Adiabatic temperature course

Figure 2.3 Adiabatic temperature course as a function of time for reactions with different energies. The S-shape is only visible for lower energies.

Besides these purely static aspects, the dynamic behavior of an adiabatic batch reactor must also be considered. The adiabatic temperature course is a function of the thermal properties of the reaction mixture. The adiabatic temperature increase influences the final temperature as well as the rate of the temperature increase. For highly exothermal reactions, even for small increase in conversion, the increase in temperature is important (see Section 2.4.3). 

Different factors may strongly affect the behavior of autocatalytic reactions, especially if we consider the adiabatic temperature course that is used to predict the TMRad. Such effects are shown by numerical simulations using the Berlin model. 

Figure 12.5 Effect of the degree of autocatalysis on the adiabatic temperature course using different values of the parameter P 0, 5, 10, and 100. The initial temperature is 100°C. The dashed line represents a temperature alarm level set at 110°C.

Figure 12.6 Effect of the initial conversion of the substance on the adiabatic temperature course. These numerical simulations were performed with a parameter P of 10.

Figure 12.11 Adiabatic temperature course of an autocatalytic reaction (solid line) compared to the zero-order approximation (dashed line). Both reactions have a maximum heat release rate of lOOWkg-1 at 200°C and an energy of500)g . ...

Figure 12.14 Adiabatic temperature course obtained using the kinetic data from the DSC thermograms from different starting temperatures 120, 130, 140, and 150°C. Temperature in °C, time in hours.

Figure 12.15 Adiabatic temperature course obtained from the AKTS software with the confidence interval for 10% relative error on the energy.

It is often necessary to employ more than one adiabatic reactor to achieve a desired conversion. The catalytic oxidation of SOj to SO3 is a case in point. In the first place, chemical equilibrium may have been established in the first reactor and it would be necessary to cool and/or remove the product before entering the second reactor. This, of course, is one good reason for choosing a catalyst which will function at the lowest possible temperature. Secondly, for an exothermic reaction, the temperature may rise to a point at which it is deleterious to the catalyst activity. At this point, the products from the first reactor are cooled prior to entering a second adiabatic reactor. To design such a system, it is only necessary to superimpose on the rate contours the adiabatic temperature paths for each of the reactors. The volume requirements for each reactor can then be computed from the rate contours in the same way as for a... 

Figu re 6.7 Polytropic reaction Temperature course and heat release rate of the reaction corresponding to the example substitution reaction. The reactor is initially heated to 35°C, then left heating adiabatically to 44°C (period a), where maximum cooling is switched on (period b). Finally controlled cooling is applied, once the final temperature of 100°C is reached (period c). 

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 ... 

In the chapters devoted to reactors, it was considered that a situation is thermally stable due to the relatively high heat removal capacity of reactors compensating for the high heat release rate of the reaction. We considered that in the case of a cooling failure, adiabatic conditions were a good approximation for the prediction of the temperature course of a reacting mass. This is true, in the sense that it represents the worst case scenario. Between these two extremes, the actively cooled reactor and adiabatic conditions, there are situations where a small heat removal rate may control the situation, when a slow reaction produces a small heat release rate. These situations with reduced heat removal, compared to active cooling, are called heat accumulation conditions or thermal confinement. 

This set of equations describes the behaviour of multiple, first order reactions in a tubular reactor using the relative conversion to desired product Xp and to undesired product Xx, the dimensionless temperature T and the dimensionless reactor length Z. The is characterized by the ratio of the reaction heats H in addition to kR, TR, y and p. The operating and design are determined by PC, the dimensionless cooling medium temperature Da, the dimensionless residence time in the reactor U, the dimensionless cooling capacity per unit of reactor volume and ATacp the dimensionless adiabatic temperature rise for the desired reaction, which, of course, depends on the initial concentration of the reactant A. 

The most challenging design has concerned a combustor for gas turbines [9,22]. In gas turbines, the adiabatic temperature is moderated by large excess air and the combustion intensity is in order of magnitudes higher than in furnaces, because of size constraints and, of course, because of pressure. Flameless oxidation has been sometimes described as volume combustion in contrast to surface combustion that hints to a turbulent flame front, where volumetric reaction rate is certainly much higher than in the former case. The basic question was then will a flameless oxidation system cope with the required... 

The decisive characteristic of an adiabatic temperature/time-course of a batch process is the enormous self-acceleration of the temperature rise over time. This self-acceleration process is responsible for the fact that corrective action is possible only in the initial maloperation phase. Therefore it is of great importance to have a measure at hand which indicates how long it takes for the adiabatic process to reach a phase of un-... 

