Deactivation kinetics parameter estimation

An experimental design was developed which uncoupled the overall problem into a number of smaller parameter estimation problems. This approach reduced confounding between parameters, for both start-of-cycle and deactivation kinetics. 

The deactivation kinetics were determined through a series of seven separate parameter estimation problems. As with the start-of-cycle case, separate estimating problems resulted from uncoupling the reactions of each carbon number by properly selecting the charge stock. This allowed the independent determination of submatrices in the rate constant matrix Dp [Eq. (37)]. 

Due to the strong interaction between the physical and chemical mechanisms, particularly when catalyst deactivation is present, the parameter estimation becomes very difficult. The kinetic parameters are normally obtained from laboratory scale reactors and when used in pilot plant studies, have to be tuned (1, 2) or even re-evaluated (3, 4) to obtain reasonable predictions. The transport parameters are estimated... 

The kinetic and deactivation models were fitted by non-linear regression analysis against the experimental data using the Modest software, especially designed for the various tasks -simulations, parameter estimation, sensitivity analysis, optimal design of experiments, performance optimization - encountered in mathematical modelling [6], The main interest was to describe the epoxide conversion. The kinetic model could explain the data as can be seen in Fig. 1 and 2, which represent the data sets obtained at 70 °C and 75°C, respectively. The model could also explain the data for hydrogenated alkyltetrahydroanthraquinone. 

Based on the obtained results, immobilized enzyme prepared at pH 4 (CALB-4) and 5 (CALB-5) were selected for thermal stability studies at 60 °C. Table 2 shows the kinetic parameters of thermal deactivation at 60 °C estimated by fitting deactivation model, Eq. 2, to experimental data. It can be observed that the deactivation profiles of CALB-4 and CALB-5 were similar, as ki and 2 are almost the same. However, by comparing the half-lives of CALB-4 and CALB-5 to CALB-7A, it can be observed that the biocatalyst prepared at pH 7 is 3- and 3.8-fold more stable than the ones prepared at pH 4 and 5, respectively. Considering that CALB has an optimum pH between 7 and 8 [35], when the enzyme is adsorbed on coconut fiber at pH 7, a favorable molecule conformation is preserved, being, therefore, more thermal stable than CALB-4 and CALB-5. Therefore, lipase immobilized at pH 7 was selected for fiirther kinetic, operational, and thermal stability studies. 

Experimental data of stearic acid decarboxylation in a laboratory-scale fixed bed reactor for formation of heptadecane were evaluated studied with the aid of mathematical modeling. Reaction kinetics, catalyst deactivation, and axial dispersion were the central elements of the model. The effect of internal mass transfer resistance in catalyst pores was found negligible due to the slow reaction rates. The model was used for an extensive sensitivity study and parameter estimation. With optimized parameters, the model was able to describe the experimentally observed trends adequately. A reactor scale-up study was made by selecting the reactor geometry (diameter and length of the reactor, size and the shape of the catalyst particles) and operating conditions (superficial liquid velocity, temperature, and pressure) in such a way that nonideal flow and mass and heat transfer phenomena in pilot scale were avoided. 

The ODE-model was solved numerically during the estimation of the kinetic, adsorption, and deactivation parameters. 

Mathematical Approaches. - The complexity of mathematical modeling of catalyst deactivation is mainly due to developing kinetic equations of the deactivation phenomena and measurement or estimation of the various parameters. When two or more different deactivation processes occur at the same time, this adds another level of difficulty and complicates the interpretation of experimental results. 

Complete lineshape analysis of the ABCj DEF2 exchange process observed in the n.m.r. spectra of 2,6-disubstituted homotropylidenes has been employed in the evaluation of the thermodynamic parameters for Cope rearrangement, The phenyl groups at the 2,6-positions of the barbaralane (155) destabilize the transition state relative to the unsubstituted hydrocarbon (154) as evidenced by the AGj g values, respectively 9.3 and 7.6 ( 0.1) kcalmol" Kinetic data for the Diels-Alder addition of acrolein to cydohexa-1,3-diene, and its reverse reaction, in the gas phase have been interpreted in favour of a biradical mechanism. Both the heat and entropy of formation of the endo-adduct have been estimated. Structural modification of 2,3-dimethylenenorbornane (156) or of 2,3-dimethylenenorbornene (158) by the introduction of oxygen in place of C-7, as in (157) and (159) respectively, leads to a decrease in rate of Diels-Alder reaction of the dienes with dimethyl acetylenedi-carboxylate. The double bond in (158) likewise resulted in deactivation relative to (156), and epoxidation of the endocyclic double bond in (158) also afforded an s-cis-diene of decreased reactivity. 

Table 1. Estimated parameters for deactivation and hydrogenation kinetics of naphthalene hydrogenation according equations 6-8 with 95% confidence interval.

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