Fixed-bed Reactor Model Research Articles

Performance analysis, statistical modeling, and multiple response optimization of a novel fixed-bed quartz reactor packed with Ba-Pt@γ-AL2O3 using response surface methodology

In the present study, a novel fixed-bed continuous reactor with a preheating chamber was designed to be utilized for the practical application of removal studies of dangerous pollutants, especially NOX removal by NOX Storage Reduction (NSR) catalysts on a laboratory scale. The reactor's design and operational parameters, including outer wall temperature (50–600 °C), volumetric flow rate (0.3–3 L/min), wall temperature time (0.16–10 min), and granule surface area inside the preheating chamber (0–270 cm2), were statistically modeled and optimized using Response Surface Methodology (RSM). For more logical and effective parameter optimization, the ratio of gas and catalyst temperatures and pressure drop to the reactor outer wall temperature (GT/ROWT, CT/ROWT, and PD/ROWT) were also included in the optimization process. Experimental results showed that gas temperature, catalyst temperature, and pressure drop ranged from 31 to 177 °C, 51–585 °C, and 7–153 Pa, respectively. Optimal conditions were determined to be an outer wall temperature of 230 °C, a volumetric flow rate of 3 L/min, a wall temperature time of 0.16 min, and a granule surface area of 67.3 cm2. The results demonstrated that outer wall temperature, flow rate, time, and surface area of granules have significant and interaction effects on the responses and should be considered when researchers assess the removal efficiency of thermal catalysts.

Numerical Study to Define Initial Thermal Integration Window for Methane Oxidative Coupling with Dehydroaromatization Reactors

Oxidative coupling of methane and methane dehydroaromatization are attractive one-step conversion routes to make valuable platform chemicals more sustainable. Both processes require elevated temperatures above 600°C, good heat management, and the use of heterogeneous catalysts. None of these reactions are yet commercial due to many technical challenges. This work explores the potential of combining these two processes under one umbrella to overcome some of the technical challenges and make these processes more attractive. It focuses on the recuperative autothermal reactor coupling as one of the possible integration options. A tube-in-tube reactor design is proposed in which OCM is in the inner tube and MDA is in the outside. A numerical study is carried out using pseudohomogenous ideal fixed bed reactor models with literature kinetics. A systematic tabulated approach is used to simplify, visualize, and structure the design process and view the design options. Practical constraints such as reactor sizing, pressure drop, reaction performance, and axial temperature profile are investigated. The effect of heat transfer coefficient, diluents, catalyst profiling, and flow direction have been investigated to alter the axial temperature profile, avoid thermal run away, and improve the performance. Multiple thermally coupled OCM-MDA reactor design candidates are identified. This is the first time that the thermal coupling of OCM and MDA has been identified and quantified. These candidates are merely a starting point toward exploring the full coupling opportunities between OCM and MDA toward reaching the ultimate and more attractive option of full mass and heat integration in the same reactor.

Modelling of fixed bed and slurry bubble column reactors for Fischer–Tropsch synthesis

Abstract An extensive review of slurry bubble column reactor and fixed bed reactor steady state models for Fischer–Tropsch synthesis is presented in this work. Material, energy and momentum balance equations are presented here along with the relevant findings of each study for modelling purposes. For fixed bed reactor models, one-dimensional and two-dimensional models can be differentiated, with the latter being better at predicting hot spots and thermal runaways, although the computational effort required solving them is also higher. Fixed bed reactors can also be classified as pseudo-homogeneous or heterogeneous models, the former considering that all phases are in thermal and chemical equilibrium, and the latter having different profiles for the catalyst particles, generally including a pellet model. For slurry bubble column reactors, single-class and double-class bubble models can be differentiated. The double-class bubble models represent better churn-turbulent regimes at the expense of a higher computational effort.

