Multidimensional modeling of a microfibrous entrapped cobalt catalyst Fischer‐Tropsch reactor bed

Thermal management of highly exothermic Fischer‐Tropsch synthesis (FTS) has been a challenging bottleneck limiting the radial dimension of the packed‐bed (PB) reactor tube to 1.5 in. ID. A computational demonstration of a novel microfibrous entrapped cobalt catalyst (MFECC) in mitigating hot spot formation has been evaluated. Specifically, a two‐dimensional (2‐D) model was developed in COMSOL^®, validated with experimental data and subsequently employed to demonstrate scale‐up of the FTS bed from 0.59 to 4 in. ID. Significant hot spot of 102.39 K in PB was reduced to 9.4 K in MFECC bed under gas phase at 528.15 K and 2 MPa. Improvement in heat transfer within the MFECC bed facilitates higher productivities at low space velocities (≥1000 h^?1) corresponding to high CO conversion (≥90%). Additionally, the MFECC reactor provides an eightfold increase in the reactor ID at hot spots ≤ 30 K with CO% conversions ≥ 90%. This model was developed for a typical FTS cobalt‐based catalyst where CO₂ production is negligible. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1723–1731, 2018     

Particle scale study of heat transfer in packed and bubbling fluidized beds

The approach of combined discrete particle simulation (DPS) and computational fluid dynamics (CFD), which has been increasingly applied to the modeling of particle‐fluid flow, is extended to study particle‐particle and particle‐fluid heat transfer in packed and bubbling fluidized beds at an individual particle scale. The development of this model is described first, involving three heat transfer mechanisms: fluid‐particle convection, particle‐particle conduction and particle radiation. The model is then validated by comparing the predicted results with those measured in the literature in terms of bed effective thermal conductivity and individual particle heat transfer characteristics. The contribution of each of the three heat transfer mechanisms is quantified and analyzed. The results confirm that under certain conditions, individual particle heat transfer coefficient (HTC) can be constant in a fluidized bed, independent of gas superficial velocities. However, the relationship between HTC and gas superficial velocity varies with flow conditions and material properties such as thermal conductivities. The effectiveness and possible limitation of the hot sphere approach recently used in the experimental studies of heat transfer in fluidized beds are discussed. The results show that the proposed model offers an effective method to elucidate the mechanisms governing the heat transfer in packed and bubbling fluidized beds at a particle scale. The need for further development in this area is also discussed. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

CFD analysis of hydrodynamic, heat transfer and reaction of three phase riser reactor

Catalytic cracking reaction and vaporization of gas oil droplets have significant effects on the gas solid mixture hydrodynamic and heat transfer phenomena in a fluid catalytic cracking (FCC) riser reactor. A three-dimensional computational fluid dynamic (CFD) model of the reactor has been developed considering three phase hydrodynamics, cracking reactions, heat and mass transfer as well as evaporation of the feed droplets into a gas solid flow. A hybrid Eulerian-Lagrangian method was applied to numerically simulate the vaporization of gas oil droplets and catalytic reactions in the gas-solid fluidized bed. The distributions of volume fraction of each phase, gas and catalyst velocities, gas and particle temperatures as well as gas oil vapor species were computed assuming six lump kinetic reactions in the gas phase. The developed model is capable of predicting coke formation and its effect on catalyst activity reduction. In this research, the catalyst deactivation coefficient was modeled as a function of catalyst particle residence time, in order to investigate the effects of catalyst deactivation on gas oil and gasoline concentrations along the reactor length. The simulation results showed that droplet vaporization and catalytic cracking reactions drastically impact riser hydrodynamics and heat transfer.     

