04 Mass Balance 1 Students
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Transcript of 04 Mass Balance 1 Students
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Mass Balance 1
1st Semester, 2015/16 Session
Dr. Yeoh Hak Koon
DEPARTMENT OF CHEMICAL ENGINEERING
UNIVERSITY OF MALAYA
(KKEK 1123 Chemical Process Principles 1)
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Motivation / Background
What to start with?
Recipe to make chocolatecakes?
What to buy for DIY skate
boards?
How much budget to allocatefor refugees?
How to sort out this mess?
What is the growth rate of theMalaysian population?
We add fresh water to a fish
pond and remove some dirty water. How much is enough tomaintain the oxygen level in thepond?
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Learning outcomes
At the end of this class, you should be able to
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Derive the general
mass balance equation
Choose a suitable
basis for calculations
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A ‘basis’ reflects the size of
the process
It is convenient to pick aneasy basis, e.g.
one cake
100 moles of reactant 1 tonne of product
1 person
1 week
Example: we want to know
how much A, B and C toproduce a product. What is agood basis?
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Picking a ‘basis’ of calculation
ProcessA
B
C
Product
1 tonne of A 1 mole of B
100 tonnes of C 1 mole of Product
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Often we also pick whatever
given as the basis because
the given numbers areconvenient enough
it is not required to considerother sizes, e.g. we are onlyinterested in this case, not ageneral case
Examples:
Find the other flow rates:
Do the C, N and P balancefor a given park. Monthly datafor the fertilizer applied and waste collected are available.
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continued …
Process100 mol/h A
BProduct
Basis:
Basis: 1 month?Basis: 1 hectare?
Basis: 1 kg C?
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Common use of basis
To determine or compare unit production cost.
e.g. How much to produce 1 ton of something?
To scale-up or scale-down the flowsheet.e.g. If we have results for 1 ton of product, what are the numbersfor 2000 ton/day?
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Process0.5 t A
0.7 t B
0.2 t C
1 t productProcess
? A
? B
? C
2000 tpd
product
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Suppose we are interested
in the changes in the massof water in an aquarium:
Pick a volume that will capture
the item of interest
Avoid picking a volume thatchanges in shape or size
Consider ALL inlet and outletstreams that cross the boundariesof the control volume only
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1. Control volume = where to focus
Water in
Water out
This is called the
“ ontrol volume”
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Accumulation = ?
= change, i.e. final – initial
Example: control volume: your bank
account
accumulation of wealth =final sum – starting sum
Question: accumulation
over how much time?
e.g. you accumulate RM1k
Rate of accumulation:better reflects the situation
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2. Rate of accumulation
Over 1 year? Over 1 day?
Must accumulation > 0?
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For a general quantity Q
that changes with time t,what is its rate ofaccumulation at any giventime?
Clearly, if t is large, we get only
an average rate of accumulation
In general, the rate ofaccumulation of a quantity Q at anyinstant is given by
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continued …
Q
time t
Q1
Q2
t
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3. What decides rate of accumulation?
In-class activity
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4. Application to mass balance
For a given control volume:
Rate of accumulation of mass of a chemical species S =
Rate of accumulation of the total mass =
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Steady state = conditions in
the control volume do notchange with time
Unsteady state = conditionsin the control volume change
with time
Mathematically, steady
state occurs when
Classic application: howdoes this apply to the mass balance of a species S notinvolved in any chemicalreactions?
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5. Steady or unsteady state?
Q
Time
Steady state
nste dy
state
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A cylindrical tank contains 3.3 m
deep of concentrated HClsolution. The internal diameterof the tank is 9.0 m, and theoverflow line is 6.5 m from thebase of the tank.
Feeding rate of the same HClsolution into the tank is at 48m3 /h continuously.
When the HCl is transferred tothe road tanker, the pump down
rate is 30 m3 /h.
Questions:
1. If no road tankers cometo take the HCl solution,how many more hours areleft before the tank
overflows?
2. When one road tankeris taking the HCl, how fast will the tank level change?
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Test yourself
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Always helpful if you
sketch out the problem:
Basis of calculation:
Control volume:
Assumption:
What to balance?
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Solution
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Let
V = volume of HCl in the tank (m3) A = cross sectional area of the tank (m2) = density of HCl (kg/m3)
Case 1: no tanker coming
Overall mass balance gives
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solution (continued) …
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solution (continued)
Case 2: when one tanker is drawing out the HCl
Overall mass balance:
Going through the same route, we obtain a reduced rate of rise ofthe liquid level:
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The tank will still overflow
it just takes a longer time.
What to do?
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Pick a convenient basis!
For a chosen control volume:
Overall mass balance (as rates):
Species mass balance (as rates):
At steady state:Rate of accumulation = 0
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Summary
Basis of calculation
setsthe size of the process
Accumulation = (in – out) + (gen – con)
Accumulation = in – out