Cited by (27)
Effects of the collision integral, thermal diffusion, and the Prater number on maximum temperature in macroporous catalysts with exothermic chemical reaction in the diffusion-controlled regime
2007, Chemical Engineering Science
The classic Prater equation is useful to estimate intrapellet temperatures in packed catalytic tubular reactors when the dimensionless Prater number is relatively small (i.e., the magnitude of ). However, for strongly exothermic chemical reactions, both thermal diffusion and the temperature dependence of important physicochemical properties of reactive gas mixtures should be included in the analysis of coupled heat and mass transfer within macroporous catalytic pellets. In the diffusion-limited regime, intrapellet temperature increases could be much greater than those predicted by the Prater equation. The analysis of thermal diffusion in pseudo-binary Lennard-Jones gases with temperature-dependent physicochemical properties reveals that steady-state predictions for exothermic reactions might not be possible when the Prater number is on the order of unity, because core temperatures are more than one order of magnitude larger than temperatures on the external catalytic surface. For reference, the Prater equation predicts that the maximum intrapellet temperature is two-fold larger than that on the external catalytic surface when , which severely underestimates realistic temperature increases by a factor of 5 or 6 (i.e., when ) for the synthesis of methanol from carbon monoxide and hydrogen. The largest increases in intrapellet temperature occur when all of the following conditions are satisfied; (i) chemical reactions are strongly exothermic, (ii) physicochemical properties of the reactive gas mixture exhibit temperature dependence, (iii) the Prater number approaches unity, and (iv) Soret diffusion enhances the molar flux of (i.e., in pseudo-binary mixtures) into the central core of macroporous catalysts as a consequence of negative thermal diffusion coefficients.
Measurement of gas composition at the center of a porous pellet during adsorption and catalytic reaction under dynamic conditions
1997, Journal of Catalysis
Gas composition is measured at the center of one-dimensional porous platinum/alumina pellets during carbon monoxide adsorption and catalytic oxidation. The apparatus is based on a single-pellet diffusion reactor that has been modified to allow continuous gas analysis and miniaturized in order to reduce the time constants of gas flow and mixing. Analysis of the CO adsorption response demonstrates that the centerplane volume and sample leak perturb the system only slightly and in a manner that can be accounted for during data analysis. A detailed kinetic model described previously is able to predict the qualitative features of the external concentration responses during carbon monoxide oxidation. However, the model is not able to predict major features of the responses measured at the pellet center, demostrating that the reactor is able to provide stricter tests of kinetic models than reactors in which only external compositions can be measured.
Nonuniform activity distribution in catalyst particles: Benzene hydrogenation on supported nickel in a single pellet diffusion reactor
1995, Chemical Engineering Science
A single pellet diffusion reactor (SPDR) of new design has been used to investigate the influence of nonuniform distributions of active ingredient on the Ni-catalyzed hydrogenation of benzene. Five different distributions, ranging from preferential shell-loading to uniform to preferential core loading, have been studied under isothermal conditions. Analysis of results has been carried out using a simple one-dimensional diffusion/reaction analysis, which the configuration of the SPDR is set to mimic. The rate of the reaction follows an Eley-Rideal model, effectively positive fractional-order under the experimental conditions, for which kinetics the nonuniform distribution problem has not been studied experimentally before. Preferential shell-loading yields the highest catalytic effectiveness but because of the complex interactions between the reaction kinetics and the activity profiles within the pellets, there is no simple relationship between diffusion lengths and effectiveness even for large values of the Thiele modulus.
Uniqueness of the steady state for an mth order reaction in a non-isothermal pellet with variable transport coefficients
1985, Chemical Engineering Science
A temperature overshoot on a catalyst pellet
1985, Chemical Engineering ScienceSee AlsoHistofix ® - Safe Konservierungsmittel gebrauchsfertig für die klinische Diagnostikscinexx | Das WissensmagazinStereoselective synthesis of beta-amino- and Microcos-piperidines : An approach to the total synthesis of (+)-MicroconineVerfahren zur selektiven Hydrierung von aromatischen Gruppen in Gegenwart von Epoxygruppen专利检索-环氧乙烷的制备专利检索查询-专利查询网
An unexpected temperature overshoot was found for a Pd on alumina catalyst pellet in its course towards a new steady state, after a change in concentration of one of the reactants. The reaction mixture consisted of ethylene, hydrogen and nitrogen as inert. A speculative model is introduced, which can explain these overshoots by a slow adsorption of one of the reactants on the active sites of the catalyst.
