Waste water treatment: Reactors

• Introduce the concept of mass balance • Identify the different reactor types... Ouput rate Input rate Decay rate rate Conservation of Mass • Mass cannot be created nor destroyed.. An i

Mass Balance

and Reactors

• Introduce the concept of mass balance

• Identify the different reactor types

Ouput rate

Input

rate

Decay rate

rate

Conservation of Mass

• Mass cannot be created nor destroyed

• Atoms are conserved but molecules may change to other forms

Steady state Accumulation = 0

Conservative Decay rate = 0 } Input rate = Ouput rate

Mass Balance- General Equation

Input,

Co

System boundary

Decay

Transform Transfer

Chemical Biological

Aerobic degradation

Anaerobic degradation

Photodegradation

Radioactive decay

Hydrolysis

Combustion

Oxidation-reduction Sedimentation

Volatilization

Sorption

Bio uptake

Ion exchange

Filtration

Types of Reactors

Q,

C V

V

to

t1

Q

t2

Q

• Packed bed Reactors

Q,

Co

Q, C

Q, C

Q,

Co

to

t1

Q

t2

Q

Batch Reactor

VkC dt

dC

o

e C

C −

=

V,k,Co V,k,C

An industrial facility generates 1.2 m3 of waste with a toxic chemical at

a level of 25 ppm Regulations allow the disposal of the waste into the marine environment only if the chemical at a level that does not

exceed 0.5 ppm The industry decided to employ a chemical reaction (k = 0.45 day-1) using a batch reactor with a detention time of 7 days

Is the reaction time sufficient to meet the regulatory limits?

Example

Using the equation for batch reactors with C = 0.5, Co =25 and k

=0.45, the value of t would be 8.7 days Therefore, 7 days will not

be sufficient to reduce the concentration of the chemical to 0.5 ppm

Solution

Completely-Mixed Tank Reactor (CSTR

(

Under steady-state conditions

out, Cout

CSTR

V k

Input

rate

Ouput rate

= + Decay rate

outV

= QoutCout

kV Q

Q

C C

out

in

in out

+

=

+

Assume the decay rate is first-order = kCV

The concentration inside the reactor is the same as the effluent concentration because of complete mixing

Design a CSTR to treat the industrial wastewater described

in the sketch

CSTR

k= 0.45 d -1

V=?

Q= 0.05 m 3 /hr

Co= 25ppm

Q= 0.05 m 3 /hr C= 0.5 ppm

Example

Applying the steady-state equation for CSTR

3 7

130 )

5

0 24

45

0 (

) 5 0 05 0 ( ) 25 05

0

(

m kC

CQ Q

C

V

kCV CQ

Q

C

o

o

=

×

×

−

×

=

−

=

+

=

Solution

Plug-Flow Reactor

) Q / V ( k

e Co

=

dVkC )

dx x

C C

( Q C

Q dt

] 2

dx ) x / C ( C C [

dVd

−

∂

∂ +

−

=

∂

∂ + +

dVkC

dx x

C Q

t

C

∂

∂

−

=

∂

∂

C

dC k

Q

dV = −

∫

−

=

Co

L

dC k

Q dx

A

At steady-state

Design a plug flow reactor to treat the industrial wastewater

described in the sketch

Plug flow

k= 0.45 d -1

V=?

Q= 0.05 m 3 /hr

Co= 25ppm

Q= 0.05 m 3 /hr C= 0.5 ppm

Example

Applying the steady-state equation for plug reactors

) 05 0 / ( 24

45 0

25

5

e−

=

The required volume of the reactor is 10.43 m3 This volume is about 12 times smaller than that needed for the case of a CSTR

Solution

Plug-Flow with dispersion

L

) 2 / (

2 )

2 / (

2

) 2 / (

) 1

( )

1 (

4

aPe aPe

Pe

ae C

C

−

−

− +

=

At steady-state with a continuous mass inflow, Wehner and

Wilhelm found:

Pe= Peclet number=vxL/D

D=dispersion coefficient

vx=axial velocity= Q/A

L=length of the reactor

tR= retention time= V/Q

5 0

4









 +

=

Pe

t k

Determine the effluent concentration for the PFD reactor shown

below if the reactor has a length of 5 m, width 1.4 m and depth 1.49

m Assume the dispersion coefficient is 1 m2/hr

Plug flow

k= 0.45 d -1

V=10.43 m 3

Q= 0.05 m 3 /hr

Co= 25ppm

Q= 0.05 m 3 /hr C= ?

Example

Solution

hr

m A

Q

v

x

x 0.024 /

49 1 4 1

05 0

=

×

=

1

5 024 0

=

×

=

=

D

L v

5 11

) 12

0

6 208 019

0 4 1 ( )

4 1

=

Pe

t k

hr Q

V

05 0

43 10

=

=

=

ppm C

Thus e

a e

a

ae C

C

aPe aPe

Pe

o

76 4 ,

19

0 )

1 ( )

1

(

4

) 2 / (

2 )

2 / ( 2

) 2 /

(

=

=

−

− +

1 The centroid (actual retention time)

∑

∑

=

i

i i

C

C

t t

2

2

C

C t

i

i

i −

= σ

∑

∑

2

2 2

t

σ

=

σθ

2 The variance

3 The normalized variance

4 The normalized variance is related to the dispersion number by

Experimental determination of dispersion coefficient

For a pulse injection of ideal tracer, moment analysis can be used

to determine the dispersion coefficient following the steps below

) 1

( ) (

2

x x

x

e L

v

D L

v

−

−

=

θ

σ

Dispersed plug flow through a compartmented aeration tank was analyzed by injecting a pulse of lithium chloride tracer in the influent From the time and output concentration data listed, plot C (kg/m3) versus time (min)-response curve Calculate the location of the

centroid of the distribution, variance of the curve , normalized

variance, and the reactor dispersion number D/vxL

Example

0 0 105 89 210 33.5 315 6

15 0 120 95 225 25.8 330 4.6

30 0 135 88 240 20 345 3.5

45 3.5 150 78.2 255 15.4 360 2.6

60 16.5 165 65 270 12.1 375 1.7

75 46.5 180 55.2 285 9.5 390 0.7

90 72 195 43 300 7.5 405 0

The response curve is shown in the figure below

0 20

40

60

80

100

time, min

Solution

The centroid (actual retention time)

∑

∑

=

i

i i

C

C

t t

2

2

C

C t

i

i i

−

= σ

∑

∑

2

2 2

t

σ

=

σθ

Using Excel a table similar to the one shown is generated

min

152 795

120770

=

=

t

7 3682 )

152 ( 795

σ

16

0 )

152

(

7

3682

2

2 = =

σθ

The variance

The normalized variance

The normalized variance is related to the dispersion number by

The dispersion number can be found by trial and error or using the figure shown in the slide

For , the dispersion number is 0.0875

Knowing the length and axial velocity one can

determine the dispersion coefficient of the reactor

16 0

2 =

θ

σ

D/v x L σθ2

0.09 0.164 0.085 0.156 0.088 0.161 0.087 0.159 0.0875 0.160

) 1

( ) (

2

x x

x

e L

v

D L

v

−

−

=

θ

σ