54
Chapter 3
and
r# =y;'
(3.14)
Since the rate of production of all substrates is negative a numerical sign is used in (3.14) to obtain
yield coefficients, which are all positive. In this definition of the yield coefficient the first index
j
in
iji always refers to the reference rate
. 1
Yield coefficients are measured in many consistent set of
units, g g
' 1
or mole mole'1
, or for carbon containing compounds C-moles (C-mole)'1
, and as
discussed in Section 2.2.3 they represent a very important set of design parameters for design and
optimization of fermentation processes.
With the above definition of the yield coefficient a stoichiometric equation for growth of biomass
X
on glucose QH
12
0
6
(or per C-mole: CH
2
0) as the carbon and energy source can now be written:
-C H îO-YJOO
2
-YwNH
3
-y „ i51-.
... + Y„^ + ^ C O
2
+ Yv^ + .
... + yïwH2O =
0
(3.15)
Capital letters are used to denote substrates other than glucose, 0
2
and the nitrogen source, which is
taken to be NH3. Likewise capital letters are used for metabolic products other than C02. In (3.15)
the rates are all scaled by the rate of consumption of glucose in units of 1
C-mole = 30 g. Thus, if
Ysn = 0.05 then 0.05 moles of NH, is consumed every time 30 g = 1 C-mole glucose is consumed by
the chemical reaction (3.15). From (3.15) other yield coefficients, for example the
respiratory
quotient
RQ, which is frequently used in control of industrial scale aerobic reactions are easily
found:
RQ =
Vo
(3.16)
In all stoichiometric calculations in this textbook the chemical formula for the biomass
X
is written
on the basis of one C-mole biomass:
^ C H A N A ft.
..
(3.17)
Likewise all other carbon containing species
Si,
Sj .
..,
Pu P2
....are written on the basis of 1
C-
mole. With this convention a carbon balance gives:
1
+
+
Y*2
+ 1
1
- =
Y sx
+
+
Y sp,
+
K p t
+ *
*
*
(3.18)
Water has been included in the general stoichiometry (3.15), but since the reaction is carried out
in aqueous solution and since the concentration of substrates and products rarely exceeds 5 wt %
the water produced adds so little to the total medium that it can be neglected when calculating the
In the literature one often finds another notation for the yield coefficient, namely
for Yp.