Kinetics temperature profiles

Fig. 4a shows several kinetic temperature profiles as a function of time "measured at a fixed station in the lattice. Curve C is the average kinetic temperature of planes 71 to 75 taken from Fig. 3. Other curves are explained in the figure caption. The general rise of these curves beyond was due to thermal diffusion (curve D), as discussed above. These results may be compared with the experimental measurements of McNelly et al. [14]. The similarities between our results and McNelly s are striking, especially our profile A and McNelly s at 14.3 K in their Fig. lb our first sound pulses and corresponded to their "ballistic" phonon pulses L and T, and our heat pulse H H> to their "new pulse. Our second sound velocities, viz., Ci/JZ, etc., were also in agreement with...

The overall benefits of this high efficiency combustor over a conventional bubbling- or turbulent-bed regenerator are enhanced and controlled carbon-bum kinetics (carbon on regenerated catalyst at less than 0.05 wt %) ease of start-up and routiae operabiUty uniform radial carbon and temperature profiles limited afterbum ia the upper regenerator section and uniform cyclone temperatures and reduced catalyst iaventory and air-blower horsepower. By 1990, this design was well estabUshed. More than 30 units are ia commercial operation. 

Much of the variation was caused by the difference in temperature profiles, which were in turn caused in large measure by differences between kinetic models. 

Figure 8.1.4r Simulated temperature profiles with true kinetics and coolant temperature as parameters. ...

This involves knowledge of chemistry, by the factors distinguishing the micro-kinetics of chemical reactions and macro-kinetics used to describe the physical transport phenomena. The complexity of the chemical system and insufficient knowledge of the details requires that reactions are lumped, and kinetics expressed with the aid of empirical rate constants. Physical effects in chemical reactors are difficult to eliminate from the chemical rate processes. Non-uniformities in the velocity, and temperature profiles, with interphase, intraparticle heat, and mass transfer tend to distort the kinetic data. These make the analyses and scale-up of a reactor more difficult. Reaction rate data obtained from laboratory studies without a proper account of the physical effects can produce erroneous rate expressions. Here, chemical reactor flow models using matliematical expressions show how physical... 

This paper surveys the field of methanation from fundamentals through commercial application. Thermodynamic data are used to predict the effects of temperature, pressure, number of equilibrium reaction stages, and feed composition on methane yield. Mechanisms and proposed kinetic equations are reviewed. These equations cannot prove any one mechanism however, they give insight on relative catalyst activity and rate-controlling steps. Derivation of kinetic equations from the temperature profile in an adiabatic flow system is illustrated. Various catalysts and their preparation are discussed. Nickel seems best nickel catalysts apparently have active sites with AF 3 kcal which accounts for observed poisoning by sulfur and steam. Carbon laydown is thermodynamically possible in a methanator, but it can be avoided kinetically by proper catalyst selection. Proposed commercial methanation systems are reviewed. 

The main disadvantage of this technique is that it relies on very accurate temperature measurement, particularly near the top of the temperature profile, so that the position of the 5°F point can be established and the tangent accurately constructed. Also, the end of the bed is predicted only from kinetic considerations when, in fact, other factors may be more important. In practice, however, although this introduces some scatter into successive measurements—as does variation in the duty required of the methanator—the technique has proved very satisfactory. 

Extraordinarily precise kinetic data are required to detect the further temperature dependence of an activation parameter. If A// is temperature-dependent, then the temperature profile will be curved. By analogy with the equation relating AH and AC , we may define the heat capacity of activation by... 

Figure 1. Typical reactor temperature profile for continuous addition polymerization a plug-flow tubular reactor. Kinetic parameters for the initiator 1 = 10 ppm Ea = 32.921 kcal/mol In = 26.492 In sec f = 0.5. Reactor parameter [(4hT r)/ (DpCp)] = 5148.2. [(Cp) = heat capacity of the reaction mixture (p) = density of the reaction mixture (h) = overall heat-transfer coefficient (Tf) = reactor jacket temperature (r) = reactor residence time (D) = reactor diameter].