NMR imaging of low pressure,gas‐phase transport in packed beds using hyperpolarized xenon‐129

Gas‐phase magnetic resonance imaging (MRI) has been used to investigate heterogeneity in mass transport in a packed bed of commercial, alumina, catalyst supports. Hyperpolarized ¹²⁹Xe MRI enables study of transient diffusion for microscopic porous systems using xenon chemical shift to selectively image gas within the pores, and, thence, permits study of low‐density, gas‐phase mass‐transport, such that diffusion can be studied in the Knudsen regime, and not just the molecular regime, which is the limitation with other current techniques. Knudsen‐regime diffusion is common in many industrial, catalytic processes. Significantly, larger spatial variability in mass transport rates across the packed bed was found compared to techniques using only molecular diffusion. It has thus been found that that these heterogeneities arise over length‐scales much larger than ～100 µm. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4013–4019, 2015     

A mathematical model for the dehydrogenation of methylcyclohexane in a packed bed reactor

A model for the dehydrogenation of methylcyclohexane in a tubular reactor over an industrial catalyst Pt-Sn/Al₂O₃ has been established. This model takes into account the axial dispersion at the inlet of the catalytic bed reactor as well as the heat transfer at the wall of the reactor. The heat transfer at the wall is satisfactorily represented by using a heat transfer coefficient correlation for which the parameters are obtained by fitting to the experimental data. The model provides a good representation of the radial and axial temperature profiles in the packed bed and can be also used to calculate the conversion.     

气体流动条件下钴基催化剂固定床的传热

在气体流量4~8 Nm3/h、气体分布器进口温度190~210℃、加热管壁温约240℃的条件下,对气体流动时活性组分呈蛋壳型分布的钴基催化剂固定床的传热进行了实验研究,建立了二维拟均相传热模型,利用正交配置法和Levenberg-Marquardt法对其求解,得到了钴基催化剂床层径向有效导热系数及壁给热系数的关联式,并将传热参数与由气体处于静态时固定床的有效导热系数计算而得的固定床传热参数值进行了比较,在气体入口温度范围内考察了其对固定床传热参数的影响. 结果表明,实验所得传热参数与文献值的最大偏差绝对值均在15%以内.     

耦合传质的羰基化固定床反应器传热模拟分析

固定床反应器中进行强放热反应时, 反应器的热点温度对操作参数变化敏感,容易引起飞温,导致转化率下降,影响催化剂寿命。为强化羰基化固定床反应器内热质传递与化学反应的协同性,建立考虑颗粒内扩散影响的羰基化固定床反应器拟均相一维传热模型,考察操作参数对床层热点温度、反应转化率、床层温升的影响。不仅体现传热传质和反应的协同作用,而且影响关系明晰、求解方便。为保证反应转化率,本实验条件下确定催化剂颗粒直径小于等于1.5 mm。反应器入口温度/冷却剂油温既要满足床层热稳定性需求,又要使反应转化率和床层温升都在合理范围内。模拟结果表明在床层入口温度升高的同时,可通过降低冷却剂油温获得良好的反应转化率和较小的床层温升。在此基础上,考察入口环氧乙烷浓度对反应转化率和床层温升的影响。本研究可为固定床反应器满足转化率要求、床层合理温升而选择催化剂颗粒直径、床层入口温度、冷却剂油温和床层入口浓度等操作参数提供计算依据。     

Cold flow experimental study and computer simulations of a compact spouted bed reactor

Spouted beds are a very interesting class of gas–solid contactors that possess excellent heat transfer and mixing characteristics, while they are particularly suited to process coarse particles. Proper design of such beds requires the prediction of various hydrodynamic characteristics, such as the minimum spouting velocity and maximum spoutable height. Contrary to their typical initial applications, spouted beds have been finding recently more frequent use on the one hand at endothermic processes and on the other hand using much finer particle sizes. In the current work, the hydrodynamic characteristics of a laboratory scale spouted bed of 0.05 m diameter have been investigated via cold flow studies using olivine particles of 3.55–5.00 × 10⁻⁴ m size. Hydrodynamic parameters have been measured at this compact geometry and fine particle size and were compared with common literature correlations. An empirical correlation was derived to predict the fountain height for the studied fine particle spouted bed. Computer simulations have been further used to investigate the heat transfer characteristics of the bed under endothermic reactive conditions, using methane reforming as a case study. Given sufficient external heat supply, a spouted bed operating at a well-mixed regime can efficiently drive even highly endothermic reactions.     

