04 mass balance 1 students

7/21/2019 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)



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



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?



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”



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?



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



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



Always helpful if you

sketch out the problem:

Basis of calculation:

Control volume:

Assumption:

What to balance?

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Solution



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) …



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?



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

04 mass balance 1 students

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