CEE 370 Environmental Engineering Principles Lecture #32 - - PowerPoint PPT Presentation

David Reckhow CEE 370 L#32 1

CEE 370 Environmental Engineering Principles

Lecture #32 Wastewater Treatment III: Process Modeling & Residuals

Reading M&Z: Chapter 9

Reading: Davis & Cornwall, Chapt 6-1 to 6-8

Reading: Davis & Masten, Chapter 11-11 to 11-12 Updated: 26 November 2019

Print version

David Reckhow

CEE 370 L#32

2

Microbial Biomass in a CMFR

dm dt = (C Q ) (C Q ) r V

A i=1 n Ai i in j=1 n Aj j

• ut

A

∑ ∑

− −

CA V

CA0 Q0 CA Q0

General Reactor mass balance

But with CMFRs we have a single outlet concentration (CA) and usually a single inlet flow as well

David Reckhow

CEE 370 L#32

3

Batch Microbial Growth

CA V

1 V dM dt = - r

A A

A i=1 n Ai i in j=1 n Aj j

• ut

A

dM dt = (C Q ) (C Q )

• r V

∑ ∑

−

Because there isn’t any flow in a batch reactor:

A A

dC dt = - r

And: Batch reactors are usually filled, allowed to react, then emptied for the next batch

General Reactor mass balance

X kX

For 1st order biomass growth

David Reckhow

CEE 370 L#32

4

Batch Microbial Growth

 Observed behavior

Time Lag Stationary Death Exponential Growth Covered in lecture #17

David Reckhow

CEE 370 L#32

5

Exponential Growth model

where, X = concentration of microorganisms at time t t = time µ = proportionality constant or specific growth rate, [time─1] dX/dt = microbial growth rate, [mass per volume-time] N r t dN/dt

D&M Text

X dt dX

gr

µ ≡      

Covered in lecture #17

David Reckhow

CEE 370 L#32

6

• Exp. Growth (cont.)

ln X X = t

• 

     µ

X = X e

• t

µ

• r

X dt dX

gr

µ ≡       dt X dX

gr

µ ≡      

Covered in lecture #17

David Reckhow

CEE 370 L#32

7

Substrate-limited Growth

 Also known as resource-limited growth

 THE MONOD MODEL

where, µmax = maximum specific growth rate, [day-1] S = concentration of limiting substrate, [mg/L] Ks = Monod or half-velocity constant, or half saturation coefficient, [mg/L]

S K SX X dt dX

S gr

+ = ≡      

max

µ µ

S K S

S +

=

max

µ µ

and

David Reckhow

CEE 370 L#32

8

Monod Kinetics

0.5*µm KS

Covered in lecture #17

Substrate Utilization & Yield

David Reckhow

CEE 370 L#32

9 H&H, Fig 11-38, pp.406

 Related to growth by Y, the yield coefficient

 Mass of cells produced

per mass of substrate utilized

 Just pertains to cell growth

dt dS dt dX S X Y = ∆ ∆ ≡

dt dS Y dt dX

gr

=      

Microbial Growth

 Monod kinetics in a chemostat (batch reactor)

 Where

 dS/dt = rsu = actual substrate utilization rate  k = maximum substrate utilization rate = μmax/Y  S = concentration of substrate (Se in H&H)  KS = half-saturation constant  Y = cell yield = dX/dS

David Reckhow

CEE 370 L#32

10

e S e su

S K XS k r + = S K SX X dt dX

S gr

+ = ≡      

max

µ µ S K XS Y dt dS

S +

=

max

µ

& Divide by Y Substitute for dS

dt dS Y dt dX

gr

=      

Death

 Bacterial cells also die at a characteristic

first order rate with a rate constant, k

 This occurs at all times, and is

independent of the substrate concentration

David Reckhow

CEE 370 L#32

11

X k dt dX

d d

− =      

Overall model: chemostat

 Combining growth and death, we have:  And in terms of substrate utilization

David Reckhow

CEE 370 L#32

12

X k S K SX dt dX dt dX dt dX

d S d gr net

− + =       +       =      

max

µ X k dt dS Y dt dX

d net

−       =       dt dS dt dX Y

gr

÷       ≡

See: M&Z equ 9.3

Activated Sludge Flow Schematic

David Reckhow

CEE 370 L#32

13

Aeration

Basin

V,X Settling

Tank Xo So X S Xe S Qr Xr Q Qw Xr S

 Conventional

Return activated sludge Waste activated sludge

Influent Effluent

Q+ Qr

Efficiency & HRT

 Efficiency of BOD removal  Hydraulic Retention Time, HRT (Aeration Time)

