受平衡约束的平行反应体系的催化剂粒内反应-扩散过程模拟

以甲烷化体系为例，研究了受平衡约束的平行反应的催化剂粒内状态。采用正交配置法求解催化剂的一维、二维反应－扩散非等温模型。模拟结果表明，由于甲烷化反应与变换反应交互作用，导致变换反应在催化剂粒内正、逆反应均存在。内扩散效率因子不能准确描述催化剂内表面利用率，应考虑粒内参数分布。     

YL 型银催化剂粒内扩散作用的研究

本文应用在不同粒度的银催化剂上所获得的乙烯氧化反应动力学的研究结果,求取了 YL 型工业银催化剂的粒内有效因子。应用等温和非等温的扩散—反应模型,通过数值法算得了乙烯在银催化剂颗粒内的有效扩散系数,并考察了粒内温度分布对催化剂粒内有效因子的影响。     

不规则形状A301氨合成催化剂内扩散有效因子

对于不规则形状A301氨合成催化剂,测定了其形状系数和球化的当量直径及高压下本征动力学方程,用SPSR法测定了不规则催化剂颗粒的曲折因子,根据多组分单一反应等温球形A301氨合成催化剂内反应-扩散-维模型,用正交配置法结合解非线性方程组的Broyden拟牛顿法求解了模型,获得了催化剂粒内各组分的浓度分布和催化剂的内扩散有效因子.利用所测得的高压下A301催化剂的总体速率对模型进行了检验,模型计算值和实验值吻合,表明球化模型和所得当量直径、曲折因子等模型参数可用于描述A30l催化剂内的反应-扩散过程及工程设计计算.     

多孔球形催化剂颗粒的随机网络模型

提出了一种多孔球形催化剂颗粒随机网络构造方法,并以等温一级不可逆反应为例,对催化剂孔道网络内发生的反应扩散过程进行了模拟计算。模拟结果表明,计算出的曲折因子既是孔网络配位数的函数,又随Thiele模数的变化而不同,在纯扩散条件下测得的有效扩散系数只能应用于扩散影响不严重的反应扩散区域。同时对在不同的网络模型上的模拟结果进行了分析,并对各自得出的结论之间存在的分歧进行了解析。     

假瞬态洁求解中温变换B109催化剂效率因子

建立了描述工业催化剂粒内浓度和温度分布的扩散数学模型.借助假瞬态法,提出了非等温扩散模型的有效解法.本文对16组宏观实验速率,获得了各组分的浓度和温度分布,及中温变换B109催化剂效率因子的数值解.采用该法能在不修改边界条件的情况下,求解催化剂颗粒内存在“死区”的定解问题.计算结果合理,计算速度快.     

LB型节能催化剂上高温变换反应本征动力学及工业化测定

运用正交实验设计安排了LB型节能催化剂高温变换反应本征动力学实验,测得不同温度、不同流量、不同水碳比、不同反应气体摩尔分数下LB型节能催化剂上CO高温变换反应本征动力学数据。用甲酸盐机理模型和幂函数模型拟合实验数据,确定了本征动力学模型参数。进行了本征动力学模型统计检验,表明所建模型无论局部还是整体都是显著和可信的。在此基础上,进行了大型合成氨装置上LB型节能催化剂高变反应工业化测定,按多组分单一反应等温球形催化剂一维非均相反应-扩散模型,利用配置法结合解非线性方程组的Merson法求解模型,得到了工业反应器中催化剂床层温度、内扩散有效因子、CO转化率和摩尔分数随床层相对高度的分布,模拟结果与工业化测定结果吻合。     

假瞬态洁求解中温变换B109催化剂效率因子

建立了描述工业催化剂粒内浓度和温度分布的扩散数学模型.借助假瞬态法,提出了非等温扩散模型的有效解法.本文对16组宏观实验速率,获得了各组分的浓度和温度分布,及中温变换B109催化剂效率因子的数值解.采用该法能在不修改边界条件的情况下,求解催化剂颗粒内存在“死区”的定解问题.计算结果合理,计算速度快.     