Multicomponent mass diffusion in porous pellets: Effects of flux models on the pellet level and impacts on the reactor level. Application to methanol synthesis

A heterogeneous model has been derived for a fixed packed‐bed reactor producing methanol. Several closures for the intra‐particle mass diffusion fluxes; Maxwell–Stefan, Wilke, dusty gas and Wilke–Bosanquet, have been compared on the level of the catalyst pellet and the impacts of the different particle flux closures on the reactor performance are investigated. A preparatory study of the transport phenomena on the pellet level is recommended prior to any large‐scale reactor simulation to determine what are the rate determining transport mechanisms. Hence, if Knudsen diffusion is apparent on the level of the pellet, a combined bulk and Knudsen diffusion model should naturally be used in the reactor simulations as well, because Knudsen diffusion can influence significantly on the reactor conversion. Minor differences are observed between the diffusion flux models on both pellet and reactor level. Hence, for the reactor operation conditions applied in this study, the Wilke model is a good approximation to the rigorous Maxwell–Stefan model, and similarly, the Wilke–Bosanquet model is an appropriate model to use in replacement for the dusty gas model. Moreover, variable pressure and viscous flow can be neglected in the pellet model, as the effect of these contributions are not visible at neither pellet or reactor level. © 2011 Canadian Society for Chemical Engineering     

固定床内石灰石煅烧与传递过程的数值模拟

将固态颗粒填料床视为由规则颗粒堆积而成的松散多孔介质,在推导出传热控制机制下微元体综合速率的基础上,采用局部热不平衡假设建立了一维固定床中石灰石热分解反应与传热、传质耦合的数学模型,运用有效容积法对其离散求解,并采用文献中实验数据对模型进行验证. 计算了不同条件下颗粒物料层内气体和固体骨架的温度场、产物气体浓度场以及固体转化率分布,以得到多孔介质体系内固有化学反应时的传热传质规律. 研究结果对具有强吸热反应的固定床反应器的设计和运行具有一定的参考作用.     

烧结矿余热回收竖罐内气固传热特性

以自制气固传热实验装置为操作平台,实验研究了烧结矿颗粒填充床内的气固传热特性。结果表明:气体表观流速和烧结矿颗粒直径是影响颗粒床层内气固传热过程的主要因素。气体表观流速越大,颗粒直径越小,床层内气固传热系数就越大。当烧结矿颗粒直径和气体表观流速一定时,床层内烧结矿颗粒温度的升高导致床层气固传热系数的增加和传热Nusselt数的减小。由于计算误差较大,现有的经验关联式不适用于求解烧结矿颗粒床层内的气固传热过程。基于量纲分析法,并结合实验测量数据拟合得出了能够描述烧结矿颗粒床层内气固传热特性的实验关联式,平均计算误差为4.22%,显示了良好的预测性能。     

Exact universal uniqueness criteria for the adiabatic tubular packed bed reactor

Exact, universal a priori bounds and regions of multiplicity for the entire tubular packed bed reactor are developed by application of a technique reported in Chang and Calo, Chem. Engng Sci. 1979 34 285 to a cascade two-phase cell model for an nth order chemical reaction with interphase resistance to mass and heat transport, Le ≠ 1 (or Le = 1) and either lumped parameter catalyst particles or with intraparticle concentration gradients with uniform temperature. Both the more common case of interphase heat transfer greater than interphase mass transfer rate and the inverse case of particle over-temperature have been considered. In all cases it has been shown that the reactor conservation equations can be decoupled at certain points along the bed determined by the Lewis number, and that questions of multiplicity and uniqueness reduce to consideration of a single algebraic equation which is actually a form of the two-phase adiabatic CSTR. Also as for the CSTR, the topology of the adiabatic packed bed reactor is shown to be the simple cusp catastrophe. The application of the resultant criteria is quite simple and represents a practical step in the design procedure for highly exothermic reactions in packed beds. A flow chart of a suggested procedure is included.     

