4 reactors

Changha Lee
School of Chemical and Biological Engineering
Seoul National University
http://artlab.re.kr
고도산화환원 환경공학 연구실
Advanced Redox Technology (ART) Lab
Chapter 5. Reactors
All the figures and tables in this material are from the reference below unless specified otherwise.
Reference: Bruce E. Rittmann and Perry L. McCarty, "Environmental Biotechnology: Principles
and Applications", McGraw-Hill, 2001.

5. Reactors
√ Reactors
• Many different types exist for environmental engineering,
generally designed as suspended growth or biofilm reactors
- Suspended growth reactors make use of suspended cells,
also called: suspended-floc, dispersed-growth, slurry reactors
- Biofilm reactors make use of cells in biofilms attached on surfaces,
also called: fixed-film, attached-growth, immobilized reactors
√ Engineers must understand
• Kinetics of substrate removal by different types of microorganisms
• Fundamental properties of different reactor types

√ Factors influencing the choice among the different reactor types:
• Physical & chemical characteristics of the wastewater
• Concentrations of contaminant
• Presence or absence of oxygen
• Efficiency of treatment and system reliability required
• Climatic conditions under which the reactor will operate
• Number of different biological processes involved in the overall treatment system
• Skills & experience of those who will operate the system
• Relative costs at a given location and time for construction and operation of
different possible reactor configurations
√ The aims of this chapter are to understand
• How to construct mass balances for different reactors,
• How to use of mass balances to derive basic equations that describe the relationship between
reactor size and treatment performance.
5. Reactors

√ Typical reactors used in environmental application
• Basic reactors
• Biofilm reactors
5.1 Reactor Types

√ Batch reactors:
• The simplest suspended-growth reactor
• Biochemical reactions take place without new additions until the reaction is complete.
• Commonly used in laboratory-scale
• Kinetics of contaminant removal is similar to that of an ideal plug-flow reactor.
5.1.1 Suspended Growth Reactors
filling
drawing
• Cyclic operation in a single reactor :
1) Fill, 2) React (aerobic/anoxic or anoxic/aerobic),
3) Settle, 4) Draw, 5) Idle
• SBR can also employ several batch reactors operated
in parallel
√ Sequencing Batch Reactor (SBR):

√ Advantages of SBR:
• Total capital costs are significantly reduced due to the elimination of clarifiers and
recirculation facilities.
• Operating flexibility is greatly increased, since the cycle format can be easily modified at
any time to offset i) change in process conditions, ii) influent characteristics or iii)
effluent objectives.
• Process reliability is greatly improved because the SBR process is not affected
by hourly, daily, or seasonal feed variations.
• Since only one vessel is used for all proces operations, plant extension is simplified.
• Better resistance to sludge bulking, since the biomass undergoes cyclic feast-famine
conditions, which have been proven to produce better settling sludge than continuous
flow.

√ Continuous-Flow Stirred-Tank Reactor(CSTR),
or completely mixed reactor :
• Used to culture organisms or to study basic biochemical phenomena in the laboratory
(Chemostat)
• Liquid or slurry stream is continuously introduced, and liquid contents are continuously
removed from the reactor
• Concentrations of substrates and microorganisms are the same everywhere throughout
the reactor (Ideal CSTR); it makes analysis of CSTR comparatively simple.
• Sometimes referred to tubular reactor or piston-flow reactor.
• In the ideal PFR,the flow moves through the reactor with no mixing with earlier or
later entering flows.
• Hence if one knows the flow rate to the reactor and itssize, the location of the
element at any time can be calculated.
• Unlike the CSTR, the concentartions of substrates and microorganisms vary throughout
the reactor.
• An ideal PFR is difficult to realize in practice, because mixing in the direction of flow is
impossible to prevent .
√ Plug-Flow Reactor (PFR)