Un modèle simple de réaction-diffusion-conduction thermique dans et autour d'une particule poreuse. Partie II: Diffusion externe
1976, The Chemical Engineering Journal
On étudie le cas général où une réaction chimique, au sein d'une particule poreuse, est en compétition avec des phénomènes de diffusion externe et interne et avec des phénomènes de conduction thermique externe et interne.
On écrit que la “résistance” globale est la somme d'une résistance externe et d'une résistance interne et on évalue la fraction externe φe de résistance.
On définit une efficacité globale ηe, par rapport aux concentrations et à la température externes, mesurées, et on exprime ηe en fonction de l'efficacité interne ηi, définie dans la première partie. Cette relation générale entre ηe et ηi est valable pour une réaction chimique quelconque et elle implique seulement que les variables C et T soient séparables (cf. la première partie).
Dans le cas particulier d'une réaction du premier ordre dans une particule isotherme, on étudie la multiplicité des points de fonctionnement dûe à l'échauffement dans la couche limite. On propose un critère de multiplicité, qui est en excellent accord avec celui proposé par Hlavacek et Kubicek.
Comme exemple d'application de la méthode, on décrit la procédure à suivre pour déterminer la loi cinétique de vitesse d'une réaction quelconque, même dans le cas général où la mesure de cette vitesse est perturbée par des phénomènes diffusionnels externes et internes et par des effets thermiques.
The general case of chemical reactions in a porous particle subject to competition between external and internal diffusion and thermal conductivity is studied.
The overall “resistance” is expressed as the sum of the external and internal resistances and the fractional external resistance is calculated. An overall efficiency ηe is defined with respect to the measured values of the external temperature and concentration. ηe is expressed as a function of the internal efficiency which was defined in Part I. This general relationship between ηe and ηi is valid for any chemical reaction and only requires that the variables C and T be separable (cf. Part I).
In the special case of an isothermal first order reaction in a porous particle the multiplicity of operating points due to the heating in the boundary layer is studied. A criterion of multiplicity is proposed which is in excellent agreement with that proposed by Hlavacek and Kubicek.
To illustrate the use of the method the procedure of determining the kinetics of any reaction is described even in the general case where rate measurements are affected by internal diffusion and thermal effects.
Recommended articles (6)
Synthesis of SAPO-34/graphite composites for low temperature heat adsorption pumps
Journal of Energy Chemistry, Volume 22, Issue 2, 2013, pp. 245-250
Low temperature heat adsorption pumps represent the innovative cooling systems, where cold is generated through adsorption/desorption cycle of water by a suitable adsorbent with good adsorption and high thermal conductive properties. In this work, the hydrothermal synthesis of zeolite SAPO-34 on thermal conductive graphitic supports, aiming at the development of highly performing adsorbent materials, is reported. The synthesis was carried out using as-received and oxidized commercial carbon papers, and graphite plate. Composites were characterized by XRD, SEM and also by a thermogravimetric method, using a Cahn microbalance. The water adsorbing capacity showed typical S-shape trend and the maximum water loading was around 25 wt%, a value close to water adsorption capability of pure SAPO-34. These results are very promising for their application in heat adsorption pumps.
Mathematical modeling of CO oxidation on Pd(100) at near-atmospheric pressures: Effect of mass-transfer limitations
Surface Science, Volume 691, 2020, Article 121488
A 3D convection-diffusion-reaction model was developed to describe CO oxidation in a continuous-flow catalytic reactor containing a Pd(100) single crystal surface. The model was studied with the help of the pseudo-arclength continuation algorithm, which is based on a matrix-free Newton–Krylov method and enables a one-parameter continuation of stationary solutions of large systems. The model was used to simulate the 3D spatial distributions of CO and CO2 during “light-off” experiments and the oscillations in CO oxidation over Pd(100) detected by the planar laser-induced fluorescence (PLIF) method. With realistic values of parameters the developed model can reproduce almost quantitatively the experimental reaction rates and the PLIF images measured under steady-state conditions and during self-sustained oscillations under near-atmospheric pressure conditions. The formation of a boundary layer and the essential decrease of CO concentration near the Pd(100) single crystal surface were demonstrated after the catalytic ignition and in a high activity branch of the oscillatory cycle indicating the mass-transfer limited regime.
