Modeling and stability of catalytic fixed bed reactors

The existence of a multiple or oscillatory condition in a packed bed reactor, with a strongly exothermic reaction, is reviewed. The following cases are discussed: simultaneous heat and mass transfer within and outside a catalyst particle, axial mixing in tubular reactors and a recycle reactor. It is shown that the condition describing multiplicity can be estimated solely on the basis of the CSTR analysis. A correspondence between stability and parametric sensitivity is presented.     

Steady state multiplicity behavior of an isothermal axial dispersion fixed-bed reactor with nonuniformly active catalyst

An isothermal, heterogeneous fixed-bed reactor packed with nonuniformly active catalyst pellets where a biomolecular Langmuir-Hinshelwood reaction occurs, is studied using an axial dispersion model. A catalyst activity distribution given by a Dirac delta function, where the active catalyst is deposited at a specific location within the pellet, is considered. This includes the common case of externally coated pellets with external mass transfer resistance. The steady state multiplicity behavior of this reactor, and its limiting cases: CSTR, PFR and pseudohomogeneous axial dispersion, are examined in detail. The nonlinearity of the reaction kinetics provides two sources of multiplicity, through the heterogeneous nature of the reactor and the presence of axial dispersion in the fluid phase. Their roles in determining reactor multiplicity behavior are fully explored. It is shown that this system can admit at most nine steady state solutions. The limiting behavior of the heterogeneous axial dispersion model as Pe → 0 or ∞ is not represented fully by the CSTR or PFR models because of ignition phenomenon. Finally, the effects of mixing on reactor conversion are discussed.     

Mass transfer characteristics of wire-mesh honeycomb reactors

The mass transfer characteristics in honeycombs made of catalyst-deposited metal wire meshes (wire-mesh honeycomb; WMH) were studied to test the prediction that WMH has better flow distribution and a higher rate of interphase mass transfer than the conventional ceramic type of honeycomb module. The WMH module was constructed from alternating layers of flat and corrugated wire-mesh sheets packed within a frame. Wire-mesh sheets were coated with aluminum particles using electrophoretic method. Thermal sintering at 800°C and then calcinations at 500°C yielded a porous layer of Al/Al₂O₃ composite particles that were firmly attached on the wire surface. The alumina-protected wire meshes were further deposited with Pt/TiO₂ catalyst powder by washcoating method. The oxidation of ethyl acetate was monitored as model reaction. A one-dimensional model was established and the parameters of intrinsic first-order kinetics were regressed from the reaction results obtained in the region controlled by chemical reaction, after which interphase mass transfer coefficients were regressed in other region. Three expressions for the Sherwood number that are typically used for honeycomb, wire-mesh gauze and packed bed reactors were examined to determine the optimal expression for WMHs. The mass transfer coefficient in the WMH was found to be quite different from that in the conventional ceramic honeycomb reactor and much higher than that in the wire-mesh gauze reactor. The best-fit results were obtained with packed-bed expression, Sh=1.06Re^0.50Sc^1/3, indicating the mechanism of reaction in the WMH is most similar to that in a packed bed. The optimal Sh expression was then used to predict the behavior of systems with a larger channel size or longer bed; the model predictions showed good agreement with experimental results from real WMH reactors.     

Liquid-solid mass transfer in a rotating packed bed reactor with structured foam packing

A rotating packed bed (RPB) reactor has substantially potential for the process intensification of heterogeneous catalytic reactions. However, the scarce knowledge of the liquid–solid mass transfer in the RPB reactor is a barrier for its design and scale-up. In this work, the liquid–solid mass transfer in a RPB reactor installed with structured foam packing was experimentally studied using copper dissolution by potassium dichromate. Effects of rotational speed, liquid and gas volumetric flow rate on the liquid–solid mass transfer coefficient (k_LS) have been investigated. The correlation for predicting k_LS was proposed, and the deviation between the experimental and predicted values was within ± 12%. The liquid–solid volumetric mass transfer coefficient (k_LSa_LS) ranged from 0.04–0.14 1⁻¹, which was approximately 5 times larger than that in the packed bed reactor. This work lays the foundation for modeling of the RPB reactor packed with structured foam packing for heterogeneous catalytic reaction.     

