sum of individual particle processes. The arrangement of particles within a bed defines a void space between the particles. The flow through the void space of a packed bed is modelled as a flow through a porous media taking into account interaction between the solid and the gaseous phase by heat and mass transfer. Experiments for drying and pyrolysis of a packed bed were carried out for validation in a temperature range of T=120–530 °C. The temperatures and the mass loss due to drying and pyrolysis were recorded during the experiments. The measured mass loss of the packed bed due to drying were well predicted by the constant evaporation temperature model of the particles and thus, indicating, that the drying process is transport limited by heat transfer for large wood particles in a temperature range of T=120–530 °C. A comparison between experiments and predictions of pyrolysis yielded reasonable agreement for temperatures above T=300 °C. For temperatures of T≈200 °C the deviations were not acceptable. However, the results show, that a particle resolved approach is well suited to describe packed bed processes.     

Adsorption in columns packed with porous adsorbent particles having partially fractal structures

A mathematical model is constructed and solved that could describe the dynamic behavior of the adsorption of a solute of interest in single and stratified columns packed with partially fractal porous adsorbent particles. The results show that a stratified column bed whose length is the same as that of a single column bed, provides larger breakthrough times and a higher dynamic utilization of the adsorptive capacity of the particles than those obtained from the single column bed, and the superior performance of the stratified bed becomes especially more important when the superficial velocity of the flowing fluid stream in the column is increased to accommodate increases in the system throughput. This occurs because the stratified column bed provides larger average external and intraparticle mass transfer and adsorption rates per unit length of packed column. It is also shown that increases in the total number of recursions of the fractal and the ratio of the radii between larger and smaller microspheres that make up the partially fractal particles, increase the intraparticle mass transfer and adsorption rates and lead to larger breakthrough times and dynamic utilization of the adsorptive capacity of the particles. The results of this work indicate that highly efficient adsorption separations could be realized through the use of a stratified column comprised from a practically reasonable number of sections packed with partially fractal porous adsorbent particles having reasonably large (i) total number of recursions of the fractal and (ii) ratio of the radii between larger and smaller microspheres from which the partially fractal particles are made from. It is important to mention here that the physical concepts and modeling approaches presented in this work could be, after a few modifications of the model, applied in studying the dynamic behavior of chemical catalysis and biocatalysis in reactor beds packed with partially fractal porous catalyst particles.     

Production of oxygen enriched air by rapid pressure swing adsorption

A novel rapid pressure swing adsorption (RPSA) process is described for production of 25–50% oxygen enriched air. The embodiment consists of one or more pairs of adsorbent layers contained in a single adsorption vessel. The layers undergo simultaneous pressurization-adsorption and simultaneous depressurization-purge steps. A total cycle time of 6–20 seconds is used. The process yields a very large specific oxygen production rate and a reasonable oxygen recovery for production of 20–50 mole% oxygen enriched gas.It is demonstrated by a simple mathematical model of isothermal single adsorbate pressure swing ad(de)sorption concept on a single adsorbent particle that the specific production rate of a PSA process cannot be indefinitely increased by reducing the cycle time of operation when adsorbate mass transfer resistances are finite.     

A Heterogeneous Multiscale Dynamic Model for Simulation of Catalytic Reforming Reactors

The present work aims to establish a generic reforming reaction scheme to evaluate the performance of catalytic reforming systems with the aid of a one‐dimensional heterogeneous dynamic model. The novelty of the numerical model stems from the direct inclusion of interphase (fluid‐to‐particle surface), intraparticle (within particle), and intrareactor heat and mass transport resistances under transient conditions. The developed model accounts for the multicomponent gas mixture physicochemical properties and correlations for calculating mass and heat transfer coefficients. Effective macroscopic properties within the particle are calculated by incorporating diffusivities and conductivities of the porous network characteristics accounting for Knudsen and molecular transport as well as tortuosity and porosity of the overall porous path. The industrial case of a steam‐methane reforming multitubular reactor was studied as the most representative case of the generic reaction scheme, with all mass/energy resistances present under severe pressure and temperature conditions. It was shown that there are notable diffusional limitations within the particle, whereas there are also temperature and partial pressure gradients due to the heat and mass transport resistances in the particle film layer. It is further demonstrated that the proposed model can be utilized as a versatile design tool for catalytic reactor development and optimization.     

