Lecture 3 – Materials Lecture 3 – Materials BalancesBalances

Introduction to Environmental EngineeringLecture3

Dr. Jawad Al-rifai

The accounting of all mass in a chemical/Environmental process is referred to as a mass (or material) balance.

‘day to day’ operation of process for monitoring operating efficiency

Making calculations for design and development of a process i.e. quantities required, sizing equipment, number of items of equipment

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M.B. with a Single MaterialM.B. with a Single Material

Conservation of Mass – mass is neither created nor destroyed

Mass Flow – therefore mass flowing into a box will equal the flow coming out of a box

◦Black box – schematic representation

X0 X1

0

1

M.B. with a Splitting Single M.B. with a Splitting Single MaterialMaterial

One or more effluent

One or more Feed Source / influent

X0X1

X2

01

2

X0

X1

X2

[Accumulation]= [In]– [Out] +[Produced] – [Consumed]

State of Mixing-Steady StateState of Mixing-Steady State

1. Steady state The rate of input= rate of out put, mass

rate of accumulation is Zero

◦Conservation: In many problems conservation is assumed Material of concern is not consumed or produced

No chemical, biological or radioactive decay◦Ex. Salt in Sewer & stream

M.B. equation 0 = [In] – [Out] + 0 - 0

[In]= [Out]

State of Mixing- State of Mixing- Reactions/ loss Reactions/ loss processprocess

2. Reactions/ loss process

dM/dt = [d(in)/dt – d(out)/dt]+ r

r=-KVCn

◦ K; reaction rate constant; S-1 or d-1

◦ C: Concentration of substances◦ n: reaction order◦ V: volume◦ - Indicate disappearance of substances

The reaction rate is often complex function of T, P

[Accumulation]= [In]– [Out] + [Produced] –

[Consumed]

[Accumulation]= [In]– [Out] + [Produced] –

[Consumed]

Complex Processes with a Single Complex Processes with a Single MaterialMaterial

General Rules for solving M.B. Problems1. Draw the system as a diagram2. Add the available information3. Draw a dotted line around the component

being balanced4. Decide material to be balanced5. Write the basic M.B. equation6. If only one missing variable, solve7. If more that one unknown, repeat the

procedure

ExampleExample

A completely mixed lake receives two inflows: natural stream flow 0.1 m3/s, wastewater discharge 0.054 m3/s and has a constant volume of 2 x 106 m3.Given:◦ 1)     the wastewater has 20 mg/L NH3-N ◦ 2)     stream has 1 mg/L NH3-Nbacteria in the lake convert NH3 to NO3

- by a process called nitrification.

-rN = k*CN

where k = a first-order rate constant = 0.03 day-1 and CN = concentration of ammonia-nitrogen mg/L

FIND: lake and outflow NH3-N Assume steady-state, non-conservative mass balance:

Ammonia is very toxic to fish, 1 mg/L NH4-N. Does the amount of natural nitrification in the lake allow wastewater discharge of 20 mg/L ammonia-N?

Complex Processes with a Single Complex Processes with a Single MaterialMaterial

◦QW*CNW + QN*CNN - QTCN - V*k*CN = 0

◦where QW = wastewater flow, = 0.054 m3/s

◦CNW = wastewater ammonia-N = 20 mg/L

◦QN = stream flow = 0.1 m3/s

◦CNN =stream ammonia-N = 1 mg/L

◦QT = lake outflow = QW +QN = 0.154 m3/s

◦CN = lake and outflow ammonia-N = ?

◦V = lake volume = 2 x 106 m3 ◦ = 150 days

Complex Processes with a Single Complex Processes with a Single MaterialMaterial

find CN: by rearranging mass balance:QTCN + V*k*CN = QW*CNW + QN*CNN

CN (QT + V*k) = QW*CNW + QN*CNN

Divide everything by QT;CN (1 + V/ QT *k) = (QW*CNW + QN*CNN)/ QT

CN =[ 1 / (1+ (V/QT)*k)]*[(QWCNW + QN*CNN)/QT] CN = [ 1/(1+ (t)*k)]*[(QW*CNW + QN*CNN)/QT]

CN = [1 /(l +(150d * 0.03d-1))]*[(0.054m3/s*20 mg/L + 0.1 m3/s*1 mg/l)/0.154m3/s]

CN = 1.4 mg/L ammonia-nitrogen1.4 mg/L ammonia-N > 1 mg/L standard.

Complex Processes with a Single Complex Processes with a Single MaterialMaterial

Aside:What is the detention time of water in the lake (Hydraulic Residence Time)?

◦Define detention time, in the book:

= V/Q = volume/flow rate = time2 x 106 m3/(0.1 m3/s + 0.054 m3/s)*(1 day/86,400

s) = 150 days

Batch cycleBatch cycle

Sequence of operations/steps repeated according to a cycle

Batch cycle timeBatch size

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Typical simple flowsheet Typical simple flowsheet arrangementarrangement

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reactorSeparation & purification

Fresh feed(reactants, solvents,reagents, catalysts etc)

product

Recycle of unreacted material

Byproducts/coproductswaste

Mass balance filtration/centrifugeMass balance filtration/centrifuge

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feed suspension

wash water/solvent

solid

waste water

filtrate

FiltrationFiltrationPaul Ashall, 2008

F1

5000 kg DM water

Impurity 55 kgWater 2600 kgAPI 450 kg

Water 7300 kgImpurity 50 kgAPI 2kg

Water 300 kgAPI 448 kgImpurity 5 kg

Mass balance - drierMass balance - drierPaul Ashall, 2008

feed product

water/evaporated solvent

Mass balance – extraction/phase Mass balance – extraction/phase splitsplit

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A + B

S

A + B

S + B

A – feed solvent; B – solute; S – extracting solvent

Example (single stage extraction; Example (single stage extraction; immiscible solventsimmiscible solvents))

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E1feed

solvent

raffinate

extract

Mass balance – absorption unitMass balance – absorption unit

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feed gas stream

feed solvent

waste solvent stream

exit gas stream

Multiple unitsMultiple units

E – evaporator; C – crystalliser; F – filter unitF1 – fresh feed; W2 – evaporated water; P3 – solid product;

R4 – recycle of saturated solution from filter unit

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R4

E C FF1

W2

P3