√ Comparison of CSTR and PFR
• The high rate of substrate utilization at the entrance of reactor inPFR
because the substrate concentrations are highest at the entrance.
- If other conditions are the same, a higher S gives a higher rate of reaction.
So a PFR generally produces a higher conversion of S in a given volume than a CSTR.
(advantage of PFR)
- It exceeds the ability to supply sufficient oxygen (high DO demand at the entrance and
low DO demand at the exit) in an aerobic system. Thus the aerators for PFR should be
designed to provide more oxygen in the inlet region. (disadvantage of PFR)
- It results in excess organic acid production and pH problems,
e.g., destruction of methanogens at low pH in an anaerobic system.
(disadvantage of PFR)

• In CSTR, the S in the reactor is the same as S in the effluent.
So the fresh feed is immediately dispersed into an environment of low S.
In PFR, the S decreases along the length of reactor.
- If no biomass enters PFR, no biological reaction would occur and the reactor
washes out.
- On the other hand, the influent to a CSTR is mixed with reactor fluid containing
biomass so that a CSTR can be sustained even in the absence of biomass in
the feed.
- Processes for in situ biodegradation of contaminants in ground waters often operate
similar to PFR. Here, mixing in the direction of flow (longitudinal) is generally small,
making plug flow the natural outcome.

• The CSTR is more stable than a PFR in response to toxic and shock loadings.
- If a concentrated pulse of a toxic substance enters a PFR, the concentration remains
high as it moves along the PFR. Because of high concentration, the toxic substance may
destroy an appreciable quantity of the biomass in the system and cause a long term
upset in PFR performance.
- With a CSTR, the pulse of toxin is dispersed rapidly throughout the CSTR and its
concentration level is reduced so that the metabolic processes of microorganisms may
be only slightly affected by the diluted toxin.
- In general, a CSTR gives a more uniform effluent under varying feed conditions.
• The CSTR and PFR are idealized models that are difficult to achieve in large scale
biological reactors.
- In actual CSTR, short-circuiting of fluid and stagnant zones may occur because of
incomplete mixing with the bulk of the reactor fluid.
- In PFR, aeration of the fluid causes longitudinal mixing and a distribution of residence
times. Thus, long biological reactors with aeration are often better simulated by an axial
dispersion model or a CSTR in series model.
- Tracer techniques are useful in establishing an appropriate hydraulic model for a biological
reactor.

√ Practical aspects of reactor design
• The deviation from two idealized flow patterns :
I) Dead Zone (Stagnant zone)
2) Channeling of fluid
3) Short-circuiting caused by
i) density current in plug-flow reactor
ii) inadequate mixing in a CSTR
• This type of flow should be avoided since it always lowers the performance of the unit.
• The problems of non-ideal flow are intimately tied to those of scale-up.
• Often the uncontrolled factor differs widely between large andsmall units.
Therefore ignoring this factor may lead to gross errors indesign.

√ Reactor arrangements
5.1.3 Reactor Arrangement

• Reactors in series:
- When different types of treatment are needed.
e.g., organic oxidation (1st reactor) nitrification (2nd reactor)denitrification (3rd reactor)
- To create plug-flow characteristics.
• Reactors in parallel:
- They are used to provide redundancy in the system so that some reactors can be out
of service, while others on a parallel track remain in operation.
- When the total flow to be treated far exceeds the capacity of the largest practical units
available.
- It maintains more of a completely mixed nature, compared to the more plug-flow nature of
reactors in series.
5.1.3 Reactor Arrangement

e- donor e- acceptor nitrogen source
5 7 2 2 2 3 2
6 5 3 4
0.02C H O N  0.06N  0.12CO  0.0133HCO
 0.1067H O
0.0333C H COO
 0.12NO
 0.02NH 
 0.12H 

√ Reactor design
• Mass balance is the key to design and analysis of microbiological processes
- It provides the critical information on what must be addedto and removed
from the process.
- It determines the amount of chemicals to satisfy the energy,nutrient, and environmental
needs of the microorganisms.
e.g., the process for biological denitrification
bacteria
0.02 mole biomass is produced from 0.0333 mole substrate, 0.12 mole nitrate,
and 0.02 mole ammonia
5.2 Mass Balances

