chapter 5. reactors

7/23/2019 Chapter 5. Reactors

1/22

Dr. BUNRITH SENG

Chapter 5

Reactors

Mobile : +81 (0) 80 3259 9952

E-mail: [email protected]; [email protected]

Department of Civil Engineering, Zaman University

No. 8, St. 315, 12151 Phnom Penh, Cambodia

Zaman UniversityDepartment of Civil Engineering

No. 8, St. 315, 12151 Phnom Penh, Cambodia


2/22

2

Type of Reactors

Batch Reactor/Mixed-Batch Reactor

Plug Flow Reactor (PFR) Continuous-Flow Stirred Tank Reactor (CFSTR),

Completely Stirred Tank Reactor (CSTR)

We have already learned the reaction orders and rateconstants. In addition to this knowledge, in order to analyzeand estimate the performance of wastewater treatmentprocesses and to design these, the knowledge of reactor isnecessary.

Type of Reactor


3/22

3

Batch Reactor

Bath Reactor

o The reactants are initially changed into a reactor (no inputand no output during the reaction)o Well-mixed (the concentration of the reactant or products

is same throughout the reactor at any time)o After a certain period (reaction time), the resultant

mixture is then dischargedo Unsteady state operation where the concentrations of

reactions and products change with time.

Qin

V (m3)

t (h)Cin QoutCout


4/22

4

Plug Flow Reactor

Plug Flow Reactor (PFR)

o The flow of fluid through the reactor is orderly (no mixingor no diffusion along the reactor)

o Laterally (perpendicular to the axis of the reactor), nodistribution of concentrations

Q

V (m3)

Q

t (h)

Cin

Cout


5/22

5

Continuous-flow Stirred Tank Reactor

Continuous-Flow Stirred Tank Reactor (CFSTR)

o the contents in the reactor are well stirred or mixedo the concentration or reactants and products in the effluent

are same as those in the reactor

Q

V (m3)

Q

t (h)

CinCout

Cout


6/22

6

Mass (Material) Balance

The starting point for designing the reactor and analyzing thereactor is the mass balance for any reactant (or product).

The material balance is expressed by:

CONSUMED

AofRate

PRODUCED

AofRate

OUT

ARate

IN

AofRate

DACCUMULATE

AofRate

inX

outX

Reaction


7/227

Mass Balance for CFSTR

Qin (m3/h)

V (m3)

Qout

t (h)

C

rVQCQCdt

dCV

0

Accumulation Inflow Outflow Disappearance

C (kg/m3)

C0(kg/m3)

* Each term has a dimension of[M/T], (kg/h)

In Case of one CFSTR


8/228

At Steady state condition

0dt

dC rVQCQC 0

0

When reactor rate follows a zero order (-r = k0)

TkCQ

VkCC 0000 T: Hydraulic retention time

When reactor rate follows a first order (-r = k1C)

Tk

C

k

V

Q

C

VkQ

QCC

1

0

1

0

1

0

11

T: Hydraulic retention

time

Mass Balance for CFSTR (Cont.)


9/229


In Case of CFSTR in Series

For First Order Reaction with respect to reactor 1

Tk

CC

1

01

1

With respect to reactor 2

TkC

C

11

2

1

1

With respect to reactor N

TkC

C

N

N

11 1

1

N

N

N

N

TkC

C

C

C

C

C

C

C

C

C

1012

3

1

2

0

1

1

1.......


10/2210


Example: A new disinfection process destroys coliform (coli)organisms in water by using a completely mixed-flow reactor. The

reaction is first-order with k = 1.0 day1. The influent concentration is100 coli/mL. The reactor volume is 400 L, and the flow rate 1600 L/d.What is the effluent concentration of coliforms?

