Falsification of Kinetic Parameters by Transport Limitations and Its Role in Discerning the Controlling Regime

Reactions occurring on the surface of a porous catalyst are accompanied by transport of heat and mass in the pores of the catalyst and across the boundary layer at the external surface. Under the conditions normally encountered in catalytic reactors, heat and mass fluxes can be large enough to cause finite gradients of concentration and temperature in the solid as well as in the film. In such instances the resulting rate of reaction is governed by both the kinetics of the reaction and the transport process (or processes) which gives rise to the gradient. Hence the dependence of the overall or global rate on temperature and the partial pressures of the reacting species can no more be expressed by the intrinsic kinetics of the reaction but is influenced also by the transport parameters of the system. In other words, in the presence of finite transport limitations the catalyst exhibits kinetics falsified by transport processes. This has been referred to as “disguised kinetics” by Wei [l]. Carberry [2] has examined the implications of this disguise in determining the operating regime of a process.     

Computer modelling and numerical analysis of hydrodynamics and heat transfer in non-porous catalytic reactor for the decomposition of ammonia

Chemical reactors exhibit very complex behaviours such as multiple steady states, oscillations, etc. resulting from complex linkage between the transport processes and the non-linear chemical reaction kinetics. Ammonia is a potential hydrogen source for a number of fuel cell applications for small scale power generation useful for portable equipments. In the present work, we analyse the fluid dynamics and heat transfer in catalytic microreactor systems for the decomposition of ammonia over a monolayer Ni non-porous catalyst. The overall model for this convective-diffusive-reactive system consists of a flow model, a mass transport model, an energy conservation model and a reaction kinetics model for ammonia decomposition. The flow model is described by the Stokes equation for a creeping flow regime. The mass transport and energy conservation models are based on convective-diffusion equations. The rate of ammonia decomposition can be measured as a function of the catalyst activity and ammonia concentration. A standard Galerkin finite element technique has been applied for the solution of the flow equations. A slightly perturbed form of the mass continuity equation is used to satisfy the Ladyzhenskaya-Babuška-Brezzi stability criterion. For the solution of convection-diffusion equations, a streamline inconsistent upwind finite element scheme has been chosen to avoid any spurious oscillations. C⁰-continuous 9-noded Lagrangian biquadratic isoparametric finite elements are used for the approximation of the field variables. A second-order Taylor-Galerkin time-stepping scheme has been chosen for the temporal discretisation of the flow equations whilst an implicit theta method has been used for convection-diffusion equations. The results are presented in the form of velocity vectors and concentration, temperature contours and are examined for stability, convergence and theoretical consistency.     

Optimal catalyst activity profiles in pellets—VII. The case of arbitrary reaction kinetics with finite external heat and mass transport resistances

The theory of optimal catalyst activity profiles is extended to include the most general case of a nonisothermal catalyst pellet, where an irreversible reaction occurs in the presence of finite external heat and mass transport resistances. Similar to our previous results for related cases, it is again found that the optimal catalyst activity distribution is given by a Dirac delta function; i.e. for optimum performance, all the active catalyst should be deposited at a specific position within the pellet. In some instances, this position is the external surface of the pellet. Some general results are first obtained about the optimal location of the catalyst for an arbitrary rate expression, and are then applied to two specific rate expressions of practical interest—the m-th order kinetics (m ⩾ 0) and the bimolecular Langmuir—Hinshelwood kinetics. The effects of physico-chemical parameters on the optimal location are analysed in detail. The possibility of enhancing catalytic effectiveness, by choosing the operating variables appropriately, is also discussed.     

光热驱动多孔氧化铈热化学循环解水制氢非热质平衡模型

热化学循环太阳燃料技术过程所涉及的多孔介质中复杂反应及热质传递过程,尚未建立较为完善的数学模型。以多孔氧化铈热化学循环解水过程为研究对象,将颗粒尺度的氧输运与宏观尺度的热质输运相耦合,提出完整的光热驱动条件下多孔介质非热质平衡模型,实验数据对比验证了动力学及热质输运模型的可靠性,分析了两种尺度(颗粒及床层)下,非热平衡效应、入射辐射热流、反应物浓度对动态过程的影响。入射辐射在床层的体积效应下,轴向的温度梯度使得缺陷反应的热力学平衡控制最大氧空位浓度出现在床层前侧,在缺陷反应的动态过程中,氧化过程相较于还原反应更快,提高多孔载氧体反应器的产物H₂浓度应主要从还原阶段中反应过程及条件出发。可为该类问题的建模和过程设计提供较为完整的理论基础和参考路径。     

