Semibatch reactor material balance

Unsteady material and energy balances are formulated with the conservation law, Eq. (7-68). The sink term of a material balance is and the accumulation term is the time derivative of the content of reactant in the vessel, or 3(V C )/3t, where both and depend on the time. An unsteady condition in the sense used in this section always has an accumulation term. This sense of unsteadiness excludes the batch reactor where conditions do change with time but are taken account of in the sink term. Startup and shutdown periods of batch reactors, however, are classified as unsteady their equations are developed in the Batch Reactors subsection. For a semibatch operation in which some of the reactants are preloaded and the others are fed in gradually, equations are developed in Example 11, following. 

There are a variety of limiting forms of equation 8.0.3 that are appropriate for use with different types of reactors and different modes of operation. For stirred tanks the reactor contents are uniform in temperature and composition throughout, and it is possible to write the energy balance over the entire reactor. In the case of a batch reactor, only the first two terms need be retained. For continuous flow systems operating at steady state, the accumulation term disappears. For adiabatic operation in the absence of shaft work effects the energy transfer term is omitted. For the case of semibatch operation it may be necessary to retain all four terms. For tubular flow reactors neither the composition nor the temperature need be independent of position, and the energy balance must be written on a differential element of reactor volume. The resultant differential equation must then be solved in conjunction with the differential equation describing the material balance on the differential element. 

For semibatch operation, the term fraction conversion is somewhat ambiguous for many of the cases of interest. If reactant is present initially in the reactor and is added or removed in feed and effluent streams, the question arises as to the proper basis for the definition of /. In such cases it is best to work either in terms of the weight fraction of a particular component present in the fluid of interest or in terms of concentrations when constant density systems are under consideration. In terms of the symbols shown in Figure 8.20 the fundamental material balance relation becomes ... 

In this chapter, we first consider uses of batch reactors, and their advantages and disadvantages compared with continuous-flow reactors. After considering what the essential features of process design are, we then develop design or performance equations for both isothermal and nonisothermal operation. The latter requires the energy balance, in addition to the material balance. We continue with an example of optimal performance of a batch reactor, and conclude with a discussion of semibatch and semi-continuous operation. We restrict attention to simple systems, deferring treatment of complex systems to Chapter 18. 

In a typical slurry bubble column operation, the liquid velocity is one order of magnitude lower than the one of gas, and in general, is very low. This mode of operation can be approximated by a semibatch operation. The semibatch operation is frequently used and is the case where the liquid and the catalyst comprise a stationary phase (sluny) in the reactor. In this case, the material balance, eq. (3.122) is used along with the overall rate based on the bulk gas-phase concentration (see Section 3.4.6). In the following, the semibatch operation is presented. 

The semibatch reactor is a cross between an ordinary batch reactor and a continuous-stirred tank reactor. The reactor has continuous input of reactant through the course of the batch run with no output stream. Another possibility for semibatch operation is continuous withdrawal of product with no addition of reactant. Due to the crossover between the other ideal reactor types, the semibatch uses all of the terms in the general energy and material balances. This results in more complex mathematical expressions. Since the single continuous stream may be either an input or an output, the form of the equations depends upon the particular mode of operation. 

A schematic illustration of the hydroformylation reactor is provided in Figure 3.2.2. The material balance on a semibatch reactor can be written for a species... 

Semibatch Reactor (SBR) In semibatch operation, a gas of limited solubility or a liquid reactant may be fed in gradually as it is used up. An ideal isothermal single-phase semibatch reactor in which a general reaction network takes place has the following general material balance equation ... 

Consider the reaction Ag -I- B C taking place in a semibatch reactor with a concentration Cg and an active volume V. Assume the reaction is first order to A and to B and that the gas-phase resistance is negligible. The unsteady-state material balance for A is... 

In the analysis of batch reactors, the two flow terms in equation (8.0.1) are omitted. For continuous flow reactors operating at steady state, the accumulation term is omitted. However, for the analysis of continuous flow reactors under transient conditions and for semibatch reactors, it may be necessary to retain all four terms. For ideal well-stirred reactors, the composition and temperature are uniform throughout the reactor and all volume elements are identical. Hence, the material balance may be written over the entire reactor in the analysis of an individual stirred tank. For tubular flow reactors the composition is not independent of position and the balance must be written on a differential element of reactor volume and then integrated over the entire reactor using appropriate flow conditions and concentration and temperature profiles. When non-steady-state conditions are involved, it will be necessary to integrate over time as well as over volume to determine the performance characteristics of the reactor. 

At the time Kladko s article (5) was prepared, market conditions dictated that it would not be financially remunerative to develop a continuous process for producing B by the reaction discussed in Illustration 10.1 and other illustrations in this chapter. Consequently, they considered the possibility of using a semibatch reactor with continuous addition of cold feed to maintain the temperature of the reactor contents within prescribed limits. The basic problem was considered in Illustration 8.11. However, in addition to the material balance aspects of the design, we now wish to consider the heat transfer requirements for operation in accordance with the filling schedule outlined earlier. For the conditions indicated in Illustration 8.11 (isothermal, 163°C) determine the direction and magnitude of the heat transfer requirements. 

In developing the solution to Illustration 13.1, we utilized a variation of the traditional material balance on a batch reactor that is often useful in the analysis of biochemical transformations carried out in batch and semibatch modes of operation. In particular, we took into account variations in the volume of the broth in the bioreactor by first converting concentrations of biomass and substrate into the total quantities of these materials present in the bioreactor. In so doing we were implicitly recognizing that the proper form of a material balance on species i for variable-volume situations is... 

In this semibatch operation a batch of liquid is taken into a reactor and a stream of gas passed through it (Figure 16.2d). The problem here is usually one of calculating the time needed for a given conversion in a reactor of known volume. The following material balance can be written ... 

Fluid-Fluids dnd Fluid-Fluid-Solids 503 A material balance on oxygen for this semibatch reactor gives (see Equation 16.25). 

The material balances in a semibatch polymerization reactor for a copolymer system are as follows ... 

For semibatch or semiflow reactors all four of the terms in the basic material and energy balance relations (equations 8.0.1 and 8.0.3) can be significant. The feed and effluent streams may enter and leave at different rates so as to cause changes in both the composition and volume of the reaction mixture through their interaction with the chemical changes brought about by the reaction. Even in the case where the reactor operates isothermally, numerical methods must often be employed to solve the differential performance equations. 

There are five primary reactor designs based in theory batch, semibatch, continuous-stirred tank, plug flow, and fluidized bed. The operating expressions for these reactors are derived from material and energy balances, and each represents a specific mode of operation. Selected reactor configurations are presented in Fig. 1. 

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