Longitudinal temperature profile

Longitudinal temperature profile and conversion in a reactor for the hydrogenation of nitrobenzene... 

What does the longitudinal temperature profile look like for given inlet temperatures and/or wall temperature profiles Are the hot spots excessive for reasons of selectivity, catalyst deactivation, etc ... 

This problem indicates the considerations that enter into the design of a tubular reactor for an endothermic reaction. The necessity of supplying thermal energy to the reactor contents at an elevated temperature implies that the heat transfer considerations will be particularly important in determining the longitudinal temperature profile of the reacting fluid. This problem is based on an article by Fair and Rase (1). 

Figure 6.9 Temperature profiles in the FEHE (a) longitudinal temperature profile and (b) temperature-enthalpy diagram.

Butakov found that high-temperature polymerization can proceed under stable conditions if the reactor is constructed in the form of a horizontal elongated spiral. This reactor is characterized by longitudinal temperature profiles with a clearly defined hot point . 

The graphs also show that for a cross-sectional profile, the temperature differences around the cross section of the tube are lower in the case of the HRS. In the case of the recuperative system, there is a noticeable (around 25°C) temperature difference between the top and bottom sides of the tube. This difference is due to heating by the upper, hotter part and cooling by the lower, colder part of the tube. In the case of HRS, the temperature difference between both ends of the tube is negligible, because of cyclic work of the system and uniform, symmetrical, and longitudinal temperature profile. However, higher temperature at the bottom side, than that on the top, can be observed in contrast with the recuperative system. In this case it is because the considered measurement point is located closer to the lower part of the tube. This difference is negligible and in the result, the cross-sectional temperature profile is also more uniform. 

Longitudinal temperature profile of the radiant tube for recuperative and regenerative systems at different reference point temperature Ttrp (a) 840°C, (b) 880°C, (c) 950°C, and (d) 1000°C. 

In order to compare both systems, the effective energy from the radiant tube resulting from radiative heat flux, some assumptions were done due to different maximum temperatures on the right side longitudinal temperature profiles. Temperature profiles were displaced to have the same maximum temperature. This temperature was chosen as the average temperature, Tavmax/ from maximum values, Tmax/ in each test. All temperature points were multiplied by factor f, Equation 24.1. 

Longitudinal temperature profiles corrected to the same average maximum temperature. 

Figure10.2 Longitudinal temperature profiles at autothermal operation for a H2-air mixture of equivalence ratio 0.6 in (a) a 250 pm gap size ceramic-frame microreactor and (b) a 300 pm gap size thin stainless-steel-based frame microreactor, for different thermal spreaders (material indicated) of thickness 3.2 mm adhered to the framework (redrawn from [6, 7]).

The longitudinal temperature profile is given by the model already presented in the general introduction concerning the axial heat balance along the reactor. 

The smaller contribution to solvent proton relaxation due to the slow exchanging regime also allows detection of second and outer sphere contributions (62). In fact outer-sphere and/or second sphere protons contribute less than 5% of proton relaxivity for the highest temperature profile, and to about 30% for the lowest temperature profile. The fact that they affect differently the profiles acquired at different temperature influences the best-fit values of all parameters with respect to the values obtained without including outer and second sphere contributions, and not only the value of the first sphere proton-metal ion distance (as it usually happens for the other metal aqua ions). A simultaneous fit of longitudinal and transverse relaxation rates provides the values of the distance of the 12 water protons from the metal ion (2.71 A), of the transient ZFS (0.11 cm ), of the correlation time for electron relaxation (about 2 x 10 s at room temperature), of the reorienta-tional time (about 70 x 10 s at room temperature), of the lifetime (about 7 x 10 s at room temperature), of the constant of contact interaction (2.1 MHz). A second coordination sphere was considered with 26 fast exchanging water protons at 4.5 A from the metal ion (99), and the distance of closest approach was fixed in the range between 5.5 and 6.5 A. 

The equations describing the concentration and temperature within the catalyst particles and the reactor are usually non-linear coupled ordinary differential equations and have to be solved numerically. However, it is unusual for experimental data to be of sufficient precision and extent to justify the application of such sophisticated reactor models. Uncertainties in the knowledge of effective thermal conductivities and heat transfer between gas and solid make the calculation of temperature distribution in the catalyst bed susceptible to inaccuracies, particularly in view of the pronounced effect of temperature on reaction rate. A useful approach to the preliminary design of a non-isothermal fixed bed catalytic reactor is to assume that all the resistance to heat transfer is in a thin layer of gas near the tube wall. This is a fair approximation because radial temperature profiles in packed beds are parabolic with most of the resistance to heat transfer near the tube wall. With this assumption, a one-dimensional model, which becomes quite accurate for small diameter tubes, is satisfactory for the preliminary design of reactors. Provided the ratio of the catlayst particle radius to tube length is small, dispersion of mass in the longitudinal direction may also be neglected. Finally, if heat transfer between solid cmd gas phases is accounted for implicitly by the catalyst effectiveness factor, the mass and heat conservation equations for the reactor reduce to [eqn. (62)]... 