• System boundary; a control volume
5.2 Mass Balances

Component entered Component left Component destroyed or formed
Fig.5.2-a Influent stream Effluent stream or sludge waste stream Within the reactor system
Fig.5.2-b Influent stream effluent stream In the reactor
Fig.5.2-c
Reactor effluent
stream
Settling tank effluent stream or
sludge recycle line
In the settling tank
• Components that enter
(or leave) the controlvolume
5.2 Mass Balances

- The mass balance is defined in terms of rates of mass change in the control volume.
- Each component must have its own mass balance
Components : COD, TOC, biomass, oxygen, electron acceptor, nitrate, ammonium etc.
- In the development of equations useful for a reactor system, mass balances on several different
components of interest and around several different control volumes sometimes are required.
• Reaction rates affect the size of the treatment system
5.2 Mass Balances
Rate of mass accumulation in control volume =
rate(s) of mass in - rate(s) of mass out + rate(s) of massgeneration
Accumulation : total mass of the component or the reactor volume x the concentration
Mass in / out : mass crossed the control-volume boundaries
Generation : formation of the component of interest within the control volume
If negative, component destroyed rather than being formed
endogenous respiration or predation
If positive, bacteria cells produced through consumption

rate(s) of mass in - rate(s) of mass out + rate(s) of massgeneration
This equation may take many mathematical forms, depending upon
i) The nature of control volume,
ii) The manner in which mass flows into and out of the control volume,
iii) What kind of reactions generate or destroy the component.
5.2 Mass Balances

• A batch reactor operated withmixing
- the control volume consists of the entire reactor
- uniformly distribution of components throughout the reactor
- constant reactor liquid volume with time
- only component concentrations changing with time.
The rate of mass accumulation = Vdc/dt
• Selection of the components
- bacteria
- limiting substrate: the electron donor
• Assumption
- sufficiently high concentration of all other bacterial requirements such as electron
acceptor and nutrients
- At time=0, microorganism concentration in the reactor = X0 (mg/l),
rate limiting substrate concentration in the reactor = S0 (mg/l)
5.3 A Batch Reactor

rate of mass in - rate of mass out + rate(s) of massgeneration
=0 =0
mass of substrate accumulating = mass of substrate generated
if no substrate added or removed
a
X
q̂S
dt
dS
 
qˆS
dt K S
K S
V
dS
V( Xa)
ut
dt
V
dS
V
r
a
ut X
r 
qˆS
KS
√ Mass balance for substrate
If rate of substrate utilization follows Monod kinetics
5.3 A Batch Reactor

rate of mass in - rate of mass out + rate(s) of massgeneration
=0 =0
a
S
dt
d X a
S
dt
V
d X a




 b  X
K  S




 b  X a
K  S
  ˆ
 V  ˆ
S
X dt
syn dec b
K S
 
1 dX a
     ˆ
a
dt
V
dX a
 VX 
√ Mass balance for microorganisms
If the organism growth rate follows Monod kinetics,
5.3 A Batch Reactor

√ Initial conditions
0
a
a S0 S0
X 0 X
a
X
dS
 
q̂S
S
dt
dt K S
d X a 

 
 b  X a
K  S
  ˆ
• Interdependence between Xa and S, both of which vary with time
• In order to solve for Xa and S as functions of time, all above equations should be
considered simultaneously.
• Due to the nonlinear Monod forms, the systems of above equations cannot be solved
analytically. It must be done with a numerical solution.
• If organism decay is considered to be negligible (b =0),
an analytical solution can be obtained. This is reasonable for cases of batch growth
where the organism decay is small while they are growing rapidly.
5.3 A Batch Reactor

• Assumption :
The organism decay is negligible while the microorganisms are growing rapidly.
X a  X a
0
 Y S0
 S 
X a  YS
5.3 A Batch Reactor
S0 S0
Xa0 Xa
0
a
X
dS
 
q̂S
S
dt
dt K S
d X a
X a
K  S
  ˆ
Let’s solve the differential equations.
S
dt
X a =  Y
K  S
  ˆ
dXa
dt
dS
∧ ∧
  q Y

