Material Balances
Lecture 1
Biochemical Engineering
Review of
Thermodynamics
• System – any matter
identified for
investigation
• Surroundings – the
remainder of the
universe
• Boundary – separates
system from
surroundings
▫ May be real and tangible
or virtual and nominal
Types of System
• Process – causes changes in the system or
surroundings
• Batch process – operates in a closed system
• Semi-batch process – allows either input or
output of mass
• Fed-batch process – allows input of material to
the system but not output
• Continuous processs – allows matter to flow in
and out of the system
Equilibrium vs Steady-state
• Steady-state
▫ Describes a process in which the properties of the
system (T, p, V, …) doesn’t vary with time
• Equilibrium
▫ Describes a system in which all opposing forces
are counter-balanced, leading to insignificant
changes in the properties of the system
Law of Conservation of Mass
• Given component A, what if Mass in ≠ Mass out?
▫ Something is wrong with the measurements
▫ The system has a leak
▫ Component A is consumed/generated within the
system
▫ Component A accumulates in the system
General Mass Balance
• For component A
Mass in
Mass out
Mass
generated
Mass
consumed
Mass
accumulated
Sample Problem
A continuous process is set up for treatment of
waste water. Each day, 105 kg cellulose and 103 kg
bacteria enter the feed stream, while 104 kg
cellulose and 1.5 x 104 kg bacteria leave the
effluent. The rate of cellulose digestion by the
bacteria is 7 x 104 kg/day. The rate of bacterial
growth is 2 x 104 kg/day; the rate of bacterial lysis
is 5 x 102 kg/day. Write balances for cellulose and
bacteria in the system
Types of Material Balance
• Differential Balance
▫ Used for continuous processes
▫ Based on flow rates
• Integral Balance
▫ Used for batch, semi-batch and fed-batch
▫ Based on the quantity or mass, usualy over a
specified time period
Simplified General Mass Balance: the
Steady-state
At steady-state, does mass in = mass out?
With reaction
Without reaction
Total mass
Yes
Yes
Total moles
No
Yes
Mass of a molecular specie
No
Yes
Moles of a molecular specie
No
Yes
Mass of an atomic specie
Yes
Yes
Moles of an atomic specie
Yes
Yes
Material
𝑚𝑎𝑠𝑠 𝑖𝑛 + 𝑚𝑎𝑠𝑠 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑 = 𝑚𝑎𝑠𝑠 𝑜𝑢𝑡 + 𝑚𝑎𝑠𝑠 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑑
Procedure for material balance
calculation
1. Draw a clear process flow diagram
2. Select a set of units and state it clearly
3. Select a basis for calculation and state it clearly
4. State all assumptions applied to the problem
5. Identify which components of the system are
involved in reaction
A fermentation slurry containing Streptomyces kanamyceticus
cells is filtered using a continuous rotary vacuum filter. Slurry is
fed to the filter at the rate of 120 kg/h; 1 kg slurry contains 60 g
cell solids. To improve filtration rates, particles of diatomaceous
aerth filter aid are added at a rate of 10 kg/h. the concentration
of kanamycin in the slurry is 0.05% by weight. Liquid filtrate is
collected at a rate of 112 kg/h; the concentration of the
kanamycin in the filtrate is 0.045% (w/w). Filter cake
containing cells and filter aid is removed continuously from the
filter cloth.
(a)
What percentage water is in the filter cake?
(b) If the concentration of kanamycin dissolved in the liquid
within the filter cake is the same as that in the filtrate, how
much kanamycin is absorbed per kg filter aid?
1. Draw a clear
process flow
diagram
2. Select a set of
units and state it
clearly
3. Select a basis for
calculation and
state it clearly
4. State all
assumptions
applied to the
problem
5. Identify which
components of
the system are
involved in
reaction
Xanthan gum is produced using Xanthomonas
campestris in batch culture. Laboratory experiments
have shown that for each gram of glucoses utilized by
the bacteria 0.23 g of oxygen and 0.01 g ammonia are
consumed, while 0.75 g gum, 0.09 g cells, and 0.27 g
gaseous CO2 and 0.13 g H2O are formed. Other
components of the system such as phosphate can be
neglected. Medium containing glucose and ammonia
dissolved in 20,000 L water is pumped into a stirred
fermenter and innoculated with X. campestris. Air is
sparged into the fermenter; the total amount of offgas recovered during the entire batch culture is 1250
kg. because xanthan gum solutions have high viscosity
and are difficult to handle, the final gum
concentration should not be allowed to exceed 3.5%
wt.
(a) How much glucose and ammonia are required?
(b) What percentage air is provided?
1. Draw a clear
process flow
diagram
2. Select a set of
units and state
it clearly
3. Select a basis
for calculation
and state it
clearly
4. State all
assumptions
applied to the
problem
5. Identify which
components of
the system are
involved in
reaction