Steady state behavior of moving bed reactors

A relatively simple model for a moving bed reactor in which ignition takes place is presented and the steady state problem is solved analytically and numerically. The dependence of multiplicity and the nature of the solution on the parameters of the system are investigated. Some similarities in the analyses between fixed bed reactor theory and moving bed reactor theory are shown.     

Comparison between simulated moving bed and reverse flow chromatographic reactors for equilibrium limited reactions

A staged linear model, containing five parameters, is developed to compare equivalent simulated moving bed chromatographic reactors (SMBCR) and reverse flow chromatographic reactors (RFCR). A first order reversible reaction and linear adsorption equilibrium, with preferential adsorption of the reactant is assumed. The analysis uses simple, easily computable analytical solutions that rigorously represents the transients in the cyclic steady state for both the RFCR and the SMBR. A comparison between the two types of reactors is carried out to determine the maximum conversion attainable and the range of operation where these systems have advantages over conventional steady state reactors. It is found that the maximum conversion of both reactors is similar. The range of operation in terms of amount of catalyst and range of switching times favors the RFCR, while the conversion at low separation factors favors the SMBCR.     

Selectivity of aging catalyst in static,moving and fluidized bed reactors

The catalyst decay theory of Wojciechowski is applied to a simplified mechanism of catalytic gas oil cracking. The resulting patterns of selectivity predicted for a static bed reactor are presented in detail and general conclusions are drawn. It is shown that selectivity in gas oil cracking is bounded by optimum and minimum performance envelopes which confine the range of possible product distributions. For the simple cases considered, moving and fluidized bed reactors show selectivity patterns which invariably fall on the optimum performance envelope.     

Trickle bed reactors: Effect of liquid flow modulation on catalytic activity

The effect of slow ON-OFF liquid flow modulation on the oxidation of aqueous solutions of ethanol using a 0.5% Pd/Al₂O₃ commercial egg-shell catalyst was investigated in a laboratory trickle bed reactor (TBR). In this mode of operation, the catalyst was cyclically exposed to oxidative and reductive environments.The study was carried out under different gas and liquid flow rates, cycle periods and splits. Cycling results have been compared with the steady-state experiments performed at the corresponding average liquid flow rate. Significant improvements over the continuous operation were obtained when the catalyst was exposed to a short surplus of oxygen (to minimize deactivation by overoxidation in the kinetic regime) after a longer time of working in the mass transfer limited regime. According to the results presented here, it is recommended to work with high liquid flow rates and moderate gas flow rates to ensure complete wetting of the catalyst during the ON cycle and to minimize the overoxidation process during the OFF cycle.     

Laminar radial flow electrochemical reactors. I. Flow fields

The velocity fields of three laminar radial flow electrochemical reactors are modeled using numerical and semi-analytical techniques. The capillary gap cell configuration is modeled using Galerkin finite element (GFEM) analysis and the asymptotic form of its velocities presented. An approximate asymptotic expression for entry length is also derived and compared to predicted entry lengths from the GFEM. Qualitative agreement is achieved. Two areas of flow separation are observed, their location being a function of gap width, flow Reynolds number (Re) and inlet pipe diameter. The rotating electrolyzer (REL) flow field is also simulated with the GFEM model. The insensitivity of the REL radial velocity profiles as a function of flow rate is shown. The shape of the radial velocity profiles and the degree of separation of the radial velocity jets are shown to be determined by the Taylor number (being the ratio of half-gap width over the theoretical boundary layer thickness). The asymptotic entry length solution is shown to provide a better estimate for this cell than for the capillary gap cell. Unlike the previous cells the pump cell shows less asymptotic behavior and is therefore more difficult to simulate. The GFEM approach is usually too costly for this cell and therefore perturbation techniques are applied. The resulting semi-analytical solution adequately represents laminar pump cell velocity profiles over a broad range of parameter values and is very short and easy to implement. One high Taylor number simulation is performed using the GFEM and the previously reported decoupling of electrodic mass transfer is interpreted via velocity profiles.Nomenclature a gap width - Q volumetric flow rate (m³ s^–1) - r dimensionless radius - R radius (m) - Re Reynolds number (v _c a/v) - Re _gap gap Reynolds number (a ²/v) - Re rotational Reynolds number (R ₀ ² /v) - Sc Schmidt number (v/D) - spin dimensionless group (Equation 8) - t time (s) - v _c characteristic velocity (m s^–1) two defined: for FEM analysis it wasQ/b ² for Perturbation analysis 6Q/(2R _in a) - v _r dimensionless radial velocity - v _z dimensionless axial velocity - v dimensionless azimuthal velocity - V velocity (m s^–1) - z dimensionless axial distance Greek symbols Taylor number (Equation 7) - ratio of characteristic lengths (a/R _o ) - viscosity (kg m^–1 s) - constant - density (kg m^–3) - azimuthal direction - kinematic viscosity (m² s^–1) - angular velocity (rad s^–1)     

