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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
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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)
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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)
Ref: http://www.water-msc.org/e-learning/file.php/40/moddata/scorm/203/Lesson%204_04.htm
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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)
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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
Ref: http://www.water-msc.org/e-learning/file.php/40/moddata/scorm/203/Lesson%204_04.htm
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)
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
→ 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
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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
≠
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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 ∀=−−−−−
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
( ) 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 ∀−−=
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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
∀( )
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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−
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
+
=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
--
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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 -
. . . .
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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
. . . .
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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
. . . .
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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
+++=
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
( )( ) ( )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
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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
Ref: Tchobanoglous and Scroeder, 1985, Addison-Wesley Publishing Company
PLUG FLOW REACTORS (PFR)
Ref: http://www.water-msc.org/e-learning/file.php/40/moddata/scorm/203/Lesson%204_04.htm
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
→ 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
Ref: Tchobanoglous and Scroeder, 1985, Addison-Wesley Publishing Company
→ 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
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
→ 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
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
( ) 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
Ref: Tchobanoglous and Scroeder, 1985, Addison-Wesley Publishing Company
@ steady-state conditions
0t
c =∂∂
RtccQr
∂∂=
∂∀∂=
0t
c =∂∂
rcQtc +
∂∀∂−=
∂∂
PFR
steady-state conditions
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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 .
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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.
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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.
MU- Department of -Env.Eng.- Enve 301 Course Notes- Dr. Bilge Alpaslan Kocamemi
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
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