Exothermic reaction temperature rise factors

Theoretical work has been done on the effectiveness factor for nonisothermal particles. Fig. 3.13.1-1 shows the results of the computations by Weisz and Hicks [1962] for y = EIRT = 20. For > 0.1, that is, for sufficiently exothermic reactions, the effectiveness factor can exceed the value of 1. In such a case the temperature rise, which increases the value of the rate constant, would more than offset the decrease in reactant concentration Cas, so that fA averaged over the particle exceeds that at surface conditions. The converse is true for endothermic reactions. 

The chemical reaction rate is generally a function of a reactant concentration and temperature. In the case of an exothermic reaction, unless the heat of reaction is removed, an increase in temperature may result in a runaway reaction. For most homogeneous reaction, the rate is increased by a factor of 2 or 3 for every 10°C rise in temperature. This is represented by... 

It is more common to find that AH° and AS° have the same sign (Table 17.2, III and IV). When this happens, the enthalpy and entropy factors oppose each other. AG° changes sign as temperature increases, and the direction of spontaneity reverses. At low temperatures, AH° predominates, and the exothermic reaction, which may be either the forward or the reverse reaction, occurs. As the temperature rises, the quantity TAS° increases in magnitude and eventually exceeds AH°. At high temperatures, the reaction that leads to an increase in entropy occurs. In most cases, 25°C is a low temperature, at least at a pressure of 1 atm. This explains why exothermic reactions are usually spontaneous at room temperature and atmospheric pressure. 

For exothermic reversible reactions the situation is different, for here two opposing factors are at work when the temperature is raised—the rate of forward reaction speeds up but the maximum attainable conversion decreases. Thus, in general, a reversible exothermic reaction starts at a high temperature which decreases as conversion rises. Figure 9.5 shows this progression, and its precise values are found by connecting the maxima of the different rate curves. We call this line the locus of maximum rates. 

Such reactions have been used to explain the three limits found in some oxidation reactions, such as those of hydrogen or of carbon monoxide with oxygen, with an "explosion peninsula between the lower and the second limit. However, the phenomenon of the explosion limit itself is not a criterion for a choice between the critical reaction rate of the thermal theory and the critical chain-branching coefficient of the isothermal-chain-reaction theory (See Ref). For exothermic reactions, the temperature rise of the reacting system due to the heat evolved accelerates the reaction rate. In view of the subsequent modification of the Arrhenius factor during the development of the reaction, the evolution of the system is quite similar to that of the branched-chain reactions, even if the system obeys a simple kinetic law. It is necessary in each individual case to determine the reaction mechanism from the whole... 

Figure 3.6 shows that, for exothermic reactions (0 > 0), the effectiveness factor may exceed unity. This is because the increase in rate caused by the temperature rise inside the particle more than compensates for the decrease in rate caused by the negative concentration gradient which effects a decrease in concentration towards the centre of the particle. A further point of interest is that, for reactions which are highly exothermic and at low value of the Thiele modulus, the value of tj is not uniquely defined by the Thiele modulus and the parameters 0 and e. The shape of... 

For exothermic reactions (fi > 0) a sufficient temperature rise due to heat transfer limitations may increase the rate constant Ay. and this increase may offset the diffusion limitation on the rate of reaction (the decrease in reactant concentrations CA), leading to a larger internal rate of reaction than at surface conditions CAs. This, eventually, leads to 17 > 1. As the heat of reaction is a strong function of temperature, Eq. (9.24) may lead to multiple solutions and three possible values of the effectiveness factor may be obtained for very large values of /I and a narrow range of catalytic reactions, (3 is usually <0.1, and therefore, we do not observe multiple values of the effectiveness factor. The criterion... 

In an exothermic reaction the temperature increases as the conyersion increases. At low conversions the rising temperature increases the rate more than it is reduced by the fall in reactants concentration. Normally the conversion will be greater than for isothermal operation. However, undesirable side reactions and other factors may limit the permissible temperatures. In these cases successful design depends on effective removal of the heat of reaction to prevent excessive temperatures (hot spots). In general, the same methods are employed as for adding energy in endothermic reactions. 

The temperature rise of an exothermic reaction is dependent on three factors the heat of the reaction, the heat capacity of the system, and the heat loss of the system The temperature rise of a reaction in a system with no heat loss, the adiabatic temperature rise ( N T), is dependent on the heat of the reaction and the heat capacity of the system, and independent of scale To determine the adiabatic temperature rise of this system, the CDMP/sulfuric acid solution, prewarmed to 30°C, was added all at once to a dewar flask containing the nitric acid/sulfuric acid solution which was also prewarmed to 30°C We observed a temperature rise of 17°C over a period of 4 minutes, with a temperature drop of 1 5°C over the next 4 minutes (Figure 3) We therefore estimated the AT to be about 18.5°C Since this temperature rise was, in theory, independent of scale, we could predict that the large scale nitration reaction would not rise to a temperature of exothermic activity Based on these results, we considered this revised nitration procedure to be safe upon scale up to the pilot plant ... 

