Decomposition kinetic model

The value of the method can be seen by reconsidering responses to the four basic questions of the TG decomposition kinetic model. The first question concerned whether the formulation components were thermally sensitive, and at what operational hold times the constant temperature decomposition was under 2%. From Fig. 4.27, the model predicted that an operating temperature in the range of 90-100°C... 

Kinetic Models Used for Designs. Numerous free-radical reactions occur during cracking therefore, many simplified models have been used. For example, the reaction order for overall feed decomposition based on simple reactions for alkanes has been generalized (37). 

The Cu-, Co- and Fe-ZSM-5 catalysts are active systems for the decomposition of N2O, but their behaviour differs with respect to conditions and gas atmospheres. They all seem to obey a (nearly) first order dependency towards pmo> which can be rationalised by the two step kinetic model given by eqs. (2) and (3). A step like eq. (3) is quite well feasible, since the TM ions in ZSM-5 can be coordinated by several ligands simultaneously [18,22], The resulting rate expression is given by eq. (7). 

The kinetics of the CTMAB thermal decomposition has been studied by the non-parametric kinetics (NPK) method [6-8], The kinetic analysis has been performed separately for process I and process II in the appropriate a regions. The NPK method for the analysis of non-isothermal TG data is based on the usual assumption that the reaction rate can be expressed as a product of two independent functions,/ and h(T), where f(a) accounts for the kinetic model while the temperature-dependent function, h(T), is usually the Arrhenius equation h(T) = k = A exp(-Ea / RT). The reaction rates, da/dt, measured from several experiments at different heating rates, can be expressed as a three-dimensional surface determined by the temperature and the conversion degree. This is a model-free method since it yields the temperature dependence of the reaction rate without having to make any prior assumptions about the kinetic model. 

The authors showed that the Grabke-type kinetic model can explain the results at a low carbon activity for Ni-Cu catalysts, but that at higher carbon activities, the rates for the Ni0 9Cu0 j catalysts are higher than the model-predicted rates. Low-temperature decomposition of methane over the silica-supported Ni catalyst has been reported by Kuijpers et al. [101]. It was demonstrated that at temperatures as low as 175°C, methane adsorbed on the Ni catalysts dissociates completely into adsorbed carbon atoms and hydrogen. 

A series of kinetic studies on the carbon filament formation by methane decomposition over Ni catalysts was reported by Snoeck et al. [116]. The authors derived a rigorous kinetic model for the formation of the filamentous carbon and hydrogen by methane cracking. The model includes the following steps ... 

Equilibrium studies under anaerobic conditions confirmed that [Cu(HA)]+ is the major species in the Cu(II)-ascorbic acid system. However, the existence of minor polymeric, presumably dimeric, species could also be proven. This lends support to the above kinetic model. Provided that the catalytically active complex is the dimer produced in reaction (26), the chain reaction is initiated by the formation and subsequent decomposition of [Cu2(HA)2(02)]2+ into [CuA(02H)] and A -. The chain carrier is the semi-quinone radical which is consumed and regenerated in the propagation steps, Eqs. (29) and (30). The chain is terminated in Eq. (31). Applying the steady-state approximation to the concentrations of the radicals, yields a rate law which is fully consistent with the experimental observations ... 

The kinetic models for these reactions postulate fast complex-formation equilibria between the HA- form of ascorbic acid and the catalysts. The noted difference in the rate laws was rationalized by considering that some of the coordination sites remain unoccupied in the [Ru(HA)C12] complex. Thus, 02 can form a p-peroxo bridge between two monomer complexes [C12(HA)Ru-0-0-Ru(HA)C12]. The rate determining step is probably the decomposition of this species in an overall four-electron transfer process into A and H202. Again, this model does not postulate any change in the formal oxidation state of the catalyst during the reaction. 

The reaction with CoII(ACAC)2 was studied in more detail and the rate law was established. The reaction was found to be first-order with respect to the substrate and the catalyst concentrations, and the partial pressure of 02. The corresponding kinetic model postulates reversible formation of a H2DTBC-Con(ACAC)2 02 adduct which undergoes redox decomposition in the rate-determining step. Hydrogen peroxide is also a primary... 