Heat Effects in ZLC Experiments

The problem of nonisothermal desorption in a zero length column (ZLC) experiment is considered theoretically. Simple analytical expressions for the ZLC desorption curve are derived for certain limiting situations in which the governing equations reduce to a linear form. More general numerical solutions are calculated for a wide range of experimental conditions assuming both negligible mass transfer resistance and finite mass transfer resistance controlled by intraparticle diffusion. A simple criterion for negligible thermal effects is developed. It is shown that when the ZLC technique is applied to the measurement of diffusion in unaggregated zeolite crystals, as originally intended, heat effects are generally insignificant. However, when applied to the measurement of macropore diffusion in relatively large adsorbent particles heat effects can become important and may cause major modification of both the desorption rate and the shape of the desorption curve. A recent experimental ZLC study carried out with commercial adsorbent particles, under conditions of macropore diffusion control, showed an anomalous dependence of the desorption rate on both temperature and particle size. These effects can be qualitatively explained by the nonisothermal model. A more precise quantitative representation of these experiments will require a more refined model incorporating a nonlinear equilibrium isotherm as well as intraparticle diffusional resistance.     

Unsteady heating and radiation effects of small particles in a thermal plasma

Based on exact solutions for the heat flux to a particle exposed to a thermal plasma given in a previous paper, initial unsteady heating (including heating of the solid phase, melting of the solid phase, heating of the liquid phase, and evaporation) and radiation effects are considered. Closed-form solutions can be obtained for particles with infinite thermal conductivities. The results show that the time periods required for the various steps are all proportional to the square of the particle radius, suggesting that reduced time periods which are independent of the particle radius are appropriate bases for comparison. Results are presented for three materials (alumina, tungsten, and graphite) and three types of plasmas (argon, argon-hydrogen mixture, and nitrogen). It is shown that evaporation (or sublimation) is by the slowest step among all processes in a plasma reactor if complete evaporation (or sublimation) of the particles is desired. Studies of the temperature history of particles with finite thermal conductivities show that temperature gradients within the particles depend on the ratio of the particles' thermal resistance to that of the plasma. In spite of the difference in initial heating, the analytical expressions based on infinite thermal conductivities predict the correct total time spent for both heating and evaporation even for low-conductivity materials such as alumina. The effect of radiation losses from a particle during heating becomes important for large particles, for high-boiling-point materials, and for low enthalpy differences between the plasma and the particle surface.On leave from the Department of Engineering Mechanics, Tsinghua University, Beijing, P.R.C.     

Modeling and experimental studies on combustion characteristics of porous coal char: Volume reaction model

A generalized single‐particle model for the prediction of combustion dynamics of a porous coal char in a fluidized bed is analyzed in the present work using a volume reaction model (VRM). A fully transient nonisothermal model involving both heterogeneous and homogeneous chemical reactions, multicomponent mass transfer, heat transfer with intraparticle resistances, as well as char structure evolution is developed. The model takes into account convection and diffusion inside the particle pores, as well as in the boundary layer. By addressing the Stefan flow originated due to nonequimolar mass transfer and chemical reactions, this work enables a more realistic analysis of the combustion process. The model, characterized by a set of partial differential equations coupled with nonlinear boundary conditions, is solved numerically using the implicit finite volume method (FVM) with a FORTRAN code developed in‐house. The use of a FVM for solving such an elaborate char combustion model, based on the VRM, was not reported earlier. Experiments consisting of fluidized‐bed combustion of a single char particle were carried out to determine the internal surface area of a partially burned char particle and to enable model validation. Predicted results are found to compare well with the reported experimental results for porous coal char combustion. The effects of various parameters (i.e., bulk temperature and initial particle radius) are examined on the dynamics of combustion of coal char. The phenomena of ignition and extinction are also investigated. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 299–315, 2010     

