Axial steady state temperature profiles

Baddour [26] retained the above model equations after checking for the influence of heat and mass transfer effects. The maximum temperature difference between gas and catalyst was computed to be 2.3°C at the top of the reactor, where the rate is a maximum. The difference at the outlet is 0.4°C. This confirms previous calculations by Kjaer [120]. The inclusion of axial dispersion, which will be discussed in a later section, altered the steady-state temperature profile by less than O.S°C. Internal transport effects would only have to be accounted for with particles having a diameter larger than 6 mm, which are used in some high-capacity modern converters to keep the pressure drop low. Dyson and Simon [121] have published expressions for the effectiveness factor as a function of the pressure, temperature and conversion, using Nielsen s experimental data for the true rate of reaction [119]. At 300 atm and 480°C the effectiveness factor would be 0.44 at a conversion of 10 percent and 0.80 at a conversion of 50 percent. 

This figure clearly illustrates that the range within which multiple steady states can occur is very narrow. It is true that, as Hlavacek and Hofmann calculated, the adiabatic temperature rise is sufficiently high in ammonia, methanol and oxo-synthesis and in ethylene, naphthalene, and o-xylene oxidation. None of the reactions are carried out in adiabatic reactors, however, although multibed adiabatic reactors are sometimes used. According to Beskov (mentioned in Hlavacek and Hofmann) in methanol synthesis the effect of axial mixing would have to be taken into account when Pe < 30. In industrial methanol synthesis reactors Pe is of the order of 600 and more. In ethylene oxidation Pe would have to be smaller than 200 for axial effective transport to be of some importance, but in industrial practice Pe exceeds 2500. Baddour et al. in their simulation of the TVA ammonia synthesis converter found that the axial diffusion of heat altered the steady-state temperature profile by less than 0.6°C. Therefore, the length of... 

To simplify the energy balance, the work done on the reacting fluid is neglected and constant heat capacity and reaction enthalpy is assumed. The steady state temperature profile of the fluid without the influence of axial conductivity can be calculated by considering the energy balance (Equation 5.31) simultaneously with the material balance (Equation 5.32). 

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. 

Fig. 4 Steady-state axial profile for the shell, metal and tube temperature corresponding to Fig. 3.

The axial screw temperature profiles for the screw speeds are shown in Fig. 10.21. These profiles were constructed from the data set shown in Fig. 10.20 by using the data collected at steady state. As shown in this figure, the temperature profile would approximate the model developed by Cox and Fenner [30], but the temperature distribution is more complicated than this simple model. 

It has been demonstrated that kg can be estimated by analogy with the Graetz-Nusselt problem governing heat transfer to a fiuid in a duct with constant wall temperature (SH= Nut) [30] and that the axial concentration profiles of NO and of N H 3 provided by the 1D model are equivalent and almost superimposed with those of a rigorous multidimensional model of the SCR monolith reactor in the case of square channels and of ER kinetics, which must be introduced to comply with industrial conditions for steady-state applications characterized by substoichiometric NH3 NO feed ratio, that is, a[Pg.401]

Comparison of steady-state profiles shows that neglecting axial mass diffusion has very little effect on the temperature and concentration profiles even though the axial gradients are significant. However, Figure 16 shows that neglecting the axial thermal dispersion in the gas does affect the solution... 

Figure 21 shows the simulated dynamic behavior of the gas temperatures at various axial locations in the bed using both the linear and nonlinear models for a step change in the inlet CO concentration from a mole fraction of 0.06 to 0.07 and in the inlet gas temperature from 573 to 593 K. Figure 22 shows the corresponding dynamic behavior of the CO and C02 concentrations at the reactor exit and at a point early in the reactor bed. The axial concentration profiles at the initial conditions and at the final steady state using both the linear and nonlinear simulations are shown in Fig. 23. The temporal behavior of the profiles shows that the discrepancies between the linear and nonlinear results increase as the final steady state is approached. Even so, there are only slight differences (less than 2% in concentrations and less than 0.5% in temperatures) in the profiles throughout the dynamic responses and at the final steady state even for this relatively major step-input change.

A detailed experimental exploration of temperature profiles in the reactor packed with the CuO catalyst showed near at the extinction boundary three steady-state axial temperature profiles which were easily reproducible (Fig. 19). There is no simple explanation of these effects so far 55). 

Fig. 1.24. Steady-state, axial temperature profiles for the gasoline reformerin Figure 1.21. (a) High load 33 kWi Hv (b) low load 3 kWlhv ...

Steady State Axial Temperature Profiles In Wall Cooled Fixed Bed Reactors... 

Steady-State Behaviour The dashed line in Figure 2 shows a typical experimental axial temperature profile for conditions listed in Table I. The banded region in the vicinity of the hot spot includes those points (labelled a, b and c) in which radial temperature profiles were also measured using moving thermocouples. There, the upper and lower lines represent the highest measured temperature and the wall temperature, respectively, at those axial points. 

Figure 2. Typical steady-state axial temperature profiles. Key -A-A-, simulated catalyst surface temperature -V-V-, simulated gas temperature and...

The sensitivity of the axial temperature profile to the feed and salt bath temperatures is shown in Figures 6 and 7, respectively. Figure 6 shows the response to a ramp decrease in the feed temperature by 2 C over a period of 10 minutes. For small perturbations (up to 5°C), the hot spot travels downstream and passes through a maximum value before reaching its new steady-state. When the disturbance is reversed, the hot spot moves upstream in a similar manner and returns to the former steady-state. 

Imagine two solid bars brought into contact as indicated in Fig. 2-14, with the sides of the bars insulated so that heat flows only in the axial direction. The materials may have different thermal conductivities, but if the sides are insulated, the heat flux must be the same through both materials under steady-state conditions. Experience shows that the actual temperature profile through the two materials varies approximately as shown in Fig. 2-14b. The temperature... 

Figure 1 shows an example of the time development of the spatial profiles of Ethanol concentration, temperature and fluid velocity for a 10m reactor tube with Ea=340 kJ/mol and ko=6.46E21/sec [6], Heat transfer is kept constant at 4kJ/s/m2/K. Steady state is reached at about lOOsec. The bath temperature of 500°C is too low for complete oxidation under these conditions. Pivot spacing increases with reactor length and the axial mixing coefficients D are 0.5m2/sec. The fluid velocity is constant beyond z=2m. 

The effects of axial mixing and of overall heat transfer are shown in figure 2, where the curves 1 and 2 show the steady state profiles at zero axial mixing, while curves 0 and 3 are calculated with D=0.5m2/s. Curves 2 and 3 are calculated from the temperature dependent overall heat transfer coefficients of [4] which are higher than the value of 4kJ/s/m2/K used for... 

Simulations performed at the same conditions, but without axial heat conductivity, showed identical temperature profiles as the ones given in Fig. 10, while results at a low mass flow, typically 0.83 kg m7 sec, showed a temperature of the solid phase at the inlet of the reactor that is lower than the temperature calculated from the model with axial heat conductivity. This phenomenon was also observed by Lie et al. [35] and indicates that axial heat conduction in the solid phase can be neglected under steady-state conditions when the fluid flow is large enough. 

Figure 3 Effect of feed temperature on the steady-state axial temperature profile during hydrogenation of cyclohexene over 2% Pd/C (To = 70-76 °C, P = 138 bar, H2/cyclohexene = 1 1, CO2 = 90%, Olefin WHSV = 20 h ).

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