Batch reactor rate constants from

Example 7.5 Suppose the consecutive reactions 2A B C are elementary. Determine the rate constants from the following experimental data obtained with an isothermal, constant-volume batch reactor ... 

If the rate equation is to be employed in its integrated form, the problem of determining kinetic constants from experimental data from batch or tubular reactors is in many ways equivalent to taking the design equations and working backwards. Thus, for a batch reactor with constant volume of reaction mixture at constant temperature, the equations listed in Table 1.1 apply. For example, if a reaction is suspected of being second order overall, the experimental results are plotted in the form ... 

Develop a batch-reactor design equation from the mass balance. To find the required holding time, a relationship between reaction time and the rate of conversion of acetylene must be developed. This may be developed from a mass balance on the batch reactor. Since the molar density of the reacting mixture is not constant (there is a net change in the number of moles due to reaction), the pressure of the reactor will have to change accordingly. 

EP.2 The reaction occurs in a batch reactor and determines the specific rate constant from the following experimental data. 

Example. Fitting the rate constant from the full curve of concentration of C vs. time for a batch reactor experiment... 

The microautoclave solvent activity tests measure coal conversion in a small batch reactor under carefully controlled conditions. The tests are described as Kinetic, Equilibrium and SRT. The Kinetic and Equilibrium Tests measure coal conversion to tetrahydrofuran solubles at conditions where conversion should be monotonically related to hydrogen transfer. The Kinetic Test is performed at 399°C for 10 minutes at an 8 to 1 solvent to coal ratio. The combination of high solvent ratio and low time provide a measure of performance at essentially constant solvent composition. The measured conversion is thus related to the rate of hydrogen donation from solvent of roughly a single composition. In contrast, the Equilibrium Test is performed at 399°C for 30 minutes at a 2 to 1 solvent to coal ratio. At these conditions, hydrogen donors can be substantially depleted. Thus performance is related to hydrogen donor... 

The data given below are typical of the polymerization of vinyl phenylbutyrate in dioxane solution in a batch reactor using benzoyl peroxide as an initiator. The reaction was carried out isothermally at 60 °C using an initial monomer concentration of 73 kg/m3. From the following data determine the order of the reaction and the reaction rate constant. Note that there is an induction period at the start of the reaction so that you may find it useful to use a lower limit other than zero in your integration over time. The reaction order may be assumed to be an integer. 

A common laboratory device is a batch reactor, a nonflow type of reactor. As such, it is a closed vessel, and may be rigid (i.e., of constant volume) as well. Sample-taking or continuous monitoring may be used an alternative to the former is to divide the reacting system into several portions (aliquots), and then to analyze the aliquots at different times. Regardless of which of these sampling methods is used, the rate is determined indirectly from the property measured as a function of time. In Chapter 3, various ways of converting these direct measurements of a property into measures of rate are discussed in connection with the development of the rate law. 

For a constant-volume batch reactor operated at constant T and pH, an exact solution can be obtained numerically (but not analytically) from the two-step mechanism in Section 10.2.1 for the concentrations of the four species S, E, ES, and P as functions of time t, without the assumptions of fast and slow steps. An approximate analytical solution, in the form of a rate law, can be obtained, applicable to this and other reactor types, by use of the stationary-state hypothesis (SSH). We consider these in turn. 

For a first-order reaction, the integrated form of the rate equation for a constant volume batch reactor, from Table 1.1 in Volume 3, is ... 

Ridelhoover and Seagrave [57] studied the behaviour of these same reactions in a semi-batch reactor. Here, feed is pumped into the reactor while chemical reaction is occurring. After the reactor is filled, the reaction mixture is assumed to remain at constant volume for a period of time the reactor is then emptied to a specified level and the cycle of operation is repeated. In some respects, this can be regarded as providing mixing effects similcir to those obtained with a recycle reactor. Circumstances could be chosen so that the operational procedure could be characterised by two independent parameters the rate coefficients were specified separately. It was found that, with certain combinations of operational variables, it was possible to obtain yields of B higher than those expected from the ideal reactor types. It was necessary to use numerical procedures to solve the equations derived from material balances. 

