Material
balances (mass balances) are based on the fundamental “law of conservation of
mass (not volume, not moles)”. In particular, chemical engineers are concerned
with doing mass balances around chemical processes.
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Doing a ‘mass
balance’ is similar in principle to accounting. In accounting, accountants do
balances of what happens to a Company’s money. Chemical engineers do a mass
balance to account for what happens to each of the chemicals that is used in a
chemical process.
Thus far,
we have learned about the process variables that we need to describe the
chemicals entering a process stream. Now, we must learn how to
a)
Specify a process stream
b)
Specify a process unit
c)
Do a mass balance on a process unit
d)
Do a mass balance on a sequence of
process units.
Classification of Processes
A.
Based
on how the process varies with time.
a. Steady-state
process is one that does not change with time. Every time we take a
snapshot, all the variables have the same values as in the first snapshot.
b. Unsteady-state (Transient) process
is one that changes with time. Every time we take a snapshot, many of the
variables have different values than in the first snapshot.
B.
Based
on how the process was built to operate.
a.
A
Continuous process is a
process that has the feed streams and product streams moving chemicals into and
out of the process all the time. At every instant, the process is fed and
product is produced. Examples are an oil refinery, a power grid and a steady
salaried job.
b.
A
Batch process is a process
where the feed streams are fed to the process to get it started. The feed
material is then processed through various process steps and the finished
products are created during one or more of the steps. The process is fed and
products result only at specific times. Examples are making a batch of a
product, like soup or a specialty chemical.
c.
A
Semi-batch process (also called
semi-continuous) is a process that has some characteristics continuous and
batch processes. Some chemicals in the process are handled batch-wise. Some
chemicals are processed continuously.
Types of Balances
a.
Differential Balance is a balance taken at a specific
instant in time. It is generally applied to a continuous process. If the process is at steady state, a differential
balance applied at any time gives the same result.
We will apply differential balances
to steady-state continuous processes.
Each term in a differential balance
represents a process stream and the mass flow rate of the chemical(s)
in that stream.
b.
Integral balance is a balance taken at two specific
instants in time. It describes what has happened over the time period between
the two points. An integral balance is generally applied to the beginning and
the end of a batch process. It accounts for what happens to the batch of
chemicals.
We will apply integral balances to
batch processes.
Each term in an integral balance represents
a process stream and the mass of
the chemical(s) in that stream.
The Mass Balance Equation
The
law of “conservation of mass” states that mass
cannot be created or destroyed. We will use this law in the form of a
general mass balance equation to account for the total mass all of the
chemicals that are involved in the process. The total mass balance equation can
be written as
INPUT
-
OUTPUT = ACCUMULATION
I -
O = A
If
the process is at steady-state,
there is no accumulation of mass within the process. In CHEN 200, we will deal
only with steady-state processes. Thus
INPUT
= OUTPUT
I
=
O
When
we apply this equation to a process, it is best to write it as
S Masses entering via feed streams
= SMasses exiting via product streams
We
understand that we must include the mass
of every chemical in every stream. The above equation can applied to
batch and continuous processes as
SMass in = SMass out for a
batch process, and
SMass in by flow = SMass out by flow for a continuous process.
If
the process involves chemical reaction(s), we must account for the formation of
product chemicals and the consumption of feed chemicals. We must remind
ourselves that the law of conservation of mass means total mass. For this case,
we must write a mass balance for each chemical and account its formation and
consumption as follows
S Mass in + Mass formed by
reaction = SMass out + Mass used by reaction
Or,
written more simply as
in
+ formed = out + consumed
What
balances can one write?
1.
A
mass balance can be written using the total mass in each process stream. This
is called a total balance.
2.
A
separate mass balance can be written for each chemical component involved.
These are called component balances.
Example:
A process unit involves 3 chemical components. How many mass balances can be
written?
Solution: We can write 4 balances. We can write a
total balance and 3 component balances.
Independent
balances: Not all balances are independent since the total balance in the sum
of all of the component balances.
Thus, the number of independent balances we can
write = the number of components.
Which
of the following must be conserved in a chemical process?
Total
mass
Mass
of a chemical
Total
moles
Moles
of a chemical
Mass
of a specie
Moles
of a specie
Mass
of an element
Moles
of an element
What’s
next? You need to develop skill at using
a systematic approach to solving mass balance problems. And later, skill at
using a systematic approach to solving mass and energy balance problems.
Where am I? Where am I going ? How do I get there?
To
answer the first question, you need to
1.
Read,
study and understand the problem.
2.
Draw
a flow sheet for the process.
3.
Label
it with all given information, including symbols for the unknowns
4.
Note
any special relationships.
To
accomplish this step, you need to learn
1.
The
information needed to specify a stream.
2.
How
to use symbols to represent the required stream data.
3.
How
to determine the mass of each component in a stream (each mass will be a term
in a mass balance)
Required Stream Information
1. Stream name & symbol (1)
2. Component masses/ stream composition (n)
3. Stream temperature and pressure (these
are needed only when an energy balance is being done, phase behavior is
included or to specify chemical properties.
How to represent the required
information
1. Specify
each stream and total mass
--- Select a stream name & symbol
a) Use a single Capital letter to
represent the total mass( or mfr) of the stream.
b) Select a stream name to clearly
identify the stream, by the location or purpose of the stream on the flow
sheet.
c)
Put
the mass/mfr on the flow sheet using an equation symbol = value (if the mass
is known) or symbol = ? (if the value is unknown)
Example: The reactor is fed with 25
kg/s of a hot feed stream and a recycle
stream. Label the reactor inputs.
Solution: The reactor has two input
streams. We draw and label them as
NOTE: The total mass balance will be written
using the symbols selected for the stream names.
Next
we must learn how to represent the component masses so we can write the
component balances.
2. Component masses/ stream composition
A component mass can be represented directly, using a lower case letter and a
subscript, or indirectly using the fractional composition times the stream
total (use and reserve x,y,z for fractional composition).
Note
that a component mass can be calculated
as the product of the total and the fractional composition.
Example1:
Stream F contains 500 kg of O2 and 700 kg of CH4. Label
the stream.
Solution:
Note that the component masses must add to the total. The total mass in F is
1200 kg. Thus,
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Stream F F=1200 kg
m O2 = 500 kg
m CH4 = 700 kg
Example2:
1200 kg of a mixture of O2 , N2 and CH4 are fed to a process. The stream has
20% O2 by mass. Label the
stream.
(
Note the Mass of i in the stream is F xi )
Solution:
The composition is partially known. Note that the fractional compositions must
add to 1.0. Thus, we can write two alternatives
Using
fractional composition
 |
Feed
Stream F, F=1200 kg
xO2 = 0.2
xN2 = ?
xCH4 = 1. – 0.2 -
xN2 = 0.8 - xN2
or
using component masses
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Feed
Stream F, F=1200 kg
mO2
= 240 kg
mN2 = ?
mCH4 = 1200 - 240
- mN2 = 960 - mN2
Some
Suggestions for Component Labeling
1. If the stream composition is unknown
(or if some of the component masses are known) represent the component masses
directly and use a lower case letter for each chemical.
E.g. If stream F contains chemicals
a, b and c, label the flow rates as
F, aF, bF
and cF=F- aF - bF
2. If the stream composition is known
from fractional compositions, represent the component masses directly and label
as in 2.
3. If stream composition is partially
known with fractional compositions and the total is known, represent the
component masses indirectly and use
lower case x,y,z for each fractional composition.
4. Avoid the creation of a product of
two unknowns—this will result in a non-linear equation.
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