Biomedical Engineering Reference
In-Depth Information
where the subscript 0 denotes for the inlet, whereas no subscript indicating the outlet.
Note:
Q
is the net heat transfer into the system, including through electric conversion and
subtraction of the frictional thermal loss by the fluid mixture. Heat of reaction is not in either
Q
or
W
s
.
In most cases, the kinetic energy and gravitational energy can be neglected, other than in
an electro-hydro facility, or for simple flow loop calculations. Thus, Eqn
(3.126)
can be simpli-
fied to
X
N
S
X
N
S
d
ð
nU
Þ
¼ Q
W
s
þ
F
j0
H
j0
F
j
H
j
(3.127)
d
t
j
¼1
j
¼1
The energy balance equation for an open system is reduced to that for closed system if
there is no flow in or out of the system, i.e. F
0. When chemical reaction occurs, internal
energy changes and so are the enthalpies according to the species change. Equation
(3.127)
can be simplified as
X
¼
H
j
N
S
V
X
N
R
X
N
S
d
T
d
t
d
ð
pV
Þ
¼ Q
W
s
F
j0
H
j0
þ
r
i
DH
R
i
þ
C
P
j
n
j
(3.134)
d
t
j
¼1
i
¼1
j
¼1
which is the general energy balance equation. It is applicable to both flow (i.e. open) and
batch (closed) systems. The assumptions we have made to obtain this equation are that the
elevation and kinetic energy change can be neglected, and that the contents in the control
volume (or system) are either condensed matters (solids and/or liquids) or ideal gases.
Therefore, Eqn
(3.134)
is valid in almost all the situations where reactors are used. On the
left hand side of Eqn
(3.134)
, the first term resembles the enthalpy change; the second term
can be thought of as the heat of generation due to reaction; the third and the fourth terms
together can be thought of as the accumulation of energy (which is not exactly true). On
the right hand side of Eqn
(3.134)
, they are the net energy rate being transferred to the system.
Therefore, the interpretation can help us remember the general energy equation.
Ideal reactors are defined as well mixed, i.e. no concentration, pressure, or temperature
gradients in the reactor, except along the axial direction of a tubular reactor or PFR where
absolutely no mixing is assumed. The idealization is meant to simplify the reactor analysis,
thus obtaining an estimate quicker. There are three types of ideal reactors: batch, PFR, and
CSTR. A batch reactor is a reactor, in which the contents are only changing with time. While
CSTR has a similar appearance as a batch reactor, its contents are not changing with time at
all with constant feed and withdrawing that were absent in a batch reactor. PFR is like
a tubular reactor, the contents are changing only along the direction of flow.
Bioprocess engineers are commonly faced with problems of optimizing a facility or
a process equipment. We often approach the problem by either maximizing the profit or
minimizing the cost of operation.
Further Reading
Fogler, H. S. (2006). Elements of Chemical Reaction Engineering (4th ed.). Prentice-Hall.
Levenspiel, O. (1999). Chemical Reaction Engineering (3rd ed.). New York: John Wiley & Sons.
Sandler, S. I. (2006). Chemical, Biochemical, and Engineering Thermodynamics (4th ed.). New York: John Wiley & Sons.
Schmidt, L. D. (2005). The Engineering of Chemical Reactions (2nd ed.). New York: Oxford University Press.
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