Drying and pyrolysis of wood particles: experiments and simulation

The objective of this study is to develop a flexible and stable numerical method to predict the thermal decomposition of large wood particles due to drying and pyrolysis. At a later stage, this model is applied to each particle of a packed bed and thus, forms the entire packed bed process as a sum of individual particle processes. Therefore, this approach can deal with particles of different sizes, shapes and properties. A general formulation of the conservation equations allows the geometry of a fuel particle to be treated as a plate, cylinder or sphere. The various processes such as heat-up, drying and pyrolysis are described by a set of one-dimensional and transient conservation equations for mass and energy. This allows for simultaneous processes e.g. reactions in time and covers the entire range between transport-limited (shrinking core) and kinetically limited (reacting core) reaction regimes. The particles interact with a gas phase by heat and mass transfer taking into account the Stefan correction due to the gas outflow during conversion. Experiments carried out span a temperature range between T=300 and 900 °C for particle sizes varying between 8 and 17 mm. A comparison between measurements and predictions of drying models yielded satisfactory agreement only for the constant evaporation temperature model and thus, indicating, that the drying process is transport limited by heat transfer for large wood particles. Likewise, predicted results of pyrolysis for the above-mentioned range of temperatures and sizes agreed satisfactorily with measurements.     

Single-particle electrophoresis for studying the adsorption of cationic polymers onto anionic particles

Understanding the adsorption of polymers onto particles is crucial for many technological and biomedical applications. Even though polymer adsorption on particles is a dynamic process, most experimental techniques can only study the adsorption indirectly, in equilibrium and on the ensemble level. New analysis methods are required to overcome these limitations. We investigated the use of single-particle electrophoresis to study the adsorption kinetics of cationic polymers onto anionic particles and compared the resulting data to a theoretical model. In this approach, the electrophoretic mobility of single polystyrene (PS) particles, exposed to different concentrations of poly(2-guanidinoethyl methacrylate), was measured as a function of time. The polymer adsorption leads to an electrophoretic mobility change of the PS particle over time, from the initial negative value to a positive value at equilibrium. By fitting the kinetics data to the Langmuir model, the adsorption rate, desorption rate and equilibrium constant were determined. Finally, the adsorption kinetics of several other polymers was investigated. This showed that the presented technique enables direct analysis and comparison of the kinetics of polymer adsorption on the single-particle level.     

铈离子改性Y型分子筛吸附剂对苯中噻吩动态吸附及其主要影响因素的研究

通过固定床吸附实验考察了吸附剂的粒径、空速与浓度及床层温度等操作参数对苯中噻吩吸附的影响。结果表明,上述因素分别通过改变内、外扩散过程的传质阻力以及其物理吸附行为来影响噻吩的脱除。最佳的参数是,吸附剂粒径为0.2~0.3 mm,空速为0.85 h^-1,床层温度为室温。在此条件下,CeY吸附剂能将噻吩浓度为500 mg/L苯溶液中的噻吩完全脱除,其噻吩的穿透时间和吸附量可达400 min和4.61 mg/g以上。     

Effect of Operation Symmetry on Pressure Swing Adsorption Process

In a multi-bed pressure swing adsorption (PSA) process, cycle steps with gas flow transferring from one bed to another such as equalization, purge, etc. are generally practiced to enhance the product recovery. However, if the flows for the connected beds in these steps are not balanced, the PSA process may not operate in a symmetrical manner. In the modeling of the PSA process, most of the simulations consider only one bed and assume that the rest of the beds would behave in a same way. In order to assess the impact of bed symmetry on the PSA performance, a new PSA model capable of studying bed symmetry in a two-bed system is developed. Experimental results from this paper show that uneven equalization flow can result in a lower product purity and a peculiar purity curve at different equalization levels. This phenomenon can be successfully predicted by this model. Simulation results also show that in large-scale PSA units, asymmetrical operation can cause drastically different temperature profiles in different adsorbers and hence a much lower performance. This paper demonstrates the importance of maintaining operation symmetry in PSA processes.     

Physicochemical influences on electrohydrodynamic transport in compressible packed beds of colloidal boehmite particles

Production and processing of colloidal particles require a deeper understanding of the surface charge of particles and the interaction of mass and charge transport in packed beds. The assessment of fundamental parameters is rather complex due to the additional influence of the particle charge on the structure of a packed bed. The combination of different measurement techniques (streaming potential and electroosmosis) allows for separating the effects, based on the postulation of a new method to quantify the ratio of surface conductance to liquid conductance. The purpose of this paper is to investigate the influence of pH value and compression on the electrohydrodynamic transport parameters.     

