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Rate Expression (rate + expression)
Selected AbstractsKinetic isotope effects for the H2 + C2H , C2H2 + H reaction based on the ab initio calculations and a global potential energy surfaceINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 5 2010Liping Ju In the present paper, kinetic isotope effects of the title reaction are studied with canonical variational transition state theory on the modified Wang Bowman (MWB) potential energy surface (PES) (Chem Phys Lett 2005, 409, 249) and the ab initio calculations at the quadratic configuration interaction (QCISD (T, full))/aug-cc-pVTZ//QCISD (full)/cc-pVTZ level. The calculated rate constants for the isotopic variants of this title reaction on the MWB PES have good agreement with those of the present ab initio calculations over the temperature range of 20,5000 K for the forward reactions and 800,5000 K for the reverse reactions, respectively. In particular, the forward rate constants for the title reaction and its isotopically substituted reactions have negative temperature dependences at about 40 K. Rate expressions are presented for all the studied reactions. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 289,298, 2010 [source] Reaction kinetics for the degradation of phenol and chlorinated phenols using Fenton's reagentENVIRONMENTAL PROGRESS & SUSTAINABLE ENERGY, Issue 1 2006Asim K. De Abstract Fenton's reaction is an advanced treatment technology often used for the removal of hazardous and refractory organic compounds from industrial wastewaters. It can effectively be used to degrade phenol and chlorophenols. The initial contaminant concentrations as well as the concentration of hydrogen peroxide and ferrous ions in aqueous solution have a significant effect on the effective degradation of contaminants. For a particular concentration of initial substrate in solution there should be an optimum level of ferrous ion concentration in the reaction medium. Based on experimental observations, a probable mechanism for Fenton's degradation kinetics has been proposed and a rate equation developed. From the rate expression, OH· radical reaction rate constants for the degradation of three compounds,phenol and o- and p-chlorophenols,in Fenton reaction were calculated to have values of 2.53 × 107, 2.38 × 107, and 2.45 × 107 m3 mol,1 s,1, respectively. © 2005 American Institute of Chemical Engineers Environ Prog, 2005 [source] Supercritical water oxidation of quinoline in a continuous plug flow reactor,part 2: kineticsJOURNAL OF CHEMICAL TECHNOLOGY & BIOTECHNOLOGY, Issue 6 2006Lisete DS Pinto Abstract The results of a detailed investigation into the kinetics of quinoline oxidation in supercritical water are presented. The novel kinetic data presented were obtained in a continuously operated, plug flow reactor where parameters such as temperature, pressure, residence time and stoichiometric ratio of oxidant to quinoline were investigated and detailed in the companion paper (Pinto LDS, Freitas dos Santos LMF, Al-Duri B and Santos RCD, Supercritical water oxidation of quinoline in a continuous plug flow reactor,part 1: effect of key operating parameters. J Chem Technol Biotechnol). An induction time was experimentally observed, ranging from 1.5 to 3.5 s, with longer times observed in experiments carried out at lower temperatures. A pseudo-first-order rate expression with respect to quinoline concentration (with oxygen excess) was first adopted and the activation energy of 234 kJ mol,1 and a pre-exponential factor of 2.1 × 1014 s,1 were estimated. Furthermore, an integral power rate model expression was established, attributing a reaction order for quinoline as 1 and for oxygen as 0.36. An activation energy and pre-exponential factor for this model were determined as 224 kJ mol,1 and 3.68 × 1014 M,0.36 s,1, respectively. A global rate expression was then regressed for the quinoline reaction rate from the complete set of data. The resulting activation energy was 226 ± 19 kJ mol,1 and the pre-exponential factor was 2.7 × 1013 ± 2 M,0.1 s,1. The reaction orders for quinoline and oxygen were 0.8 ± 0.1 and 0.3 ± 0.1, respectively. It was shown that the least-squares regression method provided the best-fit model for experimental results investigated in this study. Copyright © 2006 Society of Chemical Industry [source] High-temperature kinetics of the homogeneous reverse water,gas shift reactionAICHE JOURNAL, Issue 5 2004F. Bustamante Abstract The high-temperature rate of reaction of the homogeneous, reverse water,gas shift reaction (rWGSR) has been evaluated in quartz reactors with rapid feed preheating under both low- and high-pressure conditions. The form of the power-law rate expression was consistent with the Bradford mechanism. The Arrhenius expressions for the reaction rate constant, corresponding to the empty reactor, were in very good agreement with the low-pressure results of Graven and Long, but yielded rate constants roughly four times greater than those obtained in our packed reactor and those reported by Kochubei and Moin and by Tingey. Reactor geometry was not responsible for these differences because computational fluid dynamics simulations revealed similar residence time distributions and comparable conversions when the same kinetic expression was used to model the rWGSR in each reactor. Most likely, the empty NETL reactor and the Graven and Long reactor did not attain an invariant value of the concentration of the chain carrier (H) at low reaction times, which led to an overestimation of the rate constant. Conversions attained in an Inconel® 600 reactor operating at comparable conditions were approximately two orders of magnitude greater than those realized in the quartz reactor. This dramatic increase in conversion suggests that the Inconel® 600 surfaces, which were depleted of nickel during the reaction, catalyzed the rWGSR. © 2004 American Institute of Chemical Engineers AIChE J, 50: 1028,1041, 2004 [source] Kinetic behavior of ethylene/1-hexene copolymerization in slurry and solution reactorsJOURNAL OF POLYMER SCIENCE (IN TWO SECTIONS), Issue 11 2005Long Wu Abstract The copolymerization of ethylene and 1-hexene over a spherical polymer/MgCl2 -supported TiCl4 catalyst was studied as a function of the polymerization temperature from 40 to 100 °C in a slurry reactor and from 120 to 200 °C in a solution reactor with triethylaluminum (TEA) as a cocatalyst (1.0,6.8 mmol). The activities increased from 40 to 80 °C and then declined monotonically with increases in the temperature during the slurry and solution polymerizations. The kinetic behavior in the slurry and solution operations was described by the same rate expression. The modeling results indicated that the catalyst had at least two different types of catalytic sites; one site was responsible for the acceleration,decay nature of the activity profiles, whereas the second site resulted in long-term activity. The apparent activation energy for site activation in the slurry operation was 69.9 kJ/mol; no activation energies for site activation could be estimated for the solution operation because the activation process was essentially instantaneous at the higher temperatures. The activation energies for deactivation were 100.3 kJ/mol for the slurry operation and 31.2 kJ/mol for the solution operation. The responses to TEA were similar for the slurry and solution operations; the rates increased with increasing amounts of TEA between 1.0 and 3.4 mmol and then decreased with larger amounts of TEA. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2248,2257, 2005 [source] Kinetics of lactose hydrolysis by ,-galactosidase of Kluyveromyces lactis immobilized on cotton fabricBIOTECHNOLOGY & BIOENGINEERING, Issue 2 2003Quinn Zhengkun Zhou Abstract A mathematic model for describing the Michaelis-Menten-type reaction kinetics with product competitive inhibition and side-reaction is proposed. A multiresponse nonlinear simulation program was employed to determine the coefficients of a four-parameter rate expression. The rate expression was compared with the conventional Michaelis-Menten reaction rate models with and without product inhibition. Experimental data were obtained using ,-galactosidase of Kluyveromyces lactis immobilized on cotton fabric in a batch system at a temperature of 37°C and at various initial concentrations of dissolved lactose ranging from 3,12.5% (w/v). The reaction is followed by concentration changes with time in the tank. Samples were obtained after the outlet stream of the packed bed reactor is mixed in a well-stirred tank. High-performance liquid chromatography (HPLC) was applied to monitor the concentrations of all