Influence of elevated pressure and particle lyophobicity on hydrodynamics and gas–liquid mass transfer in slurry bubble columns

This article reports on the influence of elevated pressure and catalyst particle lyophobicity at particle concentrations up to 3 vol % on the hydrodynamics and the gas‐to‐liquid mass transfer in a slurry bubble column. The study was done with demineralized water (aqueous phase) and Isopar‐M oil (organic phase) slurries in a 0.15 m internal diameter bubble column operated at pressures ranging from 0.1 to 1.3 MPa. The overall gas hold‐up, the flow regime transition point, the average large bubble diameter, and the centerline liquid velocity were measured along with the gas–liquid mass transfer coefficient. The gas hold‐up and the flow regime transition point are not influenced by the presence of lyophilic particles. Lyophobic particles shift the regime transition to a higher gas velocity and cause foam formation. Increasing operating pressure significantly increases the gas hold‐up and the regime transition velocity, irrespective of the particle lyophobicity. The gas–liquid mass transfer coefficient is proportional to the gas hold‐up for all investigated slurries and is not affected by the particle lyophobicity, the particle concentration, and the operating pressure. A correlation is presented to estimate the gas–liquid mass transfer coefficient as a function of the measured gas hold‐up: $k_{\rm l}a_{\rm l}/\varepsilon_{\rm g} = 3.0 \sqrt{Du_{\rm b}/d_{\rm b}^3}\;{\rm s}^{-1}$ . © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Optimization and simulation of the Sabatier reaction process in a packed bed

The Sabatier reaction in a testing packed bed was investigated experimentally and theoretically, and was used to convert waste carbon dioxide and hydrogen to provide needed water for closing the life‐support loop on orbit in space. A three‐dimensional model including fluid flow, gas dispersion, heat and mass transfer, and chemical reaction was developed by coupling some semi‐empirical correlated equations in chemical engineering science into computational fluid dynamics theory. Good agreements between the simulating results and experimental data for the effect of some parameters on reaction verified this model, for example, heat exchange between reactor and atmosphere, the material property of reactor, the catalyst deactivated and gas mass flux and so on. By using this model as the designing tools, an optimized packed bed is proposed. Compared with the testing packed bed, the relevant reactor length can be reduced from 220 to 150 mm with the same hydrogen conversion and lower pressure drop. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2879–2892, 2016     

Steady‐state behavior of liquid fuel hydrazine decomposition in packed bed

A general theoretical model is presented to analyze the steady‐state decomposition process of liquid monopropellants in packed beds for thruster systems. Additionally, an experiment studying the decomposition of liquid hydrazine in a packed bed is used to validate this model. The liquid droplet evaporation rate is determined through calculating the gas‐liquid mass transfer for the mixture temperatures lower than the liquid propellant boiling point and solving the gas‐liquid or liquid‐solid heat transfer equations at the temperature exceeding the boiling point. The process of liquid propellant decomposition in packed beds are simulated based on the Naive–Stokes equation for the mixture model integrated with the developed liquid evaporation rate, in which both the heterogeneous catalytic reaction coupled with the diffusion of reactants in the pore of catalyst, and the homogenous decomposition reactions are considered. The calculated results for the axial distribution of the temperature are in good agreement with the experimental data. © 2014 American Institute of Chemical Engineers AIChE J, 61: 1064–1080, 2015     

Modeling of transient heterogeneous two-dimensional catalytic packed bed reactor

A two-dimensional transient catalytic packed bed model, incorporating all transport parameters and resistances, along with boundary conditions based on a catalytic single pellet has been developed. Thermal conduction through the solid phase is included in the model. The overall steady state reactor performances of packed bed reactor using a model proposed in this study are compared with those from different models which are often used for a packed bed reactor. The model presented is very useful in the presence of internal temperature and concentration gradients in the catalyst pellets. The dynamic behavior in feed temperature change is examined during ethane hydrogenolysis. A transient thermal runaway is observed by feed temperature decrease. The sensitivities of the computation to each physical parameter and the effects of some simplifying assumptions in the model are also analyzed. The magnitude and position of hot spot in catalytic packed bed reactor are relatively sensitive to thermal parameters and characteristic parameters of a catalyst pellet.     