Exact criteria for uniqueness and multiplicity of an nth order chemical reaction via a catastrophe theory approach

The development of a simple, generalized technique for the exact determination of regions of unique and multiple solutions to certain nonlinear equations via a catastrophe theory-implicit function theorem approach, is presented. The application of this technique to the nth order chemical reaction in the nonadiabatic and adiabatic CSTR yields exact, explicit bounds for all n ≥ 0. To our knowledge, this is the first report of exact, explicit bounds for these systems, except for n = 0, 1 for the adiabatic CSTR, and n = 1 for the nonadiabatic CSTR. For the nonadiabatic CSTR, these bounds show that the higher the reaction order, the smaller the region in parameter space for which multiplicity can occur for all γ and x_2c, (dimensionless activation energy and coolant temperature, respectively). This behavior is similar to that reported by Van den Bosch and Luss[1] for the adiabatic CSTR. The zeroth order reaction in the nonadiabatic CSTR exhibits more complex behavior and assumes characteristics of both high and low reaction orders insofar as increasing and/or decreasing the uniqueness space, in comparison to all other n > 0.An exact implicit bound between regions of uniqueness and multiplicity is also derived for the nth order reaction in a catalyst particle with an intraparticle concentration gradient and uniform temperature, and is fully demonstrated for the first order reaction. In addition, explicit criteria, sufficient for uniqueness and multiplicity of the catalyst particle steady state, stronger than those of Van den Bosch and Luss, are also developed by combining the present technique with bounds suggested by these authors.     

Scale-up analysis of autothermal operation of methane oxidative coupling with La2O3/CaO catalyst

The exothermicity of oxidative coupling of methane (OCM) renders a cooled packed-bed reactor impractical or impossible. Recently, we proposed an adiabatic autothermal reactor as a solution to this problem and reported the first results for stable autothermal operation (AO) with feed at ambient temperature. AO on the ignited branch is possible only in the region of steady-state multiplicity. High per-pass conversion and productivity requirements demand a stable ignited branch at the lowest possible feed temperature and high flow rate. To achieve OCM scale-up, many conditions must be satisfied simultaneously. Using a kinetic model for La₂O₃/CaO catalyst, we examine the impact of space time, feed methane to oxygen ratio, feed temperature, particle size, inter-phase heat and mass transfer gradients, pore-diffusion, bed scale heat/mass dispersion on the region of AO for large scale adiabatic packed-bed reactors. We show that while it is possible to achieve CH₄ conversion of about 20% and C₂ selectivity of about 80% in scaled-up reactors, these values are sensitive to the design and operating parameters.     

ADIABATIC GAS ABSORPTION AND STRIPPING WITH CHEMICAL REACTION IN PACKED TOWERS

In the design of adiabatic gas absorption, the temperature distribution within the column is an important consideration. Temperature influences the degrees of heat and mass transfer through the thermodynamic phase equilibrium relationships and reaction rates. The capacity of an absorber is limited through the formation of a temperature plateau. Gas absorption in a chemically reactive solvent in an adiabatic packed column is modelled rationally for the first time taking into account the major heat effects. An iterative computational method for computing packed bed height is presented. The design procedure is illustrated by sample calculations for carbon dioxide (CO₂) absorption in monoethanolamine (MEA).     

Katalytische Abluftreinigung: Verfahrenstechnische Aufgaben und neue Lösungen

Catalytic air purification; Challenges and new solutions. The integration of regenerative heat exchange into the catalyst bed allows for the autothermal operation of catalytic air purification with a low content of combustible gas. Concentrations corresponding to an adiabatic temperature rise of less then 20 °C can be processed without an additional heat source; in case of higher concentratons a side stream withdrawal allows for the utilization of the total heat of combustion at the highest reactor temperature. The feedback of heat due to the integrated heat exchange gives rise to an unusual reactor behaviour. An analogy of fixed bed reactor operation with countercurrent heat exchange is used to derive simple equations for reactor design and operation. If conventional catalyst packings are replaced by monolithic catalysts, substantial reduction in pressure loss and/or packed bed volume can be obtained. The corresponding relations are briefly discussed.     

Characterisation of flow and heat transfer patterns in low aspect ratio packed beds by a 3D network-of-voids model

Using an illustrative sphere packing assembly, it is demonstrated that flow structure and wall heat transfer patterns in low aspect ratio fixed bed reactors are more realistically modelled by properly accounting for the discrete void fraction variations. A 3D network-of-voids (NoV) model has been devised to characterise and examine the discrete flow and heat transfer phenomena in a low aspect ratio packed bed with d_t/d_p = 1.93. The model as formulated is deliberately designed to be not too complicated so as not to place severe demands on computational resources. Hence, the model can potentially easily be applied to simulate the typically large sets of tubes (often comprising more than 10,000) in the case of industrial multi-tubular reactors, where every tube is different due to the random insertion of the packing particles. Because of its simplicity, the model offers an opportunity of coupling the individual catalyst pellet level transport with the complex interstitial flows at the reactor scale. Illustrative studies of this NoV model on a random packed bed of spheres predict large variations of discrete in-void angular velocities and consequently wall heat transfer coefficients within a single tube. The wide variations of wall heat transfer coefficients imply that the different angular sections of the tube will transfer heat at radically different rates resulting in potentially large temperature differences in different segments of the tube. This may possibly result in local temperature runaway and/or hot spot development leading to several potentially unanticipated consequences for safety and integrity of the tube and hence the reactor. The NoV model predictions of the overall pressure drop behaviour are shown to be consistent with the quantitative and qualitative features of correlations available in the literature.     