Visible-light-driven photodegradation of xanthate in a continuous fixed-bed photoreactor: Experimental study and modeling

Photocatalysis has been widely employed as a promising method for wastewater treatment. However, existing studies are primarily conducted in batch reactors. To the best of our knowledge, a continuous reactor has not been used to degrade xanthate residual in mineral beneficiation wastewater. In this work, a continuous fixed-bed photoreactor (CFPR) was first designed, and Bi2WO6 photocatalysts coated on silica sands were used to degrade sodium isobutyl xanthate (SIBX) under visible light irradiation. The effects of various parameters, including catalyst loading, pH level, initial SIBX concentration, wastewater flow rate, calcium ion (Ca2+) concentration, magnesium ion (Mg2+) concentration, and zinc ions (Zn2+), on the degradation efficiency, were systematically investigated. The results show that the photodegradation percentage of SIBX increases with increasing catalyst loading, decreasing initial concentration, and decreasing flow rate within the scope under investigation. Additionally, low concentrations (30 mg·L−1) of Ca2+ and Mg2+ ions favor the photodegradation of SIBX, whereas excessive Ca2+ and Mg2+ ions (240 mg·L−1) inhibit photocatalytic activity. The presence of Zn2+ ions inhibits photodegradation percentage. Furthermore, the photodegradation percentage is slightly higher at alkaline than at acidic pH. The maximum degradation percentage reached 95.40 % after 70 min of visible light irradiation under optimal conditions. In addition, a fixed bed reactor model considering surface reaction kinetics and mass transfer constraints was established by combining the Langmuir-Hinshelwood (L-H) kinetic equations and the series resistance theory. This model can accurately estimate the intrinsic kinetic parameters and can well predict degradation efficiency with a root-mean-square-error (RMSE) of 4.24 %. Finally, the bottleneck for improving the performance of the reactor can be identified under different conditions.

Impact of heat transport properties and configuration of ceramic fibrous catalyst structures for CO2 methanation: A simulation study

Fibrous catalysts have shown to enhance mass transfer when applied to potentially limited reactions, and exhibit promising characteristics for heat transfer as well. However, heat removal seems to be the main limitation to process intensification when applying fibrous catalysts to an exothermic reaction. This paper investigates strategies to improve the heat transfer behavior of ceramic paper catalysts, by applying them to the exothermic reaction of CO2 methanation. A fixed-bed reactor model was used to simulate and study the development of temperature profiles, as well as the efficiency losses caused by insufficient heat removal. Different strategies were implemented in simulations to evaluate their impact on the management of reaction heat and hot-spots. The results bring forward the advantages and versatility of catalytic ceramic papers and other fibrous catalysts, as alternatives for process intensification, and to improve overall reactor performance in exothermic reaction applications.

Validation of a Fixed Bed Reactor Model for Dimethyl Ether Synthesis Using Pilot-Scale Plant Data

The one-dimensional (1D) mathematical model of fixed bed reactor was developed for dimethyl ether (DME) synthesis at pilot-scale (capacity: 25–28 Nm3/h of syngas). The reaction rate, heat, and mass transfer equations were correlated with the effectiveness factor. The simulation results, including the temperature profile, CO conversion, DME selectivity, and DME yield of the outlet, were validated with experimental data. The average error ratios were below 9.3%, 8.1%, 7.8%, and 3.5% for the temperature of the reactor, CO conversion, DME selectivity, and DME yield, respectively. The sensitivity analysis of flow rate, feed pressure, H2:CO ratio, and CO2 mole fraction was investigated to demonstrate the applicability of this model.

