Influence of Particle Size and Single‐Tube Diameter on Thermal Behavior of Fischer‐Tropsch Reactors. Part II. Eggshell Catalysts and Optimal Reactor Performance

The optimal combination of particle and tube size for simulation of a single tube of a wall‐cooled multitubular Fischer‐Tropsch (FT) reactor with cobalt as catalyst was determined. The maximum size of the tubes, realized without temperature runaway, enhances with increasing particle size until an optimal value is reached, thereby improving the production rate of liquid fuels per tube. Reasons for this are that heat transfer to the cooled tube wall for a given tube size is considerably enhanced by increasing the particle size and that the influence of pore diffusion on the effective rate of FT synthesis gets stronger with rising particle size, which reduces the temperature sensitivity of the reactor and decreases the danger of a temperature runaway. The simulations indicate that the use of FT eggshell catalysts is not an option for fixed‐bed reactors. The temperature sensitivity of the reactor is strongly enhanced, which decreases the maximum tube size and with that the productivity per tube. All these effects are valid in general for wall‐cooled fixed‐bed reactors. Respective criteria are presented.     

Radiation Matters in Fixed‐Bed CFD Simulations

Fixed‐bed reactors often operate at elevated temperatures, where radiation can be a significant heat‐transfer mechanism. Particle‐resolved CFD models fixed‐bed reactors on a very detailed macroscopic level. In this study, the contribution of radiative heat transfer is investigated in a 500‐mm bed of 7‐hole pellets. At industrially relevant temperatures (250 – 800 °C) and with a steam‐reforming gas‐phase mixture, the S2S and DOM radiation models were applied. Neglecting radiation results in temperatures being up to 6 % lower. In this case, the main driver is surface‐to‐surface (S2S) radiation. Additional modeling recommendations are given.     

Simulation and Analysis of a Tubular Fixed‐Bed Fischer‐Tropsch Synthesis Reactor with Co‐Based Catalyst

A two‐dimensional pseudohomogeneous reactor model is proposed to simulate the performance of fixed‐bed Fischer‐Tropsch synthesis (FTS) reactors by lumped thought. A CO consumption kinetics equation and a carbon chain growth probability model were incorporated into the reactor model. The model equations discretized by a two‐dimensional orthogonal collocation method were solved by the Broyden method. Concentration and temperature profiles were obtained. The validity of the reactor model against the pilot plant test data was investigated. Satisfactory agreements between model prediction values and experiment results were obtained. Further simulations were carried out to investigate the effect of operating conditions on the reaction behavior of the fixed‐bed FTS reactor.     

CFD方法在固定床反应器传热研究中的应用

固定床反应器是一种常见的化学和生化反应器,由于内部结构十分复杂,固定床内的局部流动和传热过程研究一直是一个颇具挑战性的问题。有效参数法是长期以来固定床传热研究的常用方法,但是由于对固定床内温度场缺乏准确的了解,目前为止许多基于有效参数法的传热模型的普适性仍然存在问题。计算流体力学（CFD）的数值模拟方法是近年来应用于固定床流动和传热研究的一种新的研究方法,它通过数值方法求解流动和传递的微分方程组而获得流场和温度场。CFD数值模拟方法能够提供精确的局部流动和传递信息如速度分布、压力分布、温度分布、组分浓度分布等。本文综述和分析了CFD方法在固定床反应器的流动和传热研究领域的最新进展,讨论了CFD方法在该领域的应用前景。     

Three‐dimensional CFD‐PBM coupled model of the temperature fields in fluidized‐bed polymerization reactors

A three‐dimensional (3‐D) computational fluid dynamics model, coupled with population balance (CFD‐PBM), was developed to describe the gas–solid two‐phase flow in fluidized‐bed polymerization reactors. The model considered the Eulerian–Eulerian two‐fluid model, the kinetic theory of granular flow, the population balance, and heat exchange equations. First, the model was validated by comparing simulation results with the classical calculated data. The entire temperature fields in the reactor were also obtained numerically. Furthermore, two case studies, involving constant solid particle size and constant polymerization heat or evolving particle‐size distribution, polymerization kinetics, and polymerization heat, were designed to identify the model. The results showed that the calculated results in the second case were in good agreement with the reality. Finally, the model of the second case was used to investigate the influences of operational conditions on the temperature field. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

A 2‐D observer to estimate the reaction rate in a stopped flow fixed bed reactor for gas phase olefin polymerization

A two‐dimensional high gain observer has been constructed to estimate the reaction rate parameters in a laboratory scale stopped flow fixed bed reactor for gas phase ethylene polymerization. The observer is based on the heat balances of a validated model of the reactor and the measured variable is the outlet temperature of the fixed bed. To create an observable system of equations, the polymerization rate is considered in two parts, an activation energy term and a lumped parameter. The effective radial conductivity in the fixed bed and the heat‐transfer coefficient at the wall are considered separately. The polymerization rate is calculated from the observer results and is in good agreement with the measured data and calculated values. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3511–3523, 2014     

