Semibatch Reactor Modeling

When addition of reactants, together with removal of liquid and vapor, is also considered, the equations become  

SIMULATION OF SEMIBATCH REACTOR OPERATION (with l.h. hosten Consider the following set of reactions  

The reactor is a cylindrical vessel with a diameter of 0.8 m and is operated in a semibatch mode. The initial load is 0.1826 m of pure. 4 at a concentration of 17.48 kmol/m and an initial temperature of 25°C. The copper coil for heat exchange has an internal diameter of 0.015m, an external diameter of 0.019 m, a length of 14 m, and an exchange surface of 0.748 m The thermal conductivity of the copper is 1.402 kj/m h K. The diameter of the coil is 0.35 m. The paddle agitator has a diameter of 0.3 m and revolves at 150 rpm. 

A mixture of A and D, containing respectively 7.1 and 31.89 kmol/m, is fed at 25°C during 3 hours at a rate of 0.1068 m /h. Then, the reaction is continued for another 3 hours. There is no liquid withdrawal. The operating pressure is 1 bar. 

Integration of the set of equations (8.3-1) to (8.3-3), for example by means of a Runge-Kutta-Gill routine, yields concentrations, temperature, volume of the reactor contents, and vapor flow rate as functions of time. Determining the vapor flow rate requires an additional equation, expressing that, when the reactor content is boiling, the sum of the partial pressures must equal the total pressure above the liquid. When the liquid behaves in an ideal way, the vapor pressures satisfy Raoult s law  

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Specific reactor characteristics depend on the particular use of the reactor as a laboratory, pilot plant, or industrial unit. AH reactors have in common selected characteristics of four basic reactor types the weH-stirred batch reactor, the semibatch reactor, the continuous-flow stirred-tank reactor, and the tubular reactor (Fig. 1). A reactor may be represented by or modeled after one or a combination of these. SuitabHity of a model depends on the extent to which the impacts of the reactions, and thermal and transport processes, are predicted for conditions outside of the database used in developing the model (1-4). 

The model is able to predict the influence of mixing on particle properties and kinetic rates on different scales for a continuously operated reactor and a semibatch reactor with different types of impellers and under a wide range of operational conditions. From laboratory-scale experiments, the precipitation kinetics for nucleation, growth, agglomeration and disruption have to be determined (Zauner and Jones, 2000a). The fluid dynamic parameters, i.e. the local specific energy dissipation around the feed point, can be obtained either from CFD or from FDA measurements. In the compartmental SFM, the population balance is solved and the particle properties of the final product are predicted. As the model contains only physical and no phenomenological parameters, it can be used for scale-up. 

Villemiaux, J., 1989. A simple model for partial segregation in a semibatch reactor. American Institute of Chemical Engineers Annual Meeting, San Francisco, Paper 114a. 

Semibatch Model "GASPP". The kinetics for a semibatch reactor are the simpler to model, in spite of the experimental challenges of operating a semibatch gas phase polymerization. Monomer is added continuously as needed to maintain a constant operating pressure, but nothing is removed from the reactor. All catalyst particles have the same age. Equations 3-11 are solved algebraically to supply the variables in equation 5, at the desired operating conditions. The polymerization flux, N, is summed over three-minute intervals from the startup to the desired residence time, t, in hours ... 

This section is divided into three parts. The first is a comparison between the experimental data reported by Wisseroth (].)for semibatch polymerization and the calculations of the kinetic model GASPP. The comparisons are largely graphical, with data shown as point symbols and model calculations as solid curves. The second part is a comparison between some semibatch reactor results and the calculations of the continuous model C0NGAS. Finally, the third part discusses the effects of certain important process variables on catalyst yields and production rates, based on the models. 

Semibatch reactors are often used to mn highly exothermic reactions isothermally, to run gas-liquid(-solid) processes isobarically, and to prevent dangerous accumulation of some reactants in the reaction mixture. Contrary to batch of)eration, temperature and pressure in semibatch reactors can be varied independently. The liquid reaction mixture can be considered as ideally mixed, while it is assumed that the introduced gas flows up like a piston (certainly this is not entirely true). Kinetic modelling of semibatch experiments is as difficult as that of batch, non-isotherma experiments. 

Example 5.4.5.1. Application of the E-model for simulation of the coupling of I-naphthol with diazotized sulphanilic acid in a semibatch reactor (after Baidyga and Bourne, 1989b). 

Kinetic Model Discrimination. To discriminate between the kinetic models, semibatch reactors were set up for the measurement of reaction rates. The semi-batch terminology is used because hydrogen is fed to a batch reactor to maintain a constant hydrogen pressme. This kind of semi-batch reactor can be treated as a bateh reactor with a constant hydrogen pressme. The governing equations for a bateh reactor, using the product formation rate for three possible scenarios, were derived, as described in reference (12) with the following results ... 

