304-notes 8 biotreat 2013

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ENVE 304

UNIT OPERATIONS AND

PROCESSES OF WASTEWATERTREATMENT

Biological Oxidation / Growth Kinetics / Reactor types /

Mass Balances

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• Types and characteristics of

wastewaters

• Physical unit operations

• Biological oxidation

• Biological wastewater treatment

processes

• Handling & disposal of 2

TOPICS

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1.Types and characteristics of wastewaters

–Wastewater management, Environmental laws and

regulations, Types of wastewaters, Physical, chemicaland biological characteristics of WW, Main WWTP units

1. Physical unit operations

–Flow measurement, Screening , Coarse solid reduction,Grit removal, Equalization, Sedimentation, Flotation,Oxygen transfer, Aeration

1. Biological Oxidation 3

TOPICS

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Biological Oxidation

• Classification of microorganisms

• Oxidation equations – Aerobic, anaerobic, nitrification, denitrification – Required oxygen amounts

• Growth kinetics• Reaction orders• Reactor types (completely-mixed, plug-flow, etc)• Main equations and derivations in flow through

systems, in systems with recycle, operatingparameters, SVI definition

4

Learning Objectives:

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Bacterial Growth

Biomass producedcanbe measured:

VSS, Particulate

COD, Protein

content, DNA, ATP, Turbidity

measurements,

Bacterial cell

count

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0

0.03

0.06

0.09

0.12

µ ,

1 / h r

0.15

0.18

0 300 600 900 1200

So

, mg COD/L

1500

µm /2

µm

Ks

S*

Monod

Haldane

µ *

6

Bacterial Growth

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Monod equation (substrate-limited growth, no inhibition)

Haldane equation (inhibition)

7

)(S K

S

s

m

+=

µ µ

)

/

(2

i s

m

K S S K

S

++

=µ

µ K i = inhibition constant,

mg/L

µ = specific growth rate, mg new cells / mg cells.d (1/T)µm = maximum specific growth rate, mg new cells / mg cells.d

(1/T)S = concentration of growth-limiting substrate, mg/LK s = half-velocity constant, substrate concentration at one-half

the maximum specific utilization rate, mg/L

Bacterial Growth

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First order

Zero order

8

Haldane eq.

}Beyond this point, the processcannot grow and will fail.

Monod eq.

s

m

K

S µ µ =Ks >> S, then,

m µ µ =Ks << S, then,

)/21

(*

i s

m

K K

S

+= µ µ

i s K K S /* =

Bacterial Growth

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Rate of utilization of soluble substrates

kY m = µ Y

k m µ =

)( S K Y

XS r

s

m

su +−=

µ

S K

kXS r

s

su+

−=

rsu = substrate utilization rate, mg/L.d

k = maximum specific substrate utilization rate, mg substrate/mgcells.d

µm = maximum specific growth rate, mg new cells/mg cells.dY = true s nthesis ield coefficient m VSS m bsCOD

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Other rate expression for the utilization of solublesubstrates

k r su −=

kS r su −=

kXS r su −=

o

suS

S kX r −=

Rate of utilization of soluble substrates

a e o u a on o so u e

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a e o u za on o so u esubstrate

11

kY m = µ Y

k m µ =

)( S K Y

XS r

s

m

su +−=

µ

S K

kXS r

s

su+

−=

rsu = substrate utilization rate, mg/L.d

k = maximum specific substrate utilization rate, mg substrate/mgcells.d

µm = maximum specific growth rate, mg new cells/mg cells.dY = true s nthesis ield coefficient m VSS m bsCOD

Rate of biomass growth with soluble

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Rate of biomass growth with solublesubstrates

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X k Yr r d su g −−=

X k S K

kXS Y r d

s

g −+

=)(

rg = net biomass production rate, mg VSS/L.d

Y = true (synthesis) yield coefficient, mg VSS /mg bsCODX = biomass concentration, mg/Lkd = endogenous decay coefficient, mg VSS/mg VSS.d

NET GROWTH RATE

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Typical kinetic coefficients for the activated–

sludge process for the removal of organicmatter from domestic wastewater (200C)

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Total VSS And Active Biomass