Mathematical modeling of a moving bed reactor for post‐combustion CO2 capture

A mathematical model for a moving bed reactor with embedded heat exchanger has been developed for application to solid sorbent‐based capture of carbon dioxide from flue gas emitted by coal‐fired power plants. The reactor model is one‐dimensional, non‐isothermal, and pressure‐driven. The two‐phase (gas and solids) model includes rigorous kinetics and heat and mass transfer between the two phases. Flow characteristics of the gas and solids in the moving bed are obtained by analogy with correlations for fixed and fluidized bed systems. From the steady‐state perspective, this work presents the impact of key design variables that can be used for optimization. From the dynamic perspective, the article shows transient profiles of key outputs that should be taken into account while designing an effective control system. In addition, the article also presents performance of a model predictive controller for the moving bed regenerator under process constraints. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3899–3914, 2016     

Comprehensive Fischer–Tropsch reactor model with non-ideal plug flow and detailed reaction kinetics

This paper presents a detailed first principle Fischer–Tropsch reactor model including detailed heat transfer calculations and detailed reaction kinetics. The model is based on a large number of components and chemical reactions. The model is tuned to a fixed bed nearplug flow reactor but can also be applied to slurry and micro-channel reactors.The presented model is based on a cascade of ideally stirred reactors. This modelling approach is novel for Fischer–Tropsch reactors and has the advantage of being able to represent none-ideal reactors. Using a large number of components and reactions makes it possible to better represent the product slate than with conventional modelling based on distribution models.The results of the simulations emphasise that temperature control is important. Global conversion and product yields are dependent on operating conditions especially the temperature. The model is used to calculate the dimensions of an industrial reactor from a laboratory scale reactor.     

A CFD‐PBM‐PMLM integrated model for the gas–solid flow fields in fluidized bed polymerization reactors

Although the use of computational fluid dynamics (CFD) model coupled with population balance (CFD‐PBM) is becoming a common approach for simulating gas–solid flows in polydisperse fluidized bed polymerization reactors, a number of issues still remain. One major issue is the absence of modeling the growth of a single polymeric particle. In this work a polymeric multilayer model (PMLM) was applied to describe the growth of a single particle under the intraparticle transfer limitations. The PMLM was solved together with a PBM (i.e. PBM‐PMLM) to predict the dynamic evolution of particle size distribution (PSD). In addition, a CFD model based on the Eulerian‐Eulerian two‐fluid model, coupled with PBM‐PMLM (CFD‐PBM‐PMLM), has been implemented to describe the gas–solid flow field in fluidized bed polymerization reactors. The CFD‐PBM‐PMLM model has been validated by comparing simulation results with some classical experimental data. Five cases including fluid dynamics coupled purely continuous PSD, pure particle growth, pure particle aggregation, pure particle breakage, and flow dynamics coupled with all the above factors were carried out to examine the model. The results showed that the CFD‐PBM‐PMLM model describes well the behavior of the gas–solid flow fields in polydisperse fluidized bed polymerization reactors. The results also showed that the intraparticle mass transfer limitation is an important factor in affecting the reactor flow fields. © 2011 American Institute of Chemical Engineers AIChE J, 58: 1717–1732, 2012     

Structured Porous Millireactors for Liquid‐Liquid Chemical Reactions

Milli‐scale reactors with an integrated microstructure offer a promising scale‐up approach for conventional microreactors. This study applies 3D‐printed structured porous millireactors to industrially relevant liquid‐liquid reactions. The underlying transport mechanisms are identified by quantifying interfacial heat and mass transfer. The structured reactors perform limited in Taylor flow compared to a packed‐bed reactor due to limited interfacial mass transfer. However, in stratified flow, their productivity increases significantly at a fraction of the pressure drop of a packed bed.     

Particle‐scale simulation of the flow and heat transfer behaviors in fluidized bed with immersed tube

A kind of new modified computational fluid dynamics‐discrete element method (CFD‐DEM) method was founded by combining CFD based on unstructured mesh and DEM. The turbulent dense gas–solid two phase flow and the heat transfer in the equipment with complex geometry can be simulated by the programs based on the new method when the k‐ε turbulence model and the multiway coupling heat transfer model among particles, walls and gas were employed. The new CFD‐DEM coupling method that combining k‐ε turbulence model and heat transfer model, was employed to simulate the flow and the heat transfer behaviors in the fluidized bed with an immersed tube. The microscale mechanism of heat transfer in the fluidized bed was explored by the simulation results and the critical factors that influence the heat transfer between the tube and the bed were discussed. The profiles of average solids fraction and heat transfer coefficient between gas‐tube and particle‐tube around the tube were obtained and the influences of fluidization parameters such as gas velocity and particle diameter on the transfer coefficient were explored by simulations. The computational results agree well with the experiment, which shows that the new CFD‐DEM method is feasible and accurate for the simulation of complex gas–solid flow with heat transfer. And this will improve the farther simulation study of the gas–solid two phase flow with chemical reactions in the fluidized bed. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Effects of process and design parameters on heat management in fixed bed Fischer-Tropsch synthesis reactor