Flow through packed bed reactors: 1. Single-phase flow

Single-phase pressure drop was studied in a region of flow rates that is of particular interest to trickle bed reactors . Bed packings were made of uniformly sized spherical and non-spherical particles (cylinders, rings, trilobes, and quadralobes). Particles were packed by means of two methods: random close or dense packing (RCP) and random loose packing (RLP) obtaining bed porosities in the range of 0.37–0.52. It is shown that wall effects on pressure drop are negligible as long as the column-to-particle diameter ratio is above 10. Furthermore, the capillary model approach such as the Ergun equation is proven to be a sufficient approximation for typical values of bed porosities encountered in packed bed reactors. However, it is demonstrated that the original Ergun equation is only able to accurately predict the pressure drop of single-phase flow over spherical particles, whereas it systematically under predicts the pressure drop of single-phase flow over non-spherical particles. Special features of differently shaped non-spherical particles have been taken into account through phenomenological and empirical analyses in order to correct/upgrade the original Ergun equation. With the proposed upgraded Ergun equation one is able to predict single-phase pressure drop in a packed bed of arbitrary shaped particles to within ±10% on average. This approach has been shown to be far superior to any other available at this time.     

大型径向流反应器中流体均布参数的研究

文中研究了工业规模径向反应器中流体的变质量流动规律,在直径3 m,高7 m的大型径向反应器冷模装置中测定了流道静压变化和穿孔阻力,通过数学拟合获得了动量交换系数和侧流穿孔阻力系数。实验结果表明,大型径向反应器冷模装置测得分流和集流动量交换系数Kd和Kc与前人众多的实验室小试单管结果十分相近;而大型冷模的分流和集流侧流穿孔阻力系数dξ和cξ在穿孔流速与主流道流速之比大于2之后分别比实验室小试结果提高了35%和16%左右。上述大型冷模实验研究结果对工业径向流反应器的开发有参考价值。     

滴流床反应器流体力学的研究进展

系统综述了滴流床反应器的流体力学研究现状，分析了流型的转变、床层压降和持液量的关联结果，总结了主要的反应器模型和压力对床层压降及持液量的影响，并详细讨论了操作方式对滴流床反应器流体力学的影响。     

Investigations on heat transfer and hydrodynamics under pyrolysis conditions of a pilot-plant draft tube conical spouted bed reactor

This paper describes the hydrodynamic and heat transfer performance of a pilot-plant scale conical spouted bed reactor designed for the pyrolysis of biomass wastes. The spouted bed reactor is the core of a fast pyrolysis pilot plant with continuous biomass feed of up to 25 kg/h, located at the Ikerlan-IK4 facilities.The aim of this paper is to obtain a deeper understanding of the spouted bed reactor performance at pyrolysis temperatures, in order to operate under stable conditions, improve the heat transfer rate in the reactor and minimize energy requirements. The influence of temperature on conical spouted bed hydrodynamics has been studied and wall-to-bed and bed-to-surface heat transfer coefficients have been determined.     

CFD simulation of hydrodynamics of gas–solid multiphase flow in downer reactors: revisited

In the present work, a k₁–ε₁–k₂–k₁₂ two-fluid model based on the kinetic theory of granular flow (KTGF) was employed to predict the flow behavior of gas and solids in downers, where the particles of small size as 70 μm in diameter apparently interact with the gas turbulence. The turbulence energy interaction between gas and solids was described by different k₁₂ transport equations, while the particle dissipation by the large-scale gas turbulent motion was taken into account through a drift velocity. Johnson–Jackson boundary condition was adopted to describe the influence of the wall on the hydrodynamics. The simulation results by current CFD model were compared with the experimental data and simulation results reported by Cheng et al. (1999. Chem. Eng. Sci. 54, 2019) and Zhang and Zhu (1999. Chem. Eng. Sci. 54, 5461). Good agreement was obtained based on the PDE-type k₁₂ transport equation. The results demonstrated that the proposed model could provide good physical understanding on the hydrodynamics of gas–solid multiphase flow in downers. Using the current model, the mechanism for formation and disappearance of the dense-ring flow structure and the scale-up characteristics of downers were discussed.     

