Adiabatic mode

Adiabatic temperature growth in a reaction zone is calculated using the following equation [61]  

Where q is the thermal effect of a reaction, AP is the reaction product yield from the volume unit, Cp, p are the reaction mixture average heat capacity and density respectively. 

Depending on the numerical values of the thermal effect q and reaction product yield AP of a chemical process, the increase of temperature AT in a reaction zone can be as high as dozens or even hundreds of degrees, where all the heat is released very rapidly (in seconds or fractions of a second) and in a small area  

Fast polymerisation processes, when R R, demonstrate an averaging of temperature by intensive longitudinal and cross-sectional mixing in such a way, that the MWD and average MW become similar to isothermal conditions at temperatures corresponding to the adiabatic heat of a mixture. However, adiabatic polymerisation opportunities are usually limited by substantial MW reduction at high temperatures and the occurrence of side processes, such as the destruction and crosslinking of molecules. 

The possibility of cooling a feedstock for the process, with the temperature below the boiling point of a reaction mixture, is limited by the boiling point of the cooling agent, such as liquid ethylene (183 K)). The temperature of a mixture 

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To maintain a high polymerization rate at high conversions, reduce the residual amount of the monomer, and eliminate the adverse process of polyacrylamide structurization, polymerization is carried out in the adiabatic mode. An increase in temperature in the reaction mixture due to the heat evolved in the process of polymerization is conductive to a reduction of the system viscosity even though the polymer concentration in it rises. In this case, the increase in flexibility and mobility of macromolecules shifts the start of the oncoming gel effect into the range of deep transformation or eliminates it completely. 

For isothermal and adiabatic modes of operation the energy balance equations developed above will simplify so that the design calculations are not nearly as tedious as they are for the other modes of operation. In the case of adiabatic operation the heat transfer rate is zero, so equation 10.2.10 becomes... 

The answers to these questions are contained in part in the reversible, exothermic nature of the reaction, in the adiabatic mode of operation, and in the characteristics of the catalyst. We explore these issues further in Chapters 5 and 21. 

Isoperibolic instruments have been developed to estimate enthalpies of reaction and to obtain kinetic data for decomposition by using an isothermal, scanning, or quasi-adiabatic mode with compensation for thermal inertia of the sample vessel. The principles of these measuring techniques are discussed in other sections. 

The test is primarily a screening tool relative to reactivity of substances and reaction mixtures and is highly useful for that purpose. The determined initiation temperature is approximate. The energy calculations based on temperature increase and heat capacities are semi-quantitative because of the quasi-adiabatic mode of the system operation. The method of insulating the test cell results in moderate reproducibility of temperature rise and related pressure rise. Another disadvantage is the relatively small sample quantity with respect to full scale quantities thus, there could be a problem in that the sample may not be truly representative. 

Overadiabatic mode a quasi-adiabatic mode in which the (small) energy leaks to the environment are overcompensated for by input of supplementary energy. 

Analysis of the vibrational normal modes obtained at the HF/6-31G(d,p) level of theory in terms of adiabatic modes provides the basis for a quantitative dissection of the... 

TABLE 19. Analysis of the normal modes of cyclopropane using, as internal parameter modes, adiabatic modes from Reference 163 ... 

The chemical equilibrium program is used in the adiabatic mode to calculate temperatures, heats and (crude) pressures for decomposition and oxidation. Stull (Chemical Engineering Progress, Loss Prevention, Vol. 4, p. 16, 1970) showed that these parameters are rough measures of potential reactive hazard. 

Heat, wait, and search the temperature at which the exothermal reaction is detectable is searched using a defined series of temperature steps. At each step, the system is stabilized for a defined time, then the controller is switched to the adiabatic mode. If the temperature increase rate surpasses a level (typically 0.02 Kmin-1), the oven temperature follows the sample temperature in the adiabatic mode. If the temperature increase rate remains below the level, the next temperature step is achieved (Figure 4.4). 

The adiabatic mode the reaction is performed without any exchange at all. This means the heat of reaction will be converted into a temperature increase. The temperature course can be calculated from the heat balance of the reactor ... 

The reaction is slightly exothermic, which is not favorable for the carbon monoxide equilibrium conversion when mnning shift reactors in the adiabatic mode. 

Design Study for the Multi-stage Adiabatic Mode... 

The patents quoted in Table 20 give rather broad temperature ranges. An explanation for this feature is the polymerization mode which is used for the large-scale polymerization of Nd-BR. To the best of our knowledge, adiabatic rather than isothermic modes are used. In the adiabatic mode polymerization heat is neither removed by external nor by evaporation cooling. Therefore,... 

For large (pilot plant) laboratory reactors, on the other hand, the adiabatic mode of operation is generally preferable since natural heat losses play a lesser role and heat removal or supply through the bed is more difficult. In the following part the accuracy of temperature definition in both modes of operation will be analyzed. 

Tubular reactors are commonly used in laboratory, pilot plant, and commercial-scale operations. Because of their versatility, they are used for heterogeneous reactions as well as homogeneous reactions. They can be run with cocurrent or counter-current flow patterns. They can be run in isothermal or adiabatic modes and can be used alone, in series, or in parallel. Tubular reactors can be empty, packed with inert materials for mixing, or packed with catalyst for improved reactions. It is often the process that will dictate the design of the reactor, as discussed in this entry. 

Clearly, the assets of a useful, in itself noncontradictory, and physically based CNM analysis are the internal vibrational motions and their properties as well as the amplitudes that relate internal modes to normal modes. As shown in the previous section, the adiabatic internal modes an are the appropriate candidates for internal modes. Adiabatic modes are based on a dynamic principle, they are calculated by solving the Euler-Lagrange equations, they are independent of the composition of the set of internal coordinates to describe a molecule, and they are unique in so far as they provide a strict separation of electronic and mass effects [18,19]. Therefore, they fulfil the first requirement for a physically based CNM analysis. 

An adiabatic mode analysis of measured vibrational spectra is possible with a simple perturbation theory approach that was already published in the sixties [44]. The basic equation of vibrational spectroscopy (compare with Eq. 19) can be written in matrix form according to Eq. (74)... 

Hence, the experimental situation is described by a change AF of the force constant matrix and AA in the square of the frequencies relative to the calculated force constant matrix and frequencies at some level of ab initio theory. Since AA is known from the differences between experimental and calculated frequencies, it is straightforward to calculate AF and the true force constant matrix. Once the true force constant matrix is determined, one can apply the adiabatic mode analysis in the same way as it is applied for calculated vibrational spectra. 

These examples confirm that the adiabatic mode analysis can be extended with advantage to experimental vibrational spectra provided all experimental frequencies are known. However, even in the case, in which the set of... 

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