A two-dimensional pseudo-homogeneous model of wall-cooled fixed bed Fischer-Tropsch synthesis (FTS) reactor with Co/Re/γ-Al₂O₃ catalyst was developed to study the effect of process and design parameters on heat generation and removal characteristics. The influence of liquid-phase formation on heat transport was accounted for by using two-phase correlations. The effect of intraparticle diffusion on heat generation was considered. Detailed numerical simulations were performed to analyze the effect of process and design parameters on the reactor performance in terms of heat management. Results show that thermal behavior of FTS fixed bed reactors is very sensitive and any large disturbances can lead to temperature runaway. Large tube diameters are shown to be particularly unfavorable, with d _t >5 cm resulting in axial and radial gradients greater than 20 K and 13 K, respectively. The importance of detailed reactor modeling when designing and optimizing FTS fixed bed reactors is highlighted.     

Heat Transfer in the Downer and the Riser of a Circulating Fluidized Bed – A Comparative Study

The characteristics of heat transfer were studied in both a gas‐solids concurrent downflow fluidized bed (downer) and a gas‐solids concurrent upflow fluidized bed (riser) with FCC particles. The radial and axial distribution profiles of the heat transfer coefficient between a suspended surface and the gas‐solids flow suspension were obtained using a miniature heat transfer probe, under different operating conditions. Comprising the results of the heat transfer in the downer and the riser shows that there exists some significant distinction between the heat transfer processes in the two reactors. The characteristics of heat transfer in both cases are closely related to their hydrodynamics and the distinct flow structures determinate the different heat transfer behaviors. The results also indicate that the operating conditions present some different effects in the two beds.     

Particle‐Scale Investigation of Heat Transfer in Radiation‐Driven Char Gasification

A model of the steam gasification of a single char particle driven by high‐intensity radiation was developed and experimentally verified with available measurements in the literature. This was used to explore the sensitivity of the particle surface temperature and heat‐transfer mechanisms to variations in particle diameters, radiative heat flux, and the concentration of the gasification agent H₂O under typical conditions for solar gasification reactors. The results highlight the importance of the particle diameter in influencing solar‐to‐chemical energy conversion efficiency and assist in the selection of appropriate feedstock particles to match the conditions in specific solar gasification reactors.     

Effect of Operating Parameters on Gas‐Solid Hydrodynamics and Heat Transfer in a Spouted Bed

Through a combined computational fluid dynamics and discrete element method approach, the effect of the operating parameters on the hydrodynamics and heat‐transfer properties of gas‐solid two‐phase flows in a spouted bed are extensively investigated. Considering the high velocity in the fountain region, gas turbulence is resolved by employing the large‐eddy simulation. The rolling friction model is adopted for more precise predictions of solid behavior near the wall. Subsequently, the gas‐solid flow patterns, gas‐solid velocities, and temperature evolution are investigated. Moreover, different operating conditions and geometry configurations are evaluated with respect to heat‐transfer performance. The results provide a fundamental understanding of heat‐transfer mechanisms in spouted beds.     

Design of mixed conducting ceramic membranes/reactors for the partial oxidation of methane to syngas

The performance of mixed conducting ceramic membrane reactors for the partial oxidation of methane (POM) to syngas has been analyzed through a two‐dimensional mathematical model, in which the material balance, the heat balance and the momentum balance for both the shell and the tube phase are taken into account. The modeling results indicate that the membrane reactors have many advantages over the conventional fixed bed reactors such as the higher CO selectivity and yield, the lower heating point and the lower pressure drop as well. When the methane feed is converted completely into product in the membrane reactors, temperature flying can take place, which may be restrained by increasing the feed flow rate or by lowering the operation temperature. The reaction capacity of the membrane reactor is mainly determined by the oxygen permeation rate rather than by the POM reaction rate on the catalyst. In order to improve the membrane reactor performance, reduction of mass transfer resistance in the catalyst bed is necessary. Using the smaller membrane tubes is an effective way to achieve a higher reaction capacity, but the pressure drop is a severe problem to be faced. The methane feed velocity for the operation of mixed conducting membrane reactors should be carefully regulated so as to obtain the maximum syngas yield, which can be estimated from their oxygen permeability. The mathematical model and the kinetic parameters have been validated by comparing modeling results with the experimental data for the La_0.6Sr_0.4Co_0.2Fe_0.8O_3‐α (LSCF) membrane reactor. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Investigation of radiative heat transfer in fixed bed biomass furnaces