径向反应器的研究与应用进展

介绍了径向反应器在流体流动方面的特点和优点,对径向反应器的数学模型研究的进展进行了详细的讨论,介绍了径向反应器在合成氨、CO变换、甲醇氧化重整制氢、催化重整、乙苯催化脱氢制苯乙烯等方面的应用。认为通过计算流体力学的方法,对径向反应器的流动行为进行模拟是径向反应器发展的趋势之一,结合径向反应器的优点,进一步拓展径向反应器的应用范围是其发展趋势之一。     

循环流化床流体动力特性研究

循环流化床的设计和放大需要对其流动特性进行细致地研究,文章采用RSM模型对新型的双外循环流化床流场进行了三维的数值模拟,得到了在不同入射速度下的流化床主、副床的三维的速度分布、压强分布及湍流强度分布等,给出了主床在典型位置x方向的上分布图,并与实验结果进行了对比。结果表明,在不同入射速度下RSM模型数值模拟结果与实验结果符合均较好,模拟计算可以很好地反映流化床中真实的流动状况,可以用于反应过程的性能评价,为设备优化设计和相似放大提供依据。     

Laminar radial flow electrochemical reactors. II. Convective diffusion of inert tracer

Mixing is investigated in three laminar radial flow cells (capillary gap cell (stationary discs), pump cell (one disc spinning) and the rotating electrolyser (co-rotating discs)) using numerical and semianalytical methods for inert tracer transport. Results are compared to existing data. Mixing in the three cells is modelled using finite element techniques applied to convection-dominated inert tracer transport. For the capillary gap cell modes of tracer tagging and detection are commented on with respect to which type provides the correct representation of the residence time distribution. The extent of cross-gap communication, from anode to cathode, is quantified and compared to that observed in the other radial cell designs. Two semi-analytical solutions (convection only, Taylor diffusion) are derived for inert tracer transport in this configuration and are compared to the detailed numerical results. Convection only is relevant fort _d/t _c ratios of greater than 100 and the Taylor diffusion model applies fort _d/t _c ratios of about 0.10 and only beyond a critical radius defined herein. Pump cell (PC) mixing is modelled using finite element techniques for the tracer, the velocity field being provided by a semi-analytical solution. Mixing is quantified in this cell and cross-gap communication evaluated. The large axial velocities provide for significant cross-gap mixing. The rotating electrolyser is modelled and the efficiency of separation of catholyte/anolyte streams is observed to be determined by Taylor number (Taylor number () — ratio of half-gap width divided by theoretical boundary layer thickness). The superiority of separation in this cell is quantified by definition of the zeroth wall moment and comparison with the other two radial cells. For the example modelled, cross-gap communication was less than half that of the other cells.     

Scaling down trickle bed reactors

The scaling down of trickle bed reactors for catalyst testing in deep hydrodesulphurisation (HDS) is evaluated. A multiphase micro-reactor system has been built specifically for HDS, consisting of a set of six 2 mm diameter packed beds with particles of approximately 100 μm. To confirm plug-flow behaviour (for integral conversion) and to guarantee the measurement of true kinetics, the hydrodynamics have to be investigated.

For this purpose, a ‘cold-flow’ set-up of the same dimensions as the HDS reactors, has been built. A liquid feed with a dye tracer pulse as well as gas are fed to a glass column, packed with glass particles. From the recorded outlet concentration, the influence of the gas- and liquid-flow rate on the mean residence time and residence-time distribution (RTD) have been determined.

This hydrodynamics investigation describes the deviation from plug flow in micro-scale packed beds. The results show that the deviations from plug flow are minimal. The effect of the gas-flow rate on the liquid-residence time is more pronounced in micro-packed beds than that in trickle beds with larger particles.

The RTD study presented here provides valuable insight into the behaviour of scaled-down kinetic-test facilities.     

Influence of temperature on fast-mode cyclic operation hydrodynamics in trickle-bed reactors

Despite the merits of periodic operation praised in the academic literature as one of the process intensification strategies advocated for trickle-bed reactors (TBRs), there is still reluctance to implement it in industrial practice. This can partly be ascribed to the lack of engineering data relevant to the elevated temperature and pressure characterizing industrial processes. Currently, the hydrodynamics of trickle beds under cyclic operation, especially in fast mode at elevated temperature and pressure, remains by and large terra incognita. This study proposes exploration of the hydrodynamic behavior of TBRs experiencing fast liquid flow modulation at elevated temperature and moderate pressure. The effect of temperature and pressure on the liquid holdup and pressure drop time series in terms of pulse breakthrough and decay times, pulse intensity and pulse velocity was examined for a wide range of superficial gas and liquid (base and pulse) velocities for the air-water system. The pulse breakthrough and decay times decreased, whereas the pulse velocity increased with temperature and/or pressure. The pressure drop was attenuated with increasing temperature for a given superficial gas, and base and pulse superficial liquid velocities. Experimental pulse velocity values were compared to the Giakoumakis et al. [2005. Induced pulsing in trickle beds—characteristics and attenuation of pulses. Chemical Engineering Science 60, 5183-5197] correlation which revealed that it could be relied upon at elevated temperature and close to atmospheric pressure.     

