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Damköhler Number (damköhler + number)
Selected AbstractsSoret Diffusion and Non-Ideal Dufour Conduction in Macroporous Catalysts with Exothermic Chemical Reaction at Large Intrapellet Damköhler NumbersTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 3 2007Laurence A. Belfiore Abstract The adiabatic temperature rise in catalytic pellets is predicted from a modified version of the Prater equation. Onsager reciprocal relations for coupled heat and mass transfer are violated in an analysis of thermal diffusion in macroporous catalysts with exothermic chemical reaction when Dufour conduction (i.e., the diffusion-thermo effect) is neglected. In this contribution, Dufour conduction is analyzed for both ideal and non-ideal pseudo-binary gas mixtures that simulate the production of methanol from carbon monoxide and hydrogen. In the diffusion-controlled regime at large intrapellet Damköhler numbers where intermolecular collisions provide the dominant resistance to mass transfer within the catalytic pores, temperatures in the catalytic core could be much greater than predictions based on the original Prater equation when the Prater number exceeds 0.30. The molecular flux of thermal energy includes Fourier's law, the interdiffusional flux, and Dufour conduction. Diffusional mass flux includes Fick's law and the Soret effect. All physicochemical properties of the reactive gas mixture exhibit temperature dependence. There is essentially no difference between maximum intrapellet temperature predictions that include or neglect ideal Dufour conduction when external catalytic surface temperatures range from 300-400 K and thermal diffusion enhances the flux of "smaller" reactants toward the centre of the catalyst. For "large-molecule reactants" that participate in exothermic reactions, thermal diffusion opposes Fick's law and Dufour conduction opposes Fourier's law. Under these conditions, it is demonstrated that core temperatures are overestimated by neglecting both off-diagonal coupling mechanisms (i.e., Soret diffusion and Dufour conduction). Prater numbers greater than unity and unrealistically high gas pressures are required to distinguish between maximum intrapellet temperatures for ideal and real gas simulations, where the latter consider two-body interactions for Lennard-Jones molecules in the virial equation of state. On prédit l'augmentation de la température adiabatique dans les pastilles catalytiques à partir d'une version modifiée de l'équation de Prater. Les relations réciproques d'Onsager pour le transfert de chaleur et de matière couplé sont violées dans une analyse de la diffusion thermique dans les catalyseurs macroporeux avec réaction chimique exothermique lorsque la conduction de Dufour (p.ex., l'effet de thermo-diffusion) est négligée. Dans cet article, on analyse la conduction de Dufour pour des mélanges de gaz pseudo-binaires idéaux et non idéaux qui simulent la production de méthanol à partir d'oxyde de carbone et d'hydrogène. Dans le régime à diffusion contrôlée à grand nombre de Damköhler entre les pastilles pour lesquels les collisions entre les molécules fournit la résistance dominante au transfert de matière à l'intérieur des pores catalytiques, les températures dans le noyau catalytique pourraient être bien plus grandes que les prédictions basées sur l'équation de Prater originale lorsque le nombre de Prater excède 0,30. Le flux moléculaire de l'énergie thermique inclut la loi de Fourier, le flux interdiffusionnel, et la conduction de Dufour. Le flux massique diffusionnel inclut la loi de Fick et l'effet Soret. Toutes les propriétés physicochimiques du mélange de gaz réactif montre une dépendance thermique. Il n'y a essentiellement pas de différence entre les prédictions des températures maximales entre les pastilles qui incluent ou négligent la conduction de Dufour idéale quand les températures de surface catalytiques externes sont comprises entre 300 et 400 K; la diffusion thermique améliore le flux des réactifs «plus petits» vers le centre du catalyseur. Pour les «réactifs composés de grandes molécules» qui participent aux réactions exothermiques, la diffusion thermique s'oppose à la loi de Fick et la conduction de Dufour à la loi de Fourier. Dans ces conditions, il est démontré que les températures de noyau sont surestimées en négligeant les deux mécanismes de couplage hors-diagonales (c.