the sugars (reactants as well as products). The four-parameter rate model is featured with a term to describe the formation of trisaccharides, a side-reaction of the enzymatic hydrolysis. The proposed model simulates the process of lactose hydrolysis and the formation of glucose and galactose, giving better accuracy compared with the previous models. © 2002 Wiley Periodicals, Inc. Biotechnol Bioeng 81: 127,133, 2003. [source] A Kinetic Model for Suspended and Attached Growth of a Defined Mixed CultureBIOTECHNOLOGY PROGRESS, Issue 3 2005Kawai Tam Kinetic experiments were carried out in a semicontinuous wastewater treatment process called self-cycling fermentation (SCF) using a defined mixed culture and various concentrations of synthetic brewery wastewater. The same consortium, which had been previously identified as Acinetobacter sp., Enterobacter sp., and Candida sp., were used in these experiments. The overall rate of substrate removal was attributable to both suspended microbes and the biofilm that formed during the treatment process. A rate expression was developed for the SCF system for a range of synthetic wastewaters containing glucose and various initial concentrations of ethanol and maltose. The data indicated that substrate removal by the suspended cells was directly related to the biomass concentration. However, substrate removal by the biofilm was apparently not affected by the biofilm thickness and was a function of substrate concentration only. [source] Kinetics of liquid phase synthesis of ethyl tert -butyl ether from tert -butyl alcohol and ethanol catalyzed by ,-zeolite supported on monolithINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 5 2002S. Assabumrungrat This paper compared the performance of ,-zeolite and Amberlyst-15 catalysts on a liquid phase synthesis of ethyl tert -butyl ether (ETBE) from ethanol (EtOH) and tert -butyl alcohol (TBA) ,-Zeolite was synthesized and deposited on monolith support. Its structure was confirmed by an XRD measurement and its composition was analyzed by an XRF measurement. It was found that even though the catalytic activity of ,-zeolite was lower than that of Amberlyst-15, the selectivity of ETBE was much higher than that of Amberlyst-15, resulting in almost the same level of ETBE yield. The dehydration of TBA to isobutene (IB) was the major side reaction. The kinetic study of the reaction catalyzed by ,-zeolite supported on monolith was carried out by using a semibatch reactor. The effect of external mass transfer was investigated by varying stirring speeds. The activity-based rate expressions were developed taking into account of water inhibition. Three temperature levels of 323, 333, and 343 K were performed in the study to obtain the parameters in the Arrhenius's equation and the Van't Hoff's equation. © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 34: 292,299, 2002 [source] Rate constants for the reaction of Cl atoms with O3 at temperatures from 298 to 184 KINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 2 2002Simon D. Beach Using the standard, low pressure, discharge-flow technique, with resonance fluorescence in the vacuum ultraviolet to observe Cl atoms, rate constants have been determined for the reaction of Cl atoms with O3 at temperatures down to 184 K. The measured rate constants for 298,184 K fit the Arrhenius expression k(T) = (3.1 ± 1.35) × 10,11 exp((,280 ±100 K)/T) cm3 molecule,1 s,1. The results extend the data on this key atmospheric reaction to slightly lower temperatures. The data are in fairly good agreement with those currently in the literature but suggest that the rate constant is approximately 15% lower than that given by currently recommended rate expressions at the lowest temperatures found in the stratosphere.