Reactor kinetics, with temperature

Example 3.5 A 1-in i.d coiled tube, 57 m long, is being used as a tubular reactor. The operating temperature is 973 K. The inlet pressure is 1.068 atm the outlet pressure is 1 atm. The outlet velocity has been measured to be 9.96 m/s. The fluid is mainly steam, but it contains small amounts of an organic compound that decomposes according to first-order kinetics with a half-life of 2.1s at 973 K. Determine the mean residence time and the fractional conversion of the organic. 

Reaction rates almost always increase with temperature. Thus, the best temperature for a single, irreversible reaction, whether elementary or complex, is the highest possible temperature. Practical reactor designs must consider limitations of materials of construction and economic tradeoffs between heating costs and yield, but there is no optimal temperature from a strictly kinetic viewpoint. Of course, at sufficiently high temperatures, a competitive reaction or reversibility will emerge. 

Finally, the oxidation reaction has to been run under strict conditions of temperature, which are impossible to be operated in a batch reactor. Indeed, utility stream in the Shimtec reactor was heated to 47 °C, which first initiates the reaction, accelerates its kinetics, and then controls the temperature when the heat of the reaction is too important. In a batch reactor, working with such UF temperature is impossible because of security constraints. It would certainly lead to a reaction runaway. We now consider this question in the next section. 

In this article, a dynamic reaction kinetics for propylene epoxidation on Au/Ti02 is presented. Au/Ti02 catalyst is prepared and kinetics experiments are carried out in a tube reactor. Kinetic parameters are determined by fitting the experiments under different temperatures, and the reliability of the proposed kinetics is verified by experiments with different catalyst loading. 

When a 1 1 mixture of NO and NO2 (i.e., NO2/NOx=0,5) is fed to the SCR reactor at low temperature (200 °C) where the thermodynamic equilibrium between NO and NO2 is severely constrained by kinetics, the NO2 conversion is much greater than (or nearly twice) the NO conversion for all three catalysts. This observation is consistent with the following parallel reactions of the SCR process [6] Reaction (2) is the dominant reaction due to its reaction rate much faster than the others, resulting in an equal conversion of NO and NO2. On the other hand, Reaction (3) is more favorable than Reaction (1), which leads to a greater additional NO2 conversion by Reaction (3) compared with the NO conversion by Reaction... 

A pulse reactor system similar to that described by Brazdll, et al( ) was used to obtain the kinetic data. The reactor was a stainless-steel U-tube, composed of a l/S" x 6 preheat zone and a 3/8" X 6 reactor zone with a maximum catalyst volume of about 5.0 cm. The reactor was Immersed In a temperature controlled molten salt bath. 

The desired product is P, while S is an unwanted by-product. The reaction is carried out in a solution for which the physical properties are independent of temperature and composition. Both reactions are of first-order kinetics with the parameters given in Table 5.3-2 the specific heat of the reaction mixture, c, is 4 kJ kg K , and the density, p, is 1000 kg m . The initial concentration of /I is cao = 1 mol litre and the initial temperature is To = 295 K. The coolant temperature is 345 K for the first period of 1 h, and then it is decreased to 295 K for the subsequent period of 0.5 h. Figs. 5.3-13 and 5.3-14 show temperature and conversion curves for the 63 and 6,300 litres batch reactors, which are typical sizes of pilot and full-scale plants. The overall heat-transfer coefficient was assumed to be 500 W m K. The two reactors behaved very different. The yield of P in a large-scale reactor is significantly lower than that in a pilot scale 1.2 mol % and 38.5 mol %, respectively. Because conversions were commensurate in both reactors, the selectivity of the process in the large reactor was also much lower. 

No rate enhancement was observed when the reaction was performed under microwave irradiation at the same temperature as in conventional heating [47]. Similar reaction kinetics were found in both experiments, presumably because mass and heat effects were eliminated by intense stirring [47]. The model developed enabled accurate description of microwave heating in the continuous-flow reactor equipped with specific regulation of microwave power [47, 48]. Calculated conversions and yields of sucrose based on predicted temperature profiles agreed with experimental data. 

LES/FDF-approach. An In situ Adaptive Tabulation (ISAT) technique (due to Pope) was used to greatly reduce (by a factor of 5) the CPU time needed to solve the set of stiff differential equations describing the fast LDPE kinetics. Fig. 17 shows some of the results of interest the occurrence of hot spots in the tubular LDPE reactor provided with some feed pipe through which the initiator (peroxide) is supplied. The 2004-simulations were carried out on 34 CPU s (3 GHz) with 34 GB shared memory, but still required 34 h per macroflow time scale they served as a demo of the method. The 2006-simulations then demonstrated the impact of installing mixing promoters and of varying the inlet temperature of the initiator added. 

