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Lecture 3 – Materials Balances. Introduction to Environmental Engineering Lecture3 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

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Lecture 3 materials balances

Lecture 3 – Materials Balances

Introduction to Environmental Engineering

Lecture3

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

Paul Ashall, 2008


M b with a single material

X0

X1

0

1

M.B. with a Single Material


M b with a splitting single material

X1

X1

X0

1

X0

0

X2

X2

2

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

M.B. with a Splitting Single Material


State of mixing steady state

  • Steady state destroyed

  • 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-Steady State


State of mixing reactions loss process

2. destroyedReactions/ 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]

State of Mixing- Reactions/ loss process


Complex processes with a single material

  • General Rules for solving M.B. Problems destroyed

    • Draw the system as a diagram

    • Add the available information

    • Draw a dotted line around the component being balanced

    • Decide material to be balanced

    • Write the basic M.B. equation

    • If only one missing variable, solve

    • If more that one unknown, repeat the procedure

Complex Processes with a Single Material


Example

A completely mixed lake receives two inflows: destroyed

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-N

    bacteria 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?

Example


Complex processes with a single material1

  • Q destroyedW*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

  • t = 150 days

Complex Processes with a Single Material


Complex processes with a single material2

find C destroyedN: 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-nitrogen

1.4 mg/L ammonia-N > 1 mg/L standard.

Complex Processes with a Single Material


Complex processes with a single material3

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

  • Define detention time, t in the book:

    t = V/Q = volume/flow rate = time

    2 x 106 m3/(0.1 m3/s + 0.054 m3/s)*(1 day/86,400 s) = 150 days

Complex Processes with a Single Material


Batch cycle

Batch cycle

Paul Ashall, 2008


Typical simple flowsheet arrangement

Recycle of unreacted material (Hydraulic Residence Time)?

reactor

Separation &

purification

product

Fresh feed

(reactants, solvents,

reagents, catalysts etc)

Typical simple flowsheet arrangement

waste

Byproducts/coproducts

Paul Ashall, 2008


Mass balance filtration centrifuge

wash water/solvent (Hydraulic Residence Time)?

solid

feed suspension

Mass balance filtration/centrifuge

filtrate

waste water

Paul Ashall, 2008


Filtration

5000 kg DM water (Hydraulic Residence Time)?

F1

Water 300 kg

API 448 kg

Impurity 5 kg

Impurity 55 kg

Water 2600 kg

API 450 kg

Filtration

Water 7300 kg

Impurity 50 kg

API 2kg

Paul Ashall, 2008


Mass balance drier

water/evaporated solvent (Hydraulic Residence Time)?

product

feed

Mass balance - drier

Paul Ashall, 2008


Mass balance extraction phase split

A + B (Hydraulic Residence Time)?

A + B

S + B

S

Mass balance – extraction/phase split

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

Paul Ashall, 2008


Example single stage extraction immiscible solvents

feed (Hydraulic Residence Time)?

raffinate

E1

solvent

extract

Example (single stage extraction; immiscible solvents)

Paul Ashall, 2008


Mass balance absorption unit

exit gas stream (Hydraulic Residence Time)?

feed solvent

feed gas stream

Mass balance – absorption unit

waste solvent stream

Paul Ashall, 2008


Multiple units

E (Hydraulic Residence Time)? – evaporator; C – crystalliser; F – filter unit

F1 – fresh feed; W2 – evaporated water; P3 – solid product; R4 – recycle of saturated solution from filter unit

W2

R4

E

C

F

F1

P3

Multiple units

Paul Ashall, 2008


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