KINETIC RATE LAWS

1
KINETIC RATE LAWS

• Chemical kinetics is the study of changing
  chemical properties in a reaction with time.
• Typical questions involving kinetics
• How fast does a chemical disappear from an
  environmental compartment or from a waste
  treatment system?
• What will be the chemical concentration in a
  given compartment at any time?
• How fast does a chemical exchange between various
  compartments?

2
Equilibrium and Rate Constant

• A typical reaction aA bB ..? cC dD ..
• Equilibrium constant
• Rate of the reaction
• k is the rate constant, ? ? is called the order
  of the reaction.
• Units of k depend on concentration units of A and
  B.
• Time to one half disappearance of reactant is
  called half life.

3
Differential and Integral Rate Laws
4
Atmospheric Lifetime - Definition
First order reaction A ? B C.
Second Order Reaction A B ? C D
5
Complex Atmospheric Reactions
A ? Pr (k1) A B ? Pr
(k2) A C D ? Pr
(k3)
RA - ?A/ ?t k1A k2 AB k3 ACD
Atmospheric life time for A is
6
Different Types of Reactors
7
Conservation of Mass Lavoisier Principle
For nothing is created, either in the
operations of art, or in those of nature, and one
can state as a principle that in every operation
there is an equal quantity of material before and
after operations that the quality and quantity
of the simple principles are the same and
that there are nothing but changes, modifications
-- Antoine Lavoisier Traite Elementaire de
Chemie (1978).
8
Mass Balance for a Reactor
9
Dynamic Mass Balance (CSTR)
Qin, Cin
(mass transfer)
V CCout
kmt A Cout
Qout, Cout
Accumulation Input Output
If Qin Qout 0 and C(t0) C0
10
Dynamic Mass Balance (PFR)
k
u
?
w
dx
Accumulation Input Output over volume W? dx
Dividing by dx and taking the limit as dx ? 0 we
get
If C (x 0) C0
11
API Separator An Example of CSTR

• Large wastewater streams resulting from coking,
  sulfur recovery, steam cracking, hydrocracking,
  crude desalting etc.
• Need to recover most organics and also render
  water less toxic before discharge.
• Sludge settles and VOCs are emitted through the
  air/water interface. VOC emissions from the
  organic layer floating on top of the aqueous
  phase account for most of the emissions from a
  refinery. Next in line are leaks from valves and
  other areas.
• Methods of estimating air emissions from a
  refinery operation
• Flux chamber
• Diffusion modeling
• EPA emission factor approach.

12
An API Separator Tank
13
Methods of Measuring Air Emissions
Flux chamber method
Micrometeorological method
14
Flux Chamber Method
Flux is in (mass)/(area.time) Qg is the sweep gas
flow rate (volume/time) Ac is the cross-sectional
area of chamber (length2) C is the concentration
in the sweep gas at exit (mass/volume)
15
Micrometeorological method
where 1 and 2 refer to two heights, y2 gt y1
? is the von Karmans constant (0.4).
V2 andf v1 are velocities at the two heights C2
and C1 are the concentrations at the two heights.
16
Emission sources in a manufacturing plant
Air emissions

• Primary reactors, refining towers.
• Secondary from primary units wastewater
  treatment unit.
• Often partially or fully covered losses to air
  from junction boxes, equalization basins,
  clarifiers, aeration basins.
• Common mechanism mass transfer driven by
  gradient with resistance in the air-side and
  water-side of the air/water interface.

Ground level
Q, Cin
Wastewater C Cout
Q, C
Q Cin Q C KL Ac C Obtain C from mass balance
above W KL Ac C
17
Air Pollution in An Urban Area
18
Mass Balance
In Out Accumulation S A Q Ci0 Q Ci V
(dCi/dt) Note A XY V XYZ
With initial condition, C C0 at t 0
19
Steady state conditions
(X/uZ)
Ci
Ci0
S
20
Indoor air pollution
Add reaction (loss) term to overall mass balance
Solve for C
21
Assumptions in Urban Air Pollution Models

• Atmospheric turbulence mixes the air totally in
  the vertical direction up to H.
• Turbulence strong enough in the upwind direction
  to make concentration uniform in the whole volume
  of air over the city and not higher in the
  downwind distance than the upwind side.
• velocity in the x-direction and constant
  independent of time, location or elevation.
• Background concentration is constant.
• Emission rate S is constant over the whole area.
• Pollutant is conservative (non-reactive).

22
Atmospheric Concentration of a Pollutant in a City
23
Example CO from automobile traffic in Los
Angeles
Note that
STOT EvLd/(?t), where Ev is vehicle emission
rate (?g/km), Ld is travel distance (km), and ?t
is duration of travel (h). Calculated STOT 1 x
108 mol/h. QCio 2 x 106 mol/h., V 1 x 1012 m3,
Q 5 x 1011 m3/h, C0 1.2x10-5 mol/m3 .
24
Diurnal trend for CO in Los Angeles from
automobile emissions
25
(No Transcript)
26
Annual Average Concentration
?
Concentration for that meteorology
Frequency of occurrence of that meteorology
Annual Average Concentration


(all meteorologies)
Example u 3 m/s, H 1000m, 40 of time
concentration is 25 ?g/m3 and U 6 m/s, H 1000
m, 60 of time concentration is 8 ?g/m3 .
C (average) (25)(0.4) (8)(0.6) 15 ?g/m3
27
Maximum hourly CO levels in Los Angeles
http//www.chevron.com/prodserv/fuels/bulletin/mot
orgas/ch2.shtml
28
.