Solution and Parameter Identification of a Fixed-Bed Reactor Model for Catalytic CO2 Methanation Using Physics-Informed Neural Networks

In this study, we develop physics-informed neural networks (PINNs) to solve an isothermal fixed-bed (IFB) model for catalytic CO2 methanation. The PINN includes a feed-forward artificial neural network (FF-ANN) and physics-informed constraints, such as governing equations, boundary conditions, and reaction kinetics. The most effective PINN structure consists of 5–7 hidden layers, 256 neurons per layer, and a hyperbolic tangent (tanh) activation function. The forward PINN model solves the plug-flow reactor model of the IFB, whereas the inverse PINN model reveals an unknown effectiveness factor involved in the reaction kinetics. The forward PINN shows excellent extrapolation performance with an accuracy of 88.1% when concentrations outside the training domain are predicted using only one-sixth of the entire domain. The inverse PINN model identifies an unknown effectiveness factor with an error of 0.3%, even for a small number of observation datasets (e.g., 20 sets). These results suggest that forward and inverse PINNs can be used in the solution and system identification of fixed-bed models with chemical reaction kinetics.

Dehydration of 2,3-Butanediol to 1,3-Butadiene and Methyl Ethyl Ketone: Modeling, Numerical Analysis and Validation Using Pilot-Scale Reactor Data

This work presents the numerical analysis and validation of a fixed bed reactor model for 2,3-butanediol (2,3-BDO) dehydration. The 1D heterogeneous reactor model considering interfacial and intra-particle gradients, was simulated and numerical analysis of the model was conducted to understand the characteristics of the reactions in a catalyst along the reactor length. The model was also validated by comparing predicted performance data with pilot-scale plant data operated at 0.2 bar, 299–343 °C and 0.48–2.02 h−1 of weight hourly space velocity (WHSV). The model showed good agreement with the temperature profile, 2,3-BDO conversion and selectivity of target products. In addition, sensitivity analyses of the model were investigated by changing feed flow rate, feed composition, and inlet temperature. It was found that stable and efficient operation conditions are lower than 0.65 h−1 of WHSV and 330–340 °C of inlet temperature. Additionally, the reactor performance was not affected by 2,3-BDO feed concentration above 70%.

A Simplified Method for Modeling of Pressure Losses and Heat Transfer in Fixed-Bed Reactors with Low Tube-to-Particle Diameter Ratio

This manuscript presents a simplified method of modeling fixed-bed reactors based on the porous medium. The proposed method primarily allows the necessity of precisely mapping the internal structure of the bed—which usually is done using real object imaging techniques (like X-ray tomography) or numerical methods (like discrete element method (DEM))—to be avoided. As a result, problems with generating a good quality numerical mesh at the particles’ contact points using special techniques, such as by flattening spheres or the caps method, are also eliminated. The simplified method presented in the manuscript is based on the porous medium method. Preliminary research has shown that the porous medium method needs modifications. This is because of channeling, wall effects, and local backflows, which are substantial factors in reactors with small values of tube-to-particle-diameter ratio. The anisotropic thermal conductivity coefficient was introduced to properly reproduce heat transfer in the direction perpendicular to the general fluid flow. Since the commonly used fixed-bed reactor models validation method based on comparing the velocity and temperature profiles in the selected bed cross-section is not justified in the case of the porous medium method, an alternative method was proposed. The validation method used in this work is based on the mass-weighted average temperature increase and area-weighted average pressure drop between two control cross-section of the reactor. Thanks to the use of the described method, it is possible to obtain satisfactorily accurate results of the fixed-bed reactor model with no cumbersome mesh preparation and long-term calculations.

Experimental and simulation study of the temperature distribution in a bench‐scale fixed bed Fischer–Tropsch reactor

AbstractThe temperature distribution in a bench‐scale fixed bed Fischer–Tropsch reactor using Co‐based catalyst was investigated under conditions of 2 MPa and 458 K at various syngas partial pressures and space velocities. The single‐tube reactor had a diameter of 0.05 m, which is representative of the diameters used in industrial applications. With a special designed temperature measurement, the detailed temperature distribution in a bench‐scale reactor was reported for the first time. The changes of maximum temperature in the bed and hot spot region were discussed at different N2 flow rate and gas hourly space velocity. A 2D pseudo‐homogeneous fixed bed reactor model was developed using ANSYS Fluent. A position‐dependent heat‐transfer coefficient, which considered more accurate in temperature prediction, was applied. The model was validated against both the reaction results and the measured temperatures. The inferred properties within the reactor were analyzed to give insight as to how to increase the reactor production capacity.

