Thermokinetic system

The data required for the emergency vent design includes [191] (1) the thermokinetic and pressure history monitored under near adiabatic conditions, (2) the character of the type of vented system (vapor, gassy, or hybrid), (3) the phase of the vented material (vapor, liquid, or two-phase), and (4) the degree of two-phase disengagement (turbulent, bubbly, or homogeneous). To determine these characteristics, the VSP defines the system as viscous (100 cp) or nonviscous, and also whether or not it has a foaming tendency. 

Once the cooling liquid has been chosen (i.e., Cpm fixed), the variables of mass and temperature of the cold liquid remain and depend on the desired temperature decrease (T - Te). This value can be derived from the thermokinetics of the given reaction system. 

From the temperature in the system and thermokinetic data, the time available to the maximum rate of the runaway can be calculated or determined experimentally. This represents the maximum time available to discharge the contents of the reactor. The actual time needed for dumping should be less than the maximum to add a safety factor. The driving force for dumping can be gravity or vessel pressure. 

In this chapter we give an introduction and recipe for the full Hopf bifurcation analysis for chemical systems. Rather than work in completely general and abstract terms, we will illustrate the various stages by using the thermokinetic model of the previous chapter, with the exponential approximation for simplicity. We can draw many quantitative conclusions about the oscillatory solutions in that model. In particular we will be able to show (i)that the parameter values given by eqns (4.49) and (4.50) for tr(J) = 0 satisfy all the requirements of the. Hopf theorem (ii)that oscillatory behaviour is completely confined to the conditions for which the stationary state is... 

Experiments with the system H2-02 were performed also by Horak et al. (21-23) who observed pronounced ignition-extinction phenomena. They were able to construct a reliable mathematical model based on the heat and mass balances describing the gas-to-solid heat and mass transfer. Their general conclusion is that the multiplicity phenomena may be explained in terms of thermokinetic theory. However, on the other hand, because of the high thermal capacity of the pellet, the oscillations cannot be described by this mechanism (72). Obviously we should examine a more detailed kinetic mechanism to be able to analyze successfully this phenomenon (25). 

The use of excess formic acid to destroy excess nitric acid (5M) in nuclear fuel reprocessing waste solutions at 100°C is potentially hazardous because of an induction period, high exothermicity and the evolution of large amounts of gas, mainly carbon dioxide, dinitrogen oxide and nitrogen oxide, with some nitrogen and dini-trogen tetraoxide. The system has been studied thermokinetically, and the effects of various salts (which decrease the reaction rate) and sulfuric acid (which increases the rate) were determined [1],... 

Thermal systems can be completely described using balance equations for mass, energy, and entropy in conjunction with thermophysical property relations and/or equations of state, equipment performance characteristics, thermokinetic or rate equations, and boundary/initial conditions. With the thermal system adequately described, it can be optimized by any current technique. Although the approach presented in this paper is not explicit in Second Law terms, it never-the-less will yield the optimal design and with the appropriate transformations, will yield any desired Second Law quantity. 

Acrylamide polymerization initiated by the H202-hydroxylamine system also has been described 59). The polymerization rate is proporti onal to the square root of H202 and hydroxylamine concentrations, and first order with respect to the monomer concentration. If traces of Fe (a few ppm) are added, the order with respect to the hydroxylamine concentration has been found to depend on the Fe concentration. A thermokinetic method has been applied in determining the overall activation energy... 

Several other thermokinetic blocking/reactivation schemes have been developed, a general representation of which is depicted in Fig. 6g. They were formulated for such different systems as CO/NO on Pd catalysts (101,123) and the methanol to gasoline (MTG) process on ZSM-5 (216) so that thermokinetic blocking/reactivation mechanisms describe the widest range of oscillator types. 

In 1969 Gray and Yang [70] formulated an extremely simple scheme which could reproduce these phenomena and it is described in detail in Chapter 5. Its importance lay, not so much in its application to the modelling of practical systems, but in its provision of a conceptual base for further development. It incorporated the essential features of the science, particularly thermokinetic feedback - the interaction between a branched radical chain and the reaction-generated temperature rise. 

Boyle [15] and Huff [16] first accounted for two-phase flow with relief system design for runaway chemical reactions. A computer simulation approach to vent sizing involves extensive thermokinetic and thermophysical characterization of the reaction system. Fisher [17] has provided an excellent review of emergency relief system design involving runaway reactions in reactors and vessels. Fauske [18] has developed a simplified chart to the two-phase calculation. He expressed the relief area as ... 

R15) 1980 Gray, B. F. Thermokinetic Oscillations in Gaseous System Kinetics of Physico-chemicals Oscillations, Berichte der Bunsen-Gesellschaft fur Physikalische Chemie, vol. 84, no. 4., 309-315... 

