Mass transfer advantage of hierarchical structured cobalt-based catalyst pellet for Fischer–Tropsch synthesis

The low effectiveness factor of catalyst pellet caused by high internal diffusion limitation is a common issue in fixed-bed reactor. Nevertheless, hierarchical structured catalyst provides a promising solution for the contradiction between reaction activity and diffusion efficiency in large catalyst pellets. Herein, we studied the effect of pore structure parameters of the meso-macroporous catalyst on Fischer–Tropsch synthesis performances through experiment and pellet scale reaction–diffusion simulation. The pellet simulation firstly elucidated the reason for the significant improvement on activity and product selectivity for the meso-macroporous catalyst observed in our experiment. Further optimization via pellet simulation indicated the critical influences of wax filling degree and that the perfect matching between reaction and mass transfer rates by increasing macropore size and adjusting porosity within pellet enables the C₅₊ space–time yield to the maximum. This work could provide a theoretical guideline for the engineering design of the hierarchical structured catalyst pellet.     

Effective diffusivity and optimum apparent density of vanadia catalysts for sulfur dioxide oxidation

The effective diffusivities of air and SO₂ in four industrial vanadium pentoxide catalysts were measured at steady-state using helium as the counter diffusing gas. An improved catalyst mounting technique and diffusion cell were employed. The nonsurface component of diffusion was successfully correlated using Bruggeman's model for tortuosity. and ¯a based on pore size distribution data or calculated from specific pore volume and surface. However, it was necessary to use flow porosity in place of open porosity. Since the same pore model can be used for the catalytic oxidation So₂, non-reacting flow measurements can be employed to predict effective diffusivities under reaction conditions in this case.With models for the effective diffusivity and the kinetics of the catalytic oxidation of SO₂, an optimum apparent density of the catalyst may be determined which gives the maximum rate of reaction per unit volume of catalyst. Calculations are given for the SVD catalyst.     

Steam methane reforming in a Ni/Al2O3 catalyst: Kinetics and diffusional limitations in extrudates

The true kinetics of methane steam reforming was measured in powder of Ni/Al₂O₃ catalyst (“Octolyst 1001” from Degussa) at different temperatures (733–890 K) for several operating conditions. New reaction rate constants were determined for this catalyst. The observed reaction rate was measured on catalyst extrudates to determine diffusion effects within the porous structure of the particle. A non‐isothermal model with diffusion was used to determine effectiveness factors for each reaction. The objective was to measure all necessary data to model the performance of the catalyst in a Sorption Enhanced Reaction Process (SERP) for H₂ production with in situ CO₂ capture.     

Rational design of hierarchically structured porous catalysts for autothermal reforming of methane

It is shown that the performance of a commercial, meso-macroporous catalyst for the autothermal reforming of methane on Ni/Al₂O₃ could be improved significantly by optimizing the macroporosity and the size of the macropores. The commercial catalyst, taken as a base case, contains macropores with an average diameter of 2 μm and mesopores with an average diameter of 20 nm. The kinetics of Xu and Froment (1989a) for steam reforming and the water gas shift reaction were employed, in combination with kinetics for the total oxidation of methane. Multicomponent molecular diffusion, Knudsen diffusion and viscous flow were accounted for in the modeling of transport in the macropores. At typical reaction conditions, Knudsen diffusion dominates transport in the mesopores; the effect of pore surface roughness on Knudsen diffusion was included in the simulations. Both the macropore size and the macroporosity influence the overall conversion; increases of up to 40–300% with respect to a commercial catalyst are possible. A larger macroporosity typically favors a lower CO/H₂ ratio, that is, a higher selectivity toward hydrogen, when the reverse reaction of the water gas shift reaction dominates, and vice versa. Temperature gradients in the catalyst increase with macroporosity, as a result of the lower thermal conductivity of the solid porous material, but the maximum temperature in the catalyst was around 10 K above that at the outer surface at the investigated operating conditions.     

