Mass and Energy Balance
Part 2 Mass Balance
41
Part 2 Mass balance
¾
The Concept of a Material Balance
¾
Program of Analysis of Material Balance Problems
¾
S i Material
Solving
i Balance Problems That Do Not Involve Reactions
i
¾
Solving Material Balance Problems That Involve Chemical Reactions
¾
Solving Material Balance Problems Involving Multiple Subsystems
42
The Concept of a Material Balance
¾
The concept of the macroscopic mass balance
⎧accumulation⎫ ⎧ input
⎫ ⎧ output ⎫ ⎧generation⎫ ⎧consumption⎫
⎪ with
⎪ ⎪ through ⎪ ⎪ through ⎪ ⎪ within ⎪ ⎪ within
⎪
⎪
⎪ ⎪
⎪ ⎪
⎪ ⎪
⎪ ⎪
⎪
=
−
+
−
⎨
⎬ ⎨
⎬ ⎨
⎬ ⎨
⎬ ⎨
⎬
the
the
⎪
⎪
⎪ ⎪ system ⎪ ⎪ system ⎪ ⎪ the
⎪ ⎪
⎪⎩ system
⎪⎭ ⎩⎪boundaries⎭⎪ ⎪⎩boundary ⎪⎭ ⎩⎪ system ⎪⎭ ⎩⎪ system
⎪⎭
43
Open and Closed Systems
System
¾
Open system
¾
Closed System
44
Steady-State and Unsteady-State systems
¾
An open steady
steady-state
state system
45
A open unsteady-state system with accumulation
46
Multiple Component System
¾
An open system involving two components
47
Mixing of a dilute stream of NaOH with a concentration stream of NaOH. Values
below the stream arrows are based on 1 hour of operation.
48
Let us require as to what is balanced
¾
Total mass
¾
Total mole
¾
M
Mass
off a chemical
h
i l compound
d
¾
Mass of an atomic species
¾
Moles of a chemical compound
¾
Moles of an atomic species
¾
Volume (possibly)
49
Program of Analysis of Material Balance Problems
W=?
Composition
50% EtOH
40% H2O
10% MeOH
F=100 kg
C
Composition
EtOH?
H2O?
MeOH?
wH2O
wMeOH
mH2O
mMeOH
P=60 kg
T=300C
System
Boundary
50
Mass fr.
fr
Mass
wEtOH mEtOH
Composition
80% ETOH
5% H2O
15% MeOH
Strategy for Analyzing Material Balance Problems
¾
Read the problem and clarify what is to be accomplished.
¾
Draw a sketch of the process; define the system by a boundary.
¾
Label with
i symbols the flow
f
off each stream and the associated
i
compositions
i i
and
other information that is unknown.
¾
Put all the known values of compositions and stream flows on the figure by each
stream; calculate additional compositions and flows from the given data as
necessary, Or, at least initially identify the known parameters in some fashion.
¾
Select a basis
51
Strategy for Analyzing Material Balance Problems
¾
Make a list by symbols for each of the unknown values of the stream flows and
compositions, or at least mark them distinctly in some fashion, and count them.
¾
Write down the names of an appropriate set of balances to solve; write the
balances down with type of balance listed by each one. Do not forget the implicit
balances for mass or mole fractions.
¾
Count the number of independent balances that can be written; ascertain that a
unique solution is possible.
possible If not,
not look for more information or check your
assumptions.
¾
S l the
Solve
h equations.
i
E h calculation
Each
l l i must be
b made
d on a consistent
i
b i
basis.
¾
Check your answers by introducing them, or some of them, into any redundant
material balances. Are the equations satisfied? Are the answers reasonable?
52
Example: Membrane Separation
¾
Membranes represent a relatively new
technology for the separation of gases. One
use that
h
h
has
attracted
d attention
i
i the
is
h
separation of nitrogen and oxygen from air.
Fi re illustrates
Figure
ill strates a nano-porous
nano poro s membrane
that is made by coating a very thin layer of
polymer on a porous graphite-supporting
graphite supporting
layer.
¾
Wh t is
What
i the
th composition
iti
off the
th waste
t
stream if the stream amounts to 80% of the
input.
input
53
Example: Continuous Distillation
¾
A novice manufacturer of alcohol
for gasohol is having a bit of
difficulty
y
with
a
distillation
column. The operation is shown
in Figure. Technicians think too
much alcohol is lost in the
bottoms (waste). Calculate the
composition of the bottoms and
the mass of the alcohol lost in
th bottoms.
the
b tt
54
Example: Mixing of Battery (Sulfuric) acid
¾
You are asked to prepare a batch of new
18.63 % acid as follows. A tank of old
weak
battery
acid
H2SO4
solution
contains 12.43 % H2SO4 (the remainder is
pure water). If 200 kg of 77.7% H2SO4 is
added to the tank, and the final solution
is to be 18.63 % H2SO4, how many
y
kilograms of battery acid have been
made?
55
Example: Crystallization
¾
A tank holds 10,000 kg of a
saturated solution of Na2CO3 at
30℃. You want to crystallize
y
from
this
solution
Na2CO3.10H2O
accompanying
3000
kg
without
water.
To
of
any
what
temperature must the solution be
cooled?
56
The Chemical Equation and Stoichiometry
Example Use of the Chemical Equation to Calculate the Mass of Reactants Given the Mass of Products
¾
In the combustion of heptane CO2 is produced. Assume that you want to produce 500 kg
of dry ice per hour and that 50% of the CO2 can be converted into dry ice How many
kilograms of heptane must be burned per hour?
57
Example: Application of Stoichiometry When More than One Reaction Occurs
¾
A limestone analysis: By heating the limestone you recover oxides known as lime.
lime
a.
How many pounds of calcium oxide can be made from 5 tons of this limestone?
b.
How many pounds of CO2 can be recovered per pound of limestone?
c.
How many pounds of limestone are needed to make 1 tons of lime?
58
CaCO3
92.89%
MgCO3
5.41%
Isoluble
1.70%
Limiting reactant and Excess reactant
¾
Limiting reactant is the reactant that is present in the smallest stoichiometry
amount.
C7H16+11O2 →7CO2+8H2O
¾
Excess reactant is a reactant present in excess of the limiting reactant.
% excess = 100
moles in excess
moles required to reaction with limiting reactant
59
Conversion, Selectivity and Yield
`
Conversion is the fraction of the feed or some key material in the feed that is
converted into products.
`
S l ti it is
Selectivity
i the
th ratio
ti off the
th moles
l off a particular
ti l (usually
(
ll the
th desired)
d i d) production
d ti
produced to the moles of another (usually undesired or by-product.
`
Yield
% conversion = 100
60
moles(or mass) of feed that react
moles of feed into reduced
Example: Calculation of the Limiting and Excess Reactants Given the Mass of Reactants
If you feed 10 grams of N2 gas and 10 grams of H2 gas into a reactor:
¾
a.
What is the maximum number of grams of NH3 that can be produced?
b.
What is
i the limiting
i i i reactant??
c.
What is the excess reactant?
61
Solving material balance problems that involve chemical reactions
¾
Fluid or stack gas: All the gases resulting from a combustion process including the
water vapor, sometimes known as a wet basis.
¾
Orsat analysis or dry basis: All the gases resulting from a combustion process not
including the water vapor.
62
¾
Complete combustion: the complete reaction of the hydrocarbon fuel producing
CO2, SO2, and H2O.
¾
Partial combustion: the combustion of the fuel at least some CO. Because CO
it lf can reactt with
itself
ith oxygen, the
th production
d ti
off CO in
i combustion
b ti
process does
d
not produce as much energy as it would if only CO2 were produced.
63
¾
Theoretical air (or theoretical oxygen): The amount of air( or oxygen ) required
to be brought into the process for complete combustion.
¾
Excess air (or excess oxygen): the amount of air (or oxygen) in excess of that
required
i d for
f complete
l t combustion.
b ti
¾
The calculation amount of excess air does not depend on how much material is
actually burned but what can be burned. Even if only combustion takes place.
The excess air (or oxygen ) is computed as if the process of combustion produced
only CO2.
64
The percent excess air is identical to the percent excess O2
¾
Percent excess air may also be computed as
% excess air = 100
O2 entering process − O2required
O2 required
q
or
% excess air = 100
% excess air = 100
excess O2
O2 entering − excess O2
excess air
excess O2 /0.21
= 100
required air
required O2 /0.21
65
Example: The percent excess air
¾
Fuels other gasoline are being eyes because they generate lower levels of
pollutants than gasoline. Compressed propane has been suggested as a source of
economic p
power for vehicles. Suppose
pp
that in a test 20 kg
g of C3H8 is burned with
400 kg air to produce 44 kg of CO2 and 12 kg of CO. What was the percent
excess air?
66
Example: A fuel Cell to Generate Electricity From Methane
“A Fuel Cell in Every Car” is the headline of an article in Chemical and Engineering News,
News
¾
March 5, 2001, p. 19. In essence, a fuel cell is an open system into which fuel and air are fed,
and out of which comes electricity and waste products.
products Figure is a sketch of a fuel cell in
which a continuous flow of methane (CH4) and air (O2 plus N2) produce electricity plus CO2
and H2O. Special membranes and catalysts are needed to promote the reaction of CH4.
Based on the data given in Figure, you are asked to calculate the composition of the products
¾
in P.
P
67
Example: Combustion
¾
Let us consider only the combustion of methane.
Figure shows a simple
combustion process, the mechanical details of which we can ignore.
P = ? (kgmol)
Burner
CH4 100%
CO2 = ?
F = 16.0 kg
Air
A = 300 kg
68
N2 = ?
O2
Mol %
21.0
O2 = ?
N2
79.0
90
H2O = ?
Example: Combustion of coal
¾
A local utility
y burns coal having
g the following
g composition
p
component
percent
on a dry basis. (Note that the coal analysis below is a
C
83.05
convenient one for our calculations, but is not necessarily
H
4.45
O
3.36
the only type of analysis that is reported for coal, some
N
1.08
analyses contain much less information about each
S
0.7
element). Moisture in the fuel was 3.9% and the air on the
Ash
7.36
average contained 0.0048 lb H2O/lb dry air. The refuse
Total
100.0
showed
h
d 14.0%
14 0% unburned
b
d coal,
l with
ith the
th remainder
i d
b i
being
ash. You as asked to check the consistency of the data
before they are stored in a data base.
base Is the consistency
satisfactory? What was the average percent excess air
used?
69
Solving material balance involving multiple subsystems
Example 3.16 Molecular Units in which no reaction
Occurs
¾
Acetone is used in the manufacture of many
chemicals and also as a solvent. In its later role,
many restrictions are placed on the release of
acetone vapor to the environment. You are asked
to design
g an acetone recovery
y system
y
having
g the
flowsheet
illustrated
in
Figure.
All
the
concentrations shows in Figure of both gases and
liquid are specified in weight percent in this special
case to make the calculations simpler. Calculate A,
F,W, B, and D per hour.
70
The average Orsat analysis of
the gas from the stack during a
2-hr test
Component
Percent
CO2+SO2
15.4
CO
0.0
O2
4.0
N2
80.6
Total
100.0