Reaction (124) is very weakly exothermic (AH - 50 kJ mol ), which would lead to an adiabatic temperature of reaction of the order of 300 °C. This result validates the approximation of a quasi-isothermal explosion. But, of course, a more or less important fraction of the H radicals recombine, in a homogeneous or heterogeneous way, thus... 

The most common example is the exothermic gas/solid reaction, that was discussed in section 5323, In the steady state, the temperature difference between the solid surface and the gas may be approximately equal to the adiabatic temperature rise of the reaction in Ae gas phase. This will happen when the surface temperature rises so much that not the chemical reaction but the mass transfer is rate determining. The consequences for the temperature control of the reactor are then considerable. When only the temperature of the continuous phase can be controlled effectively, the temperature of the dispersed solid, where the reactions take place, has to be calculate. Of course, it is better to measure the temperature of the solid also, if at all possible, because for an effective temperature control one needs both. 

Of course, for an accurate calculation of the temperatures, the physical constants have to be written as functions of T and an integration such as in eq. (8.2) has to be made. Nevertheless, the following approximation is elucidating. Since for gases Pr s Sc, it follows from addition of die last two equations, that the temperature of the solid particles throughout the reactor is the same, and equals approximately the entrance temperature plus the total adiabatic temperature rise, i.e. the exit temperature T ... 

The energy released when the process under study takes place makes the calorimeter temperature T(c) change. In an adiabatically jacketed calorimeter, T(s) is also changed so that the difference between T(c) and T(s) remains minimal during the course of the experiment that is, in the best case, no energy exchange occurs between the calorimeter (unit) and the jacket. The themial conductivity of the space between the calorimeter and jacket must be as small as possible, which can be achieved by evacuation or by the addition of a gas of low themial conductivity, such as argon. 

Kinetically Limited Process. Basically, this system limits the temperature rise of each adiabatically operated reactor to safe levels by using high enough space velocities to ensure only partial approach to equilibrium. The exit gases from each reactor are cooled in external waste heat boilers, then passed forward to the next reactor, and so forth. This resembles the equilibrium-limited reactor system as shown in Figure 8, except, of course, that the catalyst beds are much smaller. 

The cylinder is again placed on the non-conducting stand, and the working substance reversibly and adiabatically expanded till its temperature falls to T2. The course of. expansion is represented by the curve CD. 

In order to develop the safest process the worst runaway scenario must be worked out. This scenario is a sequence of events that can cause the temperature runaway with the worst possible consequences. Typically, the runaway starts with failure that results in an adiabatic course of exothermic reaction, inducing secondary reactions that proceed with a high thermal effect. Such a. sequence of typical events is shown in Fig. 5.4-55 (after Gygax, 1988-1990 Stoessel, 1993). It starts with, for instance, a cooling failure at time tx when the temperature is at the set level, Tv ,- Then the temperature rises up to the Maximum Temperature for Synthetic Reaction (MTSR) within the time Atn. Assuming adiabatic conditions MTSR = + ATad,R... 

A typical graph of k as a function of temperature is shown in Figure 3.6. The increasing slope shows the importance of determining a maximum allowable temperature in process equipment so that the heat removal capacity is not exceeded. Under adiabatic conditions, the temperature will reach the calculated maximum only if the reactants are depleted. The actual maximum temperature in a system with some heat dissipation will, of course, be somewhat lower than the calculated value. 

The Sikarex safety calorimeter system and its application to determine the course of adiabatic self-heating processes, starting temperatures for self-heating reactions, time to explosion, kinetic data, and simulation of real processes, are discussed with examples [1], The Sedex (sensitive detection of exothermic processes) calorimeter uses a special oven to heat a variety of containers with sophisticated control and detection equipment, which permits several samples to be examined simultaneously [2]. The bench-scale heat-flow calorimeter is designed to provide data specifically oriented towards processing safety requirements, and a new computerised design... 

Clearly, in the absence of a radial temperature or velocity gradient, no radial mass transfer can exist unless, of course, a reaction occurs at the bed wall. When a system is adiabatic, a radial temperature and concentration gradient cannot exist unless a severe radial velocity variation is encountered (Carberry, 1976). Radial variations in fluid velocity can be due to the nature of flow, e.g. in laminar flow, and in the case of radial variations in void fraction. In general, an average radial velocity independent of radial position can be assumed, except from pathological cases such as in very low Reynolds numbers (laminar flow), where a parabolic profile might be anticipated. 

---