An ionic liquid was fully immobilized, rather than merely supported, on the surface of silica through a multiple-step synthesis as shown in Fig. 15 (97). A ligand tri(m-sulfonyl)triphenyl phosphine tris(l-butyl-3-methyl-imidazolium) salt (tppti) was prepared so that the catalyst, formed from dicarbonylacetylacetonate rhodium and the ligand (P/Rh = 10), could be soluble in both [BMIMJBFq and [BMIM]PF6. The supported ionic liquid-catalyst systems showed nearly three times higher rate of reaction (rate constant = 65 min ) that a biphasic system for the hydroformylation of 1-hexene at 100°C and 1500 psi in a batch reactor, but the n/i selectivity was nearly constant the same for the two ( 2.4). Unfortunately, both the supported and the biphasic ionic liquid systems exhibited similar metal leaching behavior. 

The rates of liquid-phase reactions can generally be obtained by measuring the time-dependent concentrations of reactants and/or products in a constant-volume batch reactor. From experimental data, the reaction kinetics can be analyzed either by the integration method or by the differential method ... 

For example, Beltran and Alvarez (1996) successfully applied a semi-batch agitated cell for the determination of kL k,a, and the rate constants of synthetic dyes, which react very fast with molecular ozone (direct reaction, kD = 5 105 to 1 108 L mol-1 s l). In conventional stirred tank reactors operated in the semi-batch mode the mass transfer coefficient for ozone kLa(03) was determined from an instantaneous reaction of ozone and 4-nitrophenol (Beltran et al., 1992 a) as well as ozone and resorchinol (l,3-c//hydroxybenzene) or phloroglucinol... 

A fast exothermal reaction is to be performed in a semi-batch reactor. In order to control the temperature course of the reaction, one of the reactants is added at a constant rate, producing a constant heat flow. The reactor is cooled with water from a river (at 15 °C in winter). The cooling water should not be rejected at a temperature higher than 30 °C. 

Since the concentrations of reactants (Ma, Mp, Me and Mp,) in batch reactor are assumed to be measurable with a delay of one sampling time that is, at time k of the reactor, only information at time A — 1 is available. Thus, the EKF is applied to estimate the value of reactant concentration at current time k from their delayed measurements at sampling time k — 1. However, since it is expected to exhibit uncertainly in reaction rate constant (i.e. k and fcj) in real plant, the EKF is also used to estimate these uncertain parameters. The following equations, therefore, are appended for parameter estimation... 

Several simulations have been carried out under process parameter uncertainties e.g. in pre-exponential rate constant (ko) and activation energy (Ea). In all case studies we considered 10 time intervals when reactor temperature and switching time are optimized while minimizing the final batch operation time. Results, reported in the value of minimum batch time to obtain the desired product C and the amount of the desired product C at the end of batch operation, from on-line dynamic optimization strategy are also compared with those from the off-line strategy. 

The Livermore study used a 1.8 L upflow reactor, packed with a 1% w/w Pd/alumina catalyst, nominally 0.32 cm in diameter. (McNab and Ruiz 1998) The water supply consisted of groundwater from a well at the Livermore site and contained PCE (5-7 jig/L), TCE (500-600 tig/L), 1,1-DCE (15-25 pg/L), CT (8-15 fig/L), CF (4-10 gg/L), and 1,2-DCA (4-10 jrg/L). The water was first passed through an electrolyzer, which served as a source of hydrogen. With an average residence time of 2.3 minutes, the column showed >95% removal of chlorinated ethylenes (PCE, TCE and 1,1,-DCE) and CT. The apparent first order rate constants for all four compounds were approximately 72/hour. Chloroform was removed at a much slower rate (<32/hour) and 1,2-DCA removal was not significant. These results are also consistent with the batch studies of Lowry which showed rapid reaction of... 

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