Energy balance semibatch reactor

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. 

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. 

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 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. 

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. 

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. 

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. 

Up to now we have focused on the steady-state operation of nonisothermal reactors. In this section the unsteady-state energy balance will be developed and then applied to CSTRs, plug-flow reactors, and well-mixed batch and semibatch reactors. 

For multiple reactions occurring in either a semibatch or batch reactor, Equation (9-18) can be generalized in the same manner as the steady-state energy balance, to give... 

The performance of semibatch reactors under isothermal conditions was studied in Sec. 4-8. When the temperature is not constant, an energy balance must be solved simultaneously with the mass-balance equation. In general, the energy balance for a semibatch reactor (Fig. 3-1 c) will include all four items of Eq. (3-2). Following the nomenclature of Sec. 4-8, let Fq and iq be the total mass-flow rates of feed and product streams and Hq and the corresponding enthalpies above a reference state. Then, following Eq. (3-2) term by term, the energy balance over an element of time At is... 

There are a multitude of variations for semibatch operation. Equation (5-22) already includes restrictions that limit its application to specific operating conditions for example, constant mass-flow rates. A frequently encountered case for nonisothermal operation is one in which there is no product stream, one reactant is present in the reactor, and the temperature is controlled by the flow rate of the feed stream containing the second reactant. Figure 4-17 shows this type, and Example 4-13 illustrates the design calculations for isothermal operatioh. The energy balance for this situation reduces to... 

In this chapter, the analysis of chemical reactors is expanded to additional reactor configurations that are commonly used to improve the yield and selectivity of the desirable products. In Section 9.1, we analyze semibatch reactors. Section 9.2 covers the operation of plug-flow reactors with continuous injection along their length. In Section 9.3, we examine the operation of one-stage distillation reactors, and Section 9.4 covers the operation of recycle reactors. In each section, we first derive the design equations, convert them to dimensionless forms, and then derive the auxiliary relations to express the species concentrations and the energy balance equation. 

To express the temperature changes, we write the energy balance equation. For semibatch reactors, the expansion work is usually negligible, and assuming isobaric operation, the energy balance equation is... 

Equation 9.1.46 is the dimensionless energy balance equation for gas-phase, constant-volume semibatch reactors. The correction factor of the heat capacity is... 

Closure. After completing this chapter, the reader should be able to appi the unsteady-state energy balance to CSTRs, semibatch and batch reactor The reader should be able to discuss reactor safety using two examples on a case study of an explosion and the other the use of the ARSST to hel prevent explosions. Included in the reader s discussion should be how t start up a reactor so as not to exceed the practical stability liniit. After reac ing these examples, the reader should be able to describe how to operat reactors in a safe maimer for both single and multiple reactions. 

There is a great variety in the modes of operation of semibatch reactors and transient systems. An energy balance general enough to satisfy all these possibilities becomes unwieldy and often difficult to solve. Several authors have recommended that the energy balance be derived on a case-by-case, system-by-system basis. 

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