光热驱动多孔氧化铈热化学循环解水制氢非热质平衡模型

热化学循环太阳燃料技术过程所涉及的多孔介质中复杂反应及热质传递过程,尚未建立较为完善的数学模型。以多孔氧化铈热化学循环解水过程为研究对象,将颗粒尺度的氧输运与宏观尺度的热质输运相耦合,提出完整的光热驱动条件下多孔介质非热质平衡模型,实验数据对比验证了动力学及热质输运模型的可靠性,分析了两种尺度(颗粒及床层)下,非热平衡效应、入射辐射热流、反应物浓度对动态过程的影响。入射辐射在床层的体积效应下,轴向的温度梯度使得缺陷反应的热力学平衡控制最大氧空位浓度出现在床层前侧,在缺陷反应的动态过程中,氧化过程相较于还原反应更快,提高多孔载氧体反应器的产物H₂浓度应主要从还原阶段中反应过程及条件出发。可为该类问题的建模和过程设计提供较为完整的理论基础和参考路径。     

HEAT AND MASS TRANSFER WITH MULTIPLE PARTICLE INTERACTIONS PART II. SURFACE REACTION

A generalized treatment of heat and/or mass transport between an assemblage of particles and a surrounding continuum was developed in an earlier paper. This paper extends that analysis to chemical reactions at the particle surface. In this case the surrounding medium is assumed to contain a reactive species which diffuses to the particle surfaces and undergoes a first order reversible chemical reaction at the surface. Depletion of the reactant in the continuous phase depends on the number density of particles and the size of the assemblage of particles as well as on the transport properties and kinetics of the system. Results for finite and infinite assemblages are compared with reaction rates for a single isolated particle to elucidate the effects of particle competition for reactant on the reaction rate.     

Einfluß des stofftransportes bei der polymerisation von äthylen und 1-okten mit Ziegler-Katalysatoren

The polymerization of ethylene and 1-octene with supported Ziegler-catalysts was investigated with regard to the influence of mass transport of monomers on the kinetics, molecular weight and molecular weight distribution. In the case of the polymerization of ethylene, it was found that for certain conditions of reaction the mass transport of ethylene can influence the kinetics of polymerization respectively the catalyst efficiency strongly. The molecular weight and molecular weight distribution of the polyethylene formed are practically not affected by the conversion as well as particle size of catalyst and polymer. The molecular weight distribution however is affected by the concentration of the catalyst. The polymerization process of ethylene in suspension is distinguished by chemical and physical processes. A continuous chain initiation, for example, is based on the continuous reduction of the catalyst particles to small pieces during the course of polymerization. An apparent chain termination respectively catalyst deactivation can occur when catalyst particles are encapsulated within the growing polymer particles. The polymerization of 1 -octene for similar conditions of reaction gave polymers which were solved completely in the system used. The molecular weight distribution of the polymer formed nevertheless was very broad. This indicates that the mass transport of the monomers through the solid phase of polymer cannot be the main reason for the broad molecular weight distribution of the polymers which are produced by heterogeneous Ziegler-catalysts in suspension.     

Kinetics of sunflower oil methanolysis catalyzed by calcium oxide

The methanolysis of sunflower oil was studied in the presence of CaO previously calcined at various temperatures and the optimal temperature for CaO calcination was determined. The sigmoidal process kinetics was explained by the initial triglyceride (TG) mass transfer controlled region, followed by the chemical reaction controlled region in the latter reaction period. The TG mass transfer limitation was due to the small available active specific catalyst surface, which was mainly covered by adsorbed molecules of methanol. In the later phase, the adsorbed methanol concentration decreased, causing the increase of both the available active specific catalyst surface and the TG mass transfer rate, and the chemical reaction rate become smaller than the TG mass transfer rate.     

Video Microscopy for Fast Screening of Polymerization Catalysts

Video microscopy has been used as an effective tool for fast screening of six different metallocene/MAO supported catalyst samples. The different techniques employed for supporting the metallocene on silica gels can have an influence on the overall catalyst activity and on the activity of single catalyst particles. The kinetics of gas‐phase polymerization of ethylene with supported metallocene/MAO catalysts can be modeled by using a simple reaction scheme and neglecting mass and heat transport effects.     