Kinetics of NH3 oxidation on Pt/Al2O3: Rate enhancement and NH3 inhibition

We describe a combined experimental kinetics and modeling study for NH3 oxidation on Pt/Al2O3 and development of a predictive microkinetic model valid over a range of conditions. The NH3 oxidation rate (TOF) dependence is reported for NH3 concentrations between 10 and 25,000 ppm and temperatures below 250°C for Pt/Al2O3 powder and washcoated monoliths. The data reveal a shift from positive- to negative-order rate dependence on NH3 with the rate maximum dependent on the processing of Pt/Al2O3; unmilled Pt/Al2O3 powder exhibits a rate maximum at 500 ppm NH3, while ball-milled Pt/Al2O3 has a maximum at ~10,000 ppm. This unexpected enhancement of Pt/Al2O3 activity from milling results in a lowering of the light-off temperature (T50) by up to 100°C. Further examination rules out the extent of pore diffusion limitations as the root cause, but rather an increase in the fraction of stepped crystalline planes and destabilization of Pt oxide shown from XRD and H2-TPR characterization. The dependence of a shift in the rate maximum to higher NH3 concentrations with milling extent is shown to require single- and dual-site reaction pathways. The kinetic scheme also captures a subtle shift in the apparent NH3 reaction order for both unmilled and milled Pt/Al2O3. The microkinetic scheme is incorporated into fixed-bed and monolith reactor models which show excellent agreement with the NH3 conversion and product distribution data.

Micro-scale simulation and intensification of complex Sabatier reaction system in cylindrical catalyst bed

The methanation process based on the Sabatier reaction is becoming a key instrument in solving CO2 emissions and surplus electricity. A Sabatier fixed-bed reactor model with randomly stacked cylindrical particles was established by discrete element method (DEM), and the variation of the substances distribution, reaction characteristics and carbon deposition in the micro-scale catalyst was simulated by computational fluid dynamics (CFD). The effects of catalyst hole number and operating conditions on CO2 conversion and CH4 yield were also discussed. The result shows that as the reaction proceeds, the concentration distribution of the substances in the catalyst changes from a ring to a uniform, and the distribution of the reaction rate values in the catalyst changes from a V-shape to a U-shape. In the steady state, the catalyst is only effectively used in about 10% of the outer layer. The carbon deposition in the outer layer of the catalyst and the inlet of the reactor is more serious. And the average porosity value in the catalyst decreased by 0.012 as the reaction progressed to 1000 s. In the steady state, CH4 yield from high to low catalyst bed arrangement is 4 holes, 7 holes, 1 hole and solid. The CH4 yield can be increased by increasing the heat transfer coefficient and decreasing the inlet flow rate, and the reaction can reach a steady state faster by increasing the inlet temperature and pressure.

Insights into the catalytic CO2 methanation of a boiling water cooled fixed-bed reactor: Simulation-based analysis

This article presents the simulation-based analysis of experimental results from a catalytic fixed-bed reactor for the methanation of CO2. During previously published experiments, temperature profiles inside bidisperse catalyst-silicon carbide fixed-beds were gathered and reactant conversions at the reactor outlet measured. On the basis of the temperature profiles along the fixed-bed length and outlet reactant conversions, a procedure for the numerical characterisation of these results was developed. Primary parameters like the inserted multipoint thermocouple and the heat transfer coefficient between reactor wall and surrounding boiling water cooling are systematically investigated. Concerning the binary bidisperse fixed-beds of porous catalyst cylinders and highly thermal conductive silicon carbide, a simple numerical method for the determination of the effective heat conductivity of the bed is presented. The modelling of effective reaction rates within an industrial sized catalyst and reactor is a non-trivial task, due to interlinking aspects like intrinsic reaction rate and internal and external transport limitations. Intrinsic reaction rate, internal and external transport limitations are linked, what makes a separate investigation challenging. Thus, a step by step analysis is presented and the single effects investigated in detail. From the results of the stepwise numerical characterisation, an excellent agreement between experiments and numerics was reached. Additionally, a novel partially resolved 3D fixed-bed reactor model is presented and selected results like particle overheating presented. Overall the present numerical investigations provided a deep insight into the methanation of CO2 in a cooled fixed-bed reactor.

