Experimentation and Kinetic Model for a Fed-Batch Vessel

The fed-batch reactor model is commonly built using classical thermal and mass balance differential equations [11], Under isothermal conditions, the material balance for each measured component in the H KR of epichlorohydrin with continuous water addition is expressed by one of the following equations (Eqs. 12-17). These equations can be solved using an appropriate solver package (Lsoda, Ddassl [12]) with a connected optimization module for parameter estimation. 

Because the epoxide hydrolysis reaction is exothermic, isothermal conditions were critical to obtain good data in this parameter study. A solvent (1,2-dichloro-benzene) was used to dilute the reaction mixture in order to help maintain a constant reaction temperature. This proved especially useful when exploring higher catalyst concentrations that accelerate the rate of reaction. It will be demonstrated in Section 2.3.3.3 that the use of solvent did not alter the kinetic parameters of the HKR reaction, and thus the estimated kinetic parameters remained valid under solvent-free conditions. Water retained sufficient solubility in the mixed system to maintain homogeneity at the desired rate of addition. A slight excess of water was used to ensure complete conversion of (S)-epichlorohydrin and to compensate for any competitive hydrolysis of the (R)-enantiomer. 

It was assumed that catalyst degradation was inoperative (and subsequently confirmed by the kinetic study), thus maintaining a constant concentration and constant activity throughout the reaction. With catalyst concentration experimentally fixed, the kinetic rate equations (9-11) simplify to Eq. (18)—(20), respectively, where Ki=k [catalyst]m. 

13 and 14 plot the experimental (points) and simulated (solid lines) concentration profile versus time for (S)-epichlorohydrin, (R)-epichlorohydrin, and water under the standard HKR operating conditions using 0.5 and 0.28 mol-% catalyst (relative to racemate), respectively. Also shown is the simulated and observed evolution of epichlorohydrin ee and conversion over the course of the reaction. Fig. 15 gives the corresponding profiles for glycidol and DCP at both catalyst concentrations. 

To disconnect the kinetic rate of hydrolysis for each enantiomer of epichlorohydrin, identical experiments were performed with each pure enantiomer 

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