Ideal Flow Reactors - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 244

state, all the time derivatives are zero. Thus, for example, for species A, Eqn (5.33) is
reduced to

F A 0 F A
V ¼r A

(5.53)

Onecanobservethattheleft-handsideisthemolar rate of A fed subtracted the molar rate
of A letting out of the reactor, divided by the reactor volume. Thus, one can refer the left-
hand side as the molar supply rate per reactor volume or simply molar supply rate.
That is,

F A 0 F A
V

MS A ¼ (5.54)

And the right-hand side is the molar consumption rate (or negative molar generation rate)
of A. That is,

MC A ¼r A (5.56)

Therefore, the molar balance equation can be expressed as the molar supply rate of A to the
reactor ( MS A ) equals to the molar consumption rate of A ( MC A ) in the reactor. The solution of
a CSTR problem is thus visually illustrated in Fig. 5.11 . That is,

MC A ¼ MS A (5.57)

For a steady nonisothermal CSTR, there is one more equation needed to be solved
together,

X

N S

F j0 ðH j H j0 ÞþV X

N R

r i DH Ri ¼ UA H ðT c TÞ W s

(5.97)

j¼1 i¼1

The concentrations of reactants in a CSTR are at their lowest level in a CSTR and thus least
available to reaction. In flow reactor design, our interest is not only on the reactor volume but
type of reactors. Usually, a whole bioprocess system optimization (economic analysis) is
applied to determine whether CSTR or PFR is employed. In some cases, one can save time
by knowingly selecting the right type of reactors. Selection of PFR or CSTR depends on
the nature of the reaction mixture and type of reaction (kinetics). One important clue is
that CSTR has the highest product concentrations and lowest reactant concentrations in
the reactor, which is the opposite for PFR. The reactor feed strategy greatly affects the product
mixture. A reactor with optimum feed distribution and/or product separation can yield
significantly more desired product.

Further Reading

Fogler, H.S. 1999. Elements of Chemical Reaction Engineering , (4th ed.). Prentice-Hall.
Hill, C.G. 1977. An Introduction to Chemical Engineering Kinetics and Reactor Design , Wiley & Sons, New York.
Levenspiel, O. 1999. Chemical Reaction Engineering , (3rd Ed.). John Wiley & Sons, New York.
Schmidt, L.D. 2005. The Engineering of Chemical Reactions , (2nd ed.). Oxford University Press, New York.