The activation parameters are collected in Table III for the 1,2-dioxetanes (1) and a-peroxylactones (2). Clearly, variation of substituent structure has a minor effect on the activation parameters. A significant exception is the diadamantylidene system (lz), which is unusually thermally stable.38 Assuming a diradical mechanism for the thermal decomposition of 1,2-dioxetanes, O Neal and Richardson97 were able to reproduce the experimental activation parameters with good precision, employing thermokinetic calculations developed by Benson.9741... 

The autocatalator model is in many ways closely related to the FONI system, which has a single first-order exothermic reaction step obeying an Arrhenius temperature dependence and for which the role of the autocatalyst is taken by the temperature of the system. An extension of this is the Sal nikov model which supports thermokinetic oscillations in combustion-like systems [48]. This has the form ... 

Processes which take place within homogeneous liquids phases process are the preferred reaction systems for thermokinetic descriptions. In heterogeneous systems, which can be modelled with the help of macrokinetic formal rate laws, thermokinetic evaluation is possible, too, but only if additional information on the properties of the two phases is obtained in parallel. 

They modified an existing autoclave and a real-time digital microprocessor control system so that It could be operated In a semi-continuous mode. Various components of MSW were studied In order to obtain meaningful data, not confused by the different thermokinetics of different MSW components. Feedstocks Included wood flour, cardboard, newsprint and rice (starch), as well as the Important model compounds alpha cellulose and lignin. It was found that these MSW components could be converted to liquid oils and a high-heating value residual solid at temperatures of 325 0 to 400 0 and pressures of 1000 psl to 3000 psl. 

Systematic studies on thermokinetic wave propagation have been reported for various reactions, and different approaches have been reported to implement nonisothermal effects in the theoretical modeling [53]. Even if the details of the reaction mechanism are less well understood, the basic features of spatio-temporal pattern formation with such systems can often be modeled successfully, because the decisive effects can be approximated by a heat balance equation in which the chemistry is reduced to single variable and surface diffusion of adsorbates is neglected [54,55]. 

According to the constitutive principle of determinism the response (in the actual instant) is given by deformation and temperature in the present and the past of the body (cf. also Sects. 3.5, 4.5, and Rem. 26 in Chap. 3). This means that constitutive equations give the responses (2.4) in the actual instant as functional-independent variables of which there are histories—thermokinetic processes (2.5) in the past and present (in fluids, by deflnition, the deformations which influence the response are expressible only through volume in mass conserving system cf. Rems. 3, 4 in this chapter, 30 in Chap. 3). 

Now, in our uniform systems, an arbitrary thermokinetic process (2.5) gives some admissible thermodynamic process. Indeed, if any smooth functions (2.5) are taken we can calculate necessary values at the present time and introducing them into constitutive equations (2.6)-(2.9) we calculate the response. Heating Q is then adjusted so that the balance of energy (2.1) is satisfied (therefore this balance gives no restriction on constitutive equations for a slightly different point of view see [35, 42 6], cf. also Rem. 14 in Chap.4). Therefore, an admissible thermodynamic process is obtained and thus the constitutive admissibility principle may be... 

Memory is removed completely assuming that values of responses in the present instant are given by values of thermokinetic process T,V,m, m2 at the same present instant. The second functions, i.e., the functions (2.76)2-(2.79)2, follow for our closed system excluding m by 2.1 A), because the whole mass m is the known constant. 

In this Report the overall thermokinetic behaviour of chemical reactions is discussed wdth special reference to the stability of exothermic reactions. An almost universal property of such systems is the existence of more than one distinct mode of reaction, and hence of the possibility of sudden switches between different modes. Thus, starting from given initial conditions of temperature and pressure, a reaction may proceed at a constant low velocity (or one varying only slowly with time), whilst slightly different initial conditions lead to violent acceleration and explosively rapid change. The division between the two regimes is often distinct and well defined. Here, interest centres on the criteria that determine the onset of spontaneous ignition in exothermic systems and on the possibility of quantitative and qualitative interpretation and prediction of the features observed. 

The application of TSC to a wide variety of systems including polymers has been comprehensively reviewed [4]. Interestingly, the Arrhenius plots (or relaxation maps) of TSC relaxation modes measured for polymer systems frequently converge to a single point called the compensation point. The physical meaning of the compensation point is subject to controversy, being possibly the result of the accumulation of experimental errors. However, it has been claimed that the compensation point defines two characteristic parameters the compensation temperature and the compensation time. At the compensation temperature all modes are proposed to have the same relaxation time, and the degree of coordination between relaxation modes is an indicator of the thermokinetic state of the amorphous phase [5]. 

---