à-d. la diffusion de Soret et la conduction de Dufour). Des nombres de Prater plus grands que l'unité et des pressions de gaz élevées peu réalistes sont nécessaires pour distinguer les températures maximales entre les pastilles entre les simulations de gaz idéales et réelles, en considérant pour ces dernières les interactions à deux corps pour les molécules de Lennard-Jones dans l'équation d'état du viriel. [source] Mineral precipitation associated with vertical fault zones: the interaction of solute advection, diffusion and chemical kineticsGEOFLUIDS (ELECTRONIC), Issue 1 2007CHONGBIN ZHAO Abstract This article is concerned with chemical reactions that occur between two interacting parallel fluid flows using mixing in vertical faults as an example. Mineral precipitation associated with fluid flow in permeable fault zones results in mineralization and chemical reaction (alteration) patterns, which in turn are strongly dependent on interactions between solute advection (controlled by fluid flow rates), solute diffusion/dispersion and chemical kinetics. These interactions can be understood by simultaneously considering two dimensionless numbers, the Damköhler number and the Z -number. The Damköhler number expresses the interaction between solute advection (flow rate) and chemical kinetics, while the Z -number expresses the interaction between solute diffusion/dispersion and chemical kinetics. Based on the Damköhler and Z -numbers, two chemical equilibrium length-scales are defined, dominated by either solute advection or by solute diffusion/dispersion. For a permeable vertical fault zone and for a given solute diffusion/dispersion coefficient, there exist three possible types of chemical reaction patterns, depending on both the flow rate and the chemical reaction rate. These three types are: (i) those dominated by solute diffusion and dispersion resulting in precipitation at the lower tip of a vertical fault and as a thin sliver within the fault, (ii) those dominated by solute advection resulting in precipitation at or above the upper tip of the fault, and (iii) those in which advection and diffusion/dispersion play similar roles resulting in wide mineralization within the fault. Theoretical analysis indicates that there exists both an optimal flow rate and an optimal chemical reaction rate, such that chemical equilibrium following focusing and mixing of two fluids may be attained within the fault zone (i.e. type 3). However, for rapid and parallel flows, such as those resulting from a lithostatic pressure gradient, it is difficult for a chemical reaction to reach equilibrium within the fault zone, if the two fluids are not well mixed before entering the fault zone. Numerical examples are given to illustrate the three possible types of chemical reaction patterns. [source] Oxygen transfer effects in ,-lactamase fermentation by Bacillus licheniformis in a glucose-based defined mediumJOURNAL OF CHEMICAL TECHNOLOGY & BIOTECHNOLOGY, Issue 9 2005nar Çal Abstract The effects of oxygen transfer on the ,-lactamase production by Bacillus licheniformis were investigated in a glucose-based defined medium. The experiments were conducted in 3.0 dm3 batch bioreactor systems at three different air inlet (QO/VR = 0.2, 0.5 and 1.0 vvm) and agitation rates (N = 250, 500 and 750 min,1). During the fermentation, the concentrations of the cell, glucose, by-products, ie organic and amino acids, oxygen transfer coefficients (KLa), yield coefficients, specific rates and oxygen uptake rates (OUR) were determined, in addition to ,-lactamase activities. The highest ,-lactamase activity was obtained at QO/VR = 0.5 vvm and N = 500 min,1 and at QO/VR = 0.2 vvm and N = 500 min,1 conditions, as caA = 90 U cm,3. The highest cell concentration was obtained as CX = 0.67 kg m,3 at QO/VR = 0.5 vvm and N = 750 min,1 and at QO/VR = 0.2 vvm and N = 750 min,1 conditions. The values of KLa increased with increasing agitation and aeration rates and varied between 0.007 and 0.044 s,1, and the OUR varied between 0.4 and 1.6 mol m,3 s,1. With increasing QO/VR and/or N, the Damköhler number (ie the oxygen transfer limitation) decreased owing to the increase in mass transfer coefficients (KLa). The highest instantaneous yield of cell on substrate (YX/S) and yield of cell on oxygen (YX/O) values were respectively obtained at 0.5 vvm and 500 min,1 conditions at t = 2 h as YX/S = 0.72 kg kg,1 and YX/O = 1.49 kg kg,1. The highest instantaneous yield of substrate on oxygen (YS/O) was obtained at 0.5 vvm and 750 min,1 conditions at t = 20 h as YS/O = 8.07 kg kg,1. Copyright © 2005 Society of Chemical Industry [source] Modeling of the catalytic removal of CO and NO in dry combustion gasesAICHE JOURNAL, Issue 3 2010C. Treviño Abstract Catalytic removal of pollutants in dry combustion gases in a planar stagnation-point flow over a platinum foil is studied using both numerical and analytical tools. The governing equations have been numerically integrated with the Newton technique, and the response curve has been obtained as functions of temperature and the mixture concentrations. Using the appropriate stoichiometry, the additional oxygen needed to reduce the NO and to achieve complete oxidation of CO has been obtained. The asymptotic analysis leads to an algebraic equation for the surface coverage of empty sites as a function of two nondimensional parameters: the mass transfer number, relating the residence time to the chemical time (sort of Damköhler number), and a parameter, which relates the desorption rate to the adsorption rate of carbon monoxide and depends strongly on temperature. Critical conditions of ignition (light-off) and extinction are identified and closed form solutions are obtained for these phenomena. