Environment Engineering I

1
Environment Engineering I
AnNajah National University Civil Engineering
Department
Chapter Three
Materials Balance

• Dr. Amal Hudhud
• Dr. Abdel Fattah Hasan

2
Introduction

• Materials and Energy Balance
• A key tool in achieving a quantitative
  understanding of the behavior of Environmental
  Systems.
• Accounts for the flow of energy and material into
  and out of Environmental Systems.
• Models Production, transport, and fate of
  Pollutants and Energy in the Environment.

3
Conservation of Matter

• Matter (without nuclear reaction) can neither be
  created nor destroyed
• Its Mathematical form is called
  Materials Balance or Mass Balance
• For an environmental system
• Accumulation Input Output
• Env. System River, Pond, Pollution Control
  Device...etc.

4
Conservation of Energy

• Energy (without nuclear reaction) can neither be
  created nor destroyed
• Its Mathematical form is called
  Energy Balance

5
Control Volume (CV)

• CV boundaries to the system as imaginary blocks
  around the process or part of the process so the
  calculations are made as simple as possible.

CV
6
Useful Relations

• Density (?) M/L3 Mass M/Volume L3
• Mass (M) Density (?) x Volume (V)
• Mass Flow Rate M/T ?M/L3 x Q L3/T
• Concentration of Component A (CA) M/L3 Mass
  of A M/Volume L3
• Mass Flow Rate of Component A M/T CA M/L3 x
  Q L3/T

7
Mass Balance
In Min M/T Qin L3/T CAin M/L3
Out Mout M/T Qout L3/T CAout M/L3
Accumulation Input Output
8
Mass Balance

•  

When No Accumulation in the System ( dM/dt 0)
Steady State Conditions
9
Mass Balance for Component A
In Min M/T Qin L3/T CAin M/L3
Out Mout M/T Qout L3/T CAout M/L3
Accumulation Input Output
10
Mass Balance for Component A
For Steady State Conditions
11
Efficiency
In Min M/T Qin L3/T CAin M/L3
Out Mout M/T Qout L3/T CAout M/L3
When Qin Qout
12
State of Mixing

• Two Extreme cases (Models)
• 1. No Mixing 2.Complete Mixing

Continuous Stirred Tank Reactor (CSTR) OR
Continuous Mixed Flow Reactor (CMFR)
Plug Flow Reactor (PFR)
C inside reactor Cout
13
Including Reactions

• Conserved Substances Substances do not undergo
  chemical, biological or radioactive
  transformations.
• In case of transformations, Mass Balance will
  become
• Accumulation Rate
• Input Rate Output Rate Transformation Rate

14
Kinetics

• r Rate of Transformation or Reaction Rate
• r is used to describe the rate of formation or
  disappearance of a substance or chemical species.
• These time dependent reactions are called
  Kinetic Reactions.

15

• So, r - k Cn
• k reaction rate constant
• C concentration of substance
• n exponent or reaction order
• For first order reactions
• The rate of loss of the substance is proportional
  to the amount of substance present at any given
  time t.
• So, r - K C dC/dt (units of k s-1 or d-1)

16

• By Integration
• Co Initial Concentration
• Rearranging

17
Mass Balance for CSTR

• For completely CSTR (CMFR), with 1st order
  reaction, Mass Balance for Environmental Systems
  will be rewritten as
• For steady state conditions (dCA/dt 0 and Qin
  Qout)
• Define Q as residence time in the CSTR V/Q

18
Mass Balance for PFR

• For PFR, No mix with fluid ahead or behind
• Taking a CV for a differential element of the
  fluid..
• Mass Balance
• For 1st order reactions

19

• Define Q as residence time in PFR V/Q
• Integration of the above equation
• Also,
• u sped of flow, L system length, A x-sectional
  area of PFR