Liquid flow texture analysis in trickle bed reactors using high-resolution gamma ray tomography

Trickle bed reactor performance and safety may suffer from radial and axial liquid maldistribution and thus from non-uniform utilization of the catalyst packing. Therefore, experimental analysis and fluid dynamic simulation of liquid–gas flow in trickle bed reactors is an important topic in chemical engineering. In the present study for the first time a truly high-resolution gamma ray tomography technique was applied to the quantitative analysis of the liquid flow texture in a laboratory cold flow trickle bed reactor of 90 mm diameter. The objective of this study was to present the comparative analysis of the liquid flow dynamics for two different initial liquid distributions and two different types of reactor configurations. Thus, the hydrodynamic behavior of a glass bead packing was compared to a porous Al₂O₃ catalyst particle packing using inlet flow from a commercial spray nozzle (uniform initial liquid distribution) and inlet flow from a central point source (strongly non-uniform initial liquid distribution), respectively. The column was operated in downflow mode at a gas flow rate of 180 L h⁻¹ and at liquid flow rates of 15 and 25 L h⁻¹.     

The influence of granular flow rate on the performance of a moving bed granular filter

The goal of this study is to evaluate the effect of granular flow rate on the performance of a moving bed granular filter designed for hot gas filtration of fine char particles (dust) produced during fast pyrolysis of biomass. The filter employs a counter-current configuration, in which down-flowing granular material spreads out at the bottom of the filtration vessel to form an interfacial area where the dusty gas enters the granular bed and much of the gas cleaning is hypothesized to occur. This study uses a real-time particle counter to measure the instantaneous filtration efficiency during cold flow tests of the filter. Differential pressure measurements at various locations within the granular bed are used to assess the level of char dust hold-up over time. These experiments reveal a critical granular residence time below which the filter must be operated to achieve filtration efficiencies exceeding 99%. Operating above the critical value causes the filter to “clog” and decrease in efficiency. The clogging is characterized by a critical dust volume fraction as determined through a fixed bed filtration test. The filter is found to accumulate most of the dust at the interfacial region. Also the interfacial region is more efficient than the downcomer section of the granular bed in removing dust. Decreasing residence time of granular material in the filter reduces the hold-up of char dust in the filter, which is expected to mitigate coking reactions of organic vapors when the filter is used to remove char from fast pyrolysis gas streams.     

Modeling of fixed bed catalytic reactors

The simulation of a fixed-bed catalytic reactor requires the selection of a model, which is a set of balance equations that describes the reactor, as well as correlations for the model parameters involved. In this work general criteria, leading to a better choice of a model that fulfills the objectives of the simulation, are established. Different ways in which the parameters can be obtained are analyzed, and the numerical methods for solving the model equations are discussed.     

Dynamic responses of packed bed reactors

Amplification of process disturbances, wrong-way behavior, and extinction waves are responses to inlet disturbances of temperature, concentration or flow velocity in packed bed catalytic reactors. They can result in unexpected high temperatures that might compromise the reactor safety or performance. All of these responses are either manifestations of or are related to differential flow instability. The degree of amplification depends on the width of the reaction zone, which in turn depends on the diameter of catalyst particle. The ratio of the former and the latter determines the relative strength of convective (destabilizing) and diffusive (stabilizing) transport of heat. A modified Peclet number based on the length of the reaction zone is proposed as a criterion for the importance of disturbance amplification. Experiments and numerical analyses indicate that significant amplification under typical operating conditions of packed-bed reactors occurs for gaseous reaction systems at disturbance frequencies 0.0003-0.001 Hz and for liquid-phase reactions around 1 Hz. While simple estimates suggest that amplification that is large enough to threaten the reactor safety or to deactivate catalysts is infrequent, amplification and related responses to disturbance cannot be neglected in reactor design. Despite almost a decade of study, several questions persist about the prediction of these responses to inlet perturbations in industrial reactors.