 Same as retention time in DWT (tR)  Actual HRT is a bit different

 Isn’t used as much in design

David Reckhow

CEE 370 L#32

14

( )

• S

S S E % 100 − =

Q V = θ

R act

Q Q V + = θ

SRT – solids retention time & R

 SRT: Primary operation and design parameter

 How long does biomass stay in system  Typically equals 5-15 days

 Recycle Ratio

 Values of 0.25-1.0 are typical

David Reckhow

CEE 370 L#32

15

( )

r w r w e w c

X Q XV X Q X Q Q XV ≈ + − = θ

Q Q R

r

=

See: M&Z equ 9.10

F:M Ratio and volumetric loading

 Food-to-Microorganism Ratio (F/M)

 Typical values are 0.2-0.6 in complete mixed AS

 BOD volumetric Loading

 Typically 50-120 lb BOD/day/1000ft3 tank volume

David Reckhow

CEE 370 L#32

16

X V BOD Q M F ∗ ∗ =

XV QS M F

• =

V QS Loading

• =

M&Z equ 9.16

• Act. Sludge: Biomass Model

 Steady State mass balance on biomass

 Incorporating the chemostat model gets:  And simplifying

 Finally, we recognize that the amount of solids entering with the WW (i.e.,

Xo) and leaving in the treated effluent (i.e., Xe) is quite small and can be neglected

David Reckhow

CEE 370 L#32

17

batch r w e e

• dt

dX V X Q X Q QX dt dX V       + − − = = 0

X k S K SX dt dX dt dX dt dX

d S d gr net

− + =       +       =      

max

µ

From chemostat model

        − + + − − = = X k S K SX V X Q X Q QX dt dX V

d S r w e e

• max

µ         − + = + + − X k S K SX V X Q X Q QX

d S r w e e

• max

µ

Biomass Model II

 So it becomes  And rearranging

David Reckhow

CEE 370 L#32

18

        − + = X k S K SX V X Q

d S r w max

µ

d S r w

k S K S VX X Q − + =

max

µ

( )

r w r w e w c

X Q XV X Q X Q Q XV ≈ + − = θ

≈

c

θ 1

Earlier equation for SRT

• Act. Sludge: Substrate Model

 Steady state mass balance on substrate

 Substituting and noting that Qe=Q-Qw  And further simplifying

David Reckhow

CEE 370 L#32

19

batch w e

• dt

dS V S Q S Q QS dt dS V       + − − = = 0

From chemostat model

S K XS Y dt dS

S +

=

max

µ         + − + − = S K XS Y V S Q S Q QS QS

S w w

• max

µ

( )

        + = − S K XS Y V S S Q

S

• max

µ

Merging the biomass & substrate models



If we divide the previous equation by V and X



Multiply both sides by Y



Now insert the LH term into the earlier equation based on biomass

David Reckhow

CEE 370 L#32

20

( )

        + = − S K XS Y V S S Q

S

• max

µ

( )

S K S Y VX S S Q

S

• +

= −

max

µ

d S r w c

k S K S VX X Q − + = =

max

1 µ θ

( )

S K S VX S S YQ

S

• +

= −

max

µ

( )

d

• r

w c

k VX S S YQ VX X Q − − = = θ 1

M&Z equ 9.8 M&Z equ 9.9

Combined model II

 Now recognize that Q/V is the reciprocal of

the HRT

David Reckhow

CEE 370 L#32

21

( )

d

• c

k X S S Y − − = θ θ 1 1

Question

 All else being equal, as SRT goes up:

1.

Settleability goes down

2.

F/M goes down

3.

Waste sludge return ratio must go down

4.

Endogenous respiration becomes less important

5.