Equilibrium adsorption data from temperature-programmed desorption experiments

This work describes a novel method that enables the calculation of a series of adsorption isotherms basically from a single Temperature-Programmed Desorption (TPD) experiment. The basic idea is to saturate an adsorbent packed in a fixed bed at a certain feed concentration and temperature and to subsequently increase its temperature linearly with time, while maintaining a constant feed concentration.We measured TPD response curves for carbon dioxide on activated carbon at different heating rates for various combinations of feed concentration, molar flow rate and particle size. Response curves from an axially dispersed plug flow model were fitted to experimental data by adjustment of the Langmuir parameters. Adsorption isotherms calculated with these fitted parameters are in good agreement with adsorption data obtained by other methods over the full temperature range.The influence of heating rate on intraparticle mass transfer resistance is discussed.     

Why Does the Linear Driving Force Model for Adsorption Kinetics Work?

The Linear Driving Force (LDF) model for gas adsorption kinetics is frequently and successfully used for analysis of adsorption column dynamic data and for adsorptive process designs because it is simple, analytic, and physically consistent. Yet, there is a substantial difference in the characteristics of isothermal batch uptake curves on adsorbent particles by the LDF and the more rigorous Fickian Diffusion (FD) model. It is demonstrated by using simple model systems that the characteristics of the adsorption kinetics at the single pore or the adsorbent particle level are lost in (a) evaluating overall uptake on a heterogeneous porous solid, (b) calculating breakthrough curves from a packed adsorbent column, and (c) establishing the efficiency of separation by an adsorptive process due to repeated averaging of the base kinetic property. That is why the LDF model works in practice.     

不同尺寸ZIF-8对U(VI)的吸附性能

以经典的金属有机骨架(MOFs)材料ZIF-8为吸附剂,研究尺寸效应对铀吸附性能的影响。 通过3种方法合成不同粒径的ZIF-8,利用扫描电子显微镜(SEM)、X射线粉末衍射仪(XRD)、表面积与孔隙度分析仪等对其进行了表征,测试了相同条件下不同尺寸的ZIF-8对硝酸铀酰溶液中U(VI)吸附,分别对其吸附过程的动力学和吸附等温线进行了考察,并测试了材料的可重复利用性。 结果表明,成功制备了高结晶性、高纯度的ZIF-8,产物形貌呈菱形十二面体,颗粒均匀,粒径分别为约50 nm、150 nm及2 μm;3种ZIF-8具有单一均匀的微孔结构和与粒径高度相关的比表面积;不同尺寸的ZIF-8均能快速吸附溶液中的U(VI),在室温pH=3下,在70 min左右时即可吸附初始质量浓度为200 mg/L的U(VI)溶液中90%以上U(VI);其中较小尺寸(约50 nm)的ZIF-8吸附性能最好,单位质量ZIF-8吸附U(VI)的饱和吸附量达到520.26 mg/g;ZIF-8对U的吸附动力学上符合二级动力学方程,吸附等温线符合Langmuir模型,说明ZIF-8对U(VI)的捕获属于化学单层吸附;经过4个吸附-解吸循环后,3种尺寸的ZIF-8均依然保持了70%以上的去除率。     

氢气在单壁碳纳米管束的吸附的密度泛函研究

作者利用密度泛函理论（DFT）计算了氢气在单壁碳纳米管束（SWNTs)中管内 和管间的吸附。考察了温度,孔径以及压力对吸附的分子数密度,重量百分比,单 位体积储存能力以及超额吸附量的影响。DFT计算发现,较大的孔径有利于氢气在 SWNTs中的吸附且氢气在管隙中的吸附不可忽略。计算表明在77 K和6 MPa时,氢气 在2.719 mm的SWNTs的总的吸附的重量百分比分别可达到13.2 wt%,这约是美国能 源部（DOE）目标值的两倍,而单位体积储存能力在DOE目标值附近,而在300 K和 6 MPa时,氢气在2.719 nm的SWNTs的总的吸附的重量百分比仅为1.5 wt%。通过实 验结果与计算结果的比较表明,密度泛函理论的计算结果支持SWNTs有较高的吸附 储氢能力的实验结论。     