S(t) can be solved by reversing the above equation.
And, Xa(t) can be obtained by
a
X
dS   qˆS
dt K S
By substitution of Xa of the equation below
0
a
X  Y S0
 S 
dt K  S
dS
 
q̂S

0 0
0
0











  0
a
 a
a
 a
ln a
 ln X
Y
S0
1    SX 0
X YS
K 1
lnX  YS 0
YS
Y 
1 
 K
qˆ X  YS0
t 
By integration, subject to the initial conditions,
X a ( t )  X a
0
 Y S0
 S( t ) 
5.3 A Batch Reactor

• Effect of Xa
0 on bacterial growth and the substrate concentration
- The higher the intial concentration of biomass, the lower the substrate utilization time.
- For the lowest initial organism con., a lag period occurs before the onset of significant
substrate utilization.
- The increase of biomass between t=0 and t = t at S=0 is the same in all cases
( = ( Xa – Xa
0 ) =Y S0 = 0.6 X 100 = 60 mg/L )
0
a
a a  X  0.6(100  0)
X  X 0
 Y S 0
 S 
5.3 A Batch Reactor
lag period

5.4 A Continuous-Flow Stirred–Tank Reactor
with Effluent Recycle
• CSTR: the same as chemostat
- Continuous flow in and out
- Steady state, VdC/dt =0
• CSTR with effluent recycle
- Some of the effluent stream is recycled back at a flow rate Qr.
• How does “effluent recycle” affect the reactor performance?
-It does not affect the reactor performance at all.
-Which (the entire system or the reactor itself) is used as the control volume makes no
difference to the results.
-But, CSTR with effluent recycle can increase the total reactor volume by the volume of
recycle line (?) and increase the extent of mixing.

• Mass Balance
- For the steady-state
5.4 A Continuous-Flow Stirred–Tank Reactor
with Effluent Recycle
& 𝑋𝑎
𝑖 =
𝑄𝑋𝑎
0
+ 𝑄𝑟𝑋𝑎
𝑟
𝑄𝑖
Identical to the equation for chemostat without recycle (Chapter 3)
𝑄 + 𝑄𝑟 = 𝑄𝑖 𝑖 & 𝑄𝑋𝑎
0
+ 𝑄𝑟𝑋𝑎
𝑟
= 𝑄𝑖𝑋𝑎
𝑖
𝑖 =
𝑄 + 𝑄𝑟
𝑄𝑖
𝑄𝑖 = 𝑄 + 𝑄𝑟
= 𝑄𝑖 𝑖 𝑄𝑖 + 𝑟 = 𝑄 + 𝑟

• PFR
: the substrate and active-organism concentrations vary over the length of the reactor.
- Substrate
- Active microorganisms
5.5 A Plug-Flow Reactor
• Mass Balance

• At steady-state, influent flow rate (Q), substrate concentration (S) and active organism
concentration (Xa) do not change with time, the left sides of the equations are zero (no
accumulation
• Area of the control volume (a): A = ΔV/Δz
• Velocity of flow within the reactor (u): u = Q/A = Q/(ΔV/Δz) = Q x Δz/ΔV
- Substrate at steady-state
- Active microorganisms at steady-state
u = Q x Δz /ΔV
u = Q x Δz /ΔV
= 𝑄 𝑄 + + 𝑟
= 𝑄𝑋 𝑄 𝑋 + 𝑋 + 𝑟
= 𝑄 𝑄 + + 𝑟
= 𝑄𝑋 𝑄 𝑋 + 𝑋 + 𝑟

Apply lim that Δz approaches zero
Apply the Monod equation
𝑧 →
𝑙𝑖𝑚
If we ignore the
microorganism decay
(b=0), then analytical
solution is possible.
𝑑
𝑑𝑧
= ො
𝑞
𝐾 +
𝑋

-Substituting u = dz/dt yields an analogous differential equation to that of a batch reactor.
0
a
X  Y S0
 S 
dt K  S
dS
 
q̂S
- Integration gives
for a batch reactor
(check out the previous slide)
which is almost identical to the equation for a batch reactor.
for a batch reactor
(check out the previous slide)