This paper presents an investigation of the radiative heat transfer process in two fixed bed furnaces firing biomass fuels and the performance of several widely used models for calculation of radiative heat transfer in the free-room of fixed bed furnaces. The simple optically thin (OT) model, the spherical harmonic P₁-approximation model, the grey gas model based on finite volume discretization (FGG), and the more accurate but time consuming spectral line weighted-sum-of-grey-gases (SLW) model are investigated. The effective mean grey gas absorption coefficients are calculated using an optimised version of the exponential wide band model (EWBM) based on an optical mean beam length. Fly-ash and char particles are taken into account using Mie scattering. In the investigated updraft small-scale fixed bed furnace radiative transfer carries heat from the bed to the free-room, whereas in the cross-current bed large-scale industry furnace, radiative transfer brings heat from the hot zones in the free-room to the drying zone of the bed. Not all the investigated models can predict these heat transfer trends, and the sensitivity of results to model parameters is fairly different in the two furnaces. In the small-scale furnace, the gas absorption coefficient predicted by using different optical lengths has great impact on the predicted temperature field. In the large-scale furnaces, the predicted temperature field is less sensitive to the optical length. In both furnaces, with the same radiative properties, the low-computational-cost P₁ model predicts a temperature field in the free-room similar to that by the more time consuming SLW model. In general, the radiative heat transfer rates to the fuel bed are not very sensitive to the radiative properties, but they are sensitive to the different radiative heat transfer models. For a realistic prediction of the radiative heat transfer rate to the fuel bed or to the walls, more computationally demanding models such as the FGG or SLW models should be used.     

Optimization of Fischer‐Tropsch Process in a Fixed‐Bed Reactor Using Non‐uniform Catalysts

Optimization of Fischer‐Tropsch (FT) process in a fixed‐bed reactor is carried out using non‐uniform catalysts. The C₅⁺ yield of the reactions is maximized utilizing a combination of non‐uniform catalysts across the bed. A 1D heterogeneous model is developed to simulate the bed containing uniform and non‐uniform catalysts. It is found that the egg‐shell and surface‐layered catalysts result in higher C₅⁺ yield. Moreover, effects of cooling temperature are studied. Genetic Algorithm (GA) and Successive Quadratic Programming (SQP) methods are applied. Feed and cooling temperature are selected as decision variables together with distribution of non‐uniform catalysts along the bed. The optimization result shows 14.47 % increase in the C₅⁺ yield with respect to the base condition.     

Experimental and Theoretical Studies on Hydrogenation in Multiphase Fixed‐Bed Reactors

Multiphase fixed‐bed reactors have complex hydrodynamic and mass transfer characteristics. The modeling and scale‐up are therefore difficult. The present work focuses on the role of mass transfer on the effective reaction rate. The catalytic 1‐octene hydrogenation was taken as a model reaction. The reaction rate in the trickle‐bed reactor is by a factor of 20 smaller than (theoretically) in the absence of any mass transfer limitations. For high octene concentrations (> 10 %), the effective reaction rate is limited by the H₂ consumption, above all by the gas/liquid and liquid/solid mass transfer. For lower octene concentrations the reaction is zero order with respect to H₂ and only depends on the octene consumption, i.e., on the interplay of chemical reaction, L/S and intraparticle mass transfer of octene.     

Effects of Chaotic Temperature Fluctuations on the Heat Transfer Coefficient in Liquid‐Liquid‐Solid Fluidized Beds

The effect of chaotic temperature fluctuations on the immersed heater‐to‐bed heat transfer coefficient (h) are investigated in a liquid‐liquid‐solid fluidized bed (0.152 m ID × 2.5 m in height). The time series of temperature fluctuations are measured and analyzed by means of the multidimensional phase space portraits and Kolmogorov entropy (K), in order to characterize the chaotic behavior of heat transfer coefficient fluctuations in the bed. The overall heat transfer coefficient is inversely proportional to the Kolmogorov entropy of temperature fluctuations, as well as the fluctuation range of heat transfer coefficient (Δh_i). The Kolmogorov entropy and fluctuation range of the heat transfer coefficient (Δh_i) increase with increasing dispersed phase velocity, but decrease with increasing particle size. However, they attain their minima with variation of the continuous phase velocity as well as the bed porosity, at which point the flow regime of particles in the beds changes. The overall heat transfer coefficient is directly correlated with the Kolmogorov entropy, as well as the fluctuation range of heat transfer coefficient.