Integral method of analysis of fischer-tropsch synthesis reactions in a catalyst pellet

A generalized integral method is developed to analyze complex reactions in a catalyst pellet. This method is valid for any kinetics and takes into account both internal and external heat and mass transfer effects. The integral equations are solved for a Fischer-Tropsch kinetic model to obtain effectiveness factors. Isothermal multiplicities are observed for low values of the surface coverage parameter α(α = 1/K₁p_co,0), and low values of the parameter σ₂₁ (ratio of Thiele moduli for H₂ and CO). The effectiveness factor is mildly sensitive to the external resistances.     

Restricted diffusion of residual molecules in catalyst pores under reactive conditions

The restricted diffusion of residual molecules under catalytic conversion conditions was investigated using commercial catalysts. The effectiveness factor, η, and the effective diffusion coefficient, D_e, for residual molecules were evaluated and explicitly compared based on a pseudo-first-order reaction kinetic model and the Thiele modulus. The experimental results showed that the restrictive diffusion of heavy oil molecules is affected by the joint functions of several factors, such as the operating conditions, the size and configuration of the reactant molecules, and the average pore diameter of the catalyst. The reaction temperature has a greater influence on restrictive diffusion than the other operating factors, and the ratio of reactant molecular size to catalyst pore size is the most critical factor that determines the degree of restrictive diffusion. Moreover, a mathematical expression was derived for the restrictive factors in order to describe the relationship between the effective diffusivity and ratio of molecule-to-pore size.     

Intrinsic and Effective Kinetics of Cobalt‐Catalyzed Fischer‐Tropsch Synthesis in View of a Power‐to‐Liquid Process Based on Renewable Energy

The production of liquid hydrocarbons based on CO₂ and renewable H₂ is a multi‐step process consisting of water electrolysis, reverse water‐gas shift, and Fischer‐Tropsch synthesis (FTS). The syngas will then also contain CO₂ and probably sometimes H₂O, too. Therefore, the kinetics of FTS on a commercial cobalt catalyst was studied with syngas containing CO, CO₂, H₂, and H₂O. The intrinsic kinetic parameters as well as the influence of pore diffusion (technical particles) were determined. CO₂ and H₂O showed only negligible or minor influence on the reaction rate. The intrinsic kinetic parameters of the rate of CO consumption were evaluated using a Langmuir‐Hinshelwood (LH) approach. The effectiveness factor describing diffusion limitations was calculated by two different Thiele moduli. The first one was derived by a simplified pseudo first‐order approach, the second one by the LH approach. Only the latter, more complex model is in good agreement with the experimental results.     

Catalyst effectiveness in sulfur dioxide oxidation

The sensitivity of the relationship between catalyst effectiveness in SO₂ oxidation and the Thiele parameter to: (1) the kinetic expression with respect to the presence or absence of strong SO₃ inhibition, (2) the activation energy in the range of 16–32 kcal/g mol, (3) the conversion of SO₂ up to 90%, (4) the temperature at the exterior surface of the pellet in the range of 450–600°C, and (5) the feed composition ranging from 6–10% SO₂ in air, was investigated. A nonisothermal model was used and the calculations were carried close to equilibrium. Far from equilibrium, the relationship is essentially unaffected except by conversion at the pellet surface for the case of strong product inhibition. Close to equilibrium, the relationship is significantly influenced by conversion, temperature, and the inlet composition but the form of the kinetics is not important. The activation energy is not a significant variable. Catalyst size, surface area, and density were not specified while it was necessary to fix the ratios of the transport properties for the calculations. The properties of the American Cyanamid V₂O ₅ catalyst were used for this purpose.     

