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Nonisothermal conditions, kinetic

In the kinetic analysis of the experimental data with an autoclave, the non-linear least square method was used to estimate the rate constants under nonisothermal conditions. The simulation of liquefaction calculated by substituing the estimated values into the rate equations showed good agreement with experimental values. [Pg.225]

Grant and coworkers [8] studied the dehydration kinetics of piroxicam monohydrate using both model-free and model-fitting approaches in an effort to understand the effects of lattice energy and crystal structure. The dehydration kinetics was found to differ when determined under isothermal and nonisothermal conditions. Ultimately, the dehydration behavior of piroxicam monohydrate was determined by details of the crystal structure, which was characterized by an absence of channels and a complicated hydrogen-bonding network, and ab initio calculations proved useful in understanding the structural ramifications of the dehydration process. [Pg.265]

Most industrially relevant transformation processes are not isothermal and even in a controlled laboratory environment, it is difficult to perform experiments that are completely isothermal. The kinetics of nonisothermal phase transformations are more complex, of course, but there are some useful relationships that have been developed that allow for the evaluation of kinetic parameters under nonisothermal conditions. One such equation takes into account the heating rate, (p usually in K/min, used in the experiment [4] ... [Pg.222]

As stated in the previous section, the use of a phenomenological kinetic equation derived from Eq. (5.1), for a system that does not verify the required restrictions for its use, may lead to different kinetic expressions when trying to fit experimental results obtained under isothermal and nonisothermal conditions. In particular, it may be observed that different kinetic parameters result by varying the heating rates in nonisothermal experiments. [Pg.159]

So far it has been assumed that both reactions are first order and the pellet can be treated as isothermal. It may be obvious to note that under nonisothermal conditions the ratio of the intrinsic activation energies and, if necessary, the ratio of the external heat transfer coefficients will also affect the apparent selectivity of the catalyst. In addition, if the kinetic orders of the two reactions are different, this will also influence selectivity. [Pg.353]

So far, only isothermal operation has been considered. Under nonisothermal conditions, in Type II reactions a change of the apparent selectivity, caused by temperature variations across the pellet and/or the interphase boundary layer, may also be expected once the two reactions exhibit different activation energies. This holds irrespective of whether the kinetic order of the two reactions is equal or not. Nonisothermal Type II problems have been analyzed, for example, by 0stergaard [81]. [Pg.356]

Duff et al. [27] reported a study made by means of DSC and WAXD on SPS/ PPE blends of various compositions, precipitated from ethylbenzene solutions, compression molded at 330 °C for 2 min and then slowly cooled to room temperature. In particular, the WAXD patterns show that in sPS-rich blends (>50 50 wt%) sPS is in a 0 or (3 form, while small amounts of a are present in the 50 50 wt% blend. The kinetics of crystallization and the mechanism of nucleation of sPS were investigated under isothermal and nonisothermal conditions as a function of blend composition and molecular weights of the components. The experimental curves show that the half-time to crystallization, t j2, increases with increasing content and molecular weight of PPE, but is not influenced by the molecular weight of sPS. The crystallization kinetics were... [Pg.444]

Yeung et al. [1994] extended the studies to a general case of a bed of catalyst pellets on the feed side of a membrane reactor where the membrane is catalytically inert for an arbitrary number of reactions with arbitrary kinetics under nonisothermal conditions. Their conclusions are similar to those for the case of pellets in a fixed bed reactor [Baratti et al., 1993]. It appears that the presence of a catalytically inert membrane and a permeate su-eam do not affect the nature of the optimal catalyst distribution but may... [Pg.391]

In many catalytic systems multiple reactions occur, so that selectivity becomes important. In Sec. 2-10 point and overall selectivities were evaluated for homogeneous well-mixed systems of parallel and consecutive reactions. In Sec. 10-5 we saw that external diffusion and heat-transfer resistances affect the selectivity. Here we shall examiineHEieHnfiuence of intrapellet res ahces on selectivity. Systems with first-order kinetics at isothermal conditions are analyzed analytically in Sec. 11-12 for parallel and consecutive reactions. Results for other kinetics, or for nonisothermal conditions, can be developed in a similar way but require numerical solution. ... [Pg.452]

Such an approach is of practical value in analysing the operation of existing industrial reactors. However, when new technological processes are designed, it is necessary to investigate various nonisothermal conditions of synthesis, as well as the effect of the rheology of the system on the peculiarities of its kinetic behavior. [Pg.133]

To obtain the nonisothermal reaction kinetics, the sulfuric acid-containing coke as heated at a constant rate of 5°C/min and the volume of evolving individual reaction products was monitored vs. the change in temperature. Under the conditions of this experiment the regeneration reaction starts around 200°C and is practically completed at 450°C as indicated by the evolution of the reaction products as shown in Figure 2. [Pg.190]

Drozdetskaya GV, Gropyanov VM (1977) Calculation of kinetics of CaC03 decomposition under nonisothermal conditions. J Appl Chem USSR 50 480-483... [Pg.177]

