CHAPTER : 3 - Marmara Üniversitesi Bilişim Merkezimimoza.marmara.edu.tr/~bilge.alpaslan/enve301/Lectures/Chp_3.pdf · CHAPTER : 3 MU-Departmentof -Env.Eng.-Enve301 CourseNotes-Dr

ENVE 301

Environmental Engineering Unit Operations

CHAPTER: 3

MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi

1

Assist. Prof. Bilge Alpaslan Kocamemi

Marmara UniversityDepartment of Environmental Engineering

Istanbul, Turkey

CHAPTER: 3Types of reactors

REACTOR MODELS

REACTOR:

Containers vessels or tanks in which chemical or biological reactions are carried out.

5 principal reactor models:

1. Batch reactor


2. Complete-mix reactor(continuous–flow stirred tank reactor),(CFSTR)

3. Plug-flow reactor (PFR) (tubular-flow reactor)

4. Cascade of complete mix reactor (complete mix reactors in series)

5. Packed- bed reactor2

BATCH REACTORS

The simplest reactor type

Flow is neither entering nor leaving the reactor

The liquid contents are mixed completely and uniformly


Applications:

Used to model very shallow lake where there is at most no flow

Used to estimate reaction coefficients

BOD test

3

Ref: http://www.water-msc.org/e-learning/file.php/40/moddata/scorm/203/Lesson%204_04.htm

oC,Q C,Q

Fluid particles that enter the reactor are

instantaneously dispersed throughout the reactor

volume

Fluid particles leave the reactor in proportion to their

statistical population

COMPLETE-MIX REACTORS(CFSTR=Continuous-Flow Stirred Tank Reactor)


rVQCQCdt

dco

±−=∀

C.∀

conc of any material leaving = conc. at any point in the reactor (after steady-state conditions are reached)

4

statistical population

No conc. gradient within the system.

Material entering is uniformly dispersed throughout the reactor

Fluid particles pass through the reactor and are

discharged in the same sequence in which they entered

the reactor.

Each fluid particle remains in the reactor for a time

period equal to the theoretical detention time.

PLUG FLOW REACTOR-(PFR)



This type of flow is approximated in

long tanks with a high length/width ratio

in which longitudinal dispersion is minimal or absent.

Application:

Used to study river systems5

Ref: Tchobanoglous and Scroeder, 1985, Addison-Wesley Publishing Company

is used to model the flow regime that exists between the hydraulic flow patterns

corresponding to the complete and plug flow reactors.

CASCADE of COMPLETE MIX REACTORS(Complete Mix Reactor in Series)

n-1 n n+1


corresponding to the complete and plug flow reactors.

If the series is composed of one reactor complete mix regime prevails

If the series consists of an infinite number plug-low regime prevails

of reactors in series

Application:

In modeling rivers within small increments (segments) 6

PACKED BED REACTORS

→ These reactors are filled with some type of packing

medium ( e.g.rock, slag, ceramic or plastic)

→ With respect to flow,

completely filled (anaerobic filter)

intermittently dosed (trickling filter)


7

intermittently dosed (trickling filter)

When the pore volume of the medium flow is said to be SATURATED

is filled with a liquid

When the pore volume is partially filled flow is said to be UNSATURATED


Application:

→ Used to study the movement of water and contaminants in groundwater systems.

→ Packed bed reactors in which the packing medium is expanded by the

FLUIDIZED-BED reactors

PACKED BED REACTORS (continue)


→ Packed bed reactors in which the packing medium is expanded by the

upward movement of fluid (air or water) through the bed.

Example: Filter backwashing

8Ref: http://www.water-msc.org/e-learning/file.php/40/moddata/scorm/203/Lesson%204_04.htm

CONTINOUS FLOW STIRRED TANK (CFSTR) REACTOR

MODELS

conservative (non-reactive)

Material input may be

non-conservative (reactive)

oC,Q

∀,C

C,Q


9

NOTE

For conservative (non-reactive) material input having Co conc., eff. conc. is initially C (not Co)

due to unsteady state condition.