Catalytic hydrogenation in a packed bed bubble column reactor

The cocurrent downflow contactor reactor (CDCR) has been found to give low mass transfer resistances both in slurry and packed bed catalytic operation. The hydrogenation of propan-2-ol solutions of itaconic acid in the range 100–300 kPa and 20–70°C and of soyabean oil in the range 100–500 kPa and 130–160°C was studied using slurry (5% w/w Pd/C) and packed bed (3% w/w Pd/Al₂O₃ Raschig ring) catalyst. Mass transport and kinetic parameters were evaluated for both operational modes and while the slurry CDCR gave better mass transfer properties than the packed bed CDCR, the latter gave better mass transfer than conventional reactors and superior selectivity to the slurry CDCR. As has been observed with the slurry CDCR, the packed bed CDCR was found to operate under surface reaction rate control with negligible transport resistances. This was particularly evident for soyabean oil hydrogenation, which is well known to be transport controlled in conventional reactors.     

Gas‐Liquid Mass Transfer in a Bench‐Scale Trickle Bed Reactor used for Benzene Hydrogenation

The gas‐liquid mass transfer coefficients (MTCs) of a trickle bed reactor used for the study of benzene hydrogenation were investigated. The Ni/Al₂O₃ catalyst bed was diluted with a coarse‐grained inert carborundum (SiC) particle catalyst. Gas‐liquid mass transfer coefficients were estimated by using a heterogeneous model for reactor simulation, incorporating reaction kinetics, vapor‐liquid equilibrium, and catalyst particle internal mass transfer apart from gas‐liquid interface mass transfer. The effects of liquid axial dispersion and the catalyst wetting efficiency are shown to be negligible. Partial external mass transfer coefficients are correlated with gas superficial velocity, and comparison between them and those obtained from experiments conducted on a bed diluted with fine particles is also presented. On both sides of the gas‐liquid interface the hydrogen mass transfer coefficient is higher than the corresponding benzene one and both increase significantly with gas velocity. The gas‐side mass transfer limitations appear to be higher in the case of dilution with fine particles. On the liquid side, the mass transfer resistances are higher in the case of dilution with coarse inerts for gas velocities up to 3 · 10^–2 cm/sec, while for higher gas velocities this was inversed and higher mass transfer limitations were obtained for the beds diluted with fine inerts.     

Dynamic simulation of a cascade fluidized-bed membrane reactor in the presence of long-term catalyst deactivation for methanol synthesis

In this work, a dynamic model for a cascade fluidized-bed hydrogen permselective membrane methanol reactor (CFBMMR) has been developed in the presence of long-term catalyst deactivation. In the first catalyst bed, the synthesis gas is partly converted to methanol in a water-cooled reactor, which is a fluidized-bed. In the second bed, which is a membrane assisted fluidized-bed reactor, the reaction heat is used to preheat the feed gas to the first bed. This reactor configuration solves some observed drawbacks of new conventional dual type methanol reactor (CDMR) and even fluidized-bed membrane dual type methanol reactor (FBMDMR) such as pressure drop, internal mass transfer limitations, radial gradient of concentration and temperature in both reactors. A dynamic two-phase theory in bubbling regime of fluidization is used to model and simulate the proposed reactor. The proposed model has been used to compare the performance of a cascade fluidized-bed membrane methanol reactor with fluidized-bed membrane dual-type methanol reactor and conventional dual-type methanol reactor. The simulation results show a considerable enhancement in the methanol production due to the favorable profile of temperature and activity along the CFBMMR relative to FBMDMR and CDMR systems.     

Bed Expansion – Extending Correlations for Fluidized Beds with Inserts to Open Fluidized Beds

Bed expansion occurs during the operation of gas‐fluidized beds and is influenced by particle properties, gas properties and distributor characteristics. It has a significant bearing on heat and mass transfer phenomena within the bed. A method of predicting bed expansion behavior from other fluidizing parameters would be a useful tool in the design process, dispensing with the need for small‐scale trials. This study builds on previous work on fluidized beds with vertical inserts to produce a correlation that links a modified particle terminal velocity, minimum fluidizing velocity and distributor characteristics with bed voidage in the relationship with P as the pitch between holes in the perforated distributor plate.