X k f r d d Xd )(=

V QX X k f X k Yr r iOd d d suVSS X T /)( ,, ++−−=

VSS X d suact X T r X k Yr F ,, /)( −−=

rxd = rate of production of

cell debris, mg VSS/L.d

f d = fraction of biomass thatremains as cell debris(0.1-0.15 mg VSS/mgVSS)

rxT, VSS = total VSS production rate,

mg/L.dQ = influent flowrate, L/d

XO,i = influent nbVSS concentration,

mg/LV= volume of the reactor, L

Active fractionof biomass

Rate of celldebrisproduction

nbVSS intheinfluent

Netbiomass

growthrate

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su g bio

r r Y /−=

Net biomass yield: to estimate amount of active microorganisms

Observed yield: to estimate amount of sludge produced

suVSS X obs r r Y T

/,−=

(Considers decay of m/o)

Considers decay of m/o, includes VSScontent due to cell debris and influent

nbVSS

Biomass yield =g biomass produced

g substrateconsumed

Yield Coefficient

Synthesis (True) yield: to estimate amount of biomass produced

during cell synthesis relative to the amountof substrate degraded.

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Rate of oxygen uptake

g suO r r r 42.1−−=

rO = oxygen uptake rate, mg O2/L.d

rsu = substrate utilization rate, mg bsCOD/L.d

1.42 = COD of the cell tissue (C5H7NO2), mg bsCOD/mg VSSr = net rate of biomass growth, mg VSS/L.d

READING ASSIGNMENT: CHP 7, ESTIMATION OF BIOMASS YIELDFROM BIOENERGETICS

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Growth kinetics for nitrifiers

17

dn

n

nmn k

N K

N −

+= )(

µ µ Assuming excess

DO is available.

dn

On

nmn k

DO K

DO

N K

N −

++= ))((

µ µ

To account forthe effects of DO

µn = Specific growth rate of nitrifying bacteria, mg new cells / mg cells.d

(1/T)µnm = Maximum specific growth rate of nitrifying bacteria, mg new cells /

mg cells.d (1/T)kdn = endogenous decay coefficient for nitrifying organisms, mg VSS/mg

VSS.dK n = half-velocity constant, mg/L

N = Nitrogen concentration, mg/L

The rate of substrate utilization for

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The rate of substrate utilization indicating a slowerutilization rate in the anoxic zone

S K

kXS r

s su+

−=η

To indicate the effect of oxygen (which inhibits nitratereduction by repressing nitrate reduction enzyme):

η ))()(('

'

3,

3

3 DO K

K NO K

NOS K

kXS r O

O

NO s s

su+++

−=

The rate of substrate utilization fordenitrifiers

ƞ = Fraction of denitrifying bacteria in the biomass, mg VSS / mg VSSK S,NO3 = half-velocity coefficient for nitrate limited reaction, mg/L

K’O = DO inhibition coefficient for nitrate limited reaction, mg/L

E l

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Example

An industrial wastewater with a biodegradable solubleCOD content of 300 mg/L and nonbiodegradable VSS of 50mg/L is treated in an activated sludge process. Influentflowrate is 1000 m3/d. The biomass concentration in the

aeration basin of 105 m3

is 2000 mg/L. The biodegradablesoluble COD removal efficiency is 95%.

k = 5 d-1, K s = 40 mg/L,

Y = 0.40 g VSS/g bsCOD,k

d

= 0.10 g VSS/g VSS.d

Cell debris per dry weight = 0.10

Determine; Net biomass yieldObserved yield

VSS production rate & activebiomass fraction

R t T

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Reactor Types

Batch reactors

Complete-mix reactorsPlug-flow reactors

Plug-flow with axial dispersion

Ideal flow reactors

Non-ideal flow

reactors

Materials-balance equation in a

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Materials-balance equation in asystem boundary

Accumulation ratewithin thesystemboundary

=

Inflow rate

to thesystemboundary

-

Generation

rate withinthe systemboundary

+

Outflow

rate fromthesystemboundary

V r QC QCoV dt

dC c+−=

R t i d d

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Rate expressions and orders

k r c =

kC r c =

2kC r c =

C K

kC r c +=

Zero-order reaction

Second- order reaction

Saturation (mixed-order) reaction

Differential Method

First-order reaction

n

c kC r =

Bi l i l T t t P

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Biological Treatment Processes

23

SUSPENDED GROWTH

PROCESSES

ATTACHED GROWTHPROCESSES

Modeling Biological Treatment

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SUSPENDED GROWTH PROCESSES

ATTACHED GROWTH (BIOFILM) PROCESSES

The microorganisms responsible for treatment aremaintained in liquid suspension by appropriate mixing.

