Rate parameters from batch reactor data

Rate parameters from batch reactor data 

In this section we will briefly go over the situation where we will use batch reactor data for determining the rate constant and reaction order for a given reaction. First, we begin by collecting the concentration-time data. In gas phase reactions, pressure can be advantageously used in place of concentration. Also, the rate equations can be used in their differential or integrated forms. 

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Rate parameters from batch reactor data... 

Chapter 2 covers the basic principles of chemical kinetics and catalysis and gives a brief introduction on classification and types of chemical reactors. Differential and integral methods of analysis of rate equations for different types of reactions—irreversible and reversible reactions, autocatalytic reactions, elementary and non-elementary reactions, and series and parallel reactions are discussed in detail. Development of rate equations for solid catalysed reactions and enzyme catalysed biochemical reactions are presented. Methods for estimation of kinetic parameters from batch reactor data are explained with a number of illustrative examples and solved problems. 

To determine reaction rate parameters from the experimental data, the following differential equation was used to describe the reaction system in a constant-volume batch reactor assuming a pseudo-first-order equation for propylene epoxidation ... 

For this study, mass transfer and surface diffusions coefficients were estimated for each species from single solute batch reactor data by utilizing the multicomponent rate equations for each solute. A numerical procedure was employed to solve the single solute rate equations, and this was coupled with a parameter estimation procedure to estimate the mass transfer and surface diffusion coefficients (20). The program uses the principal axis method of Brent (21) for finding the minimum of a function, and searches for parameter values of mass transfer and surface diffusion coefficients that will minimize the sum of the square of the difference between experimental and computed values of adsorption rates. The mass transfer and surface coefficients estimated for each solute are shown in Table 2. These estimated coefficients were tested with other single solute rate experiments with different initial concentrations and different amounts of adsorbent and were found to predict... 

We can also use nonlinear regression to determine the rate law parameters from concentration-time data obtained in batch experiments. We recall that the combined rate law-stoichiometiy-mole balance for a constant-volume batch reactor is... 

The mathematical treatment of FMC data can be accomplished by standard procedures via the solution of mass balance equations, on condition that the data were converted to reaction rate data with Eq. (21). As mentioned above, this requires the determination of the transformation parameter a. Two approaches based on calibration were developed and tested. In the first approach, thermometric signals are combined with the absolute activity of IMB, which had been determined by a separate measurement using an independent analytical technique. Figure 5 shows a calibration for the cephalosporin C transformation catalyzed by D-amino acid oxidase. The activity of the IMB was determined by the reaction rate measurement in a stirred-tank batch reactor. The reaction rate was determined as the initial rate of consumption of cephalosporin C monitored by HPLC analysis. The thermometric response was measured for each IMB packed in the FMC column, and plotted against the corresponding reaction rate. From the calibration results shown in Fig. 5 it can be concluded, independently of the type of immobilized biocatalyst, that the data fall to the same line and that there is a linear correlation between the heat response and the activity of the catalyst packed in the column. The transformation parameter a was determined from... 

Now we can really see why the CSTR operated at steady state is so different from the transient batch reactor. If the inlet feed flow rates and concentrations are fixed and set to be equal in sum to the outlet flow rate, then, because the volume of the reactor is constant, the concentrations at the exit are completely defined for fixed kinetic parameters. Or, in other words, if we need to evaluate kab and kd, we simply need to vary the flow rates and to collect the corresponding concentrations in order to fit the data to these equations to obtain their magnitudes. We do not need to do any integration in order to obtain the result. Significantly, we do not need to have fast analysis of the exit concentrations, even if the kinetics are very fast. We set up the reactor flows, let the system come to steady state, and then take as many measurements as we need of the steady-state concentration. Then we set up a new set of flows and repeat the process. We do this for as many points as necessary in order to obtain a statistically valid set of rate parameters. This is why the steady-state flow reactor is considered to be the best experimental reactor type to be used for gathering chemical kinetics. 

The operational conditions, that is, the concentration of substrate and enzyme, the temperature range, and the reactor configuration are summarized in Table 13.2. The activation energy of the reaction, E, was typically obtained for a batch reactor and compared with that calculated for a CSMR. The data obtained in the CSMR at steadystate enabled us, by using a semi-log plot of reaction rate versus time, to identify a first-order mechanism of enzyme deactivation and to determine both its first-order deactivation constant, kj, and the reaction rate at time zero, r, for each substrate and temperature. It was thus possible to compare the effect of the operational parameters on the activity and stability of these two enzymes. From the Arrhenius plot of these Tq, the E,-values were determined for each substrate, and were found to match the values obtained in the batch reactors. 

The kinetics of adsorption of 1,1,1 -Irichloroethane and trichloroethylene from water on activated carbon are examined using stochastic approaches. A stochastic model, which has been developed by using the theory of the Markov process, is used to predict the rates of adsorption of 1,1,1-trichloroethane in a batch reactor. Adsorption equilibrium was represented by the linear isotherm equation. The simulation results under various adsorbent loading conditions and for various particle sizes show excellent fit between model predictions and experimental data. The intensity functions estimated from these studies can be utilized to predict batch adsorber performance under other process loading conditions. The model parameters, m 2 d J, obtained from this study can also be used in stochastic models for fixed-bed adsorbers. 

The reaction progress is monitored ofF-Une by HPLC. Flow rates, residence times and initial concentrations of 4-chlorophenol are varied and kinetic parameters are calculated from the data obtained. It can be shown that the photocatalytic reaction is governed by Langmuir-Hinshelwood kinetics. The calculation of Damkohler numbers shows that no mass transfer limitation exists in the microreactor, hence the calculated kinetic data really represent the intrinsic kinetics of the reaction. Photonic efficiencies in the microreactor are still somewhat lower than in batch-type slurry reactors. This finding is indicative of the need to improve the catalytic activity of the deposited photocatalyst in comparison with commercially available catalysts such as Degussa P25 and Sachtleben Hombikat UV 100. The illuminated specific surface area in the microchannel reactor surpasses that of conventional photocatalytic reactors by a factor of 4-400 depending on the particular conventional reactor type. 

Estimation of the kinetic parameters in Langmiiir - Hinshelwood - Hougen -Watson (LHHW) type rate equations, using experimental data sets obtained from a batch and a CSTR reactor. 

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