Example 14.1 Consider again the chlorination reaction in Example 7.3. This was examined as a continuous process. Now assume it is carried out in batch or semibatch mode. The same reactor model will be used as in Example 7.3. The liquid feed of butanoic acid is 13.3 kmol. The butanoic acid and chlorine addition rates and the temperature profile need to be optimized simultaneously through the batch, and the batch time optimized. The reaction takes place isobarically at 10 bar. The upper and lower temperature bounds are 50°C and 150°C respectively. Assume the reactor vessel to be perfectly mixed and assume that the batch operation can be modeled as a series of mixed-flow reactors. The objective is to maximize the fractional yield of a-monochlorobutanoic acid with respect to butanoic acid. Specialized software is required to perform the calculations, in this case using simulated annealing3. 

A reactor model based on solid particles in BMF may be used for situations in which there is deliberate mixing of the reacting system. An example is that of a fluid-solid system in a well-stirred tank (i.e., a CSTR)-usually referred to as a slurry reactor, since the fluid is normally a liquid (but may also include a gas phase) the system may be semibatch with respect to the solid phase, or may be continuous with respect to all phases (as considered here). Another example involves mixing of solid particles by virtue of the flow of fluid through them an important case is that of a fluidized bed, in which upward flow of fluid through the particles brings about a particular type of behavior. The treatment here is a crude approximation to this case the actual flow pattern and resulting performance in a fluidized bed are more complicated, and are dealt with further in Chapter 23. 

These processes can obviously be modeled as PETR, CSTR, batch, or semibatch reactors. However, we now must consider the flows of both fluid and sohd phases so we have amultiphase reactor because there are distinct residence times of sohd and fluid phases,... 

We have presented a general reaction-diffusion model for porous catalyst particles in stirred semibatch reactors applied to three-phase processes. The model was solved numerically for small and large catalyst particles to elucidate the role of internal and external mass transfer limitations. The case studies (citral and sugar hydrogenation) revealed that both internal and external resistances can considerably affect the rate and selectivity of the process. In order to obtain the best possible performance of industrial reactors, it is necessary to use this kind of simulation approach, which helps to optimize the process parameters, such as temperature, hydrogen pressure, catalyst particle size and the stirring conditions. 

Glaze W H, Kang J-W (1989 a) Advanced Oxidation Processes. Description of a kinetic Model for the Oxidation of hazardous Materials in Aqueous Media with Ozone and Hydrogen Peroxide in a semibatch Reactor, Industrial Engineering Chemical Research 28 1573-1580. 

The same example was solved using MINOPT (Rojnuckarin and Floudas, 1994) by treating the PFR model as a differential model. The required input files are shown in the MINOPT manual. Kokossis and Floudas (1990) applied the presented approach for large-scale systems in which the reactor network superstructure consisted of four CSTRs and four PFR units interconnected in all possible ways. Each PFR unit was approximated by a cascade of equal volume CSTRs (up to 200-300 CSTRs in testing the approximation). Complex reactions taking place in continuous and semibatch reactors were studied. It is important to emphasize that despite the complexity of the postulated superstructure, relatively simple structure solutions were obtained with the proposed algorithmic strategy. 

Glaze WH, Kang JH. Advanced oxidation processes. Description of a kinetic model for the oxidation of hazardous materials in aqueous media with ozone and hydrogen peroxide in a semibatch reactor. Ind Eng Chem Res 1989 28 1573-1580. 

The proposed model takes another approach. It was developed for multistage semibatch reactors with stationary solids and continuous co-current reactors with moving solids. It also allows for a crosscurrent stream such as gas sparged separately into any number of stages. The residence time of each stage is divided into a number of finite time intervals. Within each interval, the individual reactions are treated as successive rather than simultaneous. The model accuracy is controlled by selecting the number of intervals. 

Mitra et al. (1998) employed NSGA (Srinivas and Deb, 1994) to optimize the operation of an industrial nylon 6 semibatch reactor. The two objectives considered in this study were the minimization of the total reaction time and the concentration of the undesirable cyclic dimer in the polymer produced. The problem involves two equality constraints one to ensure a desired degree of polymerization in the product and the other, to ensure a desired value of the monomer conversion. The former was handled using a penalty function approach whereas the latter was used as a stopping criterion for the integration of the model equations. The decision variables were the vapor release rate history from the semibatch reactor and the jacket fluid temperature. It is important to note that the former variable is a function of time. Therefore, to encode it properly as a sequence of variables, the continuous rate history was discretized into several equally-spaced time points, with the first of these selected randomly between the two (original) bounds, and the rest selected randomly over smaller bounds around the previous generated value (so as... 

A model has been developed for oxidation of calcium sulfite in a three-phase, semibatch reactor, The overall rate of conversion to sulfate depends on the rates of solid dissolution and liquid phase chemical reaction. In this first treatment of the problem, gas-liquid mass transfer resistance did not affect the overall rate of oxidation. 

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