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     

NUMERICAL STUDY OF THE EFFECT OF THE WALL ON THE DISTRIBUTION OF ISOTHERMAL TWO-PHASE FLOW IN THE BED OF A HYDRODESULFURIZATION REACTOR

Numerical simulations of the isothermal two-phase flow distribution in the packed bed of a reactor used for fuel hydrodesulfurization using the commercial software Fluent are reported. As a first step, the heat and mass transfer as well as the chemical reactions are not taken into account. The reactor considered has, above the bed, a distribution tray equipped with chimneys. A Eulerian three-phase model that considers the catalyst particles as a granular static phase was used following the Holub single-slit model for particle fluid interaction to compute the liquid-solid and gas-solid drag coefficients. Physical properties of the fluids are assumed to be constant. In the present study, the tendency of the liquid to move towards the wall of the reactor was studied in a bed 11 m in depth. The simulations predict that there is no suction effect on the flow caused by the wall. As the two-phase flow moves downward through the bed, a slow radial liquid spreading takes place. However, flow distribution is not completely uniform, at least at a distance of 11 m from the inlet.     

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.     

Modelling of packed bed membrane reactors for autothermal production of ultrapure hydrogen

The conceptual feasibility of a packed bed membrane reactor for the autothermal reforming (ATR) of methane for the production of ultrapure hydrogen was investigated. By integrating H₂ permselective Pd-based membranes under autothermal conditions, a high degree of process integration and intensification can be accomplished which is particularly interesting for small scale H₂ production units. A two-dimensional pseudo-homogeneous packed bed membrane reactor model was developed that solves the continuity and momentum equations and the component mass and energy balances. In adiabatic operation, autothermal operation can be achieved; however, large axial temperature excursions were seen at the reactor inlet, which are disadvantageous for membrane life and catalyst performance. Different operation modes, such as cooling the reactor wall with sweep gas or distributive feeding of O₂ along the reactor length to moderate the temperature profile, are evaluated. The concentration polarisation because of the selective hydrogen removal along the membrane length was found to become significant with increasing membrane permeability thereby constraining the reactor design. To decrease the negative effects of mass transfer limitations to the membrane wall, a small membrane tube diameter needs to be selected. For a relatively small ratio of the membrane tube diameter to the particle diameter, the porosity profile needs to be taken into account to prevent overestimation of the H₂ removal rate. It is concluded that autothermal production of H₂ in a PBMR is feasible, provided that the membranes are positioned outside the inlet region with large temperature gradients.     

Low peclet number particle-to-fluid heat and mass transfer in packed beds

For low Peclet numbers most of the experimentally obtained particle-to-fluid heat and mass transfer coefficients in packed beds were found to be some orders of magnitude below the values predicted for a single sphere in cross flow.From theoretical considerations one should expect the transfer coefficients in packed beds to exceed the single sphere predictions as they actually do for higher Peclet numbers.The obvious discrepancy between theory and experiment can be cxplained by a simple model accounting for a nonuniform distribution of the void fraction. The model consists of a packed bed of uniformly sized particles with an average void fraction ψ, where a small part ? of the total cross-sectional area f is assumed to have a larger void fraction ψ₂. Since the same pressure drop applies to both parts of the bed, the superficial velocity will be much larger in the section with the larger void fraction, especially in the range of low Reynolds numbers.Even though in both parts of the packed bed the individual transfer coefficients are taken from a correlation which is based on the single sphere predictions (as it is valid in the range of high Peclet numbers), the apparent overall transfer coefficients for the nonuniform system become much lower, and show the same characteristic variation with Peclet number and the ratio of particle diameter to bed height as the majority of the experimental data.     

Temperature differences between phases in a moving bed reactor

Pseudo-homogeneous models of packed bed reactors assume equal temperatures and concentrations (or chemical potentials) for the solid and the fluid phases and are simpler than heterogeneous models. An analysis is presented for the degree of temperature departure between these two models under plug flow conditions with no axial dispersion. Fixed bed, cocurrent and countercurrent flow reactors are considered. The analysis yields two important parameters: α, the ratio of solid to gas thermal capacitances, and β, which is closely related to the number of interphase heat transferase units. In most industrial reactors, where β is greater than 50, the average temperature difference between phases is small, except for countercurrent reactors where gas and solid heat capacitances are nearly equal. Within this range of α, temperature differences can persist through the reactor, even with large values of β. The maximum temperature difference between phases is attained when the reaction heat effect is released in the worst case of a localized pulse in the reactor stream with the smaller thermal capacitance. These temperature difference measures can be used to estimate the validity of a pseudo-homogeneous model. This analysis is easily extended to concentration differences between phases.     