When steady-state is reached effluent conc. (C) = Co

∀,C

Response of CFSTR to Conservative (non-reactive) Tracer Input

A conservative (non-reactive) material is injected into the input flow of CFSTR on a

continuous basis, beginning at t=0 and resulting in a constant input tracer conc. Determine

the reactor output conc. as a function of time and plot the tracer-output response curve.

→ Un-steady-state condition C Co (although the material is non-reactive)

→ After steady -state condition is reached C = Co

≠


Accumulation = Inflow – Outflow + Generation

( )CCQ=dt

dc

r+QCQC=dt

dc

o

o

-∀

∀-∀since the tracer

is non-reactiveo

C,Q C,Q

∀,C

∫=∀

=∫= −

t

0t

dtQC

0CC

oC

dCbaxln

a

1dx

bax

1 +=∫ +

tQ

CCLn1

1 C0C0 ∀

=−− =

( ) tQ

LnCCCLn =+−−

( ) tQ

0CLnCCLn 00 ∀=−−−−−


( ) tQ

LnCCCLn00 ∀

=+−−

( ) tQ

LnCCCLn00 ∀

−=−−

t.Q

C

CCLn

0

0

∀−=−

( )tQ

00eC=CC ∀--

( )tQ

0

e1C

C ∀−−=

(Divide both sides to Co)

11

( )tQ-

0

e=C

C-1

∀

R3

3

t

1

sec

1

m

sec/mQ ===∀ Hydraulic retention time

(HRT)

1212

0 0

0,5 =0,393

tQ

∀ 0C

C

5,0e1 −−

t=0, C=0

( ) t.Q

0

e1C

C ∀−−=


0

0,2

0,4

0,6

0,8

1

1,2

0 2 4 6

C/C

o

1 =0,632

2 =0,865

3 =0,952

4 =0,982

5 =0,99

1e1 −−2e1 −−3e1 −−4e1 −−5e1 −−

After this time, C/C0

does not change

12

Qt/V

A reaction A B , known to be first order, is to be carried

out in a CFSTR. Water is run through the reactor at a flow rate

Q (m3/sec ) and t=0 the reactant A is added to the input

stream on a continuous basis.

Determine the output concentration of A as a function of

time and plot reactor-output response curves for reactant A.

Response of CFSTR to Non-Conservative (Reactant)

Tracer Input

oC,Q

∀,C

C,Q


time and plot reactor-output response curves for reactant A.

generationQCQCdt

dc0

+−=∀

∀−−=∀ .C.kQCQCdt

dc0 (Divide both sides to )∀

First-order rxn� r=-kC

generation term =r = -kC∴ ∀ ∀

13

Materials balance for the system:

( ) C.kCC.Q

dt

dc0 −−

∀=

( ) C.kCC.t

1

dt

dc0

R

−−=

R

R0

t

t.C.kCC

dt

dc −−=

Rt

1=

Q

∀( )


R

R0

t

)t.k1(CC

dt

dc +−=

R

R

R

0

t

)t.k1(C

t

C

dt

dc +−=

+= k

Rt1

.C-Rt0C

dtdc

)x(Qy)x(Pdx

dy =+

Integration factor= ∫ dx).x(Pe

Multiply both sides w/integration

factor

Left hand side = 14

Q(x)

]ye[d(/dxx(P ∫

R

0

R t

C=)k+

t

1(c+

dt

dc

β=+ kt

1

R

t.dt. ee β∫β =

Multiply both sides with integration factor.

