ReactorsReactors
ReactorsReactors
Reactor: a “container” where a reaction occurs Examples:
Clear well at water treatment plant (chlorine contact) Activated sludge tank at wastewater treatment plant Treated wastewater discharge into a stream:
stream = reactor Treated wastewater discharge into Cayuga lake:
lake = reactor Gas tank leaking into soil:
soil = reactor
Reactor: a “container” where a reaction occurs Examples:
Clear well at water treatment plant (chlorine contact) Activated sludge tank at wastewater treatment plant Treated wastewater discharge into a stream:
stream = reactor Treated wastewater discharge into Cayuga lake:
lake = reactor Gas tank leaking into soil:
soil = reactor
Reactor typesReactor typesWhat are your expectations?What are your expectations?
C
C
Feed Solution (glucose solution
for pipe flow)
Feed Solution (glucose solution
for pipe flow)
Peristaltic pumpPeristaltic pump
C
t
Flow with dispersion
or
t
Completely Mixed reactor
t
Pipe flow reactoror
Injection portInjection port
reactors
Advection: mean flowAdvection: mean flow
x
C
t
C
-u=
advection x
C
t
C
-u=
advection
What does it look like a short time later?
What does it look like a short time later?
xx
CC
xx
CC
Dispersion: velocity fluctuationsDispersion: velocity fluctuations
2
2
d
dispersion
D=x
C
t
C
2
2
d
dispersion
D=x
C
t
C
Fick's first lawFick's first law
Fick's second lawFick's second law
x
Cd
DJ
x
Cd
DJ
What does it look like a short time later?
What does it look like a short time later?
xx
CC
xx
CC
ReactionReaction
-kC=r=reactiont
C
-kC=r=
reactiont
C
What does it look like a short time later?
What does it look like a short time later?
xx
CC
xx
CC
Advection/Dispersion/ReactionAdvection/Dispersion/Reaction
r+u-D=2
2
d
total x
C
x
C
t
C
r+u-D=
2
2
d
total x
C
x
C
t
C
ruD 2
CC
t
Cd ruD 2
CC
t
Cd
zyx
++
zyx
++
In three dimensionsIn three dimensions
wherewhere
xx
CC
xx
CC
Reactors: Closed vs. OpenReactors: Closed vs. Open
Closed: have little dispersion across the inlet and outlet boundaries Well defined reactor volume Examples
__________________________________ ______
Open: have significant dispersion across the inlet and outlet boundaries Backmixing Example
_______
Closed: have little dispersion across the inlet and outlet boundaries Well defined reactor volume Examples
__________________________________ ______
Open: have significant dispersion across the inlet and outlet boundaries Backmixing Example
_______
tank with a small inlet and a small outlettank with a small inlet and a small outlet
lakelake
riverriver
Reactors: Defining the Control Volume
Reactors: Defining the Control Volume
tracertracer
Reactor Characterization Reactor Characterization
Time scales hydraulic residence time average time for tracer to get from
inlet to outlet
Closed systems “dead volume”
Open systems dispersion upstream “dead volume”
Time scales hydraulic residence time average time for tracer to get from
inlet to outlet
Closed systems “dead volume”
Open systems dispersion upstream “dead volume”
Q
VQ
V
t qt q
0
0
)(
)(
=
dttC
dttCt
t
0
0
)(
)(
=
dttC
dttCt
t
volumevolume
flow rateflow rate==
?
££
t qt q³³
t qt q££
Peclet Number
Ratio of advection to dispersion how far does advection carry the
fluid/width of tracer plume High Peclet means primarily
advection (_______________) Low Peclet means lots of mixing Approximation for low
dispersion (Pe>10)
UDL
Ped /
2
22
t
Pe
plug flowplug flow
Completely Mixed Flow Reactor
Closed reactor with no dead volume so theoretically t = .
What is C0? How might you check this?
