Temperature adiabatic rise

It is obvious that reducing cr (i.e., increasing the dilution), results in a reduction in the adiabatic temperature rise and, thus, can help to keep the reaction temperature within acceptable constraints. The global heat balance over the system, with all heat generation terms included, is required to obtain the actual adiabatic temperature rise. From the safety perspective, the adiabatic temperature rise is a useful design parameter, although it must be emphasized that it shows only a maximum effect and not a rate. 

Reactions in a system with a high ATad may lead to a high reactor temperature and may, for example, boil off all of a solvent diluent. As a consequence, organic materials may decompose into small, gaseous molecules, which will result in an increase in pressure. Consider, for example, an 

In order to obtain accurate results, this function should be accounted for when the temperature of a reaction mass tends to vary over a wider range. However, in the condensed phase the variation of heat capacity with temperature is small. Moreover, in case of doubt and for safety purposes, the specific heat capacity should be approximated by lower values. Thus, the effect of temperature can be ignored and generally the heat capacity determined at a (lower) process temperature is used for the calculation of the adiabatic temperature rise. 

The central term in Equation 2.5 enhances the fact that the adiabatic temperature rise is a function of reactant concentration and molar enthalpy. Therefore, it is dependant on the process conditions, especially on feed and charge concentrations. The right-hand term in Equation 2.5, showing the specific heat of reaction, is especially useful in the interpretation of calorimetric results, which are often expressed in terms of the specific heat of the reaction. Thus, the interpretation of calorimetric results must always be performed in connection with the process conditions, especially concentrations. This must be accounted for when results of calorimetric experiments are used for assessing different process conditions. 

The higher the adiabatic temperature rise, the higher the final temperature will be if the cooling system fails. This criterion is static in the sense that it gives only an indication of the excursion potential of a reaction, but no information about the dynamics of the runaway. 

As an example, for the assessment of the potential severity of the loss of control of a reaction, Table 2.3 shows the effect of typical energies of a desired synthesis reaction and decomposition and their equivalents in the form of adiabatic 

Mechanical potential energy height at 10km 200km 

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Fig. 21. Single absorption equilibrium-stage diagram where the equiUbrium curve is for 8% SO2, 12.9% the diagonal lines represent the adiabatic temperature rise of the process gas within each converter pass the horizontal lines represent gas cooling between passes, where no appreciable conversion...

The curve in Figure 21 represents SO2 equiUbrium conversions vs temperature for the initial SO2 and O2 gas concentrations. Each initial SO2 gas concentration has its own characteristic equiUbrium curve. For a given gas composition, the adiabatic temperature rise lines can approach the equiUbrium curve but never cross it. The equiUbrium curve limits conversion in a single absorption plant to slightly over 98% using a conventional catalyst. The double absorption process removes this limitation by removing the SO from the gas stream, thereby altering the equiUbrium curve. 

TABLE 23-2 Multibed Reactors, Adiabatic Temperature Rises ... 

Ethylene oxidation was studied on 8 mm diameter catalyst pellets. The adiabatic temperature rise was limited to 667 K by the oxygen concentration of the feed. With the inlet temperature at 521 K in SS and the feed at po2, o=T238 atm, the discharge temperature was 559 K, and exit Po =1.187 atm. The observed temperature profiles are shown on Figure 7.4.4 at various time intervals. The 61 cm long section was filled with catalyst. 

The screw compressor can be evaluated using the adiabatic work equation. Discharge temperature can be calculated by taking the adiabatic temperature rise and dividing by the adiabatic efficiency then multiplying by the... 

VSP experiments allow the comparison of various process versions, the direct determination of the wanted reaction adiabatic temperature rise, and the monitoring of the possible initiations of secondary reactions. If no secondary reaction is initiated at the wanted reaction adiabatic final temperature, a further temperature scan allows the... 

Adiabatic temperature rise Maximum increase in temperature that can be achieved. This increase occurs when the substance or reaction mixture decomposes or reacts completely under adiabatic conditions. The adiabatic temperature rise follows from ... 

The kinetic rate constant may be computed from the adiabatic temperature rise [38] or the isothermal heat release [37]. For a second order reaction ... 

Determine discharge temperature, Tg, using adiabatic temperature rise Equation 12-62. Use k values for gas or mixture or calculate them by Equation 12-4. 

The basic advantages of this process are (a) elimination of a mechanical device (recycle gas compressor) for controlling the adiabatic temperature rise, (b) combination of CO shift with methanation, (c) significant increase in byproduct steam recovery, and (d) significant capital advantages. 

These results have been fit to experimental data obtained for the reaction between a diisocyanate and a trifunctional polyester polyol, catalyzed by dibutyltindilaurate, in our laboratory RIM machine (Figure 2). No phase separation occurs during this reaction. Reaction order, n, activation energy, Ea, and the preexponential factor. A, were taken as adjustable parameters to fit adiabatic temperature rise data. Typical comparison between the experimental and numerical results are shown in Figure 7. The fit is quite satisfactory and gives reasonable values for the fit parameters. Figure 8 shows how fractional conversion of diisocyanate is predicted to vary as a function of time at the centerline and at the mold wall (remember that molecular diffusion has been assumed to be negligible). 