Sludge yield increases

David Reckhow

CEE 370 L#32

22

Aeration: Loadings

 Food-to-Microorganism

Ratio (F/M)

 Sludge Age or mean cell

residence time (ɵc)



Where



Q=WW flow



V=volume of aeration tank



X=MLVSS=mixed liquor volatile suspended solids (biomass concentration)



Xe=VSSe = suspended solids in wastewater effluent



XW=VSSw = suspended solids in waste sludge



Qw = flow of waste sludge



SS is sometimes used instead

• f VSS

David Reckhow

CEE 370 L#32

23

X V BOD Q M F ∗ ∗ =

( ) ( )

W W W W e e c

Q X VX Q X Q X VX ≈ + = θ

Operating Criteria

 Loading, biomass, retention time, etc

David Reckhow

CEE 370 L#32

24 H&H, Table11-4, pp.395

David Reckhow

CEE 370 L#32

25

Activated Sludge

 Mixed liquor  Return Activated sludge

• 1. Surface aerators
• 2. Bubble diffusers

David Reckhow CEE 370 L#32 26

CEE 370 Environmental Engineering Principles

Lecture #32b Wastewater Treatment IIIb: Process Modeling & Residuals

Reading: M&Z Chapter 9.11

Other Reading: Davis & Cornwall, Chapt 6-1 to 6-8 and Davis & Masten, Chapter 11-11 to 11-12 Updated: 26 November 2019

David Reckhow

CEE 370 L#32

27

Anaerobic Digester Problem

Anaerobic digesters are commonly used in wastewater

• treatment. The biological process produces both

carbon dioxide and methane gases. A laboratory worker plans to make a "synthetic" digester gas. There is currently 2 L of methane gas at 1.5 atm and 1 L of carbon dioxide gas at 1 atm in the lab. If these two samples are mixed in a 4 L tank, what will be the partial pressures of the individual gases? The total pressure?

Example 4.4 from Ray

David Reckhow

CEE 370 L#32

28 t CH CO

P = P + P = 1 atm

4 2

2

P = 1 atm 1 L 4 L = 0.25 atm      

2

P = 1.5 atm 2 L 4 L = 0.75 atm      

Solution to Anaerobic Digester Problem

First, we must find the partial pressures of the individual gases using the ideal gas law:

1 1 2 2

P V = nRT = P V

2 1 1 2

P = P V V      

For methane gas For carbon dioxide gas: And the total is:

• r

David Reckhow

CEE 370 L#32

29

Solids Balance

SRT XV Q X

w u

= = mass of organisms in tank mass of organisms removed per day

HRT V Q =

Sludge Secondary Clarifier Return Activated Sludge (RAS) Waste Activated Sludge (WAS) Aeration Tank

Qw Xu QR Q0 Q0-Qw Xe

V, X

X0

SRT=solids retention time

David Reckhow

CEE 370 L#32

30

Solids Mass Balance

 Consider aeration tank and clarifier together

 Biomass in + biomass produced due to growth = biomass out  Now using the combined growth equation without limitation to

carrying capacity:

 Combining and assuming X0 and Xe to be negligible:

( )

w w e w

X Q X Q Q dt dX V X Q + − = +

X k S K S dt dX

d s

      −         + =

max

µ

d w w s

k VX X Q S K S + = +

max

µ

We will cover this in CEE 471

David Reckhow

CEE 370 L#32

31

Substrate Mass Balance

 Consider aeration tank and clarifier together

 Substrate in + substrate consumed by biomass = substrate out  Now using the combined substrate utilization equation without

limitation to carrying capacity:

 Combining and rearranging:

( )

S Q S Q Q dt dS V S Q

w w

+ − = +

( )

S S VX Y Q S K S

s

− = +

max

µ

Note that effluent and waste sludge substrate concentrations are considered the same

X k S K S Y dt dS

d s

      −         + − =

max

1 µ

We cover this in detail in CEE 471

David Reckhow

CEE 370 L#32

32

Combined Mass Balances

 In summary the solids and substrate mass

balance equations are:

 These can be easily combined (left hand

terms are the same):

d w w s

k VX X Q S K S + = +

max

µ

( )

S S VX Y Q S K S

s

− = +

max

µ

( )

d w w

k S S VX Y Q VX X Q − − =

c

Θ 1

The mean cell residence time, or sludge age We cover this in CEE 471

David Reckhow

CEE 370 L#32

33

Sludge Treatment

 Depends on type of

sludge

 Typical process train

 Thickening or

dewatering

 Conditioning  Stabilization (usually

for wastewater)

 Disposal

 Nonmechanical

methods

 Lagoons  Sand-drying beds  Freeze treatment

 Mechanical methods

 Centrifugation  Vacuum filtration  Belt filter press  Plate filters

See also Lecture #30

David Reckhow

CEE 370 L#32

34

 Centrifuge

From Lecture #30

David Reckhow

CEE 370 L#32

35

Vacuum Filter

From Lecture #30

David Reckhow

CEE 370 L#32

36

Belt Filter Press

From Lecture #30

David Reckhow

CEE 370 L#32

37

 To next lecture