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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

slide2

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

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 Single Material
m b with a splitting single material

One or more effluent

  • One or more Feed Source / influent

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

  • 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. 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]

State of Mixing- Reactions/ loss process
complex processes with a single material

General Rules for solving M.B. Problems

      • 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:

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

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
  • t = 150 days
Complex Processes with a Single Material
complex processes with a single material2

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-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
typical simple flowsheet arrangement

Recycle of unreacted material

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

solid

feed suspension

Mass balance filtration/centrifuge

filtrate

waste water

Paul Ashall, 2008

filtration

5000 kg DM water

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 extraction phase split

A + B

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

raffinate

E1

solvent

extract

Example (single stage extraction; immiscible solvents)

Paul Ashall, 2008

mass balance absorption unit

exit gas stream

feed solvent

feed gas stream

Mass balance – absorption unit

waste solvent stream

Paul Ashall, 2008

multiple units

E – 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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