• Activated-sludge process(es)• Aerated lagoons

• Aerobic digestion

• Anaerobic contact processes• Anaerobic digestion

The microorganisms responsible for treatment areattached to an inert packing material (rock, gravel,sand, wide range of plastics, synthetic materials etc.).

• Trickling filters• Rotating biological contactors

• Packed-bed reactors, fluidized-bed reactors, expanded-bed reactors

Modeling Biological TreatmentProcesses

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COMPLETE-MIX REACTORS

MODELING


Complete-mix reactors

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V r QC QCoV dt

dC c+−=

Systemboundary

Accumulation rate = inflow rate - outflow rate +generation rate

Assumptions : well-mixed, constant volume, C and T are uniform

τ k

C

QV k

C C

+=

+=

1)/(1

00

Under steady-state conditionsand first-order reaction (r

c=

-kC)

Q, C0 Q, C

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MODELING


COMPLETE-MIX

ACTIVATED-SLUDGE PROCESS

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Biomass Mass

Balance:

[ ] V r X Q X QQQX V dt

dX g Rwewo ++−−= )(

rg = net rate of biomass production, g VSS/ m3.

d

Accumulation rate = inflow rate - outflow rate + net growthrate

Assuming; X 0 = 0 (can be neglected) and steady-state conditions

prevail;

V r X Q X QQ g Rwew =+− )(

d u s Rwew k

X

r Y

VX

X Q X QQ−−=

+− )(

1/SRT

µ =SRT

1

SRT= Solids retention

Complete mix reactors


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Rwew X Q X QQ

VX

+− )(SRT =

If no clarifier following the aeration basin,thus, no recyle; R=0, Qw=0,

τ ==QX

VX

QX

VX

e

SRT =

τ SRT == theoretical hydraulic detention time, V/Q, dτ

Biomass MassBalance:

SRT= Solids retention time, d



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-rsu/X = U = Specific substrate utilization rat

g BOD or COD/g VSS .d

d

u s k X

r Y

SRT −−=

1

S0= influent soluble substrate concentration,

g BOD or bsCOD/m3

S= effluent soluble substrate concentration,g BOD or bsCOD/m3

X

S S

VX

S S QU

X

r su

τ

−=

−== 00 )(

d k YU SRT

−=1

d

s

k S K

kS Y

SRT −

+=

1

[ ]

1)(

1

−−

+=

d

d s

k Yk SRT

SRT k K S

Biomass Mass

Balance:



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SludgeQw, XR,S

Effluent

(Q-Qw), Xe,S

Influent

Q, X0,

S0

Return activated sludge

QR, XR, S

S, X,

V

ClarifierAeration tank

Substrate Mass Balance:

V r QS QS V

dt

dS suo +−=

Assuming; steady-state conditions

))((0S K

kXS

Q

V S S

s +=−

+

−=

SRT k

S S Y SRT X

d 1

)( 0

τ [ ]

1)(

1

−−

+=

d

d s

k Yk SRT

SRT k K S



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Mixed liquor VSS concentration:

Inert material mass balance =

X0,i = nbVSS concentration in influent, g/m3

Xi = nbVSS concentration in aeration tank, g/m3

rx,i = rate of nbVSS production from cell debris,g/m3.d

rx,i

= X k f d d )(

SRT X k f SRT X X d d ii )()/(,0 += τ

X T = X + Xi

X T= total MLVSS concentration in aeration tank, g

VSS/m3

X= biomass concentration, g VSS/m3

Xi = inert VSS; nonbiodegradable VSS (nbVSS), g

VSS/m3

V r SRT V X QX V dt

dX

i xii

i

,,0 /+−=

At steady-stateconditions

τ τ

SRT X SRT X k f

SRT k

S S Y SRT X i

d d

d

T 00 )(

1

)(++

+

−=



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Mixed liquor VSS concentration:

X T = X + Xi

X T= total MLVSS concentration in aeration tank, g

VSS/m3

X= biomass concentration, g VSS/m3

Xi = inert VSS; nonbiodegradable VSS (nbVSS), g

VSS/m3

If both BOD removal and nitrification;

