An Overview of Chemical Reaction Analysis - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 135

which is then only specific to the stoichiometry of the reactions involved. One often extends
this yield factor definition to include reactants as well, in that case, the amount of species
change in the definition is always defined as the absolute value in the net change (either
increase or decrease). One often extends this yield factor definition to include reactants as
well, in that case, the amount of species change in the definition is always defined as the abso-
lute value in the net change (either increase or different).
Sometimes, one can find that the yield factor defined above is not convenient to use. For
example, counting the number of biomass or cells is not an easy task. We often use another
definition,

Mass of P that could be produced
Mass of A

YF P = A ¼ (3.70)

Because of the various forms of yield or fractional yield are used, it is recommended that the
units being always associated with the yield given. In bioprocess analysis, one often defines
the yield factor on the heat generation along the same line as the yield factor by

D H R

n j

YF H =j ¼ (3.101)

Another factor of importance is the selectivity for multiple reactions. Selectivity is defined
as the fraction of a key reactant that is turned into the desired product, i.e.

#moles of A converted to D
#moles of A reacted

S D = A ¼ (3.102)

Correspondingly, an instantaneous selectivity can be defined as

¼

r A j forming D

d ð #moles of A converted to D Þ

s D = A ¼ (3.103)

d ð #moles of A reacted Þ r A

One of the goals in using catalysts is to increase the selectivity of a desired product.
One cannot overemphasize the importance of mass (or mole) balance in reactor analysis.
It is the most used concept in bioprocess engineering:

(3.118)
It is very simple mathematically and in words, yet it takes a life to learn and master. A math-
ematical translation is given by

Accumulation ¼ flow in flow out þ generation by reaction

d n j
d t ¼

F j0 F j þ r j V (3.119)

Energy balance is performed through the first law of thermodynamics. Energy cannot be
generated nor destroyed, which is different from a particular species in a reaction mixture.
Energy balance leads to
d nU gz

H j0 þ

M j

þ 2 mu 2 þ

X

N S

u 0 þ ¼ Q W s

1
2

þ F j0 gz

0

d t

j ¼1

(3.126)

F j H j þ M j 2 gz

X

N S

u 2 þ

j ¼1