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source] Shortcut method for kinetically controlled reactive distillation systemsAICHE JOURNAL, Issue 6 2003J. W. Lee A geometric-based shortcut method for reactive distillation is addressed. The rectification body method for nonreactive distillation, the concept of critical Damköhler numbers, and the geometric design method for reactive distillation are combined with a new eigenvector analysis of pinch points. This shortcut method provides a minimum or reasonable Damköhler number for a given heat duty, as well as the design implication of how to effectively distribute reaction zones inside a column. This method can be used for a fast screening of process design alternatives and for an initialization of rigorous optimization. [source] A Simple Index to Restrain Abnormal Protrusions in Films Fabricated Using CVD under Diffusion-Limited Conditions,CHEMICAL VAPOR DEPOSITION, Issue 4 2004Y. Kajikawa Abstract Cauliflower-like protrusions formed in CVD processes under diffusion-limited conditions have been studied both experimentally and theoretically. Both approaches indicate that the difference in diffusion fluxes to the film and to the protrusions controls the growth of such protrusions. However, direct comparisons of these two approaches have never been done, probably due to the complexity of the theoretical models. To simplify model protrusion growth, we developed a one-dimensional (1D) analytical model by hypothesizing the diffusion of growth species in the boundary layer above a growing film. Based on this model, we propose a non-dimensional quantity, ksf/D, as an index of protrusion growth (D is the diffusion coefficient of the growth species, ks is the surface reaction-rate coefficient, and f is film thickness). This index represents more directly the protrusion growth than does the previously proposed index, the Damköhler number, Da,=,ks,/D, where , is boundary layer thickness. To obtain smooth, protrusion-free films, D/ks should be kept larger than the desired film thickness. By controlling the process conditions to satisfy this index, we successfully fabricated protrusion-free films with SiC deposition from dichlorodimethylsilane (DDS). [source] Experimental study of feasibility in kinetically-controlled reactive distillationAICHE JOURNAL, Issue 2 2005Madhura Chiplunkar Abstract Bifurcation studies predict limited ranges of feasibility for products in certain reactive distillations. These are closely related to the bifurcations in the singular points of dynamic models for simple reactive distillation (isobaric open evaporation with liquid phase reaction). A new dynamic model is described with constant vapor rate together with an experimental study for the reactive distillation of acetic acid with isopropanol to produce isopropyl acetate, catalyzed by Amberlyst-15 ion-exchange resin. An experimental apparatus with real-time measurement of liquid compositions based on Fourier transform infrared (FTIR) spectroscopy is described, and used to follow the composition dynamics at several initial conditions and Damköhler numbers (Da). The experimental results match model predictions that show four regions of behavior. For Da , 1, these show a stable node at acetic acid and several other fixed points as saddles. However, near Da , 2, both isopropanol and acetic acid are stable nodes and a quaternary singular point appears. The presence of two stable nodes requires the presence of a distillation boundary and, therefore, a limited feasibility for the bottom product compositions from continuous reactive distillation. For the reaction rates studied, the model predictions are closely consistent with the experimental findings, and are robust to variations in the vapor rate. These experiments are among the first to analyze the dynamics and feasibility in a kinetically-controlled reactive distillation and are consistent with previous studies for the reaction equilibrium limit, indicating the formation of a reactive azeotrope. © 2005 American Institute of Chemical Engineers AIChE J, 51: 464,479, 2005 [source] Shortcut method for kinetically controlled reactive distillation systemsAICHE JOURNAL, Issue 6 2003J. W. Lee A geometric-based shortcut method for reactive distillation is addressed. The rectification body method for nonreactive distillation, the concept of critical Damköhler numbers, and the geometric design method for reactive distillation are combined with a new eigenvector analysis of pinch points. This shortcut method provides a minimum or reasonable Damköhler number for a given heat duty, as well as the design implication of how to