τ τ τ

SRT X

SRT k

NOY SRT SRT X k f

SRT k

S S Y SRT X i

dn

xn

d d d

T

00

1

)()(

1

)(+

+++

+

−=

Ox = concentration of NH4-N in the influent that is nitrified

dn = endogenous decay coefficient for nitrifying organisms, g VSS/gVSS.d

p

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TSS produced daily :

90.080.0 −=TSS

VSS (typical biomass ratio; 0.85)

)(85.085.085.000, VSS TSS Q D

C B A P TSS X T −++++=

= net waste activated sludge produced daily, measured in terms of TSS, gTSS

0= influent wastewater TSS concentration, g/m3

VSS0 = influent wastewater VSS concentration, g/m3

Mass of MLVSS (XVSS) V = (Px,VSS) SRT

Mass of MLSS (X TSS) V = (Px,TSS) SRT

TSS X T P ,

p


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Observed Yield:

)(1)(

1 0

,0

S S

X

SRT k

SRT Y k f

SRT k

Y Y

i

d

d d

d

obs−

++

++

=

nbVSS ininfluent

Heterotrophic biomass

Celldebris

)(11)(1 0

,0

S S

X

SRT k

Y

SRT k

SRT Y

k f SRT k

Y

Y

i

dn

n

d d d

d obs

−++++++=

Nitrifying

bacteria

biomass

p

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Oxidized nitrogen:

In separate nitrification or

In combined BOD removal and nitrification

Q(NOx) = Q(TKN0) – QNe – 0.12 Px,bio

Ne = effluent NH4-N

0.12 = N content in C5H7NO2

Oxygen Requirements:

Oxygen used = bCOD removed – COD of waste sludge

RO = Q(S0-S) - 1.42 Px,bio + 4.33Q (NOx)

RO = oxygen required, kg/d

Px,bio = biomass as VSS wasted per day, kg/d

Design & Operating Parameters

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SRT = the most critical parameter of activated-sludgedesign.

It represents; the average period of time during whichthe sludge has remained in the system

r BOD removal= 3-5 d (dependent on mixed-liquor temperature)

at 18-250C= SRT ~ 3 d (to limit nitrification), even 1 d

d

s

k S K

kS Y

SRT −

+=

1SRT affects treatmentprocess performance,aeration tank volume,

sludge production, oxygenrequirements.

Solids retention time (SRT):


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Process performance and stability

Washout; S = S0 SRT = SRTmin

d

sk S K

kS

Y SRT −+= 0

0

min

1

If S0 >> K s;

Safety factor (SF) = SRTdes/ SRTmin

d md k k Yk SRT

−≈−≈ µ min

1

(SF= 2-20)


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Food to microorganisms (F/M) ratio:

X

S

VX

QS

biomassmicrobial total

rate substrateapplied total

M

F

τ 00 ===

Specific substrate utilization rate:

100

)/( E M F U = E = BOD or bsCOD process removal efficiency, (S0-S)*100/S0

X

S S U

τ

−= 0

d k YU SRT

−=1

d k E M F

Y SRT

−=100

)/(1

(g BOD or bsCOD/ gVSS.d)

F/M = 1.0 g BOD or bsCOD/ g VSS.d for high-rate systemsF/M = 0.04 g BOD or bsCOD / g VSS.d for extended-aeration


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Volumetric organic loading rate:

)/10( 3

0

kg g V

S Q Lorg =

Lorg = volumetric organic loading rate, kg BOD/m3.d

Q= influent wastewater flowrate, m3/dV= aeration tank volume, m3

S0 = influent BOD concentration, g/m3

Usually, Lorg is 0.3-3.0 kg BOD or COD /m3.d (applied to the aeration ta

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Mixed-liquor settling characteristics Should be considered while designing secondary

clarifier;Sludge volume index (SVI) : is the volume of 1 g of sludge after 30 min of settling. (suspended solids interms of MLSS)

g

mL

Lmg solids suspended

g mg LmL sludgeof volume settled

SVI == /,

)/10)(/,( 3

SVI <100 good settling sludge (desired)

SVI > 150 filamentous growth, poor settling

1)/(100

100

−=

SVI P R

w

With SVI; R required tomaintain a fixed MLSSin the aeration tank canbe determined; Pw = MLSS as expressed as percentage