COMPUTER SIMULATION OF HYDRODEMETALLATION IN FIXED-BED REACTORS

An isothermal model for hydrodemetallation (HDM) of crude oils in catalytic fixed-bed reactors is proposed. This model involves a consecutive reaction mechanism, which is capable of accounting for particle deposit profiles with interior maxima. Consistent with the fact that HDM catalysts are conglomerates formed by precipitation, the porous catalyst itself is modeled as randomly overlapping spheres of equal size. The metal is deposited as growing metal sulfide crystallites on the inner surface of the catalyst. These crystallites originate from a certain number of randomly scattered nuclei and increase in size as the deposition proceeds. The random sphere model for the catalyst and the deposit provides the changes in the catalyst pore structure—local porosity and surface area.

The mass transport within the domain of the particle is due to restricted liquid diffusion, since the diameter of the metal bearing compound (porphyrin) and the intermediate are comparable to the pore size. The diffusion restrictions taken into account are the enhanced drag imposed on a molecule by adjacent pore walls and steric partitioning.

Since the deposition process is much slower than diffusion and reaction, the pseudo-steady-state assumption can be justified. The equations of conservation for mass are solved by orthogonal collocation on finite elements. Based on this solution technique a computer simulation program of HDM is designed that allows two modes of operation: constant temperature and constant conversion. The simulation program “SIMULA” is highly flexible with regard to reaction kinetics, catalyst structure, reactor design, and operating conditions. In comparison to a base case with uniform activity, the effect of intraparticle (radial) and bed (axial) activity profiles on the conversion rate is discussed. For the case investigated, a radial distribution of activity higher at the center of the particle than at the edge can increase catalyst life by 25%, but axial distribution was less successful.     

Non-isothermal reaction-diffusion systems with thermodynamically coupled heat and mass transfer

Non-isothermal reaction-diffusion (RD) systems control the behavior of many transport and rate processes in physical, chemical, and biological systems. A considerable work has been published on mathematically coupled nonlinear differential equations of RD systems by neglecting the possible thermodynamic couplings among heat and mass fluxes, and reaction velocities. Here, the thermodynamic coupling refers that a flux occurs without its primary thermodynamic driving force, which may be gradient of temperature, or chemical potential, or reaction affinity. This study presents the modeling equations of non-isothermal RD systems with coupled heat and mass fluxes excluding the coupling of chemical reactions using the linear non-equilibrium thermodynamic approach. For a slab catalyst pellet, it shows the dynamic behavior of composition and temperature profiles obtained from the numerical solutions of non-linear partial differential equations by Mathematica for two industrial reaction systems of synthesis of vinyl chloride and dissociation of N₂O.     

HEAT AND MASS TRANSFER WITH MULTIPLE PARTICLE INTERACTIONS PART I. DROPLET EVAPORATION

A generalized treatment of heat and/or mass transport between an assemblage of particles and a surrounding continuum is presented. The unsteady state diffusive transport is shown to depend on the size and positions of the particles, and the rate processes are found to be radically different from single particle rates because of particle interactions. A three dimensional model has been developed to predict global concentration or temperature distributions by treating the particles as point sources or sinks. The conditions for which particles can be treated as isolated or as interactive members of a group are established, and correction factors are presented from which multiple particle mass transfer rates can be calculated from single isolated particle mass transfer rates. For finite assemblages the correction factors are shown to be in close agreement with results computed previously using the method of images.     

HEAT AND MASS TRANSFER WITH MULTIPLE PARTICLE INTERACTIONS PART I. DROPLET EVAPORATION

A generalized treatment of heat and/or mass transport between an assemblage of particles and a surrounding continuum is presented. The unsteady state diffusive transport is shown to depend on the size and positions of the particles, and the rate processes are found to be radically different from single particle rates because of particle interactions. A three dimensional model has been developed to predict global concentration or temperature distributions by treating the particles as point sources or sinks. The conditions for which particles can be treated as isolated or as interactive members of a group are established, and correction factors are presented from which multiple particle mass transfer rates can be calculated from single isolated particle mass transfer rates. For finite assemblages the correction factors are shown to be in close agreement with results computed previously using the method of images.     

Integrated kinetic modelling and transient FTIR studies of CO oxidation on Pt/SiO2

The reaction dynamics and multiplicity features of CO oxidation on a Pt/SiO₂ catalyst are studied via transient experiments combining Fourier transform infrared spectroscopy (FTIR) with temperature-programmed reaction (TPR) and with concentration-programmed reaction (CPR). Bifurcation diagrams of the surface and bulk concentrations and temperatures obtained in these experiments are used to develop a reaction-reactor model to interpret the results.The model integrates non-equilibrium elementary step kinetics, based on single-crystal studies, with heat and mass transport effects and reactor modelling. The model reproduces well bifurcation cross-section diagrams at various experimental conditions and simulates well the TPR and CPR experiments. A parametric sensitivity analysis reveals how changes in the parameters affect the reaction behaviour, as well as how the rate-determining step changes with the operating conditions. The results of this work demonstrate how the many interactions between the kinetics, transport processes and reactor environment affect experimental observations, and provide a method for the proper assessment of such interactions.     