Example 7.6 Suppose a liquid-solid, heterogeneously catalyzed reaction is conducted in a jacketed, batch vessel. The reaction is A B. The reactants are in the liquid phase, and the catalyst is present as a slurry. The adiabatic temperature rise for complete conversion is 50 K. The reactants are charged to the vessel at 298 K. The jacket temperature is held constant at 343 K throughout the reaction. The following data were measured ... 

Thermal Effects in Addition Polymerizations. Table 13.2 shows the heats of reaction (per mole of monomer reacted) and nominal values of the adiabatic temperature rise for complete polymerization. The point made by Table 13.2 is clear even though the calculated values for T dia should not be taken literally for the vinyl addition polymers. All of these pol5Tners have ceiling temperatures where polymerization stops. Some, like polyvinyl chloride, will dramatically decompose, but most will approach equilibrium between monomer and low-molecular-weight polymer. A controlled polymerization yielding high-molecular-weight pol)mier requires substantial removal of heat or operation at low conversions. Both approaches are used industrially. 

Rates of polymerization of isobutylene in n-hexane by TiCfi with either water or trichloracetic acid as co-catalyst at —90 to 0°C have been estimated by Plesch from the adiabatic temperature rise. His... 

CO oxidation tests on Au supported on various metal oxides were undertaken at low CO concentrations, where the adiabatic temperature rise in the bed is negligible. Since CO oxidation is highly exothermic, when high CO concentrations are present in the feed 1%), and at high conversions, the adiabatic temperature rise in the catalyst bed due to the heat of reaction may be as high as 100 C. Therefore, it is important to monitor the catalyst bed temperature when high CO concentrations are present in the feed. 

In order to derive specific numbers for the temperature rise, a first-order reaction was considered and Eqs. (10) and (11) were solved numerically for a constant-density fluid. In Figure 1.17 the results are presented in dimensionless form as a function of k/tjjg. The y-axis represents the temperature rise normalized by the adiabatic temperature rise, which is the increase in temperature that would have been observed without any heat transfer to the channel walls. The curves are differentiated by the activation temperature, defined as = EJR. As expected, the temperature rise approaches the adiabatic one for very small reaction time-scales. In the opposite case, the temperature rise approaches zero. For a non-zero activation temperature, the actual reaction time-scale is shorter than the one defined in Eq. (13), due to the temperature dependence of the exponential factor in Eq. (12). For this reason, a larger temperature rise is foimd when the activation temperature increases. 

In order to show how specific guidelines for the reactor layout can be derived, the maximum allowable micro-channel radius giving a temperature rise of less than 10 K was computed for different values of the adiabatic temperature rise and different reaction times. For this purpose, properties of nitrogen at 300 °C and 1 atm and a Nusselt number of 3.66 were assumed. The Nusselt number is a dimensionless heat transfer coefficient, defined as... 

In order to exemplify the potential of micro-channel reactors for thermal control, consider the oxidation of citraconic anhydride, which, for a specific catalyst material, has a pseudo-homogeneous reaction rate of 1.62 s at a temperature of 300 °C, corresponding to a reaction time-scale of 0.61 s. In a micro channel of 300 pm diameter filled with a mixture composed of N2/02/anhydride (79.9 20 0.1), the characteristic time-scale for heat exchange is 1.4 lO" s. In spite of an adiabatic temperature rise of 60 K related to such a reaction, the temperature increases by less than 0.5 K in the micro channel. Examples such as this show that micro reactors allow one to define temperature conditions very precisely due to fast removal and, in the case of endothermic reactions, addition of heat. On the one hand, this results in an increase in process safety, as discussed above. On the other hand, it allows a better definition of reaction conditions than with macroscopic equipment, thus allowing for a higher selectivity in chemical processes. 

Substantial heat-transfer intensification was also described for a special micro heat exchanger reactor [104]. By appropriate distribution of the gas-coolant stream, the axial temperature gradient can be decreased considerably, even under conditions corresponding to very large adiabatic temperature rises, e.g. of about 1400 °C. 

Xu et al. [124] numerically computed the adiabatic temperature rise in a micro channel due to viscous heating and expressed their results by a correlation based on dimensionless groups. They introduced a dimensionless temperature rise AT = AT/Tjgf with a reference temperature of 1 K. The correlation they found is given by... 

GP 1] [R 1] Numerical simulations prove that isothermal processing is possible in micro reactors even under severe reaction conditions which correspond to an adiabatic temperature rise up to 1400 °C [98]. 

An ignition experiment at 1-butene concentrations as high as 5% was performed to test instability in reaction behavior as an indication of unsafe operation (5% 1-butene in air 0.1 MPa 400 °C) [103]. The degree of conversion increased linearly and converged without any sign of instability. The power input corresponded to 6.5 W with an adiabatic temperature rise of more than 2000 °C. Plugging, however, was the major concern under these severe conditions. 

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