C C et
tFHIK
0
Flow With Dispersion Equation
Solution for pulse mass input with advection and dispersion in only one direction
Beware of units!!!! Adopt a consistent set! How can we get the dispersion coefficient?
e tDUtx
dtx d
tDAM
C
4)(
,
2
4
Estimating the Dispersion Coefficient
Estimating the Dispersion Coefficient
tC
tCtt n
ii
n
iii
0
0
tC
tCtt n
ii
n
iii
0
0
2
0
0
2
2 ttC
tCt
n
ii
n
iii
t
2
0
0
2
2 ttC
tCt
n
ii
n
iii
t
UD
LPe
d /
UD
LPe
d /
2
22
t
Pe
2
22
t
Pe
Pe
LUDd
Pe
LUDd
2
2
2
td
LUD
2
2
2
td
LUD
Approximation for Pe>10Approximation for Pe>10
Definition of PeDefinition of Pe
Solve for DdSolve for Dd
Substitute approximationSubstitute approximation
Mass conservation
How much tracer comes out in 10 seconds?
What are the potential errors?
What level of accuracy do you expect?
M QiCiti
i0
n
M QiCiti
i0
n
Ideal TracerIdeal Tracer
same properties as fluid viscosity temperature density non reactive
additional properties low background concentrations easily measured cheap non toxic
same properties as fluid viscosity temperature density non reactive
additional properties low background concentrations easily measured cheap non toxic
Real TracersReal Tracers
Tracer typedistinguishingproperty
analyticalinstrument
examples
salt conductivity Conductivitymeter
NaCl
Dyes color Spectrophoto-meter
methylene blue
fluorescentdye
fluorescence Fluorometer rhodamine WT
radioactiveions
radioactivedecay
Liquidscintillation
counter
C14
Dissolved gas Gas Gaschromatograph
Sulfurhexafluoride
Reactor Lab TracerReactor Lab Tracer
Sodium chloride measured with conductivity probe
Red dye # 40 so we can see it Density problem: 1.012 g/cm3
Which reactors would be affected by density difference?
How can we solve it?
Sodium chloride measured with conductivity probe
Red dye # 40 so we can see it Density problem: 1.012 g/cm3
Which reactors would be affected by density difference?
How can we solve it?
Density MatchingDensity Matching
990
1000
1010
1020
1030
1040
0 20 40 60 80 100
C (g/L)
dens
ity (
g/L
) density = 0.378C + 998.215
995
1000
1005
1010
1015
1020
1025
0 10 20 30
C (g/L)
dens
ity (
g/L
) density = 0.6985C + 998.29
glucoseglucose
Sodium chlorideSodium chloride C848.1 C
0.6985C 0.378C
998.29 0.6985C
998.215 0.378C
NaClglucose
NaClglucose
NaCl
glucose
C848.1 C
0.6985C 0.378C
998.29 0.6985C
998.215 0.378C
NaClglucose
NaClglucose
NaCl
glucose
MonitoringMonitoring
Conductivity Probe location pipe flow porous media column completely mixed flow reactor
Data acquisition conductivity probe monitored by meter that sends data to
computer computer will display a graph of conductivity vs. time output is a tab delimited text file containing
sample times conductivity
Conductivity Probe location pipe flow porous media column completely mixed flow reactor
Data acquisition conductivity probe monitored by meter that sends data to
computer computer will display a graph of conductivity vs. time output is a tab delimited text file containing
sample times conductivity
Porous Media ReactorPorous Media Reactor
What are x, A, and U for the porous media reactor?
How could we get the dispersion coefficient?
What part of our laboratory model doesn’t this equation describe?
What are x, A, and U for the porous media reactor?
How could we get the dispersion coefficient?
What part of our laboratory model doesn’t this equation describe?
e tD
Utx
d
tx d
tDA
MC
4
)(
,
2
4
Data Manipulation
What would happen if you collected data for a week?
No clear approach, perhaps eliminate data after 99% of the mass is accounted for?
No need to collect data after the effluent concentration is stable.
tC
tCtt n
ii
n
iii
0
0
tC
tCtt n
ii
n
iii
0
0
Conductivity as f(NaCl)Conductivity as f(NaCl)
Use the slope of the four point calibration curve and the baseline conductivity of each of the reactors to convert the conductivity data to NaCl concentration
Use the slope of the four point calibration curve and the baseline conductivity of each of the reactors to convert the conductivity data to NaCl concentration
600
y = 2.1680x + 6.7393
R2 = 1.0000
0
500
1000
1500
0 200 400 600
NaCl concentration (mg/L)
Con
duct
ivity
(m S
/cm
)
“Plug Flow”“Plug Flow”
Completely MixedCompletely Mixed
Porous MediaPorous Media