(eq. 0.3% ~ 3000 mg/L)

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SludgeQw, XR,S

Effluent

(Q-Qw), Xe,S

Influent

Q, X0,

S0

QR, XR, S

S, X,

V

ClarifierAeration tank

Assuming; steady-stateconditions

SECONDARY CLARIFIER

0 = X(Q + QR) - QRXR - XRQW - QeXe

(Q-Qw

=Qe

)

Mass balance around the clarifier:

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SECONDARY CLARIFIER

[ ] X X

SRT XV XQQ

R

R−

−=

)/(

Q

O R

Recycle ratio = R =

X X

X R

Q

O

R

R

−==Mass balance around the aeration tank:

Mass balance around the clarifier:

1)/(

)/(1

−−=

X X

SRT R

R

τ

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SECONDARY CLARIFIER

A

X QQSLR R )( +

=

Solids loading rate (SLR):

A= clarifier surface area, m2

ypical return sludge pumping rate: 50 - 75% of Qave

esign average capacity = 100 - 150% of the design flowrat

Return sludge concentration, XR = 4000 – 12000 mg/L

EXAMPLE

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Design a complete-mix activated sludge process to treatprimary effluent of 10000 m3/d by both BOD removal andnitrification.

Influent BOD = 150 g/m3 (bCOD/BOD=1.6)

Effluent BOD = 2 g/m3

Influent TKN = 35 mg/L,

Effluent NH4-N = 0.5 mg/L

NH4-Nin / TKNin = 0.65

SRT = 15 d

Theoretical detention time = 8 h Yn= 0.12

K s = 40 mg/L,

Y = 0.40 g VSS/g bCOD,kd = 0.08 g VSS/g VSS.d

kdn = 0.06 g VSS/g VSS.d =

Determine

• Oxygen demand in theaeration tank

• Oxygen uptake rate• Oxygen required fornitrification

• Tank biomass concentration

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PLUG-FLOW

ACTIVATED-SLUDGE PROCESS

MODELING SUSPENDED GROWTH PROCESSES

Plug-flow reactors

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Under steady-state conditions and nth-order reaction (r c = -kCn )

V r QC QC V t

C c x x x ∆+−=∆∂

∂∆+||

x x+ x∆

V ∆

= change in average concentration with

time, (mg/L.s)C = constituent concentration, mg/L

= differential volume element, L

r c = reaction rate for constituent C, mg/L.s

t

C

∂

∂

cr x

C

A

Q

t

C +

∆

∆−=

∂

∂

τ k Q

V k

Q

ALk dx

Q

Ak

C

dC L

n

C

C −=−=−=−= ∫ ∫ 00

L

Q, CQ, Co

τ k Q

V k

C

dC n

C

C −=−=∫

0

cr x

C

A

Q

t

C +

∂

∂−=

∂

∂

Non-ideal Plug-flow reactors:ith i l

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with axial

dispersion

)2/exp()1()2/exp()1(

)2/1exp(422

0 d aad aa

d a

C

C

−−−+=

C= effluent concentration, mg/LC0 = influent concentration, mg/L

a = (1+4kτd)1/2

d = dispersion factor = D/uL

D=coefficient of axial dispersion,m2/s

u=fluid velocity, m/sL= characteristic length, m

As d goes to infinity, complete-mix, if d=0 then plug-

flow.

Wehner andWilhelm equation

To check if the flow is ideal or not

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READING ASSIGNMENT:Residence time distribution (RTD) CurvesChp 4-4 (Metcalf & Eddy, 4th Ed.)

Tracer study analyses

Plug-flow reactor

Pulse dose Step input

Kinetic model of the plug-flowreactor

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reactor

Two simplifying assumptions:

- Microorganisms concentration in influent =microorganisms concentration in effluent

applies only if; SRT / Ʈ >5

then; average microorganism concentration: X

- Rate of substrate utilization through the tank;S K

S X k r

s

su+

−=

After integration, and substitution of equation for X

d

i s

k S S K S S

S S k Y

SRT −

++−

−=

)/ln()1()(

)(1

0

0

α )1(

0

α

α

+

+=

S S Si

Si= influent concentration to reactor after dilution with recycle flow

α = recycle ratio

304-notes 8 biotreat 2013

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