Temperature and concentration profiles

A schematic representation of temperature and concentration profiles in a temperature-jump experiment. All scales are arbitrary, and the matter to be emphasized is that the temperature jump occurs rapidly compared with the re-equilibration reaction. 

FIGURE 9.3 Temperature and concentration profiles at the point of maximum temperature for the packed-bed reactor of Example 9.1. 

Similar systems in which temperature and concentration profiles are identical will perform the same, i.e. yields and selectivities will be the same in both systems over the whole equipment volume. However, it is impossible to reach all similarities simultaneously. This does not mean that the same overall yields and selectivities cannot be reached. This is possible for systems that are only partially similar (or even not similar at all). 

Equations 13.2.16, 13.2.54, 13.2.56, 13.2.57, and 13.2.65 constitute the set of relations that must be satisfied simultaneously within the volume element. One manner in which these equations may be employed in stepwise fashion to determine temperature and concentration profiles is as follows. 

If ki is less temperature-dependent that 2, the optimum temperature profile is one that starts off at a high temperature to get the first reaction going but then drops to prevent the loss of too much B. Figure 3.10 sketches typical optimum temperature and concentration profiles. Also shown in Fig. 3.10 as the dashed line is an example of an actual temperature that could be achieved in a real reactor. The reaction mass must be heated up to 7. We will use the optimum temperature profile as the setpoint signal. 

If we examine the temperature and concentration profile in the radial direction for the plot in Figure 5-23, we obtain graphs approximately as those in Figure 5-24. 

The time constants for the temperature and concentration profiles in the pellet to change are at least an order of magnitude faster than the time constants for the temperature and concentration profiles in the reactor bed. 

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... 

Solution times using the homogeneous model are 15 to 25% less than that for the full two-phase analysis, although the accuracy of the results may be somewhat in question. Figure 17 shows the axial temperature and concentration profiles under type I operating conditions. Although these simulations appear similar to those obtained with the heterogeneous analysis, no direct comparison is possible, as was explained earlier. 

Simulations show negligible differences in the transient temperature and concentration profiles as a result of this quasi-steady-state approximation. The major advantage of this assumption should be apparent in control system design, where a reduction in the size of the state vector is computationally beneficial or in the time-consuming simulations of the full nonlinear model. 

Fig. 7. Sketch of the velocity, temperature, and concentration profiles according to the simple theory...

Bakhurov and Bores-kov(1947) Radial temperature and concentration profiles c Air Glass, porcelain, metals, etc. Spheres, rings, cylinders, granules 3-19 ... 

To obtain the temperature and concentration profiles along the reactor, equation 1.40 must be solved by numerical methods simultaneously with equation 1.35 for the material balance. 

Figure 1 Basic strategies for manipulating temperature and concentration profiles in chemical reactors.

The full potential of hybrid operation, employing more than one of the fundamental processes for manipulating temperature and concentration profiles, remains to be realized. Special catalysts and reactors must be developed to accommodate the conflicting demands that often arise in the design process. 

Fig. 4.2 Temperature and concentration profiles in adiabatic conditions at Q = 50 (curve 1), 30 (curves 2 and 4) and 10 (curve 3). All curves are obtained with A = 1 and 7rf) = 1 except curve 4, which is obtained with A = 1 and %0 = 0.95...

Table 1 gives the components present in the crude DDSO and their properties critical pressure (Pc), critical temperature (Tc), critical volume (Vc) and acentric factor (co). These properties were obtained from hypothetical components (a tool of the commercial simulator HYSYS) that are created through the UNIFAC group contribution. The developed DISMOL simulator requires these properties (mean free path enthalpy of vaporization mass diffusivity vapor pressure liquid density heat capacity thermal conductivity viscosity and equipment, process, and system characteristics that are simulation inputs) in calculating other properties of the system, such as evaporation rate, temperature and concentration profiles, residence time, stream compositions, and flow rates (output from the simulation). Furthermore, film thickness and liquid velocity profile on the evaporator are also calculated. 

The model describes, within the limits of measuring error, the experimental temperature and concentration profiles quite well over a wide temperature range (more than 100 C) and propylene conversion range (Table I), (Figures 2 - 4). But the reaction orders for propylene and oxygen have only a limited reliability since especially the oxygen concentration along the reactor varied only within narrow limits. Additionally, pressure and flow rate were, for the most part, held constant (Table I). 

A dynamic experimental method for the investigation of the behaviour of a nonisothermal-nonadiabatic fixed bed reactor is presented. The method is based on the analysis of the axial and radial temperature and concentration profiles measured under the influence of forced uncorrelated sinusoidal changes of the process variables. A two-dimensional reactor model is employed for the description of the reactor behaviour. The model parameters are estimated by statistical analysis of the measured profiles. The efficiency of the dynamic method is shown for the investigation of a pilot plant fixed bed reactor using the hydrogenation of toluene with a commercial nickel catalyst as a test reaction. 

In the present work a method is described to extract the information necessary for modelling from only a few dynamic experimental runs. The method is based on the measurement of the changes of the temperature and concentration profiles in the reactor under the influence of forced simultaneous sinusoidal variations of the process variables. The characteristic features of the dynamic method are demonstrated using the behaviour of a nonisothermal-nonadiabatic pilot plant fixed bed reactor as an example. The test reaction applied was the hydrogenation of toluene to methylcyclohexane on a commercial nickel catalyst. 

Figure 6.16 Temperature and concentration profiles in a catalytic distillation column.

Validation of the Global Rates Expressions. In order to validate the global rate expressions employed in the model, temperature and concentration profiles determined by probing the flames on a flat flame burner were studied. Attention was concentrated on Flames B and C. The experimental profiles were smoothed, and the stable species net reaction rates were determined using the laminar flat-flame equation described in detail by Fristrom and Westenberg (3) and summarized in Reference (8). 

Effective thermal conductivity values of porous materials Ap,efr range between 0.1 and 0.5Js IK 1 in gaseous atmospheres [6] and are only slightly larger than those for the gas phase. Straightforward combination of eqs 23 and 37 and integration leads to a simple general result that relates the temperature and concentration profile over a particle ... 

Figure 4. Temperature and concentration profiles for a partial oxidation reaction in a spherical catalyst pellet.

However, the thermal conductivity of the catalyst matrix is usually larger than that of the gas. This means that the external gas-catalyst heat transport resistance exceeds the thermal conduction resistance in the catalyst particles. The temperature and concentration profiles established in a spherical catalyst are illustrated for a partial oxidation reaction in Figure 4. 

Figure 21. Influence of the heating strategy on the temperature and concentration profiles in styrene synthesis. A) Adiabatic B) Isothermal C) Countercurrent heating. EB = ethylbenzene St = styrene.

The work of Rostrup-Nielsen is very informative, but it also raises a number of important questions. How can more realistic temperature and concentration profiles through the reactor be incorporated into a reactor deactivation model Could experimental measurements be performed to determine how sulfur is actually distributed in the catalyst pellets and in the bed and how this distribution changes as a function of time at various H2S concentrations Would it be worthwhile to consider a modification of the model by Wise and co-workers (195,233) for steam reforming in which pore... 

The temperature and concentration profiles will be similar when a = D or a/D = 1. and the ratio a/D is called the Lewis number... 

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