The next step is to assign a suitable law to the experimental reacted fractions Xi, X2 and Xs for stages 1, 2 and 3, respectively. A non-invoking mechanism method will be assumed. The integrated kinetic approach under nonisothermal conditions gives,... [Pg.99]

You have learnt about the behaviour of adsorption kinetics of a single component in a single particle. Pore, surface diffusions and their combined diffusion have been studied in some details for linear as well as nonlinear isotherm and under isothermal as well as nonisothermal conditions. Here we will study a situation where there are more than one adsorbate present in the system and the interaction between different species will occur during diffusion as well as adsorption. Analysis of multicomponent system will require the application of the Maxwell-Stefan approach learnt in Chapter 8. To demonstrate the methodology as well as to show the essential features of how multiple species interact during the course of diffusion as well as adsorption onto adsorption sites, we will first consider a multicomponent adsorption system under isothermal conditions and dual diffusion mechanism is operating in the particle. [Pg.584]

In this chapter we will consider the micropore diffusion case and the bimodal diffusion. First, we consider the single component micropore diffusion in a single crystal under isothermal conditions, and then consider how nonisothermal conditions would affect the overall adsorption kinetics. Next, we consider the bimodal diffusion case, and study two situations. In one situation, the linear isotherm is considered, while in the other we investigate the nonlinear isotherm. Finally we consider multicomponent case where we will show how non-linear isotherm and non-isothermal conditions are incorporated into the heat and mass balance equations. [Pg.604]

Nonisothermal conditions. If thermal factors are of considerable importance the system of kinetic equations (5.16) is solved together with the equation describing the temperature variation of the reaction system. As this takes place, the target functional of the calculus of variations is chosen with regard to the temperature factor... [Pg.104]

It is worth noting that the computing data imder nonisothermal conditions, along with the kinetic curves of chemical species, include also the time-dependence of the temperature of the reaction medium. [Pg.200]

Rousar, 1., and DitI, P., Kinetic characteristics of batch adsorber or ion exchange device operated under nonisothermal conditions, Chem. Eng. Commun.. 18(5), 341-354 (1982)... [Pg.982]

Many kinetic measurements are performed under nonisothermal conditions that allow for faster runs over a wider temperature range. The runs are typically carried out at a constant heating rate ... [Pg.283]

It should be noted that unlike the isothermal kinetic curves in Fig. 3.23, the shape of nonisothermal curves does not provide any clear indication of the type of the reaction model. In nonisothermal runs the temperature increases, causing the reaction rate to continuously accelerate. As a result, under nonisothermal conditions all processes exhibit kinetic curves of a sigmoidal shape. [Pg.283]

In some simple cases of reaction kinetics, it is possible to solve the balance equations of the ideal, homogeneous reactors analytically. There is, however, a precondition isother-micity if nonisothermal conditions prevail, analytical solutions become impossible or, at least, extremely difficult to handle, since the energy and molar balances are interconnected through the exponential temperature dependencies of the rate and equilibrium constants (Sections 2.2 and 2.3). Analytical solutions are introduced in-depth in the literature dealing... [Pg.68]

A. Desorption Kinetics Under Nonisothermal Conditions Thermal Desorption Spectrometry... [Pg.524]

Ziabicki proposed to analyze nonisothermal processes as a sequence of isothermal steps [170-172]. The proposed equation is a series expansion of the Avrami equation. In quasi-static conditions, provided that nucleation and growth of the crystals are governed by thermal mechanisms only, that their time dependence comes from a change in external conditions, and that the Avrami exponent is constant throughout the whole process, the nonisothermal crystallization kinetics can be expressed in terms of an observable half-time of crystallization, T]/2, a function of time, and of the external conditions applied. The following equation was derived for the dependence of the total volume of the growing crystal, E(t), with time ... [Pg.237]

Under nonisothermal conditions, however, densification kinetics may not be diffusion controlled. If the temperature is being raised, the stress to move (and to generate) dislocations will steadily decrease. Material transport by dislocation motion will occur, and the extent of this transport may be dependent primarily on the final temperature rather than on the time of the heat treatment. In other words, as the temperature is increased, a steady procession of dislocations which were previously anchored will move. The facilitation of motion of dislocations by diffusion processes may be overshadowed by the contribution of the increasing temperature. [Pg.350]

The assumption of the Energetic Kinetic Theory (EKT) is that under nonisothermal conditions the total free energy remains that of the equilibrium at the corresponding temperature (i.e., RT In ( 2/ 7) in this example), and that there is a transfer of populations between the/and b types of bonds to render this constraint feasible. The kinetic duality between the b and/units within a closed but split statistical ensemble is the reason for the nomenclature "Split Dual Kinetics," but since the free energy remains as the driving force to determine the tme kinetic expression, we favor the expression "Energetic Kinetic Theory" to describe our new model. It will become apparent shordy that the latter expression has a more general sense. The set of equations for the new statistics... [Pg.383]

The present discussion will focus on the physical principles of the measurement and how to interpret the recorded data under nonisothermal conditions. This technique is also useful to study the polymer crystallization kinetics however, this topic is beyond the scope of this discussion. Fully detailed description and... [Pg.194]


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