Page 324 - Elements of Chemical Reaction Engineering Ebook

Sec. 6.3 Algorithm for Solution to Complex Reactions 295

Another technique is often used to follow the progress for two reactions
in series. The concentrations of A, B and C are plotted as a singular poiint at
different space times (e.g., q' , T; ) on a triangular diagram (see Figure 6-4).
The vwtices correspond to pure A, B, and C.
For (k,/k2)*1 a
large quantity of B 6
can be obtained

For (k,/k,) 1
very little B can be
obtained

A C
Figure 6-4 Reaction paths for different values of the specific rates.

6.3 Algorithm for Solution to Complex Reactions

6.3.1 Mole Balances

In complex reaction systems consisting of combinations of parallel and
series reactions the availability of software packages (ODE solvers) makes it
much easier to solve problems using moles Nj or molar flow rates 5 rather than
conversion. For liquid systems, concentration may be the preferred variable used
in the mole balance equations. The resulting coupled differential equations can
be easily solved using an ODE solver. In fact, this section has been developed
to take advantage of the vast number of computational techniques IIQW available
on mainframe (e.g., Simulsolv) and personal computers (POLYMATH).
Table 6-1 gives the forms of the mole balances we shall use for complex
reactions where rA and r, are the net rates of reaction.

TABLE 6-1. MOLE BALANCES FOR MULTIPLE REACTIONS
- Gas Liquid
Reactor
Batch dN, rAv dCA =
dt dt
These are the forms CSTR V=- FA0 - FA v=uo-
CAO - cA
of the mole balances - 'A - rA
we will use for dFA - ug -
dCA -
--
multiple reactions PFRlPBR dV rA dV -
Semibatch % = rAV dCA 'OCA
dt dt = rA-- V
vg [C,, - CBI
V