First we tuned the simulation model using existing operation conditions. Product properties as well as conversion and temperature profile along the reactor axis closely coincided with the actual data after properly choosing the kinetic constants and other operation parameters. 

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. 

The objective of the present work was to determine the influence of the light intensity on the polymerization kinetics and on the temperature profile of acrylate and vinyl ether monomers exposed to UV radiation as thin films, as well as the effect of the sample initial temperature on the polymerization rate and final degree of cure. For this purpose, a new method has been developed, based on real-time infrared (RTIR) spectroscopy 14, which permits to monitor in-situ the temperature of thin films undergoing high-speed photopolymerization, without introducing any additive in the UV-curable formulation 15. This technique proved particularly well suited to addressing the issue of thermal runaway which was recently considered to occur in laser-induced polymerization of divinyl ethers 13>16. 

Recently, such a temperature oscillation was also observed by Zhang et al (27,28) with nickel foils. Furthermore, Basile et al (29) used IR thermography to monitor the surface temperature of the nickel foil during the methane partial oxidation reaction by following its changes with the residence time and reactant concentration. Their results demonstrate that the surface temperature profile was strongly dependent on the catalyst composition and the tendency of nickel to be oxidized. Simulations of the kinetics (30) indicated that the effective thermal conductivity of the catalyst bed influences the hot-spot temperature. 

The simple physical approaches proposed by Mallard and Le Chatelier [3] and Mikhelson [14] offer significant insight into the laminar flame speed and factors affecting it. Modem computational approaches now permit not only the calculation of the flame speed, but also a determination of the temperature profile and composition changes throughout the wave. These computational approaches are only as good as the thermochemical and kinetic rate values that form their database. Since these approaches include simultaneous chemical rate processes and species diffusion, they are referred to as comprehensive theories, which is the topic of Section C3. 

For infinitely fast kinetics, then, the temperature profiles form a discontinuity at the infinitely thin reaction zone (see Fig. 6.11). Realizing that the mass burning rate must remain the same for either infinite or finite reaction rates, one must consider three aspects dictated by physical insight when the kinetics are finite first, the temperature gradient at r = rs must be the same in both cases second, the maximum temperature reached when the kinetics are finite must be less than that for the infinite kinetics case third, if the temperature is lower in the finite case, the maximum must be closer to the droplet in order to satisfy the first aspect. Lorell et al. [22] have shown analytically that these physical insights as depicted in Fig. 6.15 are correct. 

Although Bowman and Seery s results would, at first, seem to refute the suggestion by Fenimore that prompt NO forms by reactions other than the Zeldovich mechanism, one must remember that flames and shock tube-initiated reacting systems are distinctively different processes. In a flame there is a temperature profile that begins at the ambient temperature and proceeds to the flame temperature. Thus, although flame temperatures may be simulated in shock tubes, the reactions in flames are initiated at much lower temperatures than those in shock tubes. As stressed many times before, the temperature history frequently determines the kinetic route and the products. Therefore shock tube results do not prove that the Zeldovich mechanism alone determines prompt NO formation. The prompt NO could arise from other reactions in flames, as suggested by Fenimore. 

A sample of the polymer to be studied and an inert reference material are heated and cooled in an inert environment (nitrogen) according to a defined schedule of temperatures (scanning or isothermal). The heat-flow measurements allow the determination of the temperature profile of the polymer, including melting, crystallization and glass transition temperatures, heat (enthalpy) of fusion and crystallization. DSC can also evaluate thermal stability, heat capacity, specific heat, crosslinking and reaction kinetics. 

Kjaer (K9) gives a very comprehensive study of concentration and temperature profiles in fixed-bed catalytic reactors. Both theoretical and experimental work is reported for a phthallic anhydride reactor and various types of ammonia converters. Fair agreement was obtained, but due to the lack of sufficiently accurate thermodynamic and kinetic data, definite conclusions as to the suitability of the dispersed plug flow model could not be reached. However, the results seemed to indicate that the... 

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