The first-order non-isothermal (FONI) reactor. A continuous, well-stirred magmatic reservoir similar to those discussed above is supposed to be thermally insulated. A dissolved element i precipitates with a temperature-dependent rate of crystallization. Crystallization rate is assumed to obey first-order kinetics with Boltzmann temperature dependence such as... 

Based on experimental results and a model describing the kinetics of the system, it has been found that the temperature has the strongest influence on the performance of the system as it affects both the kinetics of esterification and of pervaporation. The rate of reaction increases with temperature according to Arrhenius law, whereas an increased temperature accelerates the pervaporation process also. Consequently, the water content decreases much faster at a higher temperature. The second important parameter is the initial molar ratio of the reactants involved. It has to be noted, however, that a deviation in the initial molar ratio from the stoichiometric value requires a rather expensive separation step to recover the unreacted component afterwards. The third factor is the ratio of membrane area to reaction volume, at least in the case of a batch reactor. For continuous opera-... 

Rogowski, D. F., Marshall, P., and Fontijn, A., High-temperature fast-flow reactor kinetics studies of the reactions of A1 with Cl, A1 with HCl, and AlCl with CI2 over wide temperature ranges, J. Phys. Chem. 93, 1118 (1989). 

A West Texas gas oil is cracked in a tubular reactor packed with silica-alumina cracking catalyst. The liquid feed mw = 0.255) is vaporized, heated, enters the reactor at 630°C and 1 atm, and with adequate temperature control stays close to this temperature within the reactor. The cracking reaction follows first-order kinetics and gives a variety of products with mean molecular weight mw = 0.070. Half the feed is cracked for a feed rate of 60 m liquid/m reactor hr. In the industry this measure of feed rate is called the liquid hourly space velocity. Thus LHSV = 60 hr Find the first-order rate constants k and k " for this cracking reaction. 

Samples of HY zeolite were exhaustively treated with successive doses of tetramethylsilane in a static reactor at different temperatures in the range 250°-650°C. Rate data for methane evolution were obtained, and the kinetics were discussed. Silicon and some carbon were incorporated, giving gray materials parts of which were calcined in oxygen. Samples of the original H Y, the treated zeolite, and calcined materials were tested for their abilities to accept electrons from perylene and to isomerize cyclopropane and protoadamantane. The treated zeolite had good electron transfer properties but low and high activities for the isomerizations, respectively. However, the opposite was true for the calcined materials. These results are discussed in terms of the acidic properties of the modified zeolites. 

The reduction of citral is performed in situ, in the same autoclave, without any exposure of the catalyst to air. After cooling down the reactor to room temperature and reducing the hydrogen pressure, a solution of 0.9 ml of citral and 0.4 ml of tetradecane (internal standard) in 10 ml of n-heptane is introduced under hydrogen in the autoclave. The temperature and the hydrogen pressure are then raised to respectively 340K and 7.6 MPa. The kinetic of the reaction is followed with time by analysis of samples of the liquide phase. The selectivity for a product X at 100% conversion (Sx) is defined by Sx = [X]10o/[Citral]0. (Citral]0 represents the initial concentration of Citral (2 and E) and and [X]iqo represents the concentration of X at 100% conversion. 

A reaction A——>P is to be performed in a PFR. The reaction follows first-order kinetics, and at 50 °C in the batch mode, the conversion reaches 99% in 60 seconds. Pure plug flow behavior is assumed. The flow velocity should be 1 m s"1 and the overall heat transfer coefficient 1000Wm 2 K"1. (Why is it higher than in stirred tank reactors ). The maximum temperature difference with the cooling system is 50 K. 

For a safe operation, the runaway boundaries of the phenol-formaldehyde reaction must be determined. This is done here with reference to an isoperibolic batch reactor (while the temperature-controlled case is addressed in Sect. 5.8). As shown in Sect. 2.4, the complex kinetics of this system is described by 89 reactions involving 13 different chemical species. The model of the system consists of the already introduced mass (2.27) and energy (2.30) balances in the reactor. Given the system complexity, dimensionless variables are not introduced. 

Kinetics studies were conducted at 65 1°C in a jacketed batch reactor. Five hundred milliliters or 1 L of buffer was added to the reactor and heated to the assay temperature. The buffer pH was chosen according to the optima specified by the enzyme manufacturers. Corn flour (100-300 g/L) was then added to the reactor, along with a specified quantity of either soluble or immobilized amylase to initiate hydrolysis. Samples were collected at regular intervals over 30-60 min, and centrifuged to separate solids. The supernatant was analyzed for sugar content by measuring the %Brix with an optical refractometer. 

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