Reactors
Reactors
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 types
What are your expectations?
Feed Solution
(glucose solution
for pipe flow)
Injection port
C
Flow with dispersion
Peristaltic pump
t
or
C Completely Mixed reactor
t
or
reactors
C
Pipe flow reactor
t
Advection: mean flow
C
t
= -u
advection
C
x
C
What does it look
like a short time
later?
x
C
x
Dispersion: velocity fluctuations
J  D d
Fick's first law
Fick's second law C
t
What does it look
like a short time
later?
C
x
= Dd
dispersion
C
 2C
x
2
x
C
x
Reaction
C
C
t
= r = -kC
reaction
x
What does it look
like a short time
later?
C
x
Advection/Dispersion/Reaction
C
t
= Dd
total
 2C
x 2
-u
C
x
C
+r
In three dimensions
C
t
x
 D d  2C  uC  r
C
where

  
+ +
x y z
x
Reactors: Closed vs. Open

Closed: have little dispersion across the inlet and
outlet boundaries
Well defined reactor volume
 Examples




tank with a small inlet and a small outlet
__________________________________
lake
______
Open: have significant dispersion across the inlet
and outlet boundaries
Backmixing
 Example


_______
river
Reactors: Defining the Control
Volume
tracer
Q
Q
Reactor Characterization

Time scales
 
hydraulic residence time
 average time for tracer to get from
inlet to outlet



Q
“dead volume”
t£ q
dispersion upstream t ³ q
 “dead volume”
t£ q

?
flow rate
t

C
(
t
)
dt

t=
Open systems
=
volume

Closed systems

V
0

 C (t )dt
0
Peclet Number
 Ratio
of advection to dispersion
 how
far does advection carry the
fluid/width of tracer plume
 High
L
Pe 
Dd / U
Peclet means primarily
advection (_______________)
plug flow
 Low Peclet means lots of mixing
2
2

 Approximation for low
Pe  2
t
dispersion (Pe>10)
Completely Mixed Flow Reactor
Ft I
H
t K
C C e
0
 Closed
reactor with no dead volume so
theoretically t = .
 What is C0? How might you check this?
Flow With Dispersion Equation
C x ,t 
 Solution
 ( x Ut ) 2 


 4 Dd t 
M

e
A 4Dd t
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?
Estimating the Dispersion
Coefficient
Pe 
Pe 
2 2
Approximation for Pe>10
 t2
n
2
t
 i  Ci t
L
Dd / U
Definition of Pe
 t2  i 0 n
 C t
i
i 0
Dd 
LU
Solve for Dd
Pe
Dd 
LU t2
2
2
Substitute approximation
n
 t  C t
t  i 0n
i
i
 C t
i 0
i
t 2
Mass conservation
How much tracer comes out in 10
seconds?
 What are the potential errors?


n
M
What level of accuracy do you expect?
Q C t
i
i 0
i
i
Ideal Tracer

same properties as fluid
viscosity
 temperature
 density
 non reactive


additional properties
low background concentrations
 easily measured
 cheap
 non toxic

Real Tracers
Tracer type
salt
distinguishing
property
conductivity
Dyes
color
fluorescent
dye
radioactive
ions
fluorescence
Dissolved gas
Gas
radioactive
decay
analytical
instrument
Conductivity
meter
Spectrophotometer
Fluorometer
Liquid
scintillation
counter
Gas
chromatograph
examples
NaCl
methylene blue
rhodamine WT
C14
Sulfur
hexafluoride
Reactor 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?
  0.378C glucose  998.215
density (g/L)
Density Matching
1040
glucose
1030
density = 0.378C + 998.215
1020
1010
1000
  0.6985C NaCl  998.29
990
0
0.378C glucose  0.6985C NaCl
20
40
60
80
100
C (g/L)
C glucose  1.848C NaCl
density (g/L)
Sodium chloride
1025
1020
1015
density = 0.6985C + 998.29
1010
1005
1000
995
0
10
20
C (g/L)
30
Monitoring

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 Reactor
C x , t  
 What
M
A 4Dd t
  ( x Ut ) 2 




 4 Dd t 
e
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?
Data Manipulation
 What
would happen if you collected data
n
for a week?
 ti  Ci t
t  i 0n
 C t
 No
i 0
clear approach, perhaps eliminate data
after 99% of the mass is accounted for?
 No need to collect data after the effluent
concentration is stable.
i
Conductivity as f(NaCl)
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
Conductivity (mS/cm)
 Use
1500
y = 2.1680x + 6.7393
2
R = 1.0000
1000
500
0
0
200
400
600
600
NaCl concentration (mg/L)
“Plug Flow”
Completely Mixed
Porous Media