Sustainability and Stability - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 801

and

H G ¼ rðDH R Þ (16.18)

Eqn (16.14) can be reduced to

d T
d t ¼

H G H R
P N S (16.19)

j¼1 C j C Pj

The way we regrouped to H R and H G are such that H R is the heat of removal from the reactor
(via the heat exchanger jacket and the reaction mixture flowing out, subtracted by the energy
input due to the stirrer) and H G is the heat generated in the reactor due to the reaction. Noting
from Eqn (16.18), H R is linearly related to reactor temperature T (straight line), while H G is
directly proportional to reaction rate in the reactor based on Eqn (16.8) and constant D H R .
If we normalize H G and H R with ( D H R ), then H 0 G ¼ H G /( D H R ) is equivalent to the rate
of reaction in the reactor while H 0 R ¼ H R /( D H R ) is still linearly related to T.
At steady state, Eqn (16.19) is reduced to

H R ¼ H G (16.20)

And Eqn (16.13) is reduced to

DC A þ r ¼ DC A0 (16.21)

For a given kinetics, r ¼ f(T, C A ), the steady-state solutions can be obtained by two visual
ways, depending which of the two Eqns (16.20) and (16.21) is solved first.
The first approach is solving the energy balance Eqn (16.20) first to render r and/or T as
a function of reactant concentration in the reactor C A only for a given heat-exchanging capac-
ities,

, and C A0 . Combining with the mole balance Eqn (16.21) , we can completely solve the
steady states of the CSTR. In this case, the solution procedure and qualities have been dis-
cussed in Section 16.1, except the influence of feed temperature, and heat-exchanging capac-
ities. Nevertheless, we already learned how to approach the problem.
The second way is solving the mole balance Eqn (16.21) first to render r and/or C A as
a function of reactor temperature T only for a given

s

and C A0 . Table 16.1 shows the solutions
for some simple kinetic models. Combining with the energy balance Eqn (16.20) , we can
completely solve the steady states of the CSTR. Fig. 16.10 illustrates graphically how Eqn
(16.20) is used to solve for the steady-state reactor operating temperature T. For the conve-
nience of discussion, we further lump the operating parameters such that the heat of
removal, Eqn (16.17) , is reduced to

s

H R ¼ C HV ðT T H Þ (16.22)

where

V þD X

N S

UA H

C HV ¼ C j0 C Pj (16.23)

j¼1