An Overview of Chemical Reaction Analysis - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 117

We will write all reactor mass balances as

Accumulation ¼ flow in flow out þ generation by reaction (3.118)

which is an expression we will see many times in mass and/or mole balances throughout this
topic. It is very simple mathematically and in words, yet it takes a life to learn and master.
We must formulate and solve many mass balance equations in reactor analyses. We
strongly encourage the student not to memorize anything except the basic defining relations.
We stress that you should be able to derive every equation from these definitions as needed.
This is because (1) only by being able to do this will you understand the principles of the
subject; and (2) we need to make many different approximations, and remembering the
wrong equation is disastrous.
To begin apply this equation, one should always start with identifying the control volume
or system of interest. This can be the whole reactor if it is well mixed or a differential volume
at a given or arbitrary location inside a vessel. Let us consider a general case whereby the
volume of the system (control volume) under consideration is V as shown in Fig. 3.7 where
for a given chemical species j, its feed rate, withdrawing rate, and number of moles inside the
system are shown. The mole balance equation can thus be written mathematically as

d n j
d t ¼

F j0 F j þ r j V (3.119)

which corresponds term by term to the literal expression (3.118) . Therefore, one could
consider Eqn (3.119) as the general mass balance equation.

Example 3-5: Fermented Rice
Two kilograms of rice is cooked in 2 kg-water. The cooked rice and water mixture are
cooled to 30 C andmixedwith 10 g of yeast. The rice-water-yeast mixture is sealed in a vessel
undergoing anaerobic fermentation for 48 h at 30 C. The final mixture (solids, water, and
alcohol) can be eaten as alcoholic food. Assuming that the chemical formulas for rice is the
same as starch or HO(C 6 H 10 O 5 ) n H and that the alcohol content in the final mixture is 5%
(after gas released), find the total mass of the fermented rice mixture.
Solution: Figure E3-5 on the right shows a sketch to illustrate the problem. Drawing
a sketch helps us to collect the thoughts together before tackling the problem. Assuming
that all the hydrolyzed starch is converted to ethanol, the stoichiometry is then given by

/ 2

n C 2 H OH 2 n CO

5 2

HO ð C H O

5 Þ

n H þð n 1 Þ H O þ

10

6 2

2 n 46:07 2 n 44:01

F j0

V
n j

F j

FIGURE 3.7 Schematic of a control volume or system of interest for performing mass balances. A chemical
species j enters into the system at a flow rate of F j0 and leaves at a flow rate of F j . The volume of the system is V,
which contains n j moles of chemical species j.