Semibatch reactors design equations

Semibatch Reactors Design Equations for (1,0)- and (1,1)-Order Reactions... 

Semibatch reactors Design equations for (1,0)-and (l,l)-order reactions... 

Semibatch or semiflow processes are among the most difficult to analyze from the viewpoint of reactor design because one must deal with an open system under nonsteady-state conditions. Hence the differential equations governing energy and mass conservation are more complex than they would be for the same reaction carried out batchwise or in a continuous flow reactor operating at steady state. 

From this general mole balance equation we can develop the design equations for the various types of industrial reactors batch, semibatch, and continuous-flow. Upon, evaluation of these equations we cau determine the time (batch) or reactor volume (continuous-flow) necessary to convert a specified amount of the reactants to products. 

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 derive the design equation of a semibatch reactor, we write a species balanee for any speeies, say species j, that is not fed continuously into the reactor. Its molar balance equation is... 

To reduce the design equation to dimensionless form, we have to select a reference state and define dimensionless extents and dimensionless time. The reference state should apply to all operations, including those with an initially empty reactor, and should enable us to compare the operation of a semibatch reactor to that of a batch reactor. Therefore, we select the molar content of the reference state, (A tot)o. as the total moles of species added to the reactor. The dimensionless extent is defined by... 

For constant volume, gas-phase semibatch reactors, Vuit) = V (0) = and the design equation (Eq. 9.1.2) reduces to... 

These equations remain valid for bioreactors provided that one employs a suitable mathematical representation of the rate of disappearance of the substrate that is the limiting reagent. In Illustration 13.3 we employ an alternative form of the design equation to determine the holding time necessary to achieve a specified degree of conversion in a strictly batch bioreactor. This illustrative example also indicates how overall yield coefficients are employed as a vehicle for taking the stoichiometry of the reaction into account. Illustration 13.4 describes how one type of semibatch operation (the fed-batch mode) can be exploited to combine the potential advantages of batch and continuous flow operation of a stirred-tank reactor. 

Polymerization of reactants is a common occurrence in many reactions. Although this is also a parallel scheme, it will be noticed that high concentrations of A combined with low concentrations of B will favor the desired product R. Thus, a semibatch reactor (SBR) would be the preferred candidate since the above condition is met in this reactor. We will see the design equations and principles of operation of SBRs later in this chapter. On the other hand, the common BR, PFR, and MFR would all give lower selectivities because they all allow the second reaction to proceed without hindrance. 

Parallel reactions (nonreacting products) The general case Effect of reaction order One of the reactants undergoes a second reaction Parallel-consecutive reactions Plug-flow reactor with recycle The basic design equation Optimal design of RPR Use of RPR to resolve a selectivity dilemma Semibatch reactors... 

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 Chapter 3, the analytical method of solving kinetic schemes in a batch system was considered. Generally, industrial realistic schemes are complex and obtaining analytical solutions can be very difficult. Because this is often the case for such systems as isothermal, constant volume batch reactors and semibatch systems, the designer must review an alternative to the analytical technique, namely a numerical method, to obtain a solution. For systems such as the batch, semibatch, and plug flow reactors, sets of simultaneous, first order ordinary differential equations are often necessary to obtain the required solutions. Transient situations often arise in the case of continuous flow stirred tank reactors, and the use of numerical techniques is the most convenient and appropriate method. 

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... 

Three-phase reactors are operated in either the semibatch or continuous mode, and batch operation is almost never used because the gas phase is invariably continuous. The general principles of design are the same for all types of reactors for a given mode of operation, semibatch or continuous. They differ with respect to their hydrodynamic features, particularly mass and heat transfer. Thus, for simple first-order reactions. Equation 17.8 is valid for any reactor. The rate constant ky,i would be the same for all of the reactors, but specific to each reactor type is the mass transfer term k/. Hence we consider first the design of... 

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