Simulating a multiphase reactor with continuous phase transition

A novel multiphase fixed-bed reactor with continuous phase transition for benzene hydrogenation to cyclohexane has been presented by Cheng et al. (A.I.Ch.E. J. 47 (2001a) 1185; Chem. Eng. Sci. 56 (2001b) 6025; 57 (2002) 3407; A.I.Ch.E. J. 49 (2003) 225) which makes use of evaporation of volatile components to remove the reaction heat. This paper investigates issues related to the numerical simulation of the model for this novel fixed-bed reactor. The reactor is supposed to be divided into two parts subject to the phase transition point on the bed level, that is, the liquid-contacted zone at the lower part and the gas-contacted zone at the upper part. A steady-state mathematical model for the reactor is developed. All external mass and heat transfer resistances can be neglected in the case investigated, as well as temperature differences in the particles. The effects of feed inlet temperature, inlet benzene concentration, gas flow rate and liquid flow rate on the reactor performance are theoretically studied. Reliability of the model is verified by bench-scale experiments. The results show that dryout phenomena will occur in the reactor both on the bed-scale and on the pellet-scale under certain conditions.     

Studying the internal mass transfer phenomena inside a Ni/Al2O3 catalyst for benzene hydrogenation

The mass transfer phenomena occurring inside Ni/Al₂O₃ catalytic extrudates have been studied for the liquid-phase hydrogenation of benzene. The experiments were conducted in a bench scale trickle-bed reactor at 17 bar absolute pressure and temperatures between 70 and 150 °C. Kinetic, thermodynamic and hydrodynamic effects have previously been examined [K.C. Metaxas, N.G. Papayannakos, Ind. Eng. Chem. Res. 45(21) (2006) 7110–7119]. Temperature gradients inside the particle and across the liquid film surrounding catalyst particles have been checked and verified as absent. Concentration profiles of hydrogen and benzene show firstly that are consumed close to the surface of the extrudate and secondly to be in large excess along the particle radius. Catalyst particle tortuosity is estimated to be 3.75, very close to the value of 3.56 extracted from a statistical model based on nitrogen sorption hysteresis data. The effectiveness factor lies in the range of 0.19–0.35, implying strong diffusion limitations. The passivation of catalyst surface is posed as a solid reason for the modification of the true activation energy of the reaction occurred while moving from crushed catalyst particles to catalytic extrudates.     

内部部分润湿催化剂的动力学行为

The global reaction rate of benzene hydrogenation to cyclohexane accompanied by partial internal wetting of catalyst pellets was measured by a new method, which investigated both adsorption and chemical reaction. The adsorption investigation was used to establish a relationship between the extent of liquid filling of the catalyst and the bulk conditions while the chemical reaction investigation was to study the effect of partial internal wetting of the catalyst on the global reaction rate. It was shown that the extent of liquid filling in the catalyst interior showed a significant effect on the global rate, and the current state of the catalyst depended on the history, i.e. whether it was a liquid evaporation process or a vapor condensation process, and two steady states were found under certain circumstances. A mathematical model was developed, which took multicomponent diffusion, chemical reaction, pore size distribution of the catalyst and capillary condensation of condensable components in the catalyst pellet into consideration. The predicted values were in good agreement with the experimental data.     

Two-parameter model for evaluating effectiveness factor for immobilized enzymes with reversible Michaelis-Menten kinetics

A two-parameter mathematical model was developed to calculate the effectiveness factor for immobilized enzymes in porous spherical particles. The model was resolved for reversible Michaelis-Menten kinetics, including simple Michaelis-Menten and product competitive inhibition kinetics. Since only two dimensionless moduli are involved in the model, the effectiveness factor for the three kinetic equations considered can be estimated by using only one generalized graph.     