Solution:

rVQCQCdt

dCV 0

rVQCQC 0

0

CLCmLcolidL -1d1400)/100(/16000

coli/mL80C


11/2211

Mass Balance for Batch Reactor

No Inflow QC0=0

No Outflow QC = 0 rV

dt

dCV

rdt

dC

For Zero Order Reaction, -r = k0

0kdt

dC 00 CtkC CCk

t 00

1

For 1st Order Reaction, -r = k1C

Ckdt

dC1 C

C

kt 0

1

ln1


12/2212

Example: An industrial wastewater treatment process uses activatedcarbon to remove color from the water. The color is reduced as a first-

order reaction in a batch adsorption system. If the rate constant (k) is0.35 d-1, how long will it take to remove 90% of the color?

Mass Balance for Batch Reactor (Cont.)

Solution:

Let C0: Initial concentration of the colorC : concentration of color at any time tC = 0.1 C0

ktC

C0

ln

tC

C35.0

1.0ln

0

0

days6.635.030.2 t


13/22

13

Mass Balance for Plug Flow Reactor

xArQCQCdtdCSA xxx

)(

Consider a small element of the reactor and apply mass balance

Where Cxand C

x+xare substrate concentration at x=xand x=x+x

At a steady state dC/dt = 0

)( rdx

CC

A

Q xxx

0x )( rdx

dC

A

Q )( r

dV

dCQ


14/22

14

For Zero order reaction, -r = k0

0kdV

dCQ

dV

Q

kdC

0

0kdxdC

AQ

dx

Q

AkdC

0

constxQ

AkC

0

Atx = x0, C=C0

Const=C0

00 CxQ

AkC

constQ

VkC

0

At V=V0, C=C0

Const=C0

00 CQ

VkC

Mass Balance for Plug Flow Reactor (Cont.)


15/22

15

Putting x = L to obtainedeffluent concentration Ce

PuttingV (variable) = V (reactor volume)

Q

ALkCCe 00

Q

V

kCCe 00

TkCCe 00

Q

VkCCe 00

TkCCe 00

Or more directly, applying integrate!



16/22

16

For 1storder reaction, -r = k1C

CkdxdC

AQ

1

LC

Cdx

Q

Ak

C

dCe

01

0

TkLQ

Ak

C

Ce11

0

ln

Tk

e eCC 1

0

xQ

Ak

e eCC1

0

CkdV

dCQ 1

VC

CdV

Q

k

C

dCe

0

1

0

VQ

k

C

Ce 1

0

ln

Tke eCC

1

0



17/22

17



18/22

18


Example: An industry wants to use a long drainage ditch to removeodor from their waste. Assume that the ditch acts as a plug-flow

reactor. The odor reduction behaves as a first-order reaction, with therate constant k = 0.35 day1. The flow rate is 1600 L/d. How long mustthe ditch be if the velocity of the flow is 0.5 m/s and 90% odorreduction is desired?

Solution:

xQ

Ak

e eCC1

0

kTC

C

0ln

TC

C35.0

1.0ln

0

0

days58.6T

s/d86400d6.58m/s0.5L

m108.2L 5

C C S


19/22

19

Comparison between CFSTR and PFR

CFSTR

PFR

)()(0 rTrQ

VCC

The required HRT to obtained

effluent concentration of Ce

)(1

0 e

e

CFSTR CCr

T

rdV

dCQ

The required HRT to obtained

effluent concentration of Ce

dCr

TC

Ce

PFRe

0

)(

1

TCFSTRor TPFRcan be obtained as an area under the curve.To obtain same effluent concentration, Ce, PFR requiredshorter HRT than CFSTR.

C i b CFSTR d PFR (C )


20/22

20

Comparison between CFSTR and PFR (Cont.)

CMF = CSTR = CFSTR

C i b CFSTR d PFR (C )


21/22

21

Comparison between CFSTR and PFR (Cont.)

Example: Consider a first-order reaction, requiring 50% reduction inthe concentration. Would a plug-flow or a CMF reactor require the least

volume?

Solution:

C

C

k

Q

C

C

A

Q

V

V

PFR

CSTR

0

0

ln

1

For 50% conversion

20 C

C 44.1

2ln

12

PFR

CSTR

V

V

A CMF reactor would require44% more volume than a PFR


22/22

chapter 5. reactors

Documents