)ln 0
0 0
S 0
SXa
0
1
K
{(  ) ln{Xa  YS  YS}  (
u qˆ Xa
0
 YS 0
Y Xa
0
 YS 0
z

1 K 1
 ln Xa }
Y
L/u = V/Q = θ (the hydraulic detention time)
An expression for the effluent concentration (Se) from the batchreactor is obtained
by letting z = L.
)ln 0
0 0
S 0
SeXa
0
1
K
{(  ) ln{Xa  YS  YSe}  (
u qˆ Xa
0
 YS 0
Y Xa
0
 YS 0
L

1 K 1
 ln Xa }
Y
 )ln 0
0 0
S 0
SeXa
0
1
K
{(  ) ln{Xa  YS  YSe}  (
qˆ Xa
0
 YS 0
Y Xa
0
 YS 0

1 K 1
 ln Xa }
Y

• We thus see that a PFR works exactly like a batch reactor.
• In practice, however, it is difficult to operate a PFR according to the assumptions involved.
- A PFR has no mixing or short-circuiting of the fluid along the flow direction.
This is impossible to achieve in a real continuous-flow reactor.
- Wall effects slow the fluid near the wall boundaries relative to the velocity near the middle.
- Aeration or mixing to keep the biomass in suspension introduces a large amount of
mixing in all directions.
• Methods to achieve as much of a plug-flow character as possible include
i) using a very long, narrow reactor, and ii) using many reactors in series.
But, some mixing and short-circuiting are inevitable.
- If achieving the reaction kinetics represented by the theoretical kinetic equation is of paramount
importance, a batch reactor is a prudent choice, although it presents its own problems:
For example, time is required to fill and empty a batch reactor, time that might otherwise be used
for treatment. In order to minimize downtime (e.g., idle time), a batch reactor can be operated
while it is filling.

5.6 A Plug-Flow Reactor with Effluent Recycle
 If no organisms are introduced in PFR, then the system fails to do any treatment.
 using effluent recycle, a portion of microorganisms in the effluent is brought
back to the influent stream.
a a a

- Solved in the same manner as with the PFR without effluent recycle except that
Q 0
, X 0
and S0
 Qi
, X i
and Si
- Ignoring the organism decay (b=0), we have
Xa  Xa
0
 Y(S 0
 S)
0
0
0
S0
SXa
0
1
K
 ln Xa }
Y
 YS  YS} ( )ln
Xa
0
 YS 0
z

1
{(
K

1
)ln{Xa
u qˆ Xa
0
 YS 0
Y
Which are similar to the equations below for the PFR without effluent recycle

- Recycle ratio R,
𝑅 =
𝑄𝑟
𝑄
𝜃 =
𝑄
=
(1 + 𝑅)
𝑄𝑖
𝜃
1+𝑅
We have a Se as a function of 𝜽
𝑄𝑖 = 𝑄 + 𝑄𝑟
Si =
0
+ 𝑟
𝑖 =
0
+ 𝑟
+ 𝑟 =
0
+𝑅
1+𝑅
Xa
i = 𝑎
0
+ 𝑟
𝑎
𝑖 = 𝑎
0
+ 𝑟
𝑎
+ 𝑟 = 𝑎
0
+𝑅 𝑎
1+𝑅
= 𝑎
0
+𝑅( 𝑎
0
+ ( 0
)
1+𝑅

𝜃
Washout
time
• Washout time:
- A detention time below which the
effluent concentration equals the
influent concentration (S0 = Se = Si),
- In which no treatment takes place
- Similar concept to 𝜽𝒙
𝒎𝒊𝒏
for the CSTR
• The washout time increases when R
decreases
• In theory, when R approaches infinity,
the PFR with recycle becomes
identical to a CSTR.
√ Se as a function of 𝜽
with different R values

• Relative benefits of a CSTR and a PFR
with recycle
- R=8 is very similar to a CSTR ‘s performance
- CSTR improves reliability
if contaminant removal of 80
to 90% were satisfactory.
- PFR with low recycle ratio is
much more desirable if
contaminant removal of 99.9%
were required.
- There is an optimal recycle ratio that provide
low θ and high efficient contaminant removal.
• Effluent recycle with a CSTR does not
change system performance, but with a
PFR, the recycle is essential and has a
great impact on performance.