丙烯聚合建模研究:扩散作用的影响

提出了均匀分布多粒模型 (UMGM) ,用于研究单个聚丙烯粒子的增长过程。在不考虑催化剂多活性中心和失活的情况下 ,扩散作用能够在较大范围内解释丙烯聚合过程中分子量分布以及反应速率的变化。分析了扩散系数、催化剂的活性以及催化剂颗粒大小对反应的影响。仿真结果表明 ,扩散作用对高活性催化剂的影响更加显著 ,并且与催化剂粒子的大小有密切关系。本模型能够方便地扩展到多活性中心以及采用更加复杂的微观反应动力学方程 .与其他单粒子模型相比 ,UMGM模型参数物理意义明确 ,计算速度快 ,为工业反应器的建模和优化奠定了基础。     

硫中毒状态下B108中变催化剂效率因子的研究

硫中毒状态下铁铬系变换催化剂效率因子的研究,迄今尚未见报道。本文根据水煤气变换反应的特点,以均匀中毒假设为前提,建立多组分扩散模型描述稳态情形下,500ppm 硫化氢气相浓度时各反应组分在等温原粒度催化剂中的浓度分布。所有6个实验条件下的效率因子计算机求解结果表明,模型与实验值符合良好。从浓度分布和死区两方面解释了相同条件下,宏观反应速率受硫化氢影响较本征速率小38.30%的原因。研究表明,采用的实验手段是可行的,所建立的模型可用于工业过程的分析。     

多孔催化剂颗粒的内扩散效应对伴有失活的二级反应动力学的影响

采用正交配置等数学方法,研究在均匀独立失活的催化反应系统中,内扩散效应对等温球形催化剂失活速率的影响,建立适用于任何内扩散区域的二级反应、m级失活系统的失活有效因子和失活西勒模数的定量关系,对n级反应、m级失活系统也作了相应地推广.运用加压微反-色谱-数据处理机联合装置,通过分析在原颗粒丝光沸石催化剂上进行的临氢甲苯歧化反应的失活数据,研究了内扩散对二级反应失活动力学的影响规律.同时,在实验范围内,建立了一套内扩散存在下的甲苯歧化失活动力学模型.     

单颗粒催化剂上非理想体系的反应-扩散模型(Ⅰ)——非理想体系反应-扩散模型的建立

基于力平衡和通量的观点,建立了多孔催化剂上非理想体系的反应-扩散模型.该模型综合考虑了非理想气体反应体系的热力学特性和各组分通量之间的相互耦合作用;此外,该模型可根据实际情况依次简化为常规意义上的尘气模型、广义Stefan-Maxwell模型和费克扩散模型.作为单颗粒催化剂上反应-扩散过程通用模拟软件开发的基础,该模型明显优于其他常规模型.     

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.     

单颗粒催化剂上非理想体系的反应-扩散模型(Ⅰ)——非理想体系反应-扩散模型的建立

基于力平衡和通量的观点,建立了多孔催化剂上非理想体系的反应-扩散模型.该模型综合考虑了非理想气体反应体系的热力学特性和各组分通量之间的相互耦合作用;此外,该模型可根据实际情况依次简化为常规意义上的尘气模型、广义Stefan-Maxwell模型和费克扩散模型.作为单颗粒催化剂上反应-扩散过程通用模拟软件开发的基础,该模型明显优于其他常规模型.     

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.     

QUALITATIVE OBSERVATIONS OF HEAT AND MASS TRANSFER EFFECTS ON THE BEHAVIOUR OF A TRICKLE BED REACTOR

This paper examines the effect of simultaneous heat and mass transfer on the hydrogenation of cyclohexene in a trickle bed reactor with particular attention given to the problem of liquid phase evaporation and transition to the gas-phase regime of operation. The reaction rates are obtained as a function of temperature and hydrogen flow rate; the concentration of the substrate in the feed displays considerable hysteresis due to an abrupt increase of the reaction rate arising from temperature gradients within the bed and in the gas film surrounding the catalyst pellet, during the transition from the liquid to the gas-phase regime. The transition is accompanied by the change of apparent kinetics of the model reaction as well as by a change of regime and operation of the pellet. In the liquid phase a pellet originally showing inter-phase and intra-particle diffusion resistances changes into the gas-phase regime with a large resistance due to inter-phase diffusion.     

Coupling non-isothermal trickle-bed reactor with catalyst pellet models to understand the reaction and diffusion in gas oil hydrodesulfurization

In this work, a trickle-bed reactor coupled with catalyst pellet model is employed to understand the effects of the temperature and catalyst pellet structures on the reaction–diffusion behaviors in gas oil hydrodesulfurization(HDS). The non-isothermal reactor model is determined to be reasonable due to non-negligible temperature variation caused by the reaction heat. The reaction rate along the reactor is mainly dominated by the temperature,and the sulfur concentration gradient in the catalyst pellet decreases gradually along the reactor, leading to the increased internal effectiveness factor. For the fixed catalyst bed volume, there exists a compromise between the catalyst reaction rate and effectiveness factor. Under commonly studied catalyst pellet size of 0.8–3 mm and porosity of 0.4–0.8, an optimization of the temperature and catalyst pellet structures is carried out, and the optimized outlet sulfur content decreases to 7.6 wppm better than the commercial level at 0.96 mm of the catalyst pellet size and 0.40 of the catalyst porosity.     