Ceramic Fiber-Based Structures as Catalyst Supports: A Study on Mass and Heat Transport Behavior Applied to CO2 Methanation

Fibrous structures present interesting characteristics as catalyst supports for heat- and mass-transfer-limited reactions. This paper investigates the mass and heat transport behavior of ceramic fiber-based catalysts (catalytic ceramic paper) by applying them to the exothermic reaction of CO2 methanation. Catalytic experiments were carried out to fit the activity of the catalysts with known kinetics. A fixed-bed reactor model was used to determine the efficiency and efficiency losses caused by different transport phenomena, as well as to perform a sensitivity study focused on heat transfer. The results show that heat transfer limitations are the main cause for losses in reactor efficiency, with steep temperature profiles developing inside the reactor. Poor heat transfer limits the development of highly active catalysts, while pressure drop restricts the flow rate and therefore the productivity. The use of ceramic materials with higher thermal conductivity and increasing the fiber diameter are promising approaches to enhance heat transfer, reduce pressure drop, and improve overall reactor performance.

Modeling of low temperature steam reforming of flare gas to methane-rich fuel gas on Ni catalyst in different types of reactors

The results of mathematical modeling of fixed-bed catalytic reactors for low temperature low H2O/C steam reforming of propane-methane mixture and two real associated petroleum gases into methane-enriched fuel gas are reported. Three cases of practical interest were considered. In the first case, a lab-scale flow reactor, which is used for kinetic studies, was analyzed under assumption of constant wall/oven temperature. The possibility of noticeable hot and cold zones formation along the bed radius (4 mm) and length (33 mm) was predicted depending on the wall temperature and the ratios of H2O/C3H8 and C3H8/CH4. In the second case, a plant-scale adiabatic reactor was simulated, and the impossibility of conversion of flare gas with high C2+ fraction into fuel mixture with sufficiently high LHV (>31.8 MJ/m3) was predicted even if the post-removal of CO2 was assumed. In the third case, the advantages of a plant-scale tubular reactor against an adiabatic one were revealed for the reforming of “heavy” and “light” associated petroleum gas. The proposed bifunctional role of steam (first as a coolant, second as a reagent) increases the energy efficiency of tubular reformer due to recuperation of heat produced by reaction. The scheme with counter-current flows of reagent and coolant enabled to reduce twice the number of tubes in comparison with concurrent flow, but the catalyst temperature in the hot zone raised by 40°.

Mathematical Model of the Solar Pyrolysis of Biomass

Abstract The paper presents a two-dimensional computational fluid dynamics (CFD) model of lab-scale fixed-bed pyrolytic reactor. The goal of the work was to verify assumptions regarding construction and operating parameters of the pyrolytic reactor and examining heat transfer conditions and the final temperature distribution in the system taking into account the endothermic pyrolysis reactions occurrence. The impact of the most important numerical parameters on simulation results was also investigated. Model was prepared in ansys fluent 18.2 software. The studies have shown large temperature gradients both in the biomass deposit and at the reactor walls. The analysis has confirmed the validity of the proposed reactor construction concept and allowed to specify the range of thermal power value necessary for obtaining the pyrolysis process in a system with given properties and dimensions. Increasing the heat flux supplying the reactor from 160 to 480 W caused acceleration and intensification of biomass thermal decomposition, while the average final bed temperature after 10 min of heating in each case was reaching similar level. Low thermal conductivity of the bed and strong heat absorption due to pyrolysis suppress heat transfer through the bed, which causes significant temperature differences between the warmest and coldest regions of the bed. However, temperature unevenness and hence the unevenness of the pyrolysis process can provide favorable conditions for measuring the gas composition leaving the reactor due to the relatively balanced time stream of pyrolysis gases.

