Temperature distribution in reactors

The rate of energy transfer is important in determining the temperature distribution in reactors. Also, heats of reaction are significant in connection with equilibrium calculations. The following section deals with data and methods concerning heats of reaction, followed by a discussion of equilibrium conversion. 

FIG. 13. Temperature distribution in reactor block in normal case. 

If an electric current flows through a wire, ihe heat generated internally will result in a temperature distribution between the central axis and the surface of the wire. This type of problem will also arise in chemical or nuclear reactors where heat is generated internally. It is necessary to determine the temperature distribution in such a system and the maximum temperature which will occur. 

Example 8.9 Find the temperature distribution in a laminar flow, tubular heat exchanger having a uniform inlet temperature and constant wall temperature Twall- Ignore the temperature dependence of viscosity so that the velocity profile is parabolic everywhere in the reactor. Use art/P = 0.4 and report your results in terms of the dimensionless temperature... 

Non-uniform temperature distribution in a reactor assumed model based on the Fourier heat conduction in an isotropic medium equality of temperatures of the medium and the surroundings assumed at the boundary critical values of Frank-Kamenetskii number given. 

In the design of an industrial scale reactor for a new process, or an old one that employs a new catalyst, it is common practice to carry out both bench and pilot plant studies before finalizing the design of the commercial scale reactor. The bench scale studies yield the best information about the intrinsic chemical kinetics and the associated rate expression. However, when taken alone, they force the chemical engineer to rely on standard empirical correlations and prediction methods in order to determine the possible influence of heat and mass transfer processes on the rates that will be observed in industrial scale equipment. The pilot scale studies can provide a test of the applicability of the correlations and an indication of potential limitations that physical processes may place on conversion rates. These pilot plant studies can provide extremely useful information on the temperature distribution in the reactor and on contacting patterns when... 

Specific Remarks. The established dependence of the microkinetics on the oxidation state of the catalyst make clear that a) results of kinetic investigations at lower temperatures are different in respect to the mechanistic scheme from those obtained at higher temperatures, b) in a distributed catalytic system in the steady state a distribution of the catalytic steps is possible as a direct consequence of the ambient gas concentration profile and the axial temperature distribution in an extreme situation it is conceivable that at the reactor inlet, another mechanism dominates as at the reactor exit. These two facts can perhaps explain some contradictory results about the same reaction scheme which have been reported in the past by different authors. As stated recently by Boreskov (19) in a review paper, this conclusion holds true for the most catalytic systems under the technical operating conditions. 

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)]... 

The details of the transitions and the vortex behavior depend on the actual channel dimensions and wall-temperature distributions. In general, however, for an application like a horizontal-channel chemical-vapor-deposition reactor, the system is designed to avoid these complex flows. Thus the ideal boundary-layer analysis discussed here is applicable. Nevertheless, one must exercise caution to be sure that the underlying assumptions of one s model are valid. 

Further advancements in the theory of fixed bed reactor design have been made(56,57) but it is unusual for experimental data to be of sufficient precision and extent to justify the application of sophisticated methods of calculation. Uncertainties in the knowledge of effective thermal conductivities and heat transfer between gas and solid make the calculation of temperature distribution in the bed susceptible to inaccuracies, particularly in view of the pronounced effect of temperature on the reaction rate. 

The evaluation of catalyst effectiveness requires a knowledge of the intrinsic chemical reaction rates at various reaction conditions and compositions. These data have to be used for catalyst improvement and for the design and operation of many reactors. The determination of the real reaction rates presents many problems because of the speed, complexity and high exo- or endothermicity of the reactions involved. The measured conversion rate may not represent the true reaction kinetics due to interface and intraparticle heat and mass transfer resistances and nonuniformities in the temperature and concentration profiles in the fluid and catalyst phases in the experimental reactor. Therefore, for the interpretation of experimental data the experiments should preferably be done under reaction conditions, where transport effects can be either eliminated or easily taken into account. In particular, the concentration and temperature distributions in the experimental reactor should preferably be described by plug flow or ideal mixing models. 

By comparison with a fixed-bed gas-liquid reaction, a three-phase fluidized-bed reactor offers the advantage of very high effective thermal conductivity and, therefore, a more uniform temperature distribution in the reactor. Van Driesen and Stewart139 have demonstrated this for large-scale catalytic desulfurization and hydrocracking of heavy petroleum fractions. 

Figure 7 Predicted Temperature Distributions in the Reactor as a Function of the Distance along the Reactor and the Feed Rate.

Application to capacitively-coupled reactors Figure 24a shows the electron temperature distribution in an argon discharge sustained in a one-dimensional parallel plate reactor of the kind shown in Fig. 7. The temperature peaks near the plasma-sheath interface, where the product of the current and electric field (Eq. 31) is highest, and steep gradients develop in that region. Electrons which diffuse towards the electrode during the sheath potential minimum (around r = 0.25 at left electrode, see also Fig. 

Knowledge of the heat transfer characteristics and spatial temperature distributions in packed beds is of paramount importance to the design and analysis of the packed-bed catalytic or non-catalytic reactors. Hence, an attempt is made in this section to quantify the heat transfer coefficients in terms of correlations based on a wide variety of experimental data and their associated heat transfer models. The principal modes of heat transfer in packed beds consist of conduction, convection, and radiation. The contribution of each of these modes to the overall heat transfer may not be linearly additive, and mutual interaction effects need to be taken into account [23,24]. Here we limit our discussion to noninteractive modes of heat transfer. 

The wafer temperature distribution in functioning reactors has been experimentally investigated much less frequently than the flow dynamics or static thermal distributions due to problems involved with experimental temperature measurements of moving components and in varying emissivities. Recently, a scanning pyrometer has been... 

The fast-start test reactor will be used to determine the effect of hot gas temperature, gas hourly space velocity, adjacent environments, and flow patterns on the heat-up rates of catalysts and materials. The temperature progression within the reactor will be a function of the effectiveness of heat transfer between the hot gas and the catalyst. Variations in flow patterns that will drive the design of a fast-start processor include the effect of counter-current versus co-current flow of the gas streams in adjacent zones and of heating the zones in series versus parallel. The temperature distributions in adjacent zones will determine the insulation... 

Fig.l Temperature distribution in the reactor at the H2 flow rate of 88sccm KINETIC EXPERIMENTS... 

Fig. 4-34. Schematic presentation of the axial as well as the radial temperature distribution in a cooled fixed-bed reactor...

PDE 2 The law of conservation of enthalpy (mechanical energy and nuclear energy are usually not considered) describes the temperature distribution in the reactor (Equation 2.2-2) ... 

The thorough mixing of the solid leads to effective gas-solid heat exchange with an excellent heat-transfer characteristic and hence a uniform temperature distribution in the reaction space. Heat-transfer coefficients are typically 100-400 kJm h K and for small particles can be as high as 800 kJm h K. For fine particles and at high reaction rates, circulating fluidized-bed reactors with separation and recycling of the soUd are particularly suitable. 

---