Rate of heat production

Thermal runaway reactions are the results of chemical reactions in batch or semi-batch reactors. A thermal runaway commences when the heat generated by a chemical reaction exceeds the heat that can be removed to the surroundings as shown in Figure 12-5. The surplus heat increases the temperature of the reaction mass, which causes the reaction rate to increase, and subsequently accelerates the rate of heat production. Thermal runaway occurs as follows as the temperature rises, the rate of heat loss to the surroundings increases approximately linearly with temperature. However, the rate of reaction, and thus the... 

For the second-order reaction, the term representing the rate of heat production by reaction, simplifies to... 

Calorimetry. Radioactive decay produces heat and the rate of heat production can be used to calculate half-life. If the heat production from a known quantity of a pure parent, P, is measured by calorimetry, and the energy released by each decay is also known, the half-life can be calculated in a manner similar to that of the specific activity approach. Calorimetry has been widely used to assess half-lives and works particularly well for pure a-emitters (Attree et al. 1962). As with the specific activity approach, calibration of the measurement technique and purity of the nuclide are the two biggest problems to overcome. Calorimetry provides the best estimates of the half lives of several U-series nuclides including Pa, Ra, Ac, and °Po (Holden 1990). 

Therefore, there is a maximum size reactor for each set of reaction conditions. This size will now be calculated. The maximum rate of heat production will be determined first. 

The focus of our investigations of the kinetics of oxidation of Athabasca bitumen has been on the use of an aneroid calorimeter ( 1 ) for measuring rates of heat production under nearly isothermal (AT < 1.2°C in each experiment) conditions. Initial attention was given to just two of the variables that affect the kinetics of oxidation (i) temperature and (ii) pressure of oxygen. 

Experimental conditions and initial rates of oxidation are summarized in Table V. For comparison, initial rates of dry oxidation at the same temperature and pressure of oxygen predicted by Equation 9 are included in parentheses. The predicted dry rate, measured dry rate, and measured wet rates are compared in Figure 2. The logarithms of the initial rates of heat production during wet oxidation increase approximately linearly (correlation coefficient = 0.92) with the logarithm of the partial pressure of oxygen and lead to values of In k = 2.5 and r = 0.9, as compared with values of In k = 4.8 and r = 0.6 for dry oxidation at this temperature. 

Figure 2. Rate of heat production by wet oxidation relative to dry oxidation at the same temperature and pressure of oxygen.

First, the rate of heat production is again related to the sum of the rates of depositional and burning processes, and if the predominant factor affecting the overall rate is temperature, then it does not seem likely that the specific effect of water vapor on the oxidation reported here is chemical catalysis, since a lowering of activation energy for either process would result in an increase in the overall rate relative to dry oxidation. 

What would be the corresponding effect of water vapor on the overall rate of heat production The rate of heat production must now be considered as the sum of the rates of heat evolution by deposition and burning plus the rate of heat absorption by distillation i.e., the overall rate of heat production must be smaller than the dry rate ... 

Equation 23 can no longer be used to describe the initial rate of heat production for the wet oxidation process at these elevated temperatures. However, it was ejected that an equation of the form shown below would suffice ... 

Here Wx represents the initial rate of heat production for some process (or processes) that is dependent on the partial pressure of the water vapor in the calorimetric system and gives a positive contribution to the initial rate of heat production by wet oxidation (unlike the steam distillation process envisaged for wet oxidation at 225°C, which aids in the retardation of the initial rate of heat production). If this relationship were valid, then a plot of the logarithm of the initial rate Wx against the logarithm of the ratio of the partial pressure of water vapor in the system to the total pressure in the system would be linear. However, as demonstrated by Figure 3, no such simple relationship is found. 

Figure 3. Variation of the difference between the wet and the dry initial rates of heat production as a function of the partial pressure of water vapor in the system at 285°C.

Both of the above chemical studies point towards the increased importance of the burning process at 285°C in determining the initial rate of heat production. The role of water as yet remains undefined other than at the higher temperature of 285°C it appears to have the opposite effect on the bitumen sample compared to the process at 225°C i.e., it appears that water vapor encourages pathways by which the various components of bitumen react with oxygen. Preliminary calculations of the total heats evolved during the wet oxidation of bitumen sands indicate that they are independent of the partial pressure of oxygen in the system at... 

For exothermic reactions, the value of AH is by convention negative and for endothermic reactions positive. For a set of R individual reactions, the total rate of heat production by reaction is given by... 

The rate of heat production by the three reactions is written as... 

Reaction kinetics (how fast a chemical reaction will proceed, and the rate of heat production and off-gas evolution)... 

Factors that affect accumulation or rate of heat production (temperature, catalysts, pH, etc.)... 

Heat flow calorimeters simulate closely the operation of plant reactors. Removing the heat of reaction at the same rate as it is generated results in a constant reaction temperature. The temperature difference between the reactor and vessel jacket is a measure of the rate of heat production. 

The rate of heat production (dQR/dt, reaction output), where applicable as a function of temperature... 

The rate of heat production dQ ldt is the quantity of heat that is produced per unit of time. This rate is proportional to the reaction rate the latter is a function of the concentrations and the temperature. 

The main experiment followed a similar procedure. The Joule calibration yields e. The cyclohexane solution of Cr(CO)6 and piperidine was irradiated for a period t. The heat released (Q) provided A0bs H via equation 10.5. If/ / t, then Q derived from the reference experiment needs to be multiplied by t/t. Alternatively, we can simply derive the rate of temperature increase during the irradiation. This rate multiplied by e is equal to rate of heat production (Q/t), which Adamson and co-workers called F. The difference between the radiant power (P) and F gives A0bsH/t. 

During a marathon, the rate of heat production can be more than tenfold greater than at rest and sufficient to raise the core body temperature by 1°C every eight minutes, if no cooling occurs. The core temperature is normally regulated so precisely that it does not rise more than about 1°C. The main mechanism for cooling is evaporation from the skin. Endurance runners can produce one litre of sweat per hour which removes about 2.4 MJ of heat. The energy used and therefore converted into heat in a marathon is about 12 MJ... 

Ignition is dependent on various physicochemical parameters, such as the type of reactants, reaction rate, pressure, the heat transfer process from the external heat source to the reactants, and the size or mass of the reactants. The rate of heat production is dependent on the heats of formation of the reactants and products, the temperature, and the activation energy. As the process of ignition includes an external heating and an exothermic reaction of the reactants, there is a non-steady heat balance during these phases. 

Fig. B-1 presents a steady-state flow in a combustion wave, showing mass, momentum, and energy transfers, including chemical species, in the one-dimensional space of Ax between Xj and %2- The viscous forces and kinetic energy of the flow are assumed to be neglected in the combustion wave. The rate of heat production in the space is represented by coQ, where ai is the reaction rate and Qis the heat release by chemical reaction per unit mass.

Photocalorimetry is a technique for determining the ordinary enthalpy (AH) of a reaction but, unlike conventional calorimetry, the reaction is light induced,191 Essentially, the procedure involves measuring the rates of heat production in two irradiated solutions, one containing an absorbing but unreactive substance and the other containing the photosensitive compound. The difference between these rates, per mole of reaction, gives the AH for the photochemical process. 

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