5.7 Reactors with Recycle of Settled Cells
• Microorganism recycle from a settling tank :
the most widely used suspended-growth reactor.
• Any method that increases the concentration of microorganisms in the reactor
increases the reaction rate and, in this manner, decreases the required reactor
volume
• The primary advantage: a much smaller reactor volume is required.
The disadvantage: the cost of the settler and the recycling system.
Smaller reactor plus settler vs a larger reactor without a settler

5.7.1 CSTR with Settling and Cell Recycling
• Assumptions
• Mass balance for microorganisms
• Mass balance for substrates
• Solids retention time (SRT)
Applicable Equations : S, Xa
CSTR
with Settling and Cell Recycling

√ Assumptions:
• Biodegradation of substrates takes place in the reactor only,
no biological reactions take place in the settling tank, and biomass in the settler
is insignificant.
• No active microorganisms are in the influent to the reactor (Xa
0 = 0).
• The substrate is soluble so that it cannot settle down in the settling tank.

Accumulation = In – Out + Generation - Consumption
- Mass balance for microorganism:
- Mass balance for substrate:
√ Mass balance

- At steady state,
𝜃𝑥 =
active biomass in the system
production rate of active biomass
√ SRT (𝜽𝒙)
𝜃𝑥 =
active biomass in the system
remova rate of active biomass
=
𝑋
𝑄 𝑋𝑎 + 𝑄 𝑋𝑎

- If it takes Monod kinetics,
- At steady state, mass balance for microorganism
- Solving this equation for S,
= 𝐾
1 + 𝑏𝜃𝑥
𝜃𝑥 𝑌ො
𝑞 𝑏 1
- This equation is identical to the one developed for the chemostat (CSTR) without settling
and recycle (in Chapter 3)
- So then, what is unique about the CSTR with settling and microorganism recycle?
= 𝑄 𝑋𝑎 + 𝑄 𝑋𝑎 + 𝑌 𝑟 𝑏𝑋
𝑋
=
𝑌( 𝑟 )
𝑋
𝑏
1
𝜃𝑥
=
𝑌( 𝑟 )
𝑋
𝑏
𝜃𝑥 =
𝑋
1
𝜃𝑥
=
𝑌( 𝑟 )
𝑋
𝑏 = 𝑌
𝑞
ො
𝐾 +
𝑏

• For the CSTR without settling and microorganism recycle (Chapter 3)
- Usually, θx > θ in order to obtain high efficiency of substrate removal
θx = θ
• For the CSTR with settling and microorganism recycle (Chapter 5)
θx ≠ θ
√ What is unique about the CSTR with settling and microorganism recycle?

- From mass balance for substrate,
- Substituting rut,
- Since no reaction occurs in the settling tank
- From the previous equation (originally from the mass balance for microorganism),
1
𝜃𝑥
=
𝑌( 𝑟 )
𝑋
𝑏 𝑋 = 𝜃𝑥
𝑌( 𝑟 )
1 + 𝑏𝜃𝑥
= 𝑄 𝑄 + 𝑄 + 𝑟
𝑟 =
𝑄 𝑄 𝑄
= =
𝑑 𝑄 = 𝑄 + 𝑄
𝑟 =
𝑄 ( )
=
( )
𝜃
𝑋 = 𝜃𝑥
𝑌( 𝑟 )
1 + 𝑏𝜃𝑥
=
𝜃𝑥
𝜃
𝑌( )
1 + 𝑏𝜃𝑥

