Transcript Document

Mass Balance, Kinetics
& Reactors
Dr. Martin T. Auer
MTU Department of
Civil & Environmental Engineering
Some concepts and
definitions
Sustainability
In our every deliberation we must consider the impact of our
decisions on the next seven generations. Iroquois Confederacy
We seek to meet the needs of the present without compromising
the ability of future generations to meet their own needs. World
Commission on Environment and Development, 1987
Modeling: an alternative to build and measure, providing a more
rational basis for making water quality control decisions, such a
basis to include a defensible, credible, predictive framework,
within the larger framework of cost-benefit analysis.
Definition: a mathematical model
is an idealized formulation that
represents the response of a
physical system to external stimuli.
Chapra 1997, p. 10
Modeling and Environmental Engineering
…the environmental engineering equivalent
of building a bridge to nowhere.
(Thomann and Mueller 1987, p. ix)
http://www.zen39641.zen.co.uk/ps/
Modeling and Environmental Engineering
…the environmental engineering equivalent of
building a bridge that falls down.
(Thomann and Mueller 1987, p. ix)
http://www.jansenkiener.com/Bridge%20Engineering.htm
Modeling and Environmental Engineering
…the question is not will a system will respond,
but rather when and to what extent.
(Cooke et al. 1999)
and, as engineers, we might add ‘at what cost’?
Reactor Analogs – Natural Systems
Plug Flow
Reactor
Completely-Mixed
Flow Reactor
Fox River
Wisconsin
Mille Lacs Lake
Minnesota
Reactor Analogs – Engineered Systems
Plug Flow
Reactor
Completely-Mixed
Flow Reactor
Resin-Based
Water Softener
Wastewater
Primary Clarifier
Soaking Rain
Dream Car
CMF Reactor
Control Volume
Zero Order Kinetics
Oxygen in Dollar Bay
Ct = -k∙t + C0
Dollar Bay
Dissolved Oxygen (mg/L)
12
10
8
6
4
2
0
0
30
60
90 120 150 180 210 240 270 300 330 360
Day of Year
Dollar Bay
Dissolved Oxygen (mg/L)
10
y = -0.1285x + 23.752
2
8
R = 0.9759
6
4
2
Zero Order
k = 0.13 mg∙L-1∙d-1
0
0
30
60
90 120 150 180 210 240 270 300 330 360
Day of Year
First Order Kinetics
Radioisotope Decay
lnCt = -k∙t + lnC0
Pb-210
Radioisotope Concentration
1.0
0.8
0.6
0.4
0.2
0.0
0
20
10
30
40
60
50
70
80
90
100
Time (yr)
Pb-210
Radioisotope Concentration
0
k = 0.036 yr-1
-1
t0.5 = 19.25 yr
-2
y = -0.036x + 6E-16
-3
2
R =1
-4
0
20
40
60
Time (yr)
80
100
Temperature and Kinetics
Rate Coefficient (d -1)
Theta Function
4
Q
3
1.08
2
1.04
1
1.00
0
0
5
10
15
20
25
30
35
Temperature (°C)
(T 20)
kT  k20  Q
40
Temperature and Kinetics
WWTP Nitrification

2

3
Effluent Ammonia Load (MT∙d-1)
OrgN  NH3  NO  NO
J F M A M J J A S O N D
CMF Reactor
with first order decay
dC
V
 Q  Cin  Q  C  V  k  C
dt
Sonora River at Arizpe, Mexico
Image courtesy of Agustin Robles Morua
Chloride in 9 Mile Creek
For many years, Allied Chemical and its ancestors
produced soda ash … a chemical used to soften water
and in the manufacture of glass, soap, and paper. The
raw materials were two locally abundant minerals:
CaCO 3 + NaCl  Na 2 CO 3 + CaCl 2
and the products were soda ash (Na2CO3) and calcium
chloride (CaCl2) waste. The wastes were deposited in
2000 acres of lagoons along the banks of 9 Mile Creek.
The waste continually leaks from the lagoons into the
creek, making the water highly ‘salty’.
Chloride in 9 Mile Creek
Cmb 
Cup  Qup + Cin  Qin
Qup + Qin
BATCH Reactor
with first order decay
dC
V
 Q  Cin  Q  C  V  k  C
dt
dC
  k C
dt
BATCH Reactor
with first order decay
Concentration
dC
  k C
dt
Ct  C0  e
Distance or TimeTime (yr)
 k t
Batch Reactor in Pipe
Batch Reactor in Pipe
Batch Reactor in Pipe
Batch Reactor in Pipe
Batch Reactor in Pipe
Batch Reactor in Pipe
Batch Reactor in Pipe
Batch Reactor in Pipe
Batch Reactor in Pipe
Batch Reactor in Pipe
Batch Reactor in Pipe
Batch Reactor in Pipe
Concentration
PFR = Train of Batch Reactors
Distance or TimeTime (yr)
To Water Quality
CMF Reactor
dC
V
 Q  Cin  Q  C  V  k  C
dt
and, at steady state
Q
Css  Cin 
Q +V  k
Change in Css
concentration
Css,1
Css,2
time
Time-Variable Response
concentration
FG1 + k IJ  t

C t  C ss1  e Ht K
C t  C ss2
F FGH IJK I
G
1 e
J
H
K
1
+ k t
t
F
G
H
FG1 + kIJ t
FG1 + kIJ t
H K

C t  C ss1  e Ht K + C ss2  1  e t
time
I
JK
Response Time
t95%
 ln 0.05

1
+k
t95% 
3
1
t
t
+k
Rate Coefficients
‘fast’ k, 30 yr-1
‘slow’ k, 0.03 yr-1
Wastewater Treatment
Drinking Water Treatment
Grit removal, 0.5 hr
1°, 2° settling, 1-2 hr
Activated sludge, 4-8 hr
Anaerobic digestion, 15-30 d
Rapid mix, <1 min
Flocculator, 30 min
Disinfection, 15 min
Natural Systems
Onondaga Lake (0.25 yr)
Lake Ontario (8 yr)
Lake Michigan (136 yr)
Lake Superior (179 yr)
SS CMF
Application to Lakes
dP
V
 W  Q·P  V ·k ·P
dt
where W = Q∙Cin, i.e. the loading
SS CMF
Application to Lakes
dP
V
 W  Q·P  V ·k ·P
dt
v
k
 and
H
V
A
H
dP
V ·  W  Q·P  v·A·P
dt
W
@ SS , P 
Q + v·A
PF-CMF Comparison: Reactor Efficiency
PF-CMF Comparison: Sensitivity to Spikes
Mass Transport
CMF Reactor
PF Reactor
8
8
Lake
Huron
Saginaw
Bay
Advection and Diffusion
advection
alone
diffusion
alone
advection
plus
diffusion
Diffusion
PCBs
PCBs are a family of chemical compounds formed by the
addition of chlorine to biphenyl (C12H10). There are 10
substitution positions where chlorine may be added,
leading to a possible 209 unique chemical compounds
termed congeners.
3
2
2’
3’
4’
4
5
6
6’
5’
ClnH(10-n)
Congeners have been assigned numbers (1209) and
are also classified by the positions occupied by chlorine.
Referencing the substitution positions in the figure above,
three examples are:
Congener 1: 2-Chlorobiphenyl
Congener 101: 2,2’,4,5,5’-Pentachlorobiphenyl
Congener 209: Decachlorobiphenyl
Example 4.14 PCBs in Lake Superior
Dr. Perlinger’s research group
sampling on Lake Superior aboard
the U.S. EPA research vessel
Lake Guardian.
air
water