Sharp Temperature Profiles

At the other extreme, temperature profiles are very sharp (large temperature differences between trays) when the separation is easy (high relative volatility). This situation also can cause control problems. A 

A fairly easy solution to this problem is to use multiple temperature measurements over a section of the column in which the temperature profile moves and control an average temperature (Fig. 6.17). 

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Luyben, W. L., "Profile Position Control of Distillation Columns with Sharp Temperature Profiles, AIChE J. 18, 1972, p. 238. 

Figure 11.7 shows the temperature history at a fixed point in the reaction tube as a front passes. The temperature at this point is ambient when the front is far away and rises rapidly as the front approaches. Hence, a polymerization front has a very sharp temperature profile (Pojman et al., 1995b). Figure 11.7 shows five temperature profiles measured during frontal free-radical polymerization of methacrylic acid with various concentrations of BPO initiator. Temperature maxima increase with increasing initiator concentration. For an adiabatic system, the conversion is directly proportional to the difference between the initial temperature of the unreacted medium and the maximum temperature attained by the front. The conversion depends not only on the type of initiator and its concentration but also on the thermodynamic characteristics of the polymer (Pojman et al., 1996b). 

Tray temperatures are controlled in both columns. A 1 min deadtime is included in the temperature loops. In the water system, a single temperature in the methanol column is controlled. In the DMSO and chlorobenzene systems, an average temperature is controlled because of the sharp temperature profile. 

Since there is a sharp temperature profile in the acetone column, an average temperature is used by measuring the temperatures on three trays Stage 4 at 360 K, Stage 5 at 388 K, and Stage 6 at 395 K, giving an average of 381 K. 

In general ordered conformations are promoted by favourable non-covalent interactions, inflexible secondary structure, and efficiency of packing, and inhibited by loss of conformational entropy, energy of hydration, intermolecular electrostatic repulsion, structural irregularities, and branching. The balance of these opposing drives is often delicate, and may be tipped by relatively small perturbations. For example, thermally induced order-disorder transitions, which may or may not be accompanied by a gel-sol transition, have been observed for a number of polysaccharide systems (8,13,14), and show the sharp temperature profile characteristic of a co-operative process. 

The use of multiple temperature measurements was proposed by Grote and independently (but much later) by Luyben. This technique is useful for distillation columns in which a large temperamre change occurs over a few trays (a sharp temperature profile). This is found in columns where the components have widely differing boiling points (peanut butter and hydrogen would be an extreme example). 

A polymerization front has a very sharp temperature profile, and profile measurements can provide much useful information. The temperature profiles help elucidate the reasons for incomplete conversion and the stmcture of the front. Two temperature profiles measured during FP of methacrylic add are shown in Figure 8. The first profile is for benzoyl peroxide in methacrylic add at different initial temperatures. The other profile was obtained for the same monomer with tert-butyl peroxide (tBPO). Conversion is directly proportional to the... 

A polymerization front has a sharp temperature profile, (77) and profile measurements can provide much useful information. From Figure 4 it may appear that the chemical reaction is occurring in a zone about 0.5 cm in width. This is incorrect. If the chemical reaction has an infinitely high energy of activation, the chemical reaction will occur in an infinitely narrow region. In actuality, the 0.5 cm represents a pre-heat zone. The temperature below that at which significant chemical reaction occurs follows an exponential profile, which can be described with the following relationship in terms of... 

The sharp temperature profile in C2 presents control difficulties. The process gain between a single tray temperature, for example, stage 7, and reboiler heat input is very large. This means that the controller gain must be small, which results in poor load rejection. A simple solution is to measure several temperatures on trays in the column and control the average temperature. 

It is instructive to examine predictions of the Bunimovich et al. model. The temperature profiles in Fig. 16a at times within a half cycle are about the same as the profiles for 6 vol% S02 predicted by Xiao and Yuan (1996) and shown in Fig. 14a. Note that curves 1 and 5 in Fig. 16 are those at the switching time and show the inversion when the flow direction changes. The remarkable prediction of the Table XI model is the sharp variation of the S03 concentration in the melt with position in the bed that develops about 1 min after the direction changes and persists for about 13 min. Curves (c) to (f) show there is a substantial change in the complexes present in the melt with position in the bed and that the complex concentrations... 

Figure 9.18 shows experimental values of the shell thickness plotted as a function of the thickness predicted by the theoretical model. A very good agreement was obtained for large variations of the wall temperature and the amount of hexa in the formulation. Visual inspection of the shell sand revealed the presence of a distinct hard layer with a characteristic yellow color. The rest of the sand falls easily upon mold inversion, which means that the cure proceeds through the development of sharp conversion profiles. 

The design value of the overall heat transfer coefficient U between the process gas and the liquid coolant used in Chapter 5 was 142 J s-1 K-1 m-2. The resulting temperature profile is shown at the top of Figure 6.40. There is a sharp peak that occurs very near the inlet end of the reactor. This peak temperature is only about 5 K higher than the coolant because of the large value of U. In order to be able to demonstrate the use of a peak temperature controller, the value of U is drastically decreased to 14.2 J s-1 K-1 m-2, which changes the temperature profile to that shown at the bottom of Figure 6.40. Now the... 

Since the methanation reaction is strongly exothermic, a sharp temperature rise can be measured across the reaction zone in the catalyst bed. Most methanation reactors are designed with a number of thermocouples that monitor the position of the exotherm. A strong indicator of the amount and rate of methanation catalyst deactivation is the position of the temperature profile in the catalyst bed and its rate of movement over time. A record of the temperature profile should be kept to detect any movement during the first one to two years of operation. An estimate of future life can then be made. ... 

Sulfur, usually present as H2S, has to be below 0.1 ppm, but even with such low concentrations, the catalyst is slowly poisoned. The ZnO adsorbs the sulfur and it finally transforms into bulk ZnS. When the ZnO is exhausted in a given layer of the catalyst, the H2S causes deactivation of the copper by sintering. The poisoning process moves through the catalyst as a relatively sharp front and can be seen in the change of the catalyst temperature profile over time [619], [620] (Figure 64). 

In general, other native starch dispersions will be exhibit similar viscosity versus temperature profiles as in Figure 8-7, while cross-linked starch dispersions, due to limited granule rupture, will not exhibit a sharp decrease in viscosity of the segment CD. The t] versus 7 profiles of a 5% CWM STD obtained at values of cu from 1.26 to 31.38rads , 3% strain, andaheatingrateof2.1°C min (Figure 8-8)followed the equation (Tattiyakul and Rao, 2000) ... 

In near-isothermal systems, it is assumed that the heat transfer between mobile and stationary phases is slow. This causes an additional band broadening contribution to appear [53]. Such a contribution can be especially important on the front of a sharp concentration profile. On the other hand, the heat transfer between the chromatographic column and the outside is fast enough to prevent the formation of a temperature front and of an associated secondary mass transfer zone. 

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