effectively distribute reaction zones inside a column. This method can be used for a fast screening of process design alternatives and for an initialization of rigorous optimization. [source] Soret Diffusion and Non-Ideal Dufour Conduction in Macroporous Catalysts with Exothermic Chemical Reaction at Large Intrapellet Damköhler NumbersTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 3 2007Laurence A. Belfiore Abstract The adiabatic temperature rise in catalytic pellets is predicted from a modified version of the Prater equation. Onsager reciprocal relations for coupled heat and mass transfer are violated in an analysis of thermal diffusion in macroporous catalysts with exothermic chemical reaction when Dufour conduction (i.e., the diffusion-thermo effect) is neglected. In this contribution, Dufour conduction is analyzed for both ideal and non-ideal pseudo-binary gas mixtures that simulate the production of methanol from carbon monoxide and hydrogen. In the diffusion-controlled regime at large intrapellet Damköhler numbers where intermolecular collisions provide the dominant resistance to mass transfer within the catalytic pores, temperatures in the catalytic core could be much greater than predictions based on the original Prater equation when the Prater number exceeds 0.30. The molecular flux of thermal energy includes Fourier's law, the interdiffusional flux, and Dufour conduction. Diffusional mass flux includes Fick's law and the Soret effect. All physicochemical properties of the reactive gas mixture exhibit temperature dependence. There is essentially no difference between maximum intrapellet temperature predictions that include or neglect ideal Dufour conduction when external catalytic surface temperatures range from 300-400 K and thermal diffusion enhances the flux of "smaller" reactants toward the centre of the catalyst. For "large-molecule reactants" that participate in exothermic reactions, thermal diffusion opposes Fick's law and Dufour conduction opposes Fourier's law. Under these conditions, it is demonstrated that core temperatures are overestimated by neglecting both off-diagonal coupling mechanisms (i.e., Soret diffusion and Dufour conduction). Prater numbers greater than unity and unrealistically high gas pressures are required to distinguish between maximum intrapellet temperatures for ideal and real gas simulations, where the latter consider two-body interactions for Lennard-Jones molecules in the virial equation of state. On prédit l'augmentation de la température adiabatique dans les pastilles catalytiques à partir d'une version modifiée de l'équation de Prater. Les relations réciproques d'Onsager pour le transfert de chaleur et de matière couplé sont violées dans une analyse de la diffusion thermique dans les catalyseurs macroporeux avec réaction chimique exothermique lorsque la conduction de Dufour (p.ex., l'effet de thermo-diffusion) est négligée. Dans cet article, on analyse la conduction de Dufour pour des mélanges de gaz pseudo-binaires idéaux et non idéaux qui simulent la production de méthanol à partir d'oxyde de carbone et d'hydrogène. Dans le régime à diffusion contrôlée à grand nombre de Damköhler entre les pastilles pour lesquels les collisions entre les molécules fournit la résistance dominante au transfert de matière à l'intérieur des pores catalytiques, les températures dans le noyau catalytique pourraient être bien plus grandes que les prédictions basées sur l'équation de Prater originale lorsque le nombre de Prater excède 0,30. Le flux moléculaire de l'énergie thermique inclut la loi de Fourier, le flux interdiffusionnel, et la conduction de Dufour. Le flux massique diffusionnel inclut la loi de Fick et l'effet Soret. Toutes les propriétés physicochimiques du mélange de gaz réactif montre une dépendance thermique. Il n'y a essentiellement pas de différence entre les prédictions des températures maximales entre les pastilles qui incluent ou négligent la conduction de Dufour idéale quand les températures de surface catalytiques externes sont comprises entre 300 et 400 K; la diffusion thermique améliore le flux des réactifs «plus petits» vers le centre du catalyseur. Pour les «réactifs composés de grandes molécules» qui participent aux réactions exothermiques, la diffusion thermique s'oppose à la loi de Fick et la conduction de Dufour à la loi de Fourier. Dans ces conditions, il est démontré que les températures de noyau sont surestimées en négligeant les deux mécanismes de couplage hors-diagonales (c.à-d. la diffusion de Soret et la conduction de Dufour). Des nombres de Prater plus grands que l'unité et des pressions de gaz élevées peu réalistes sont nécessaires pour distinguer les températures maximales entre les pastilles entre les simulations de gaz idéales et réelles, en considérant pour ces dernières les interactions à deux corps pour les molécules de Lennard-Jones dans l'équation d'état du viriel. [source] | ||||||||||