Analysis of catalytic reaction systems under microwaves to save energy

Effects of microwaves on catalytic reaction systems are analyzed theoretically in this work. Use of microwaves is encouraged to save energy. The effects of microwave heating are analyzed theoretically by assuming that the catalyst pellet is homogeneous. The temperature and concentration profiles within the catalyst pellet were obtained by numerical simulations for the cases of microwave heating and conventional heating. In the modeling the catalyst pellet is regarded as a continuum. When a chemical reaction was conducted in a heterogeneous medium with microwave heating, the reaction rate and the yield were found to be increased compared to conventional heating under the same reaction conditions. This is due to hot spots generated by selective heating of the catalyst pellet, resulting in an increased reaction rate.     

Modeling of multicomponent mass diffusion in porous spherical pellets: Application to steam methane reforming and methanol synthesis

The main purpose of this paper is the derivation and evaluation of various diffusion flux models. For this aim, a comprehensive catalyst pellet problem has been simulated for two test cases: the steam methane reforming (SMR) and the methanol synthesis, as these two important chemical processes cover various aspects of a chemical reaction. The pressure, temperature, total concentration, species composition, viscous flow, mass and heat fluxes within the porous spherical pellet are included in the transient pellet model. Mass diffusion fluxes are described according to the rigorous Maxell–Stefan and dusty gas models, and the respectively simpler Wilke and Wilke–Bosanquet models. Simulations are performed with these fluxes defined according to both the molar averaged and mass averaged definitions. For the mass based pellet equations, a consistent set of equations is obtained holding only the mass averaged velocity. On the other hand, the closed set of molar based pellet equations hold both the molar averaged and mass averaged velocities as the fundamental energy balance and the momentum balance (Darcy law) are derived according to the mass averaged velocity definition, whereas the diffusion fluxes are defined relative to the molar averaged velocity. Identical results of the molar and mass based pellet equations were not obtained; however, the deviations are small. It is anticipated that these discrepancies are due to some unspecified numerical inaccuracies. However, efficiency factors have been computed for both processes and the values obtained compare well with the available literature data. Furthermore, efficiency factor sensitivity on parameters like pore diameter, tortuosity, temperature and pressure have been accomplished, and the classical simplifications of the pellet equations have been elucidated: isothermal condition, constant pressure, and neglecting viscous flow. The following conclusions are established for the reactor operating conditions used in the present work. The methanol synthesis: The simulation results of the methanol synthesis indicate that the classical assumptions are very fair for this process. Moreover, both Wilke and Wilke–Bosanquet models are good replacements for the more rigorous Maxwell–Stefan and dusty gas models. However, the simulation results are affected by Knudsen diffusion, thus the diffusion flux is most appropriately described by the Wilke–Bosanquet model. The SMR process: Knudsen diffusion hardly influences the results of the highly intraparticle diffusion limited SMR process. As the Wilke model does not necessarily conserve mass, we recommend the Maxwell–Stefan model because the simpler Wilke closure deviates with several percents. However, it is not elucidated whether these deviations are numerical problems arising from the large gradients of this process, or related to the choice of diffusion model. Isothermal and isobaric conditions can be assumed within the particle, but significant external temperature gradients are observed. Convective fluxes are much less than the diffusive fluxes, hence viscous flow can be neglected.     

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.     

Experimental and modeling study of the solid state polymerization of poly(ethylene terephthalate) over a wide range of temperatures and particle sizes

The solid state polymerization (SSP) of poly(ethylene terephthalate) was studied experimentally over a wide range of pellet sizes and temperatures. A comprehensive model was developed. It considered polycondensation, degradation and polycondensation of vinyl end groups together with diffusion. The reaction rate constants, diffusivities and the corresponding activation energies were obtained through parameter identification using experimental data. The effects of the reaction temperature and pellet size on the SSP time were also investigated. A decrease in the particle size decreases the concentration of the vinyl end groups and narrows the concentration distribution of end groups inside poly(ethylene terephthalate) particles. A decrease in the size of pellets also favors diffusion. Nevertheless it is preferable that the size of pellets be between 1 and 2 mm because too small pellets bring about difficulties with preparation and handling. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013