t.o

R

tt. e.C.t

1.C.e

dt

dc.e βββ =β+

( ) t.o

t

e.C.t

1

dt

e.Cd ββ

=

R

0

R t

C=)k+

t

1(c+

dt

dc


oRtdt

( ) dt.e.C.t

0tt

1C

C

e.Cd t0

R

t

0

t ββ∫=

=∫

∫ =

=

ββ

=β axea1

dxaxet

0t

te.1

.0C.Rt1tC

0C

t.e.C

15

β−

β=− βββ 1

Ct

1e

1C

t

1eCeC

0R

t

0R

t

0

t

t

β−

β=− ββ 1

Ct

1e

1C

t

1CeC

0R

t

0R

0

t

t

−+= ββ 1C

1e

1C

1CeC

tt (Divide both sides to )te

β

t=0 =1 t

eβ


β−

β+= C

teC

tCeC

0R

0R

0t

t0R

0R

t0

t e

11C

t

11C

t

1

e

CC ββ β

−β

+=

)e

11(

t

C

e

CC t

R

0t

0

t ββ −β

+=

(Divide both sides to )e

)e1(t

CeCC

t

R

0t

0t

β−β− −β

+= where kt

1

R

+=β16

CFSTR, UNSTEADY-STATE FOR NON-CONSERVATIVE REACTANT HAVING 1ST ORDER REACTION RATE

As t approaches infinity ( ) steady-state solution is approached∞

oC,Q

∀,C

C,Q

0t.e =β−


+

=β

≅k

t

1t

C

.t

CC

R

R

0

R

0t

R

0t

t.k1

CC

+=

CFSTR, steady-state, non-

conservative (reactive) reactant

having 1st order reaction rate.

17

)e1.(.t

Ce.CC t.

R

0t.0t

β−β− −β

+=

For steady-state condition (1st order reaction):

∀--∀ kCQCQC=dt

dc0

kCC ∀Q

C ∀Q

=dt

dc0

--


At steady-state 0dt

dc =

( )CCt

1=kC 0

R

-

( )CC=kCt 0R-

0RC=C+kCt

R

0

t.k1

CC

+=

18

CASCADE OF COMPLETE MIX REACTORS

(CFSTR in series)

At steady-state:

1st reactor 1101

r+QCQC=dt

dc ∀-∀

r+CQ

CQ

=dt

dc1

10

1 ∀-

∀

r+C1

C1

=0 -

. . . .


r+Ct

1C

t

1=0

11R

01R

-1 2 n

For 1st order

reaction: 111

01

1-10 kCCt

Ct RR

−= )k+t

1(CC

t

1=0

1R10

1R

-

t

kt+1CC

t

1=0

1R

1R

101R

-1R

01

kt1

CC

+=

19

2nd reactor2212

r+QCQC=dt

dc ∀-∀

r+CQ

CQ

=dt

dc2

21

2 ∀-

∀

r+Ct

1C

t

1=0

22R

12R

-

1 2 n

. . . .


For 1st order

reaction: 222

12

1-10 kCCt

Ct RR

−= )k+t

1(CC

t

1=0

2R21

2R

-

t

kt+1CC

t

1=0

2R

2R

212R

-

20

2 n

2R

12

kt1

CC

+=

1R

01

kt+1

C=C

( )( )2R1R

02

kt1.kt1

CC

++=

3rd reactor 3323r+QCQC=

dt

dc ∀-∀

r+CQ

CQ

=dt

dc3

32

3 ∀-

∀

r+Ct

1C

t

1=0

33R

23R

-

1 2 n

. . . .


For 1st order

reaction: 3kC3C3Rt

1-2C

3Rt1

0 −=

)k+t

1(CC

t

1=0

3R32

3R

-

t

kt+1CC

t

1=0

3R

3R

323R

-

21

2 n

3R

23

kt1

CC

+=

( )( )2R1R

02

kt+1kt+1

C=C

( )( )( )3R2R1R

03

kt1kt1kt1

CC

+++=

1R

01

kt1

CC

+=

( )( )2R1R

02

kt1.kt1

CC

++=

( )( )( )3R2R1R

03

kt1kt1kt1

CC

+++=


( )( ) ( )Rn2R1R

0n

th

kt+1...kt+1kt+1

C=C reactor n →

22

CFSTR in series under steady – states and

for 1st order rxn.

