Flat Temperature Profiles

In attempts to overcome the problem of flat temperature profiles, differential temperature has been used in some systems. Looking at the difference in temperature between two trays helps to reduce the influence of pressure on the temperature signals. However, it does not handle changes in pressure drop. 

This nonmonotonic behavior can lead to feedback control instability. On one side of the hump the controller should be direct acting. On the other it should be reverse acting. So we must be careful when applying differential temperature control structures. 

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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 other geometries, the time to melt is given in Table 16.10. This analysis assumes that the heat transfer is very fast in the melted zone, giving a flat temperature profile in this zone. If this is not the case, then the expression becomes more complicated. 

The heat from the environment is transfened into the particle layer by layer and become the sensible heat of the cellulose substance. This situation remains until the outside layer of particle reaches an enough high temperature of about 660K, at which, the chemical reactions start to come into effect. Due to the reaction heat needed for pyrolysis, the temperature increase is suppressed significantly, and is turned to the chemical reaction stage of rather flat temperature profiles. The tenqierature is held between 650 1C to 750 K by endothermic pyrolytic reactions, which is much lower than the environmental temperature of 1073K. 

Generally, a flat temperature profile is maintained at the outlet of the three main reactors, with GC outlet remaining 20 - 30°F lower. Maximum exotherm allowed in the three main reactors is around 50°F. GC exotherm is generally limited to 25°F. This is to ensure a more controlled and uniform deactivation of the catalyst system. 

The activity was also tested where char combustion was conducted in the regenerator. The average conditions for this run are given in Table VI. In this run 32 lbs. of char were burned, thereby exposing the acceptor to 0.73 lb. ash/lb. MgO CaO inventory. The combustion was trouble free, giving essentially flat temperature profiles and complete burnout of the carbon. No ash fusion difficulty was experienced. 

During the liquid phase FT program completed at the demonstration scale slurry column at the La Porte Alternative Fuels Development unit it was found that the system was essentially isothermal, with a temperature difference smaller than 2°C along the height of the reactor. ExxonMobil has reported that their AGC-21 FT reactor can be operated with an essentially flat temperature profile. All these publications confirmed the earlier results observed at the Rheinpreussen-Koppers demonstration scale plant the temperature gradient in the (slurry FT) reactor never amounted to more than 1°C . 

Spinning the products of combustion helps greatly. Sometimes there is too much spin, but more often there is not enough. Even with the degree of spin controlled to give a flat temperature profile in the combustion chamber, the pit bottom temperature may be 100 to 200 °F (55 to 110 °C) hotter at the opposite end than at the burner end. 

Controi Above the Load(s) With the advent of the fuel-directed burner, two temperature locations in a longitudinal direction can be held at the same or a constant difference in temperature. Therefore, firing across the width of a furnace above the product can be controlled to a nearly flat temperature profile regardless of the product size or location. 

If a long furnace is fired from one end, the cooling gases set up temperature differentials that affect the load heating rate. (See fig. 5.6.) Attaining a flat temperature profile along the length of a one-end-fired furnace requires burners with adjustable spin controlled by AT sensors. (See chap. 6.)... 

These cases show that calculating an accurate zone temperature profile is difficult. A flat temperature profile for part of a zone may be correct, but with most zones and firing rates, the temperature profile must ascend or decline to reflect the dynamic heat exchange rates in furnace zones. 

For our experimental conditions the highest value of Biot number is estimated to be 0.3. Although this value does not fulfil the classical requirements for a flat temperature profile distribution within the slab (which requires Biot < 0.1), the slab "cooling time" is practically unaffected by slab conductivity, therefore the so-called "regular regime" conditions still apply (Isachenko et al., 1987). In other words, the maximum Biot number for achieving a flat temperature profile is ... 

WhenFo = 0 then p =0 (flat temperature profile before cooling) ... 

Ciambelli P, Palma V, Palo E, Villa P (2010) Autothermal catalytic reactor with flat temperature profile. PCT Int. Appl. WO 2010/016027... 

Obviously, when a column or a section is flooded or dumping, a flat temperature profile can be obtained since there is no fractionation taking place. 

It was also noted from Tables 2.2.2 and 2.5.1 that a< 0 and p> 0 for FRRPP behavior. This made a and P counteract each other while there was a need to increase the effeet of the exotherm. It was also possible for a and p to counteract each other by having a> 0 and p< 0. For now, a combined dimensionless quantity is introduced to incorporate the opposite signs of a and p, as well as the strong effect of the reaction exotherm while keeping the result of a flat temperature profile (6< 1.01 at = 0) in the system. This quantity is symbolized by Ch (pronounced see-enye) and defined as... 

It seems to be evident that the cutoff value of -1,000 for Ch is supported experimentally and could then be used to quantitatively characterize the necessary and sufficient condition for the occurrence of the FRRPP process. A final note here is that this criterion corresponds to strict FRRPP process, wherein all aspects of polymerization control occur with a flat temperature profile. If the flat temperature profile is to be relaxed, then the cutoff value of Ch will have to be less than —1,000 but below zero. This will reach even smaller polymer-rich domain particle sizes in Fig. 2.5.2. 

Process as other polyolefin materials, using flat temperature profile of 215°C. Processing methods listed in Table 2. 

A recent experimental and modeling study of an annular reactor confirmed the good heat characteristics of this configuration resulting in fast heating and quenching and rather flat temperature profiles [46]. 

A novel monolithic reactor-heat exchanger has been constructed and operated in five different modes. Experiments were conducted with the oxidation of carbon monoxide over copper chromite pelleted catalysts. The experimental temperatures of reactants and coolants, and concentrations agree with computations with a cell model. Virtually flat temperature profiles can be obtained in the co-current mode. 

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