Differential sidestream reactors

We therefore consider a different reaction flow model as our basic targeting model—one that can address temperature manipulation by feed mixing as well as by external heating or cooling. The model consists of a differential sidestream reactor (DSR), shown in Fig. 6, with a sidestream concentration set to the feed concentration and a general exit flow distribution function. (As mentioned in Section II, the boundary of an AR can be defined by DSRs for higher-dimensional (> 3) problems). We term this particular structure a cross-flow reactor. By construction, this model not only allows the manipulation of reactor temperature by feed mixing, but often eliminates the need to check for PFR extensions. 

Combinations of basic reactor types, such as CSTRs and differential sidestream reactors (DSRs), are arranged in a specific pattern to produce a building block structure for the creation of more sophisticated reactor structures. These superstructures allow for the description of a wider variety of different achievable states. 

Figure A.l (a) Reactor symbol for a plug flow reactor (PFR), (b) reactor symbol for a continuous-flow stirred tank reactor (CSTR), and (c) reactor symbol for a differential sidestream reactor (DSR).

Derive a differential equation that expresses the concentration change in a fed-batch reactor with respect to reaction time t. A constant sidestream concentration C is available and is fed into the fed-batch at a time-dependent volumetric rate of F(t). Constant density may be assumed. 

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