Modeling of catalytic monolith reactor for reforming of hexadecane with exhaust gas
International Journal of Hydrogen Energy, Volume 38, Issue 27, 2013, pp. 11826-11839
A numerical two-phase one-dimensional mathematical model of a single channel catalytic monolith reactor was developed in this study. The model is capable of simulating a final steady state starting from an initial distribution of temperatures and concentrations. An algorithm was written in order to solve the conservation equations. In a catalytic reactor these equations are the mass and energy balances, rate equations and physical property relationships. The new method used to solve the equations was the combination of the Euler's method and central finite difference method. The advantage of this combined method is that the percentage error produced by the program code was negligible. The program code in MATLAB environment was executed to describe the profiles of temperatures and concentrations of each individual species in the gas and solid phase along the reactor. The reforming process is complicated for heavy hydrocarbons and it is not well defined. The model was applied, as far as the authors are aware for the first time, for autothermal reforming process with n-hexadecane (C16H34) feed to depict the performance of the monolith channel for hydrogen production at specified operating conditions. In this model, it was also assumed that the reactions only occur on the surface of catalyst. The temperatures and the concentrations of each species of interests (i.e. H2, CO2, CO, and C16H34) were obtained in both the gas phase and at the wall. The results obtained using reaction kinetics data from literature were successfully validated against experimental results from a different study with respect to reactor temperatures and concentrations of products H2, CO2 and CO. The influence of thermal conductivity and effective wall thickness of the solid phase, and mass flow rate of gas on wall temperatures and mole fractions of components were also investigated and the results were in agreement with literature data.
Application of continuum percolation theory for modeling single- and two-phase characteristics of anisotropic carbon paper gas diffusion layers
Journal of Power Sources, Volume 307, 2016, pp. 613-623
Percolation theory is used to model intrinsic and relative permeabilities as well as tortuosity in anisotropic carbon paper gas diffusion layers (GDL) and compared with existing results from lattice-Boltzmann (LB) simulations and experimental measurements. Although single- and two-phase characteristics of the carbon paper GDL are mainly affected by medium geometrical and topological properties, e.g., pore-size distribution, connectivity, and pore geometry, analyzing capillary pressure curves implies that the pore-size distribution of the carbon paper GDL is very narrow. This suggests that its effect on tortuosity and wetting- and nonwetting-phase relative permeabilities is trivial. However, integrated effects of pore geometry, surface area, connectivity, and tortuosity on intrinsic permeability might be substantial. Universal power laws from percolation theory predict the tortuosity-porosity and relative permeability–saturation curves accurately, indicating both characteristics not affected by the pore-size distribution. The permeability–porosity relationship, however, conforms to nonuniversality.
Modeling the oscillative behavior and carbon monoxide removal by current pulsing technique in H2/CO mixtures for Pt catalyst layer
International Journal of Hydrogen Energy, Volume 41, Issue 25, 2016, pp. 10854-10869
The main objectives of this study are to investigate the carbon monoxide (CO) poisoning and a mitigation method of high-level CO in a platinum (Pt) catalyst layer using hydrogen (H2)/CO mixture as the inlet fuel. Two separate levels of poisoning, 1000 and 10,000ppm CO at the anode fuel, are considered and investigated in detail. For this purpose, a one-dimensional transient model is developed including the diffusion of hydrogen and carbon monoxide, the conservation of adsorbed species, and ionic and electronic charges. As a result of CO poisoning, oscillations in overpotential and coverage of adsorbed species are observed for 1000ppm CO level, while the similar situation is not detected for 10,000ppm CO. Hence, the behavior of oscillations throughout the catalyst layer thickness, and the reasons are explored for the lower concentration case. For 10,000ppm CO, a mitigation technique, in which current density is pulsed from 0.1 to 2.5 A/cm2 for a period of time, is performed in order to remove the adsorbed CO from the Pt sites. It is concluded that up to 92% of CO coverage within the catalyst layer can be removed, and 70% of the catalyst layer length is determined to be completely CO-free following the application of current pulsing.
Multi-objective optimization of a residential air source heat pump with small-diameter tubes using genetic algorithms
International Journal of Refrigeration, Volume 67, 2016, pp. 134-142
Heat exchangers are key components in refrigeration and air conditioning systems. Significant research is being devoted to reduce the size, weight and cost of the heat exchangers while maintaining the same, if not better, system performance. This helps reduce the system refrigerant charge and negative environmental impacts. This work presents an optimization of an air source heat pump (ASHP) using multi-objective genetic algorithms, specifically focusing on the use of small diameter tubes in the heat exchangers. The objective is to minimize the heat exchangers' cost while maximizing the system performance. The goal is to find the potential material savings and cost reduction when using tube diameters between 3 mm and 5 mm in the heat exchangers. We show and discuss the results for R-410A, and the lower GWP R-32. The system utilizing the improved heat exchanger designs showed a cost reduction of 44%, and 47% in comparison to the baseline R-410A, and R-32 systems, respectively. Improvements in the system's COP are around 17%, and 15% for R-410A, and R-32, respectively. The system charge can be decreased to 33% for both refrigerants.
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