对苯二甲酸精制钯碳催化剂内扩散有效因子的估算

在高压磁力搅拌间歇反应釜中研究了粗对苯二甲酸在不同反应温度下,两种粒径的Pd/C催化剂上加氢精制反应的规律。按照该反应对于对羟基苯甲醛(4 CBA)是拟一级反应估算了催化剂的内扩散有效因子η值。本试验估算的η值与动力学研究拟合得到的η值吻合良好。     

Measuring absolute adsorption in porous rocks using oscillatory motions of a spring-mass system

We present an oscillation-based method to measure absolute adsorption, or total gas, contained in porous rocks without and with excess adsorption. Experiments conducted with a macroporous Berea sandstone sample in nitrogen where excess adsorption is negligible show that absolute adsorption can be obtained after the added mass of co-accelerated gas outside the sample is subtracted. In experiments conducted in propane with a crushed Niobrara shale sample with micro- and mesopores, absolute adsorption included significant excess adsorption. After subtracting both the added mass outside the sample and the gas that would be in the sample assuming no excess adsorption existed, estimated excess adsorption of propane is in good agreement with that projected based on capillary condensation of propane in the volume of mesopores.     

1D and 2D simulations of partially wetted catalyst particles: A focus on heat transfer limitations

Hydrodynamics and transport phenomena inside Trickle Bed Reactors are strongly modified when superficial liquid velocity is not sufficient to insure a perfect wetting of catalyst particles. For this reason, the impact of partial wetting on catalyst effectiveness has been widely studied in past, in case of isothermal reactions. Heat transfer limitations, inside or outside catalyst particles, have also been investigated, but only in case of total wetting.In the present study, the effect of partial wetting is quantified numerically for various kinetics, mass and heat transfer limitations. When possible, an analogy is proposed between 1D and 2D models of particles. Robust rules are proposed to take into account for partial wetting in 1D-radial models of particles.The case of partial evaporation inside catalyst pores is also studied. Evaporation phenomena is approximated following a simple approach. Performed calculations show that the effect of partial wetting can affect very strongly catalyst effectiveness factors, especially in case of evaporation in the pores. The use of 1D approximations gives a good prediction of the global catalyst efficiency, as far as boundary conditions are symmetric between heat and mass transfer. Otherwise, 1D models are not relevant anymore.     

Study on diffusion and flow of benzene, n-hexane and CCl4 in activated carbon by a differential permeation method

In this paper the diffusion and flow of carbon tetrachloride, benzene and n-hexane through a commercial activated carbon is studied by a differential permeation method. The range of pressure is covered from very low pressure to a pressure range where significant capillary condensation occurs. Helium as a non-adsorbing gas is used to determine the characteristics of the porous medium. For adsorbing gases and vapors, the motion of adsorbed molecules in small pores gives rise to a sharp increase in permeability at very low pressures. The interplay between a decreasing behavior in permeability due to the saturation of small pores with adsorbed molecules and an increasing behavior due to viscous flow in larger pores with pressure could lead to a minimum in the plot of total permeability versus pressure. This phenomenon is observed for n-hexane at 30°C. At relative pressure of 0.1-0.8 where the gaseous viscous flow dominates, the permeability is a linear function of pressure. Since activated carbon has a wide pore size distribution, the mobility mechanism of these adsorbed molecules is different from pore to pore. In very small pores where adsorbate molecules fill the pore the permeability decreases with an increase in pressure, while in intermediate pores the permeability of such transport increases with pressure due to the increasing build-up of layers of adsorbed molecules. For even larger pores, the transport is mostly due to diffusion and flow of free molecules, which gives rise to linear permeability with respect to pressure.     

Optimum washcoat thickness of a monolith reactor for syngas production by partial oxidation of methane

In this paper, syngas (hydrogen and carbon monoxide) production was investigated by a numerical model of an adiabatic monolithic reformer (e.g. for a micro fuel cell system). The study includes the thermal and diffusive properties of a washcoat of finite thickness that is modeled as a porous layer composed of a ceramic support containing catalytic active rhodium sites. It was combined with a two-dimensional radially symmetric model of a single tubular mini-channel, considering both the thermal and the diffusive transport phenomena in all domains. It was found that both the methane conversion and the hydrogen yield depended markedly on the washcoat thickness. An interesting result was obtained by implementing the common experimental conditions into the numerical model: if the inlet volume flow and the amount of catalyst per washcoat volume are constant, an optimum washcoat thickness of was found, where the hydrogen yield is maximal. For a thinner washcoat, the smaller amount of catalyst is limiting, leading to a low methane conversion. For a thicker washcoat, the limiting effect is the reduced residence time, which stems inherently from the constraint of constant volume flow, rather than the increased diffusive resistance.The demonstration of the existence of an optimum washcoat thickness is important, because it can have economic effects due to saving of the precious catalyst rhodium.     

Hydrogenation of dimethyl oxalate to ethylene glycol on a Cu/SiO2/cordierite monolithic catalyst: Enhanced internal mass transfer and stability

The design and application of a Cu/SiO₂‐based monolithic catalyst for hydrogenation of dimethyl oxalate (DMO) to ethylene glycol (EG) is presented. The catalyst was dip‐coated on cordierite with highly dispersed Cu/SiO₂ slurry prepared by ammonia evaporation method. This structure guarantees high dispersion of copper species within the mesopores of silica matrix in the form of copper phyllosilicate. The catalyst is low cost, stable, and exhibits high activity in the reaction of hydrogenation of DMO, achieving a 100% conversion of DMO and more than 95% selectivity to EG. Notably, STY_EG over the monolith is significantly enhanced compared to the packed bed Cu/SiO₂ catalysts in both forms of pellet and cylinder. It is primarily due to the relatively short diffusive pathway of the thin wash‐coat layer and high efficiency of the active phase derived from the monolithic catalyst. Theoretical results indicated that the internal mass transfer is dominated on the catalysts of pellet and cylinders. Moreover, the monolithic catalyst possessed excellent thermal stability compared to the pellet catalyst, which is attributed to the regular channel structure, uniform distribution of flow. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Evaluating the effectiveness factor from a 1D approximation fitted at high Thiele modulus: Spanning commercial pellet shapes with linear kinetics

In the present contribution a one-dimensional model (1D model) is employed to account for the effect of pellet shape in the solution of diffusion-catalytic reaction problems. The 1D model free parameter (σ) is fitted so as to match the second term of the series for the effective reaction rate at fast kinetic conditions. The performance of the model was evaluated for a large collection of pellets available commercially, covering almost all the main shapes offered by catalyst manufacturers. For isothermal linear kinetics the effectiveness factors calculated by the 1D model differ at most by 3% from those of the actual 3D pellets.     

Influence of carbon dioxide partial pressure and fluidization velocity on activated carbons prepared from scrap car tyre in a fluidized bed

The effect of carbon dioxide partial pressure and fluidization velocity on activated carbons produced by carbon dioxide activation of scrap car tyre rubber in a fluidized bed has been studied. The method consisted of carbonization at under nitrogen followed by activation at . Three types of activated carbons were produced using activated gas concentrations of 20, 60 and 100% carbon dioxide by volume, the rest nitrogen, at a constant fluidization velocity (0.0393 m/s) to investigate the influence of carbon dioxide partial pressure. Within the experimental setup and activation time of 4 h, it was observed that BET surface area and total pore volume increased with carbon dioxide partial pressure reaching and , respectively, for 100% activation with carbon dioxide. Three other types of activated carbons were produced using 100% carbon dioxide at two (0.0393 m/s), three (0.0589 m/s) and four (0.0786 m/s) times the minimum fluidization velocity (U_mf). The BET surface area and total pore volume were observed to increase with fluidization velocity (which can be viewed as an indicator of the intensity of mixing in the bed), reaching and , respectively, at four times the minimum fluidization velocity.     

Determination of adsorption and diffusion parameters in zeolites through a structured approach

Temporal analysis of products (TAP) is a transient pulse-response technique that allows to extract kinetic information from reacting and adsorbing systems. In a previous work (Chem Eng Sci 57(2002) 1835), a detailed-transport model for the Multitrack set-up, a TAP-like system, was developed, which allows studying systems with a low bed resistance. The use of structured beds, having both a low bed resistance and small sorbent particles, is required to determine adsorption and diffusion parameters when strong adsorption and slow diffusion occurs. A method is presented to extend the range of measurable adsorption and diffusion parameters in zeolitic sorbents in the TAP technique by a structured approach. Small zeolite crystals are coated on larger non-porous glass beads. Adsorption and diffusion parameters for n-butane, SF₆ and 3-methylpentane have been determined in MFI-type zeolites. Absolute diffusivity values in the zeolite coating are estimated by using a well-defined silicalite sample as a reference to determine the effective diffusion length in the coating.Two criteria have been derived, one for the characteristic time for transport through the bed, , and one for the ratio of the latter and the characteristic diffusion time in the zeolite crystal, 0.01<α<200t_bed/(1+t_bed), which should be satisfied both to be able to determine values of the zeolite diffusivity.