Temperature concentration profiles

Still with reference to the temperature-concentration profile, van Welsenaere and Froment [13] proposed a criterion based on the locus of the temperature maxima that was originally derived for homogeneous tubular reactors but whose validity for batch reactors was also proved. The criterion is discussed here with reference to Fig. 4.8, where the temperature-concentration profiles in a batch reactor are reported for Se = 0.470, 2 = 40, Tro = 7j = 1, and different values of A in the range 0.2-1.16. The maxima of the %(C) curves (continuous lines) define a new curve (dashed line), which has itself a maximum with respect to %. According to the criterion of van Welsenaere and Froment, the latter maximum defines the critical conditions for runaway, i.e., it provides the maximum value of A that allows one to have an easily controlled temperature in the reactor for any given set of the remaining parameters. In Fig. 4.8, the critical point on curve 1 is found at Ac = 0.7. 

Fig. 4.8 Temperature-concentration profiles continuous lines) at A values of (starting from the lowest curve) 0.2,0.4, 0.6, 0.7,0.8, 0.9, 1, 1.1, and 1.16 and locus of temperature maxima dashed line). Critical conditions occur at Ac = 0.7 and Tc = 1.026...

As concerns the first approach, the Thomas and Bowes criterion has been adopted since it makes use of the second and third derivatives of the temperature-time profile, which are easy to obtain numerically. On the contrary, the Adler and Enig and the van Welsenaere and Froment criteria were discarded because of the difficulty in identifying a reference temperature-concentration profile, given the presence of many different reactants and intermediates. 

If the objective in design or operation were optimizing catalyst utilization, then Figure 82 shows that the converter temperature-composition profile should follow curve (a), which corresponds to maximum reaction rate at all points. It is also obvious that in reality this ideal temperature - concentration profile cannot be achieved. For example, a synthesis gas with about 3 % ammonia concentration entering the converter cannot be heated to the ideal temperature by heat exchange because the very high temperature required does not exist in the converter system. To reach the ideal temperature, the first portion of the catalyst must initially operate adiabatically. Consideration of the service life of the catalyst requires that this maximum initial temperature not exceed that recommended by the manufacturer, usually 530 °C (cf. Section... 

The solution of the gas and liquid phase equations supplies parameters such as the droplet temperature, concentration profile within the micro-solution droplet, etc. These data may be used to predict the morphology of particles produced by the... 

Temperature concentration profiles for a quench converter and an intercooled converter. Inlet temperature 200°C, exit temperature 240°C. (Diagram courtesy of ICl.)... 

The various converter types may be characterized by the temperature profile through the catalyst bed(s) or by the temperature/concentration profile (plots of temperature vs ammonia concentration for the gas passing the converter) (see Fig. 6.6a-d below). Such profiles are often compared to maximum reaction rate profiles, see Fig. 6.5 (from [460]). It is seen from this figure that when the temperature is increased (at otherwise constant conditions, including constant ammonia concentration), then the reaction rate will increase up to a maximum value when the temperature is further increased, the rate decreases until it becomes zero at the equilibrium temperature. The temperature/concentration points where maximum rate is achieved describe a curve, the maximum rate curve, which will normally be roughly parallel to the equilibrium curve, but at 30-50 °C lower temperature. It is clear that the minimum catalyst volume would be obtained in a converter where this maximum rate curve were followed. In the early days of ammonia production, available technology limited the obtainable size of the converter pressure shell, and the physical dimensions of the converter... 

One potential problem with this approach is that heat loss from a small scale column is much greater than from a larger diameter column. As a result, small columns tend to operate almost isotherm ally whereas in a large column the system is almost adiabatic. Since the temperature profile in general affects the concentration profile, the LUB may be underestimated unless great care is taken to ensure adiabatic operation of the experimental column. 

Fig. 7. Constitutional supercooling, (a) impurity concentration profile during solidification (b) actual temperature T and equilibrium freezing temperature T...

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. 

In fact, this phenomenon has been used as the basis of a very sensitive detecting system. An example of the temperature profile of an adsorbent as a peak passes over it is shown in figure 2. Unfortunately, it was found almost impossible to produce a true simulation of the concentration profile of the peak from the temperature profile and interest in the detector declined. 

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

The axial dispersion model is readily extended to nonisothermal reactors. The turbulent mixing that leads to flat concentration profiles will also give flat temperature profiles. An expression for the axial dispersion of heat can be written in direct analogy to Equation (9.14) ... 

For the analysis of the chemical structure of flames, laser methods will typically provide temperature measurement and concentration profiles of some readily detectable radicals. The following two examples compare selected LIF and CRDS results. Figure 2.1 presents the temperature profile in a fuel-rich (C/O = 0.6) propene-oxygen-argon flame at 50 mbar [42]. For the LIF measurements, 1% NO was added. OH-LIF thermometry would also be possible, but regarding the rather low OH concentrations in fuel-rich flames, especially at low temperatures, this approach does not capture the temperature rise in the flame front [43]. The sensitivity of the CRDS technique, however, is superior, and the OH mole fraction is sufficient to follow the entire temperature profile. Both measurements are in excellent agreement. For all flames studied here, the temperature profile has been measured by LIF and/or CRDS. 

Overbeek and Booth [284] have extended the Henry model to include the effects of double-layer distortion by the relaxation effect. Since the double-layer charge is opposite to the particle charge, the fluid in the layer tends to move in the direction opposite to the particle. This distorts the symmetry of the flow and concentration profiles around the particle. Diffusion and electrical conductance tend to restore this symmetry however, it takes time for this to occur. This is known as the relaxation effect. The relaxation effect is not significant for zeta-potentials of less than 25 mV i.e., the Overbeek and Booth equations reduce to the Henry equation for zeta-potentials less than 25 mV [284]. For an electrophoretic mobility of approximately 10 X 10 " cm A -sec, the corresponding zeta potential is 20 mV at 25°C. Mobilities of up to 20 X 10 " cmW-s, i.e., zeta-potentials of 40 mV, are not uncommon for proteins at temperatures of 20-30°C, and thus relaxation may be important for some proteins. 

The reactivities of spray-dried sorbents were examined in a fast fluidized bed. The reactor was operated at a carbonation temperature of 50 °C, and a gas velocity of 2 m/s with an initial sorbent inventory of 7 kg to compare CO2 concentration profiles in effluent gas for spray-dried Sorb NH series and NX30 sorbent. Figure 5 shows the comparison of CO2 concentration profiles in effluent gas of Sorb NHR, NHR5, and NX30 in a fast fluidized-bed reactor. The CO2 removals of Sorb NHR and NHR5 were initially maintained at a level of 100 % for a short period of time and quickly dropped to a 10 to 20 % removal level. 

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). 

Vary the temperature of the heating period limit, T ax note the influence on the concentration profiles. 

Figure 5.84. The inlet temperatures were set at 350, 450 and 500 for these axial concentration profiles.

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