Handouts on the presentation of batch reactors with regards to water quality and treatment.

1. 1/29/2015
1
BATCH REACTORS
AND COMPLETELY
MIXED REACTORS
EVEN 3321 Environmental Engineering Lab
o Write & explain the general mass
balance equation.
o Solve both steady-state & transient-
state mass balance problems.
o Explain the meaning of hydraulic
retention time.
o Describe key features of batch and
completely mixed reactors.
o Explain the meaning of conservative
tracer.
LEARNING
OBJECTIVES

2. 1/29/2015
2
MASS BALANCES
Note: units are mass per unit time
o Steady-state
No accumulation of mass within “system”.
o Transient-state
(or non-steady-state, or dynamic):
Mass accumulating or disappearing from
the “system”.
o Steady≠state equilibrium
STEADY-STATE VERSUS TRANSIENT STATE

3. 1/29/2015
3
FUNDAMENTAL “REACTOR” TYPES USED TO
MODEL ENVIRONMENTAL SYSTEMS
Batch Reactors
Completely Mixed Reactors :
CFSTR-Continuous Flowing Stirred Tank Reactor
CSTR – Continuous Stirred Tank Reactors
Plug-flow Reactors (PFR)
Completely mixed reactors in series
Packed Bed Reactors
BATCH REACTOR
Accumulation = Inflow – Outflow + Reaction
For this reactor, no flow in or out.

4. 1/29/2015
4
BATCH REACTORS
FOR WATER
TREATMENT
COMPLETE-MIX REACTOR (CFSTR)
Accumulation = Inflow – Outflow + Reaction
0 at steady-state
Concentrations within reactor are same
As in effluent.
A CFSTR operated at steady-state is
called a “chemostat”.

5. 1/29/2015
5
EXAMPLE OF A CSTR IN WATER
TREATMENT
http://bluefrogsystem.com/pages/cstr.html
HYDRAULIC RETENTION TIME
o “HRT”, also called hydraulic detention time or hydraulic
residence time (દH).
o Equals the average time that water molecules remain in
the system.

6. 1/29/2015
6
RESPONSE OF A CFSTR TO STEP INPUT OF
A CONSERVATIVE TRACER
0 3દH TIME
( )H
i
t
TT eCC θ/
1 −
−=
RESPONSE OF CFSTR TO STEP INPUT
OF A CONSERVATIVE TRACER
∫∫ =
−
tC
TT
T
dt
V
Q
CC
dCT
i
00
HT
TT t
C
CC
i
i
θ
=







 −
− ln
VrQCQCV
dt
dC
TTT
T
i
−−=
0

7. 1/29/2015
7
( )H
i
t
TT eCC θ/
1 −
−=
CONSERVATIVE TRACER VERSUS TIME

8. 1/29/2015
8
HRRRH
R
kCCC
dt
dC
i
θθ −−= )1( HRRH
R
kCC
dt
dC
i
θθ +−=
( ) ∫∫ =
+−
t
H
C
HRR
R
dt
kCC
dCR
i
00
1
1 θθ
HR
RHR
H
t
C
CkC
k i
i
θ
θ
θ
=







 +−
+
−
)1(
ln
1
1
H
t
k
R
R
k
eC
C
H
H
i
θ
θ
θ
+








−
=
+−
1
1
)1(
RESPONSE OF A CFSTR TO STEP INPUT OF A
FIRST ORDER REACTANT
VrQCQCV
dt
dC
RRR
R
i
−−=
VkCR−
REACTANT VS TIME
o When t->0, then CR -> CRi (1-1)/(1 + kદH) and CR -> 0
o When t is large then 1/et/દH -> 0 and CR -> CRi (1-0)/(1 + kદH)
CR =CRi /(1 + kદH)
o Note for example when t is about 3દH
CR = 0.95CRi /(1 + kદH)
And a large residence time will result in a lower concentration of the
effluent.
H
t
k
R
R
k
eC
C
H
H
i
θ
θ
θ
+








−
=
+−
1
1
)1(

9. 1/29/2015
9
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5
CR/CRi
t/θθθθH
K=0.03 per hr
θH=0.5 hrs
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5
CR/CRi
t/θθθθH
K=0.9 per
H
t
k
R
R
k
eC
C
H
H
i
θ
θ
θ
+








−
=
+−
1
1
)1(
RESPONSE OF CFSTR TO STEP
INPUT OF A REACTANT
K=0.9 per hr
θH=0.5 hrs
K=0.03 per hr
θH=0.5 hrs
RESPONSE OF CFSTR TO STEP
INPUT OF REACTANT
0 < 3દH 3દH

10. 1/29/2015
10
)1(0 HRR kCC i
θ+−=
DETERMINING EFFLUENT REACTANT
CONCENTRATION FOR CFSTR STEADY-STATE
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
CR/CRi
Detention time (θθθθH), hrs
K=0.03 per hr
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
CR/CRi
Detention time (θθθθH), hrs
K=0.3 per hr
STEADY-STATE EFFLUENT REACTANT
CONCENTRATIONS IN CFSTR
K=0.3 per hr
K=0.3 per hr

11. 1/29/2015
11
MATHEMATICAL MODELS OF PHYSICAL
SYSTEMS SUMMARY
Accumulation = inflow + outflow + reaction
At steady-state: