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

QQ

QQ

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