Role of convection and diffusion in a single pore with adsorptive walls

The importance of intraparticle convection during and after the pressurization step of a pressure swing adsorption process is assessed by considering a single, cylindrical, closed-end pore with adsorptive walls exposed to a binary mixture of an adsorbable component and an inert gas. Gas-phase mass transfer is comprised of pore diffusion and convection, and surface diffusion occurs in the adsorbed phase. Concentration, velocity, and flux profiles are obtained inside the pore both during and after pressurization. Solutions are obtained analytically for the limiting cases of no adsorption, no diffusion, and no inert gas. Complete solutions of the material balance equations are obtained by orthogonal collocation. The pressurization rate, the adsorptive capacity of the pore wall, and the gas-phase mole fraction are varied over a wide range to study the relative importance of convection and diffusion under different conditions. Results show that convection makes a large contribution to transport in the pore except when the adsorbable component has a small mole fraction.     

Flow pattern maps for particle-fluid mixture transport in a horizontal pipe - application of a three-layer model

A modified three-layer model was applied to model particle-fluid mixture flow in a horizontal pipe, the viscoelastic properties of carrier polymer solution were taken into consideration, and the Deborah number was used to calculate solid-fluid friction factor. An energy equation was applied to determine temperature distribution of carrier fluid along a horizontal pipe to accurately represent the rheological properties of carrier fluid. During the transport process, particles quickly settle out of carrier fluid and accumulate on pipe bottom forming a particle bed, so a particle bed load flow is observed. The transport mechanisms of particles in moving particle bed are govern by fluidization, which causes the height of this layer to be small and equal to 2～5 times of particle diameter. In addition, the pressure drop is composed of solid-fluid and solid-solid friction loss, which dominate the hydrodynamic performance at different stages.     

Adsorption of large macromolecules on fine colloidal particles

A simple model of adsorption of large macromolecules on ultra-fine colloidal particles is presented. The basic assumption of the model is that the number of particles attached to a single molecule is a random quantity. Both the reversible and irreversible polymerparticle binding is considered. Also, effects of the non-ideal mixing of polymer solution with suspension and of the polymer/particle size ratio on the shape of the adsorption isotherm are examined. The predictions of the model are confronted with experimental results of the study on the adsorption of very high molecular weight polyacrylamide on fine AgI colloidal particles.     

An in situ study of the adsorption behavior of functionalized particles on self-assembled monolayers via different chemical interactions

The formation of particle monolayers by convective assembly was studied in situ with three different kinds of particle-surface interactions: adsorption onto native surfaces, with additional electrostatic interactions, and with supramolecular host-guest interactions. In the first case carboxylate-functionalized polystyrene (PS-COOH) particles were assembled onto native silicon oxide surfaces, in the second PS-COOH onto protonated amino-functionalized (NH3+) self-assembled monolayers (SAMs), and in the third beta-CD-functionalized polystyrene (PS-CD) particles onto beta-CD SAMs with pre-adsorbed ferrocenyl-functionalized dendrimers. The adsorption and desorption behaviors of particles onto and from these surfaces were observed in situ on a horizontal deposition setup, and the packing density and order of the adsorbed particle lattices were compared. The desorption behavior of particles from surfaces was evaluated by reducing the temperature below the dew point, thus initiating water condensation. Particle lattices on native oxide surfaces formed the best hexagonal close packed (hcp) order and could be easily desorbed by reducing the temperature to below the dew point. The electrostatically modified assembly resulted in densely packed, but disordered particle lattices. The specificity and selectivity of the supramolecular assembly process were optimized by the use of ferrocenyl-functionalized dendrimers of low generation and by the introduction of competitive interaction by native beta-CD molecules during the assembly. The fine-tuned supramolecularly formed particle lattices were nearly hcp packed. Both electrostatically and supramolecularly formed lattices of particles were strongly attached to the surfaces and could not be removed by condensation.