A sequential approach to modeling catalytic reactions in packed-bed reactors

A sequential modeling approach is proposed to simulate catalytic reactions in packed-bed reactors. The hydrogenation of alpha-methylstyrene and wet oxidation of phenol are selected as studied cases. The modeling scheme combines a reactor scale axial dispersion model with a pellet scale model. Without involving any fitting parameters, such an approach accounts for the non-linear reaction kinetics expression and different types of pellet-liquid wetting contact. To validate the developed modeling scheme and the parallel approach reported in the literature, the experimental observations for hydrogenation of alpha-methylstyrene to cumene have been employed. The predicted results by both approaches agree reasonably with the experimental data for both gas- and liquid-limited reaction. The proposed sequential approach was also used to simulate the dynamic performance of the reactor and pellets for the catalytic wet oxidation of aqueous phenol over a newly developed but rapidly deactivated catalyst (MnO₂/CeO₂). The simulation results for the catalytic wet oxidation process by both approaches were compared. The simulation describes the time evolution of the catalyst stability at different pellet points along the reactor axis. The performance of trickle beds and packed bubble columns over a range of operating conditions were also investigated, and packed bubble columns were found to achieve higher phenol conversion at the cost of more rapid catalyst deactivation.     

C3O1铜基催化剂甲醇合成反应动力学——(Ⅲ)平行反应的效率因子

对于铜基催化剂上甲醇合成反应,选取C0和CO_2的加氢反应作为关键反应,CO和CO_2作为关键组分,本文提出了求算C301铜基催化剂对于这两个平行反应效率因子的关键组分扩散模型,求得效率因子ζco、ζco_2的数值解.在内循环无梯度反应器中测定了5MPa压力下,Φ5×5mm柱状C301催化剂只计入内扩散影响的宏观反应速率,获得ξco、ξco_2的实验测定值.ξco、ξco_2的模型计算值与实验值比较的结果表明该模型是计算平行反应效率因子的简便而可行的方法.     

Kinetic study of reaction of hexachlorocyclophosphazene with phenol by triphase catalysis

The kinetics of the substitution reaction of hexachlorocyclotriphosphazene, (NPCl₂)₃, with phenol to synthesize the partially substituted (phenoxy) chlorocyclotriphosphazene was investigated by using triphase catalysis in an organic phase/alkaline solution. The relative reaction-rate constants and the corresponding energies, enthalpies, and entropies of activation of the sequential substitution were also estimated. The diffusional limitations involve both ion diffusion in the aqueous phase and organic reactant diffusion in the organic phase within the catalyst pellet. The particle diffusion and intrinsic reactivity limit the substitution reaction in the organic phase. The diffusion of the aqueous phase in the ion-exchange step is the main rate-limiting factor.     

Characterization and testing of sol-gel catalysts prepared as thin layers in a plate reactor

Catalytic plate reactors offer many advantages over conventional reactors, including a major reduction in size and much better temperature control. This study examines the characteristics of thin catalyst coats prepared by the sol-gel method and calcined at different conditions. Employing the catalyst as a thin layer (< 100 μm) on the surface of plate reactors reduces mass and heat transfer limitations compared with pellet catalysts and can improve the effectiveness factor. A sol-gel of Ni/Al₂O₃ catalyst, with good rheological properties and good adherence onto stainless steel substrate, was prepared and characterized. The effects of calcination temperature, nickel content and calcination environment on the catalyst properties were investigated. The results revealed that the highest catalyst surface area was obtained at 400 °C for all calcined coatings. The presence of nitrogen gas during drying and calcining seemed to increase the catalyst surface areas and improve its adherence properties. Rheological evaluation of the prepared coats proved to be an effective tool in characterizing the thin coatings. The Ni/Al₂O₃ catalyst exhibited high activity and achieved more than 80% conversion for steam reforming of methane. The reactions were not diffusion limited based on the values of activation energy.     

Pore network modeling of catalyst deactivation by coking,from single site to particle,during propane dehydrogenation

A versatile pore network model is used to study deactivation by coking in a single catalyst particle. This approach allows to gain detailed insights into the progression of deactivation from active site, to pore, and to particle—providing valuable information for catalyst design. The model is applied to investigate deactivation by coking during propane dehydrogenation in a Pt-Sn/Al₂O₃ catalyst particle. We find that the deactivation process can be separated into two stages when there exist severe diffusion limitation and pore blockage, and the toxicity of coke formed in the later stage is much stronger than of coke formed in the early stage. The reaction temperature and composition change the coking rate and apparent reaction rate, informed by the kinetics, but, remarkably, they do not change the capacity for a catalyst particle to accommodate coke. Conversely, the pore network structure significantly affects the capacity to contain coke. © 2018 The Authors. AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers. AIChE J, 65: 140–150, 2019     

活性非均匀分布催化剂颗粒的等温有效系数

本文比较了球形、圆柱形和片形的活性非均匀分布催化剂颗粒及相应的均匀分布催化剂颗粒的等温有效系数.当反应为零级、一级或二级时,活性分布趋向催化剂颗粒的外层,使有效系数增大,反之则减小.扩散效应很大时,有效系数和颗粒表面处的活性的平方根成正比.以当量有效层厚度修正西尔模数(Thiele Modulus)后,得到了适用于各种活性分布的有效系数——西尔模数曲线.据此,可以推算活性非均匀分布催化剂颗粒的有效系数.当扩散效应很大或很小时,最大偏差小于5%,在两者之间为10%.     

Rapid bistable reactions in porous catalysts

We analyze the kinetics of rapid bistable reactions (e.g., CO or hydrogen oxidation on Pt) occurring on a nm catalyst particle located inside a mesoscopic pore. Limitations for reactant diffusion inside a single pore are shown to modify the dependence of the reaction rate on the reactant pressures outside the pore. In particular, the position of the maximum reaction rate is shifted to higher CO pressures (provided that the O₂ pressure is fixed). This effect is significant if a pore is not too short. Similar effects are possible during oscillations in CO oxidation on supported nm catalyst particles.     

ISOTHERMAL EFFECTIVENESS FACTORS FOR NONUNIFORM ACTIVE CATALYST

Isothermal effectiveness factors for slab,cylinder and sphere shaped catalysts with uniform or nonuni-form intrinsic activity profiles have been investigated.In the case of zero-,first- and second-order kinetics,the effectiveness factors of pellets with increasing activity towards the pellet surface are larger than that ofuniform active catalyst,and they are proportional to the square root of the activity at the pellet surfacewith significant diffusion effect.The effectiveness factor-Thiele modulus curves which are valid for bothuniform and nonuniform catalysts have been obtained with the Thiele modulus modified by equivalent thick-hess of effective layer of the catalyst.Thus,the effectiveness factor for nonuniform active catalyst could bepredicted with a maximun deviation of 5% in the case of significant or insignificant diffusion effect but 10%in general.     

Optimization of catalyst pellet structures and operation conditions for CO methanation

A fundamental understanding of the effects of catalyst pellet structures and operation conditions on catalytic performance is crucial for the reactions limited by diffusion mass transfer. In this work, a numerical investigation has been carried out to understand the effect of catalyst pellet shapes (sphere, cylinder, trilobe and tetralobe) on the reaction-diffusion behaviors of CO methanation. The results reveal that the poly-lobe pellets with larger external specific surface area have shorter diffusion path, and thus result in higher effectiveness factors and CO conversion rates in comparison with the spherical and cylindrical pellets. The effects of operating conditions and pore structures on the trilobular catalyst pellet with high performance are further probed. Though lower temperature can contribute to larger effectiveness factors of pellets, it also brings about lower reaction rates, and pressure has little impact on the effectiveness factors of the pellets. The increase in porosity can reduce the pellet internal diffusion limitations effectively and there exists an optimal porosity for the methanation reaction. Finally, the height of the trilobular pellet is optimized under the given geometric volume, and the results demonstrate that the higher the trilobular catalyst, the better the reaction performance within the allowable mechanical strength range.     