© 2001 John Wiley & Sons, Inc. Int J Chem Kinet 34: 104,109, 2002 [source] Methane steam reforming at microscales: Operation strategies for variable power output at millisecond contact timesAICHE JOURNAL, Issue 1 2009Georgios D. Stefanidis Abstract The potential of methane steam reforming at microscale is theoretically explored. To this end, a multifunctional catalytic plate microreactor, comprising of a propane combustion channel and a methane steam reforming channel, separated by a solid wall, is simulated with a pseudo 2-D (two-dimensional) reactor model. Newly developed lumped kinetic rate expressions for both processes, obtained from a posteriori reduction of detailed microkinetic models, are used. It is shown that the steam reforming at millisecond contact times is feasible at microscale, and in agreement with a recent experimental report. Furthermore, the attainable operating regions delimited from the materials stability limit, the breakthrough limit, and the maximum power output limit are mapped out. A simple operation strategy is presented for obtaining variable power output along the breakthrough line (a nearly iso-flow rate ratio line), while ensuring good overlap of reaction zones, and provide guidelines for reactor sizing. Finally, it is shown that the choice of the wall material depends on the targeted operating regime. Low-conductivity materials increase the methane conversion and power output at the expense of higher wall temperatures and steeper temperature gradients along the wall. For operation close to the breakthrough limit, intermediate conductivity materials, such as stainless steel, offer a good compromise between methane conversion and wall temperature. Even without recuperative heat exchange, the thermal efficiency of the multifunctional device and the reformer approaches ,65% and ,85%, respectively. © 2008 American Institute of Chemical Engineers AIChE J, 2009 [source] Modeling of Kinetic Expressions for the Reduction of NOx by Hydrogen in Oxygen-Rich Exhausts Using a Gradient-Free Loop ReactorCHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 6 2003E. Frank Abstract The reduction of NOx by hydrogen under lean conditions is investigated in a gradient-free loop reactor. Using this computer-controlled reactor, the reaction rates can be measured under exact isothermal conditions. Systematic variation of the input concentrations of hydrogen, nitric oxide, oxygen as well as reaction temperature provides a complete data set of reaction rates for the given reaction system. A number of kinetic rate expressions were evaluated for their ability to fit the experimental data by using toolboxes of MATLAB. The temperature influence on reaction rate constants and adsorption equilibrium constants were correlated simultaneously using Arrhenius and van't Hoff equations, respectively. The kinetic rate expression based on a Langmuir-Hinshelwood-type model describes the data and the model can be improved by introducing a correction term in square root of hydrogen partial pressure over the range of conditions investigated. [source] Modellierung und Simulation von Chemiereaktoren , Aspekte einer zeitgemäßen IngenieurausbildungCHEMIE-INGENIEUR-TECHNIK (CIT), Issue 1-2 2005J. Hagen Prof. Abstract Die Durchführung chemischer Prozesse in der Technik unter möglichst optimalen Bedingungen setzt ein Grundverständnis für die Arbeitsweise von Chemiereaktoren voraus. Grundlage der Modellierung von Chemiereaktoren sind die Stoff- und Wärmebilanz und die Kinetik der Reaktion. Nur in einfachen Fällen lassen sich analytische Lösungen für Problemstellungen aus der Praxis durch Integration der Differentialgleichungen finden. Das in der Chemieingenieurausbildung eingesetzte Softwarepaket POLYMATH ist sehr anwenderfreundlich und einfach zu erlernen. Es wird u.,a. eingesetzt, um gekoppelte Differentialgleichungen simultan zu lösen und Datenanalyse durch Regression durchzuführen. Mit einem einmal aufgestellten Modell lässt sich der Einfluss verschiedener Reaktionsparameter auf den Gesamtprozess leicht nachvollziehbar simulieren. Modeling and Simulation of Chemical Reactors , Aspects of a Modern Education of Engineers Understanding how chemical reactors work lies at the heart of almost every chemical processing operation. Basis information for modeling and simulation of chemical reactors is needed from mass transfer, heat transfer and chemical kinetics. Only simple problems from practice can be solved analytically by means of integration of the differential equations. POLYMATH is a extremely user-friendly software package which makes modeling easy for the education of chemical engineers and chemists. POLYMATH is used to numerically solve coupled differential equations simultaneously or to find kinetic parameters in rate expressions by regression. Using an identified model the influence of various reaction parameters on the overall process can be simulated easily. [source] | |||||||||||||