For exothermic processes the reactions cause a temperature rise inside the particle. This usually leads to increased values of the rate constants. This increase of the rate constants can sometimes overcompensate for the lower concentrations (compared to those in the bulk fluid) caused by the diffusion limitations in the particle. As a result, the reaction rate becomes higher than the reaction rate that is obtained with the concentrations in the bulk phase and temperature. Consequently, the effectiveness factor exceeds 1 This effect is particularly emphasized at small values of the Thiele modulus. The catalyst effectiveness factors as a function of Thiele modulus at different values of the Prater numbers are illustrated in Figure 9.15. 

One of the most interesting features is that for > 0 (exothermic), there are regions where > 1. This behavior is based on the physical reasoning that with sufficient temperature rise caused by heat transfer limitations, the increase in the rate constant, Ic,., more than offsets the decrease in reactant concentration, C so that the internal rate is actually larger than that at surface conditions of C/ and T, , leading to an effectiveness factor greater than unity. The converse is, of course, true for endothermic reactions. 

The generation of heat inside a pellet due to reaction and its transport through the pellet can greatly affect the reaction rate. For endothermic reactions, there is a fall in temperature within the pellet. As a result, the rate falls, thus augmenting the retarding effect of mass diffusion. On the other hand, for exothermic reactions, there is a rise in temperature within the pellet. This leads to an increase in rate which can more than offset the decrease due to lowered concentration. Thus the effectiveness factor can actually be greater than one. 

Two other factors give rise to the departure of the sample s actual temperature from the desired programmed temperature. One is associated with the enthalpy of the event. An endothermic reaction will consume the heat supplied rather than raise the temperature of the sample. Conversely, an exothermic reaction can lead to the temperature getting ahead of the intended temperature. If the sample combusts, the temperature can get far ahead. The... 

Ammonia s3mthesis is a reversible and exothermic reaction without any side reaction. With the rising of temperature the reaction rate constant increases while the equilibrium constant decreases. For a given reactant composition, the reaction rate is affected by two contradictory factors thus there exists an optimum reaction temperature. 

Ben Franklin is credited with the saying, Waste not want not. I don t think that he was referring to chemical waste but chemical waste is a major factor in scale-up. In the laboratory, waste from filtrates, unused distillation fractions, etcetera is of inconsequential quantity but as the scale increases, it can mean the success or failure of a project. In the laboratory, reactions are often run in dilute solutions. On a larger scale, to minimize waste and to be able to make more material, reactions are commonly much more concentrated sometimes they are run without solvent When a solvent is used, it is best if it can be recycled. If the solvent must be disposed of, it adds to the cost and is not as environmentally friendly. When there is less solvent to act as a heat sink, heats of reaction become more pronounced. Lacking other controls, an exothermic reaction run at 20% concentration will have a much greater temperature rise than one run at 2%. The characterization of the waste is also important. Whenever possible the waste should not be contaminated with highly toxic or environmentally unfriendly chemicals. 

Fires in mines can be caused by many factors but one of the major causes is spontaneous combustion ( spon com ). Spon com occurs when air is allowed to percolate through organic materials, including coal. Through a progressive series of adsorptive, absorptive, and chemical processes, heat is produced, which causes the temperature of the material to rise. As we discussed in the introduction to this chapter, fires occur when the temperature of the material reaches its minimum self-heating temperature, where a continuous exothermic reaction is sustained and the material goes into thermal runaway. 

A typical, unsealed plot of versus the nonisothermal Thiele modulus is shown in Figure 9.10. Two additional parameters that contain the thermal factors make their appearance here the Arrhenius number EJRT which contains the important activation energy E and the dimensionless parameter P, which reflects the effect due to the heat of reaction and the transport resistances. For p = 0 (i.e., for a vanishing heat of reaction or infinite thermal conductivity), the effectiveness factor reduces to that of the isothermal case. P > 0 denotes an exothermic reaction, and here the rise in temperature in the interior of the pellet is seen to have a significant impact on E which may rise above unity and reach values as high as 100. This means that the overall reaction rate in the pellet is up to 100 times faster than would be the case at the prevailing surface conditions. This is due to the strong exponential dependence of reaction rate on temperature, as expressed by the Arrhenius relation... 

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