A new method of bimodal support preparation and its application in Fischer–Tropsch synthesis

A simple preparation method of bimodal silica was developed by introducing SiO₂ sol into large pores of SiO₂ gel pellet directly. Cobalt supported on this kind of bimodal silica support, exhibited remarkably high activity in liquid-phase Fischer–Tropsch synthesis, which was attributed to its bimodal structure having not only a higher surface area but also a larger pore size. The support with a large surface area allowed highly dispersed cobalt particle and its large pore size improved the diffusion of reactants and products.     

Effects of temperature and pressure gradients on catalyst pellet effectiveness factors—I

The dusty gas model is used to establish the effects of temperature and pressure gradients on catalyst pellet effectiveness factors for reaction systems in which species molecular weights and transport coefficients are indistinguishable and Σν_i = 0. For this class of reactions, the total molar flux of species i is shown to be expressible simply as N_i = ?cD ??_i in terms of the molar concentration, the Bosanguet diffusivity, and the mole fraction gradient. The effects of temperature and pressure gradients are reflected only in variations in molar concentration and diffusivity. Furthermore, the temperature-pressure relationship is shown to be given by the thermal transpiration equation for a pure gas.Typical numerical results are reported for first order reactions in spherical pellets under diffusive conditions ranging from the Knudsen through the bulk diffusion regimes.The variation in diffusion regime is shown to be controlled by an additional parameter α, the Knudsen to bulk diffusion ratio. Comparisons are made with the classical Weisz-Hicks nonisothermal pellet solutions based on N_i = ?D_eff?c_i. For highly exothermic reactions, effectiveness factors are 18% lower in the Knudsen regime and 30% higher in the bulk diffusion regime than are the Weisz—Hicks values. For highly endothermic reactions with a significant diffusion limitation, the effectiveness factors are 30% lower than the Weisz—Hicks values.The classical Damköehler relationship for pellet temperature rise is shown to apply in the Knudsen regime, with the maximum dimensionless center temperature given by (1 + β), where β is the heat of reaction parameter. This temperature is accompanied by a maximum dimensionless center pressure of (1 + β)^{$\text{1}\text{2}$}.In the bulk diffusion regime, the maximum center temperature is shown to be increased by the additional term β²/4. This additional temperature rise accounts for the 42% increased bulk diffusion effectiveness for highly exothermic reactions.     

Adsorption of Pt(cod)me2 onto organic aerogels from supercritical solutions for the synthesis of supported platinum nanoparticles

The thermodynamics and kinetics of adsorption of Pt(cod)me₂ onto resorcinol-formaldehyde aerogel (RFA) from supercritical carbon dioxide (scCO₂) was investigated by using high performance liquid chromatography (HPLC) to measure Pt(cod)me₂ concentrations in the fluid phase. It was found that the adsorption isotherms of Pt(cod)me₂ at 35 °C for different CO₂ pressures could be represented by modified Langmuir isotherms. The kinetics of adsorption was determined by following the Pt(cod)me₂ uptake of the RFA spheres; these data correspond closely to the behavior from a mass transfer model based on diffusion within the pore volume with the assumption of local equilibrium at the solid-fluid interface. The adsorbed Pt(cod)me₂ molecules were reduced at atmospheric pressure under flowing hydrogen at 200 °C. The resultant Pt nanoparticles were distributed uniformly on the surface and had narrow size distributions. The average particle size of the nanoparticles increased with platinum loading from 2.0 nm at 10 wt.% to 3.3 nm at 34 wt.%. The Pt nanoparticles in an RFA pellet had a uniform radial size distribution, even though the pellet was impregnated with Pt(cod)me₂ for too short a short period of time for the system to reach adsorption equilibrium. The high mobility of the atomic Pt evolved during the reduction process is believed to be responsible for this phenomenon. Performing the adsorption of Pt(cod)me₂ onto RFA at 80 °C led to concurrent reduction and Pt nanoparticle growth.