𝜃𝑥
𝜃
: 𝑺𝒐𝒍𝒊𝒅𝒔 𝒄𝒐𝒏𝒄𝒆𝒏𝒕𝒓𝒂𝒕𝒊𝒐𝒏 𝒓𝒂𝒕𝒊𝒐
- Active biomass concentration in the reactor depends on the ratio of solids retention
time to the hydraulic detention time.
In Chapter 3, for a CSTR without sett ing and recyc e,
𝜃𝑥
𝜃
= 1, so 𝑋 = 𝑌
1 + 𝑏𝜃𝑥
√ Solids concentration ratio
√ Mass rate of active biomass production
• At steady state, the mass rate of active biomass production must equal the rate at which the
biomass leaves the system from the effluent stream and the waste stream.
𝑟 𝑏𝑝 ∶ 𝑐 𝑖𝑣 𝑏𝑖𝑜𝑚 𝑠𝑠 𝑝𝑟𝑜𝑑 𝑐 𝑖𝑜 𝑟 (𝑀/𝑇)
=
𝑋
𝜃𝑥
𝑋 = 𝜃𝑥
𝑌( 𝑟 )
1 + 𝑏𝜃𝑥
=
𝜃𝑥
𝜃
𝑌( )
1 + 𝑏𝜃𝑥
𝜃𝑥 =
𝑋
𝑟 𝑏𝑝 = 𝑄 𝑋𝑎 + 𝑄 𝑋𝑎
* rnet  Xa
Net rate of cell growth
= Xa/x

√ Table 5.2
• Summary of a series of equations to design a CSTR with settling and recycle
• Assumptions for Table 5.2
- Operating at steady state
- Treating a soluble substrate
- No input of active biomass
• The equations in Table 5.2 can be used for a CSTR without a settler by letting θx = θ

√ Table 5.2

- At a constant SRT, the effluent concentration (S) remains independent on the
influent concentration (S0). Only θx affects S because all other parameters in the
equations are coefficients.
Why?
1) “Self Control”: As the influent concentration increases, so does the concentration of
active organisms in the reactor.
The increased biomass is sufficient to consume the additional substrate that is added
to the reactor.
𝑋 =
𝜃𝑥
𝜃
𝑌( )
1 + 𝑏𝜃𝑥
= 𝐾
1 + 𝑏𝜃𝑥
𝜃𝑥 𝑌ො
𝑞 𝑏 1
2) The organisms’ growth rate and SRT are equal to the inverse of each other.
𝜃𝑥 =
𝑐 𝑖𝑣 𝑏𝑖𝑜𝑚 𝑠𝑠 𝑖 ℎ 𝑠𝑦𝑠 𝑚
𝑝𝑟𝑜𝑑 𝑐 𝑖𝑜 𝑟 𝑜𝑓 𝑐 𝑖𝑣 𝑏𝑖𝑜𝑚 𝑠𝑠
= 𝜇 1 𝜇 = 𝑌
ො
𝑞
𝐾 +
𝑏
Constant SRT (θx) → Constant specific growth rate (μ) → Constant substrate (S)

5.10 Engineering Design of Reactors
𝜃𝑥
𝑑
= 𝐹 𝜃𝑥
𝑚𝑖𝑛
𝑙𝑖𝑚
𝜃𝑥
𝑑 ∶ 𝑑 𝑠𝑖𝑔 𝜃𝑥
- Conventional activated sludge treatment plants :
Medium sized treatment systems that are expected to operate reliably with fairly constant
supervision by reasonably skilled operator.
- High Rate: Highly skilled operator or the removal efficiency and high reliability is not as critical.
- Low Rate : Extended aeration
: Operator attention is quite limited
: Operators are present for a very short period time.
: “shopping center” or “apartment complex”
√ Safety factor (SF)

√ Factors to consider when selecting SF :
- High SF increases the degree of reliability of operation,
but gives higher construction cost.
- Low SF requires more continuous supervision
and operators with increased skill
5.10 Engineering Design of Reactors
- Higher SS (X) makes the reactor volume
smaller and thus less expensive for a given
𝜽𝒙
𝒅
. However, high SS may require larger
settling tanks, because increased loads of
SS to the settling reactor.

Homework
What about PFR with settling and cell recycling?
What are the differences from CSTR?

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