Calculated adiabatic reaction temperature

Calculated Adiabatic Reaction Temperature (CART) See Flame Temperature. 

We will review the basic quantities of thermodynamics energy, temperature, heat, work, and the ideal gas law. These quantities will be used to explain the principles of thermophysics and thermochemistry, which will be applied to the specific reactions of combustion and detonation. Using the thermochemical data of heats of detonation or explosion, we will see how to calculate adiabatic reaction temperatures. These data in turn will be used to analyze or predict pressures of explosions in closed vessels. We shall also see how, using thermochemical data, to predict detonation velocities and detonation pressures. 

The calculated adiabatic reaction temperature (CART) also provides some indication of a compound s potential hazard. Known explosive compounds have CART values higher than 1500K. 

Adiabatic Reaction Temperature (T ). The concept of adiabatic or theoretical reaction temperature (T j) plays an important role in the design of chemical reactors, gas furnaces, and other process equipment to handle highly exothermic reactions such as combustion. T is defined as the final temperature attained by the reaction mixture at the completion of a chemical reaction carried out under adiabatic conditions in a closed system at constant pressure. Theoretically, this is the maximum temperature achieved by the products when stoichiometric quantities of reactants are completely converted into products in an adiabatic reactor. In general, T is a function of the initial temperature (T) of the reactants and their relative amounts as well as the presence of any nonreactive (inert) materials. T is also dependent on the extent of completion of the reaction. In actual experiments, it is very unlikely that the theoretical maximum values of T can be realized, but the calculated results do provide an idealized basis for comparison of the thermal effects resulting from exothermic reactions. Lower feed temperatures (T), presence of inerts and excess reactants, and incomplete conversion tend to reduce the value of T. The term theoretical or adiabatic flame temperature (T,, ) is preferred over T in dealing exclusively with the combustion of fuels. 

Figure 2-82. Schematic representation to calculate the adiabatic reaction temperature (T ).

Except under special circumstances—for example, for systems having flame temperatures so low that dissociation is negligible in product gases, thereby causing combustion reactions to proceed essentially to completion—manual computation of adiabatic flame temperatures is very tedious. Fortunately, programs for electronic computers are now available for calculating adiabatic flame temperatures in practically all systems of interest (for example, [25]). These programs include the needed thermodynamic data and provide information on additional equilibrium properties... 

We are now equipped to determine what is called the adiabatic reaction temperature. This is the temperature obtained inside the process when (1) the reaction is carried out under adiabatic conditions, that is, there is no heat interchange between the container in which the reaction is taking place and the surroundings and (2) when there are no other effects present, such as electrical effects, work, ionization, free radical formation, and so on. In calculations of flame temperatures for combustion reactions, the adiabatic reaction temperature assumes complete combustion. Equilibrium considerations may dictate less than complete combustion for an actual case. For example, the adiabatic flame temperature for the combustion of CH4 with theoretical air has been calculated to be 2010 C allowing for incomplete combustion, it would be 1920 C. The actual temperature when measured is 1885 C. 

To calculate the adiabatic reaction temperature, you assume that all the energy liberated from the reaction at the reference temperature plus that brought in by the entering stream (relative to the same base temperature) is available to raise the temperature of the products. We assume that the products leave at the temperature of the reaction, and thus if you know the temperature of the products, you automatically know the temperature of the reaction. In effect, for this adiabatic process we can apply Eq. (4.40). 

The reaction given by Eq. (1) is very exothermic. To determine the temperature range of interest for thermodynamic analysis, the adiabatic reaction temperatures (ARTs) have been calculated for the Zr, Ti, and Hf systems (the latter two are described in the next section) using the following assumptions ... 

An additional criterion, the Calculated Maximum Adiabatic Reaction Temperature... 

The actual (unrestricted) solution has O and H (not ions, but atoms) as important reaction products, but these species have not even been considered in the adiabatic reaction temperature calculation. The conclusion is that restricting over consideration to just the species in the problem statement is unjustified ... 

The computation of the temperature of an a iabatic combustion flame is the most common adiabatic reaction temperature calculation (see Problems 14.3 and 14.9). 

Given an exothermic reaction operation, an important first step is to compute the adiabatic reaction temperature, that is, the maximum temperature attainable, in the absence of heat transfer. Note that this can be accomplished readily with any of the process simulators. Furthermore, algorithms have been presented for these iterative calculations by Henley and Rosen (1969) and Myers and Seider (1976), among many sources. 

With the reactants fed in stoichiometric amounts at 25°C and 1 atm, calculate the standard heat of reaction and the adiabatic reaction temperature. 

The final example of the section illustrates the calculation of an adiabatic reaction temperature. This type of calculation is often used to estimate the maximum temperature which can be attained in a reaction, e.g. maximum flame temperature. 

Flame Temperature. The adiabatic flame temperature, or theoretical flame temperature, is the maximum temperature attained by the products when the reaction goes to completion and the heat fiberated during the reaction is used to raise the temperature of the products. Flame temperatures, as a function of the equivalence ratio, are usually calculated from thermodynamic data when a fuel is burned adiabaticaHy with air. To calculate the adiabatic flame temperature (AFT) without dissociation, for lean to stoichiometric mixtures, complete combustion is assumed. This implies that the products of combustion contain only carbon dioxide, water, nitrogen, oxygen, and sulfur dioxide. 

Two standard estimation methods for heat of reaction and CART are Chetah 7.2 and NASA CET 89. Chetah Version 7.2 is a computer program capable of predicting both thermochemical properties and certain reactive chemical hazards of pure chemicals, mixtures or reactions. Available from ASTM, Chetah 7.2 uses Benson s method of group additivity to estimate ideal gas heat of formation and heat of decomposition. NASA CET 89 is a computer program that calculates the adiabatic decomposition temperature (maximum attainable temperature in a chemical system) and the equilibrium decomposition products formed at that temperature. It is capable of calculating CART values for any combination of materials, including reactants, products, solvents, etc. Melhem and Shanley (1997) describe the use of CART values in thermal hazard analysis. 

The reactor would be run adiabatically, but the maximum reaction temperature allowable is 400 °C, since above this temperature undesirable by-products are formed. Calculate the minimum reactor volume required to obtain 80% conversion of A. What must the heat transfer rate be in the cooling section of the reactor ... 

The heat of decomposition (238.4 kJ/mol, 3.92 kJ/g) has been calculated to give an adiabatic product temperature of 2150°C accompanied by a 24-fold pressure increase in a closed vessel [9], Dining research into the Friedel-Crafts acylation reaction of aromatic compounds (components unspecified) in nitrobenzene as solvent, it was decided to use nitromethane in place of nitrobenzene because of the lower toxicity of the former. However, because of the lower boiling point of nitromethane (101°C, against 210°C for nitrobenzene), the reactions were run in an autoclave so that the same maximum reaction temperature of 155°C could be used, but at a maximum pressure of 10 bar. The reaction mixture was heated to 150°C and maintained there for 10 minutes, when a rapidly accelerating increase in temperature was noticed, and at 160°C the lid of the autoclave was blown off as decomposition accelerated to explosion [10], Impurities present in the commercial solvent are listed, and a recommended purification procedure is described [11]. The thermal decomposition of nitromethane under supercritical conditions has been studied [12], The effects of very high pressure and of temperature on the physical properties, chemical reactivity and thermal decomposition of nitromethane have been studied, and a mechanism for the bimolecular decomposition (to ammonium formate and water) identified [13], Solid nitromethane apparently has different susceptibility to detonation according to the orientation of the crystal, a theoretical model is advanced [14], Nitromethane actually finds employment as an explosive [15],... 

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. 

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