Semibatch reactor variable volume

The CSTR operator, Rc, has an identical term to describe accumulation under transient operation. The algebraic sum of the two other terms indicates the difference of in-flow and out-flow of that species. This operator also describes semibatch or semicontinuous operation in cases where the volume can be assumed to be essentially constant. In the more general case of variable volume, V must be included within the differential accumulation term. At steady state, it is a difference equation of the same form as the differential equation for a batch reactor. 

Figure 9.1 Semibatch reactors (a) liquid phase (variable volume) and (b) gas phase (constant volume).

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... 

From the discussion in Example 5.2, semibatch operation with continuous addition of DAA to hypochlorite appears to be the preferred mode of reactor operation. Using the same nomenclature as in that example, and employing the equations summarized in Table 10.2 for different variable volume semibatch reactions, the following equation can be written for component i in reaction j ... 

The rate terms for the different reactions comprising E, r,y are given by Equations E5.3.2-E5.3.8. Using these equations. Equation El 1.2.1 can be resolved into the following set of variable volume semibatch reactor equations ... 

If the system involves more than one dependent variable (such as a semibatch unit in which both the volume and composition of the system contents vary or a reactor in which several... 

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