Adaptive Modeling of Fixed-Bed Reactors with Multicycle and Multimode Characteristics Based on Transfer Learning and Just-In-Time Learning

Multi-cycle and multi-mode are important features in fixed bed reactors due to a manifold of reasons such as catalyst regeneration and equipment updates. Unfortunately, samples are not sufficient t...

Computational Fluid Dynamics for Fixed Bed Reactor Design.

Flow, heat, and mass transfer in fixed beds of catalyst particles are complex phenomena and, when combined with catalytic reactions, are multiscale in both time and space; therefore, advanced computational techniques are being applied to fixed bed modeling to an ever-greater extent. The fast-growing literature on the use of computational fluid dynamics (CFD) in fixed bed design reflects the rapid development of this subfield of reactor modeling. We identify recent trends and research directions in which successful methodology has been established, for example, in computer generation of packings of complex particles, and where more work is needed, for example, in the meshing of nonsphere packings and the simulation of industrial-size packed tubes. Development of fixed bed reactor models, by either using CFD directly or obtaining insight, closures, and parameters for engineering models from simulations, will increase confidence in using these methods for design along with, or instead of, expensive pilot-scale experiments.

Crystallite-scale model for NOx reduction by hydrogen spillover on SBA-15 and MCM-41

The extent of hydrogen spillover on two different Pd-based catalysts supported on mesoporous SBA-15 and MCM-41 is quantitatively predicted using a crystallite-scale model, which considers the effect of size and location of crystallites, metal-support interfacial contact, and diffusivity of the adsorbed species on the support surface. The developed model, in combination with a fixed-bed reactor model predicts that in the absence of any reductant in the feed, the NO conversion is higher ( = 37 %) on the SBA-15 supported catalyst as compared to 25 % on MCM-41, which is consistent with the reported data in the literature. The difference in the catalytic activity is ascribed to the different spillover rates of hydrogen on SBA-15 and MCM-41, which is further correlated to the fraction of Pd crystallites present in the support channels. The model is also used to study the effect of cycle time, H2 concentration, Pd dispersion, and Pd loading on NO reduction under cyclic conditions. Consistent with the literature findings, the model predicts that the Pd surface area and the metal-support interfacial contact increase with an increase in the Pd loading and dispersion, which result in higher spillover and hence increase the NO conversion. Even though the present model has been developed for the H2-SCR system, it can also be extended to other catalytic systems where spillover effects are significant.

Modeling and control of a Fischer-Tropsch synthesis fixed-bed reactor with a novel mechanistic kinetic approach

A modeling and dynamic control study for a Fischer-Tropsch synthesis fixed-bed reactor under the one-dimensional pseudohomogeneous scheme representation with integration of the cooling jacket dynamic approach has been developed. The proposed reactor model contemplates the use of a novel mechanistic kinetic model based on the Langmuir theory recently reported in the literature. To ensure a good thermal behavior and an improvement reactor performance a proportional-integral controller is implemented in the cooling jacket. The robustness of the controller, the dynamic model and the mechanistic kinetic approach are evaluated and validated against the use of four different sets of initial operating conditions of temperature, pressure and gas hourly space-velocity. The results indicate the reactor model potential under the proportional-integral controller action, since it allows to completely attenuate the typical hot-spot formation in fixed-bed reactors in which highly exothermic reactions are carried out. In addition, the mechanistic kinetic model represents to a great extent the Fischer-Tropsch synthesis reaction network in terms of the syngas conversion and the light gases and heavy liquid hydrocarbons selectivity.