醋酸液相氧化燃烧反应动力学

以醋酸钴、醋酸锰为主催化剂,溴化钾为促进剂,乙酸钾为助催化剂,在半连续搅拌釜式钛材反应器中通过测定尾气中CO2和CO的生成量,对醋酸的液相催化氧化动力学进行了研究. 分别考察了空气流量、温度、催化剂总浓度、[Co]/[Mn]比、溴离子浓度、水含量等因素对醋酸燃烧损失速率的影响. 实验结果表明,增加催化剂总浓度和[Co]/[Mn]比能明显加快CO2和CO的生成速率常数,提高溴离子浓度和降低反应温度可显著抑制醋酸的燃烧损失,同时根据实验结果得出CO2和CO的反应活化能分别为88.11和127.31 kJ/mol.     

Applying Reaction Kinetics to Pseudohomogeneous Methanation Modeling in Fixed-Bed Reactors

Reactor simulations can reduce the effort when designing fixed-bed reactors for methanation processes. Several microkinetic models were developed under a variety of operating conditions. However, most production-scale fixed-bed methanation processes exceed the temperature range in which these kinetic models were obtained. In addition, heat and mass transport limitations strongly influence the reaction kinetics. In this work, microkinetic rate equations for CO and CO₂ methanation were analyzed with respect to their suitability for high-temperature, pseudohomogeneous reactor modeling. The best-suited kinetic model was fitted to the operating conditions and validated by means of CFD simulations. It is shown that the simulations match the experimental data for various operating conditions.     

Optimization of the active component distribution through the catalyst bed

A variational problem was formulated to determine the optimal axially non-uniform catalyst activity distribution along the fixed catalyst bed. It was observed that the mass transport limitations or non-isothermal temperature profile are necessary conditions for potential optimization of the catalyst distribution along the bed length. Under isothermal conditions with linear dependence of the reaction rate on concentration at a constant mass transfer coefficient, the uniform distribution is optimal. Analytical solution for the first-order reaction and numerical solutions for power-law kinetics were found.     

Hydrogenation of oleochemicals at supercritical single-phase conditions: influence of hydrogen and substrate concentrations on the process

Fatty alcohols can be produced by catalytic hydrogenation of fatty acid methyl esters. This heterogeneous catalytic reaction is normally performed in a multi-phase system. In such a system, with a low hydrogen solubility in the liquid substrate and a large mass transport resistance, the hydrogen concentration at the catalyst is low and limits the reaction rate. To overcome this limitation, we have used the unique properties of supercritical fluids, properties which are in between those of liquids and gases, making them a very suitable medium for reactions. By adding propane to the reaction mixture of hydrogen and fatty acid methyl esters (C₁₈) we have created supercritical single-phase conditions. At these single-phase conditions the concentrations of all the reactants at the catalyst surface can be controlled, and an excess of hydrogen becomes possible. In this way, extremely rapid hydrogenation can be combined with a high product selectivity.

In our lab-scale experiments the catalyst performance was studied as a function of hydrogen concentration, substrate concentration and temperature. Complete conversion of the liquid substrate was reached in a few seconds. As long as single-phase conditions remain, we have, in our experiments, tested up to 15 wt.% substrate, vapor-phase like reaction rates can be maintained. However, at these high substrate concentrations, mass transport becomes important again.

Our results show that performing hydrogenation at supercritical single-phase conditions has a large potential for this and other catalytic processes where the hydrogen concentration at the catalyst is the limiting factor.     

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。     

Convection,diffusion, and exothermic zero‐order reaction in a porous catalyst slab: Scaling and perturbation analysis

The analysis of the interaction between transport phenomena and chemical reaction inside large‐pore catalyst particles needs to include intraparticular convection as an additional mass/heat transfer mechanism. In this work, we describe by a 3D regime diagram the global behavior of a permeable catalyst slab, where an exothermic, zero‐order reaction is occurring. An order of magnitude estimate for the maximum temperature change is obtained by scaling techniques in each regime of operation. Specific operating regimes of fast mass/heat transport, dominant reaction and strong intraparticular convection, are then studied in more detail using perturbation analysis. The results include approximate concentration and temperature profiles, which allow the estimation of both the effectiveness factor and maximum temperature attained inside the catalyst in these regimes. © 2009 American Institute of Chemical Engineers AIChE J, 2009