A conventional flow apparatus shown in Figure 1 was used. It consisted of gas-flow controlling devices, tubular reactor in an electric furnace, Liebig condenser, liquid trap, etc. The temperature profile along the longitudinal axis of the reactor was measured by a thermocouple. The reaction zone is defined here as the part of the reactor above 350°C. The reaction temperature means the highest temperature in the reaction zone. 

In all above- and below-cited publications in this field (e.g. 84 ) the problem was solved in order to calculate the tensors of strain velocity and stress, to prognosticate alteration of longitudinal viscosity, profile of alteration of the thickness of material over the height of the film sleeve (by coordinate on the central line of the sleeve counted from the outlet face of the extrusion head) and configuration of the sleeve ( bubble ) and also to solve thermal problems in order to determine the dependency of melt temperature upon height (or time) and to forecast the position of the crystallization... 

Heat transfer studies on fixed beds have almost invariably been made on tubes of large diameter by measuring radial temperature profiles (1). The correlations so obtained involve large extrapolations of tube diameter and are of questionable validity in the design of many industrial reactors, involving the use of narrow tubes. In such beds it is only possible to measure an axial temperature profile, usually that along the central axis (2), from which an overall heat transfer coefficient (U) can be determined. The overall heat transfer coefficient (U) can be then used in one--dimensional reactor models to obtain a preliminary impression of longitudinal product and temperature distributions. 

For the purposes of this discussion, deposition temperature is defined as the gas temperature close to the substrate. Due to the exhaust flow in the deposition hoods and the natural rising of hot air, the deposition temperature profile is skewed above the flame s longitudinal axis. The actual temperature of the substrate in the deposition zone depends upon the substrate material — size, absorption and emissivity characteristics — as well as the dwell time of the flame on one area of the substrate and whether or not any cooling is being applied to the substrate. 

This behaviour can be explained if we consider the wall and the fluid temperatures as a function of the channel length (Figure 23). The longitudinal profiles are presented for two Reynolds numbers. For the first, with a Reynolds number much higher than 500 (fie = 4004), it is seen that the two temperature profiles are parallel as expected for uniform heat flux boundary conditions. For the second Reynolds number, smaller than 500 (Re = 381), the two profiles are no longer parallel. 

Agostini shows that for Bi > 3 the convective effects are prominent and for Bii < 0.3 the longitudinal heat flux produces an effect on the temperature profiles. The definition given by Commenge was calculated for counter-current heat exchangers and leads to different valnes. Evalnating these nnmbers would be useful in ensuring the heat flux is purely transversal. 

The form of the radial temperature profile in a nonadiabatic fixed-bed reactor has been observed experimentally to have a parabolic shape. Data for the oxidation of sulfur dioxide with a platinum catalyst on x -in. cylindrical pellets in a 2-in.-ID reactor are illustrated in Fig. 13-9. Results are shown for several catalyst-bed depths. The reactor wall was maintained at 197°C by a jacket of boiling glycol. This is an extreme case. The low wall temperature resulted in severe radial temperature gradients, more so than would exist in a commercial reactor, where the wall temperature would be higher. The longitudinal profiles are shown in Fig. 13-10 for the same experiment. These curves show the typical hot spots, or maxima, characteristic of exothermic reactions in a nonadiabatic reactor. The greatest increase above the reactants temperature entering the bed is at the center,... 

The longitudinal and transverse relaxation times for both samples 2 and 5 show in Figures 1 and 2 inverse temperature profiles typical of adsorbed systems for all the coverages except the 100% RH for sample 5. This implies a shallow Ti minimum, a drastic spreading out of the Ti curve, and may include a shoulder effect or maximum as T2 increases with temperature (20,21). Logarithmic Gaussian temperature-independent (B = constant) distributions have been used to model these systems and is discussed below. Because of the similarity of these profiles, the motional characteristics of the adsorbed water is probably similar for the different conditions listed in Figures 1 and 2. The data in Table II support this view since (except for sample 5 at 100% RH)... 

Zones, migrating along the capillary, possess different mean temperatures and thus also longitudinal temperature gradients exist and zones exhibit different longitudinal temperature distributions (temperature profiles). This is important for zone identification that is based on the measurements of conductivity, potential gradient or UV absorption. At the ideal state, the concentration and the temperature in the entire zone are constant. The actual state is, however, characterized by... 

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