( )( )( )3R2R1R kt1kt1kt1 +++

EXAMPLE 1:

V1=8.68 x 10 ^5 m3

V2=25.9x 10 ^5 m3

V3=17.28 x 10 ^5 m3

v4=8.64 x 10 ^5 m3

V5=25.92x 10 ^5 m3


EXAMPLE 1:

The river reach shown has been divided into 5 segments based on measured velocities and

depths. An industrial facility is planned just upstream of the 1st segment and it is necessary

to estimate effect of ww discharge. A series of dye experiments have been run and each of

the segments was found to behave as an approximate CFSTR. The pollutant is expected to

disappear according to 1st order reaction. For the data given determine the steady-state

pollutant con. in each segment.

30

1

3river

m/g30C

day2,0k

sec/m5Q

==

=−

23


PLUG FLOW REACTORS (PFR)



→ Are ideally mixed in lateral direction and unmixed longitudinally

→ Unrealistic assumption for most real-world systems but can be approximated closely

→ The mean HRT time = true HRT time

An effluent tracer (conservative) signal is exactly the same as the input , expect that is

transposed in time by tR. 24


→ Tracers (dyes, electrolytes, radioactive isotopes) are used to characterize the degree

of mixing.

→ must be conservative

does not participate in any reaction

it is not adsorbed or absorbed by reactor or its contents

→ are assumed to be moved about in the same manner as the water molecules


→ PF conditions are achieved by

designing long and narrow reactors,

placing baffles in a reactor

their flow pattern will mimic have liquid flow pattern.

25Ref: Tchobanoglous and Scroeder, 1985, Addison-Wesley Publishing Company

Materials Balance:

( ) ( ) ∀rxxQC-x0QC∀t∂c∂ ∆+∆+=∆ (Divide both sides to )∀∆

→ In a PF situation the mass balance must be taken over an incremental volume because a

longitudinal concentration gradient exists (since there is no longitudinal mixing.

Accumulation = Inflow - Outflow + Generation


( ) r+CCxΔA

Q=

t

cxΔ+xx -

∂∂

rx

CC

A

Q

t

c xxx +

∆

−=∂∂ ∆+

( ) r+CCΔ

Q=

t

cxΔ+xx -

∀∂∂

26

rx

c

A

Q

t

c +

∂∂−=

∂∂ rcQ

tc +

∂∀∂−=

∂∂ PFR

Unsteady-state conditions


@ steady-state conditions

0t

c =∂∂

RtccQr

∂∂=

∂∀∂=

0t

c =∂∂

rcQtc +

∂∀∂−=

∂∂

PFR

steady-state conditions


Rt∂∂∀

27

steady-state conditions

EXAMPLE 2:

A plug flow reactor (PFR) is to be used to carry out the reaction

A B

The reaction is first order and the rate is characterized as ra=-kCA

Determine the steady-state eff. conc. as a function of tR .


28

EXAMPLE 4:

EXAMPLE 3:

Determine the volume of a CFSTR required to give a treatment efficiency of 95% for a

substance that decay according to half – order kinetics with a rate constant of

0.05 (mg/L)1/2 .

The flow rate is steady at 300L/hr and the influent concentration is 150mg/L.


29

EXAMPLE 4:

Determine the volumes of two identical CFSTR reactors in series to provide the same

degree of treatment for the conditions given in Example 1.

EXAMPLE 5:

Determine the volume of a PFR to provide same degree of treatment for the conditions

given Example 1.


Volume Comparison For Examples 3-5

)m( 3∀

Example 1 Example 2 Example 3

CFSTR 2 CFSTR in series PFR

312 180 114

When the same reaction model (except for zero-order rxns) applies, regardless of the

mixing regime a PF system is always the most efficient (less volume requirement)

30

Documents

CHAPTER : 3 - Marmara Üniversitesi Bilişim Merkezimimoza.marmara.edu.tr/~bilge.alpaslan/enve301/Lectures/Chp_3.pdf · CHAPTER : 3 MU-Departmentof -Env.Eng.-Enve301 CourseNotes-Dr