The Semibatch Reactor

Introduction to Reactor Design Fundamentals for Ideal Systems 307 

Following eonsiders the material balanees of both eomponents A and B. From the material balanee Equation 5-1 

Input Output Rate Rate Disappearanee Rate of hy reaetion Aeeumulation (5-1) 

310 Modeling of Chemioal Kinetios and Reaotor Design Substituting Equation 5-134 into Equation 5-145 yields 

Equations 5-146, 5-149, and 5-152 are first order differential equations. The concentration profiles of A, B, C, and the volume V of the batch using Equation 5-137 is simulated with respect to time using the Runge-Kutta fourth order numerical method. 

Equations 5-137, 5-146, 5-149, and 5-152 can be incorporated respectively in the subprogram of a computer code as follows 

The computer program BATCH510 was developed incorporating Equations 5-156, 5-157, 5-158, and 5-159 in the subprogram of the Runge-Kutta fourth order program. The results of the simulation are 

Charge rate Charge concentration Initial volume 

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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 semibatch reactor where the incoming and outgoing mass flows are not equal to each other, and the total mass of the reacting mixture is not constant. 

Figure 4.1 Broad classification of reactor types, a) The batch reactor, b) The steady-state flow reactor, (c), d), and (e) Various forms of the semibatch reactor.

Where the composition within the reactor is uniform (independent of position), the accounting may be made over the whole reactor. Where the composition is not uniform, it must be made over a differential element of volume and then integrated across the whole reactor for the appropriate flow and concentration conditions. For the various reactor types this equation simplifies one way or another, and the resultant expression when integrated gives the basic performance equation for that type of unit. Thus, in the batch reactor the first two terms are zero in the steady-state flow reactor the fourth term disappears for the semibatch reactor all four terms may have to be considered. 

Note that this is exactly the transient CSTR equation we derived previously, and elimination of the flow terms yields the batch reactor. Keeping aU these terms and allowing Uq, v, V, and Cao to vary with time yields the semibatch reactor. 

The semibatch reactor combines attributes of the batch and the continuous-stirred tank. The reactor is essentially batch but has either a continuous input or output stream during operation. 

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. 

Physically, the semibatch reactor looks similar to a batch reactor or a CSTR. Reaction occurs in a stirred tank, with the following assumptions (1) the contents of the tank are well mixed, and (2) there are no inlet or outlet effects caused by the continuous stream. 

The semibatch reactor is one of the primary ideal reactor types since it can not be accurately described as either a continuous or a batch reactor. A semibatch reactor is usually classified as a type of transient reactor. 

The temperature-controlling features of this reaction scheme dominate selection and use of the reactor. However, the semibatch reactor does have some of the advantages of batch reactors temperature programming with time and variable reaction time control. 

Writii the Semibatch Reactor Eqaations in Terms of Concentrations. Recalling that the number of moles of A is just the product of concentration of A, C, and the volume V, we can rewrite Equation (4-51) as... 

Writing the Semibatch Reactor Equations in Ihnns of Conversion. Consider the reaction... 

Writing the Semibatch Reactor Equations in Terms of the Number of Moles. We can also solve semibatch reactor problems by leaving the mole balance equations in terms of the number of moles of each species (i.e., N, ... 

The semibatch reactor was defined in Chap. 3 (Fig. 3-1 c) as a tank type operated on a non-steady-flow basis. Semibatch behavior occurs when a tank-"flow reactor is started up, when its operating conditions are changed from one steady state to another, or when it is shut down. Purging processes in which an inert material is added to the reactor can also be classified as semibatch operation. 

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... 

The longitudinal reardor, with multiple injection of one reactant, is a special case and corresponds to the semibatch reactor. 

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