Although the above model was developed under non-catalytic conditions, some of the results may bear significance under natural conditions or in the presence of excess sulfite ions. Thus, the decomposition of the mono-sulfito complex was considered to be the rate-determining step in the catalytic cycle, but only estimates could be given for the rate constant in earlier studies. The comprehensive data treatment used by Lente and Fabian yielded a well established value for this parameter (106), which can then be used to improve previous kinetic models. Furthermore, the participation of reactions of the [Fe2(0H)(S03)]3+ complex was never considered in kinetic studies where excess sulfite ion was used over low iron(III) concentration in mildly acidic solution (pH 2.5-3.0). The above model predicts that in some cases the formation of the dimeric sulfito complex could make a substantial contribution to the spectral changes and omission of this species could lead to biased conclusions. Reevaluation of data sets reported earlier by including the reactions of [Fe2(0H)(S03)]3+ may resolve some of the controversies found in literature results. 

A unified gas hydrate kinetic model (developed at ARC) coupled with a thermal reservoir simulator (CMG STARS) was applied to simulate the dynamics of CH4 production and C02 sequestration processes in the Mallik geological zones. The kinetic model contains two mass transfer equations one equation transfers gas and water into hydrate, and a decomposition equation transfers hydrate into gas and water (Uddin etal. 2008a). 

The second question asked what would be an excessive temperature for this process. It was recommended that process hot spots (i.e., zones higher than 100°C) should be avoided. This requirement was met by keeping the heating lines, the walls of the melting pot, and the spray head thermally jacketed to maintain the appropriate internal soak temperature. As a result, the model presented a potential for hot spots at the skin surfaces of the lines and equipment walls. This needed to be investigated for its decomposition potential, and in fact, after several batches were processed, the flexible heat-traced lines had to be discarded because of a buildup of a blacked residue on the inner tubing walls. The kinetic model predicted how many batches could be run before this necessary replacement maintenance was required. 

To illustrate these issues better, the pressure at the center of fall-off (F ) is presented in Fig. 20. As seen from this figure, the unimolecular decompositions of small molecules are at their low-pressure limits at atmospheric pressure, and at process temperatures, = feo [M]- Decompositions of larger molecules, on the other hand, are closer to their high-pressure limits. It is important to recognize that the unimolecular decompositions of hydrocarbons from CH4 to CaHg exhibit differing degrees of fall-off under process conditions, and this must be properly accounted for in the development of accurate detailed chemical kinetic models. 

Many mechanistic implications have been discussed, but we will concentrate here only on the most important structures in the context of dihydrogen-cation complexes. Deuterium-labeled methane and methyl cations were employed to examine the scrambling and dissociation mechanisms. The protonated ethane decomposition yields the ethyl cation and dihydrogen. Under the assumption that the extra proton is associated with one carbon only, a kinetic model was devised to explain the experimental findings, such as H/D scrambling. ... 

For the initiation by azo initiators only the dependence kp / kt0 5=f ([M]) has to be considered in a kinetic model [10]. Accordingly, an initiator exponent of 0.5 and a monomer exponent of 2 are valid. By adding amine the decomposition velocity of APS is increased by an orders of magnitude. The chain side reactions with the monomer and termination by chlorine atoms are then significantly suppressed which results in a monomer exponent of 2 and higher molar masses of the homopolymer [11]. The kinetics of 2.3 order in monomer and 0.47 order in initiation [59], explained by partial cyclization and termination of cyclized radicals, could not be confirmed. 

Equation (8) has been used to describe the progress of the homogeneous polymerization up to conversions of approximately 60%. Experimental and calculated conversion-time curves were in good agreement, even for the case of changing experimental conditions during the polymerization [51]. For the heterophase polymerization experimental and modeled conversion-time curves coincide well if a kinetic model based on first order initiator decomposition was applied and consideration of gel effect for conversions greater than 35% was included [13]. 

When several temperature-dependent rate constants have been determined or at least estimated, the adherence of the decay in the system to Arrhenius behavior can be easily determined. If a plot of these rate constants vs. reciprocal temperature (1/7) produces a linear correlation, the system is adhering to the well-studied Arrhenius kinetic model and some prediction of the rate of decay at any temperature can be made. As detailed in Figure 17, Carstensen s adaptation of data, originally described by Tardif (99), demonstrates the pseudo-first-order decay behavior of the decomposition of ascorbic acid in solid dosage forms at temperatures of 50° C, 60°C, and 70°C (100). Further analysis of the data confirmed that the system adhered closely to Arrhenius behavior as the plot of the rate constants with respect to reciprocal temperature (1/7) showed linearity (Fig. 18). Carsten-sen suggests that it is not always necessary to determine the mechanism of decay if some relevant property of the degradation can be explained as a function of time, and therefore logically quantified and rationally predicted. 

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