Non-steady-flow Semibatch Reactors

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. 

The mass-balance equations for semibatch operation may include all four of the terms in the general balance, Eq. (3-1). The feed and withdrawal streams from the reactor cause changes in the composition and volume of 

In general the conversion of reactant is not a very useful term for seihib atch operatidhbecause when reactant is present initially in the reactor and is added and deleted in feed and exit streams, there may be ambiguity about the total amount upon which to define x. Instead we shall formulate Eq. (3-1) in terms of the mass fraction w of reactant. If Fq is the total mass feed rate and Fj, is the withdrawal rate, the mass balance for the reactant is 

If the feed-stream conditions and the initial state in the reactor are known, Eq. (4-12) can always be integrated, although numerical procedures may be required. An important case in which analytical integration is possible is when the feed and exit flow rates, feed composition, and density are all constant and the reaction is first order. Piret and Mason have analyzed single and cascades (reactors in series) of stirred-tank reactors operating under these restrictions. The results are a reasonable representation of the behavior for many systems under startup and shutdown periods. With constant density, the concentration accounts fully for changes kt. amount of reactant. Also, constant density along with constant flow rates means that the reactor volume V will remain constant. Under these restrictions Eq. (4-12) may be written 

CHAPTER 4 HOMOGENEOUS REACTOR DESIGN ISOTHERMAL CONDITIONS 

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Fig. 3-1 Ideal stirred-tank reactors classified according to method of operation (a) flow (steady-state), (b) batch, (c) semibatch (non-steady-flow)...

The stirred-iank reactor may be operated as a steady-state flow type (Fig. 3-lu), a batch type (Fig. 3- b), or as a non-steady-state, or semibatch, reactor (Fig. 3-lc). The key feature of this reactor is that the mixing is complete, so that the properties of the reaction mixture are uniform in all parts of the vessel and are the same as those in the exit (or. product) stream. This means that the volume element chosen for the balances can be taken as the volume V of the entire reactor. Also, the composition and temperature at which reaction takes place are the same as the composition and temperature of any exit stream. 

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 operating under non-steady-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. 

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. 

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