Data mining macrokinetic approach based on ANN and its application to model industrial oxidation of p-xylene to terephthalic acid

Considering that kinetics and thermodynamics are coupled with heat and mass transfer effects being present in the liquid-phase catalytic oxidation of p-xylene to terephthalic acid (OXTA) in an industrial type of continuous stirred tank reactor (CSTR) and that the time evolution of the concentration of all the interest intermediate and final products of OXTA in the industrial CSTR cannot be obtained to estimate macrokinetic parameters, a novel data mining macrokinetic approach based on artificial neural network (ANN) was proposed to develop the macrokinetic model of OXTA in the industrial CSTR, which mines intrinsic kinetics and transport phenomena information from the sample data collected from OXTA in the industrial CSTR. Firstly, the reaction orders of OXTA are estimated by the mass transfer-free experiment data in the laboratory semi-batch stirred tank reactor. The kinetics of OXTA in the industrial CSTR is assumed to be zeroth-order with respect to gaseous reactants, 0.65-order with respect to p-xylene, and first-order with respect to the other liquid reactants, respectively. Secondly, ANN is employed to model the influence of the reaction parameters on the rate constants of OXTA in the industrial CSTR. Based on the sample data collected from OXTA in the industrial CSTR, heuristic differential evolution algorithm is employed to adjust the weights and thresholds of the rate constant ANN in such a way that it minimizes the prediction error of the macrokinetic model, and thus the optimal weights and thresholds are obtained and the macrokinetic model of OXTA in the industrial CSTR is developed. The reliability of the macrokinetic model was investigated and the satisfactory results were obtained. Further, a generalized macrokinetic approach for multi-phase reaction in industrial reactor was suggested too.     

Analysis of the CSTR with two-phase flow under phase equilibrium conditions

A mathematical model of the flow gas-liquid continuous stirred tank reactor (CSTR) is presented under the assumption of thermodynamic equilibrium of the two-phase flow. Phase equilibrium was calculated using the Redlich-Kwong-Soave (RKS) equation of state. An efficient algorithm based on homotopy method was used to obtain a numerical solution of the system of nonlinear algebraic equations of the model. By an example of the liquid-phase hydrogenation of benzene, steady states were analyzed in isothermal and adiabatic regimes and at partial removal of heat released as a result of exothermic reaction. It was shown that under certain conditions, a multiplicity of stationary solutions is possible due to nonlinearity of the kinetic reaction, on the one hand, and deviation of the reaction mixture properties from the ideal state, on the other hand.     

双催化层固定床甲烷化反应器CFD模拟

温度分布直接影响着固定床甲烷化反应器的甲烷产量和设备安全性。以年产12.75亿立方煤制天然气绝热甲烷化反应器为研究对象,在建立真实设备三维模型的基础上,利用ANSYS-CFX有限元数值模拟的方法,建立多孔介质内化学反应、热交换与质量传递的气-固两相反应器模型,获得了双段固定床甲烷化反应器内部温度、压力、速度场的分布规律及甲烷产率分布。对不同床层结构对应的特征场分布进行了探索,分析了床层结构对各特征场分布的影响,确定了床层结构优化方案,MCR催化剂床层出口处支撑延长的结构更有利于温度场沿反应器径向的均匀分布和甲烷质量分数的提高。对反应器入口温度、空速、压力对特征参数分布的影响进行了研究,提出了针对本工艺的允许入口参数波动范围。     

Lateral mixing in trickle bed reactors

Knowledge of lateral mixing is essential to understand heat and momentum transfer parameters in both single-phase liquid and two-phase gas-liquid co-current down flow through packed bed columns. The reactors through which gas and liquid concurrently flow downwards through a bed of catalytic packing are called trickle bed reactors. Experimental data on lateral mixing coefficients from both the heat transfer and radial liquid distribution studies are obtained over a wide range of flow rates of gas and liquid using glass spheres (4.05 and 6.75 mm), ceramic spheres (2.59 mm), and ceramic raschig rings (4 and 6.75 mm) as packing materials covering trickle flow, pulse flow, and dispersed bubble flow regimes. In the present work, an expression for estimation of lateral mixing coefficient (αβ)_L is derived using the data on radial liquid distribution studies. The agreement between the values of (αβ)_L obtained from heat transfer studies and from radial liquid distribution studies using the experimental data shows that there exists an analogy between the heat transfer and radial liquid distribution in packed beds. Since (αβ)_L is an important variable for estimation of various heat and mass transfer parameters, a correlation for (αβ)_L based on present heat transfer study is proposed. The agreement between the (αβ)_L values estimated from the proposed correlation and experimental values is satisfactory with a standard deviation (s.d.) of 0.119.