Kinetic Analysis of Isothermal Data

The thermal cracking of propane was studied at atmospheric pressure and 800°C in a tubular reactor with plug flow and operated in the integral mode. The 

THERMAL CRACKING OF PROPANE. CONVERSION VERSUS SPACE TIME DATA 

The global reaction, propane products is considered to be irreversible. When first order is assumed, the rate equation may be written 

This reaction is carried out in the presence of a diluent, steam. The diluent ratio is k (moles diluent/moles hydrocarbon). Furthermore, 1 mole of propane leads to 2 moles of products in other words, the molar expansion Sa= 1. The relation between the propane concentration and the conversion has to account for the dilution and expansion and is obtained as follows. For a feed of Fao moles propane per second, the flow rates in the reactor at a certain distance where a conversion Xa has been reached may be written 

From (9.1-1) it follows that the slope of the tangent of the curve Xa versus V/Fao is the rate of reaction of A at the conversion Xa. The rates are shown in Table 9.2.1-2. The kare calculated by both the integral and the differential method of kinetic analysis. 

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The main approaches which have been used in kinetic analysis of isothermal data for decompositions and other reactions of solids are listed below and explained in greater detail in Sections 5.4.5. to 5.4.7. 

The two major methods used predominantly in the kinetic analysis of isothermal data on solid-catalyzed reactions conducted in plug-flow PBRs are the differential method and the method of initial rates. The integral method is less frequently used either when data are scattered or to avoid numerical or graphical differentiation. Linear and nonlinear regression techniques are widely used in conjunction with these major methods. 

Gaisford S, Hills AK, Beezer AE, Mitchell JC. Thermodynamic and kinetic analysis of isothermal microcalorimetric data applications to consecutive reaction schemes. Thermochimica Acta 1999 328(l-2) 39-45. 

Non-isothermal curves of a thermal reaction can satisfy the kinetic equations developed for the kinetic analysis of nth-order reactions , even if they follow a quite different mechanism. The results of comparative studies led to the conclusion that the actual mechanism of a thermal process cannot be discriminated from the kinetic analysis of a single TG trace [a.52]. Besides, both activation energy and pre-exponential factor, given in equation (2), may be mutually correlated. As a consequence of this correlation, any TG curve can be described by an apparent kinetic model instead of the appropriate one for a certain value of the apparent activation energy. Therefore, the kinetic analysis of TG data cannot be successful unless the true value of the activation energy is known. 

After switching from fast cooling to isothermal conditions at time zero, the measured heat flow rate exponentially approaches a constant value (-10.3 mW) with a time constant of about 3 seconds for this DSC. The observed crystallization peak is often symmetric, and then the time of the peak maximum (nunimum) is a measure of crystallization half time. Integration of the peak yields the enthalpy change, which can be transformed into relative crystallinity by dividing by the limiting value at infinite time. To obtain development of absolute crystallinity (mass fraction) the curve has to be divided by the enthalpy difference between crystal and liquid at the crystallization temperature, which is available from ATHAS-DB [124], The commonly applied Kolmogorov-Johnson-Mehl-Avrami (KJMA) model for the kinetic analysis of isothermal crystallization data is based on volume fractions. Therefore, the mass fraction crystallinity, Wc, as always obtained from DSC, should be transformed into volume crystallinity. 

Although there are experimental and interpretative limitations [189, 526] in the kinetic analysis of non-isothermal data, DTA or DSC observations are particularly useful in determining the temperature range of occurrence of one or perhaps a sequence of reactions and also of phase changes including melting. This experimental approach provides, in addition, a useful route to measurements of a in the study of reactions where there is no gas evolution or mass loss. The reliability of conclusions based on non-isothermal data can be increased by quantitatively determining the... 

References to a number of other kinetic studies of the decomposition of Ni(HC02)2 have been given [375]. Erofe evet al. [1026] observed that doping altered the rate of reaction of this solid and, from conductivity data, concluded that the initial step involves electron transfer (HCOO- - HCOO +e-). Fox et al. [118], using particles of homogeneous size, showed that both the reaction rate and the shape of a time curves were sensitive to the mean particle diameter. However, since the reported measurements refer to reactions at different temperatures, it is at least possible that some part of the effects described could be temperature effects. Decomposition of nickel formate in oxygen [60] yielded NiO and C02 only the shapes of the a—time curves were comparable in some respects with those for reaction in vacuum and E = 160 15 kJ mole-1. Criado et al. [1031] used the Prout—Tompkins equation [eqn. (9)] in a non-isothermal kinetic analysis of nickel formate decomposition and obtained E = 100 4 kJ mole-1. 

Stoichacmetry and reaction equilibria. Homogeneous reactions kinetics. Mole balances batch, continuous-shn-ed tank and plug flow reactors. Collection and analysis of rate data. Catalytic reaction kinetics and isothermal catalytic radar desttpi. Diffusion effects. 

The kinetic analysis of the whole set of transient data collected over the powdered SCR catalyst has been addressed using the dynamic ID isothermal heterogeneous plug-flow model of the test microreactor (Chatterjee et al., 2005 Ciardelli et al., 2004a) described in Section IV. 

Figure 5. First order kinetic analysis of conversion rate data on the MY720-DDS system cured Isothermally at 177 C and 153 C.

The usual starting point for the kinetic analysis of non-isothermal data is ... 

In the following kinetic analysis of the cure of TGDDM with DDS at elevated temperatures, the equations are developed from both DSC and MR data (in some circumstances collected simultaneously (de Bakker et al, 1993)), and enable quantitative estimation of the reactive-group profile at any time during isothermal (and in some cases temperature-ramped) cure. 

At the same time, a scientist needs not only the mathematical tool which could help him to calculate the isotherm or kinetic curve determined by a particular model. It is much more important to have a tool which helps in the analysis of experimental data how far can phenomena taking place in the experimental system can be explained in the framework of a particular model Moreover, with automated and computerised experimental devices currently available, one should naturally expect to have also the software, which is designed so as to provide him with the option of interactive and easily understandable way to analyse the results. 

The cured and the liquid polymers degrade essentially by the same mechanism (see Equation 6.1). The kinetic analysis of the isothermal and dynamic thermogravimetric data of the liquid polysulfide polymer cured with ammonium dichromate is explained by a kinetic model based on random initiation, followed by rapid termination by disproportionation. The average overall activation energy obtained by different methods for the decomposition is 145.3 kj/mole ... 

Fundamental kinetic studies are by preference performed in isothermal rather than in non-isothermal reaction conditions because frequently, as cure proceeds, parallel reactions with different activation energies occur, changing the relative rates of reactions with temperature. In theory, one non-isothermal experiment comprises all the kinetic information normally enclosed in a series of isothermal experiments, which makes the kinetic analysis of non-isothermal DSC data very attractive. The criteria forjudging the kinetic parameters derived from non-isothermal experiments must be its... 

Analysis of isotherms and kinetic data reveal some general and particular regularities of the sorption of cation modifying doi)es depending on the nature of... 

Due to length limitation of this chapter, many theoretical approaches on the phenomenological aspects of polymer crystallization have to be skipped. The isothermal and non-isothermal kinetic analysis of overall crystallization appears as technically important in the data treatment of DSC measurements. Some theoretical considerations on the metastable aspects of crystal morphologies and their evolution under various circumstances appear as practically important and case sensitive (see Chap. 1). In this sense, a combination of this chapter with other contributions of this book will provide reader a broad cutting-edge knowledge about our basic understanding of polymer crystallization. 

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