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Modelling of the removal of livestock- related airborne contaminants via biofiltration Dennis McNevin and John Barford Department of Chemical Engineering University of Sydney Australia

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Modelling of the removal of livestock-related airborne

contaminants via biofiltration

Dennis McNevin and John Barford

Department of Chemical Engineering

University of Sydney

Australia

Biofiltration

ORGANICMATERIAL

ODOROUS AIR

WATER,NUTRIENTSCLEAN AIR

HUMIDIFIER

Mathematical model

aqueous phase

gaseous phase

z

z+dz

solid support

biofilm

Solid filter medium

bulk density of the dry solid (g per m3 dry solid)voidage of the dry solid (m3 space per m3 dry solid)water content of the solid (m3 water per g dry solid)interfacial area available for heat and mass transfer (m2 per g dry solid)partition coefficient (g.m-3 compound j in the gas phase at equilibrium with 1 g.m-3 compound j adsorbed onto the solid)

s

dry

W

a

j

Equations

• Differential balances or transport equations mass, heat

• Equilibrium expressions

physical, chemical

• Rate expressions

mass & heat transfer, microbial activity

• Air phase behaviour

pressure, density

Bioconversions aerobic

Organic carbon oxidation

VOC CO2 + H2O chemoheterotrophs

Nitrification

NH4+ NO2

- Nitrosomonas spp.

NO2- NO3

- Nitrobacter spp.

Sulfide oxidation

S2- SO42- Thiobacillus spp.

Aqueous phase mass balances

Aqueous species divided into four groups:

dissociating non-dissociating

volatile NH3, H2S, CO2 VOC, O2, N2

non-volatile

HNO2, HNO3,H2SO4

Ca2+, Cl-

Volatile, non-dissociating species

j = VOC, O2, N2

• Diffusion

• Bulk flow

• microbial production/consumption

• mass transfer from air/biofilm interface

C

tD

C

z

u C

zr

k a

WC Cl j

l jl j l l j

jl j

l j l j,

,, , ,

, , 2

2

Non-volatile, non-dissociating species

j = Ca2+, Cl-

• Diffusion

• Bulk flow

C

tD

C

z

u C

zl j

l jl j l l j,

,, ,

2

2

Dissociating species

C Cl j l k

k, ,

j k

NH3 NH4+, NH3

H2S H2S, HS-, S2-

CO2 H2CO3, HCO3-, CO3

2-

HNO2 HNO2, NO2-

HNO3 HNO3, NO3-

H2SO4 H2SO4, HSO4-, SO4

2-

Volatile, dissociating species

j = NH3, H2S, CO2

• Diffusion

• Bulk flow

• microbial production/consumption

• mass transfer from air/biofilm interface

,

,, , ,

, ,

C

tD

C

z

u C

zr

k a

WC Cl j

l jl j l l j

jl j

l j l j 2

2

Non-volatile, dissociating species

j = HNO2, HNO3, H2SO4

• Diffusion

• Bulk flow

,

,, ,C

tD

C

z

u C

zrl j

l jl j l l j

j 2

2

Interfacial equilibrium

• Partition coefficient for mass

• Antoine equation for temperature

jg j

l j

C

C

,

,

log P ab

c TH O2

Chemical equilibriumDissociation

• Water

• Acids

• Bases

H O H OH2 K H OHw

HA H A

KH A

HAA

B H O BH OH 2

KBH OH

BB

Chemical equilibriumElectroneutrality

n Cj l jj

n j, 0

j H+ NH4+ Ca2+ OH- Cl-

nj +1 +1 +2 -1 -1

j HCO3- CO3

2- HS- S2- NO2-

nj -1 -2 -1 -2 -1

j NO3- HSO4

- SO42-

nj -1 -1 -2

Mass transfer

• Air phase

Wakao & Kaguei (1982)

• Aqueous phase (diffusion controlled)

Sh Sc 2 11 1 3 0 6. Re/ .

kD

l jl j

biofilm,

,

kD Sh

g jg j

particle,

,

Heat transfer

• Air phase

Wakao & Kaguei (1982)

• Aqueous phase (diffusion controlled)

Nu 2 11 1 3 0 6. Pr Re/ .

h ll

biofilm

hNu

gg

particle

Gross rate of biomass growth

Monod (1942)

dxdt

x xC

K Ck

grossk k k k

l j

k j l jj

max ,

, ,

Cl,j

0.5max

max

K

Net rate of biomass growth

Endogenous or maintenance metabolism

gives a “true” growth rate:

k = VOC oxidisers, nitrifiers, sulfide

oxidisers

dxdt

dxdt

xk

net

k

grosskend

k

Microbial substrates

For each micro-organism, three substrate

requirements are considered:

• anabolism– carbon source

• catabolism (energy source)– electron donor– electron acceptor

Case study Nitrification

• Anabolism (balanced for carbon)

• Catabolism

5 2 5 7 2CO biomass C H NO ...

NH O NO H H O4 2 2 2

32

2

Bioconversion rates

Bioconversion rates are linked to gross

biomass growth rates:

Yj/x = moles compound j per g biomass

r Ydxdtj

conj xcon k

grossk

/

r Ydxdtj

prodj xprod k

grossk

/

pH and growth rate

k

kopt H H

1 2

1

/

/ /

1

0-log -logpHopt

opt

pH

Temperature and growth rate

k

kopt

kopt

ER T T

exp1 1

1/Topt

1/T0

lnopt

Numerical solution

• P.D.E.’s converted to O.D.E.’s by discretising the spatial dimension with finite (backward) differences

• Biofilter height divided into n equal elements. In the ith element:yz

y yZ

i i

1

2

2

1 1

2

2yz

y y y

Z

i i i

Numerical solution (cont.)

• System of O.D.E.’s and algebraic equations solved by SPEEDUP (Aspen Technology, 1994)

• Modified Gear’s method integrator selected

Comparison with experimental data

Hodge & Devinny (1995)

• Compost biofilter for removal of ethanol

• Solid medium characteristics: = 0.45

W = 60 %

= 247 000 g dry compost per m3

= 0.001 m (a = 0.004 m2g-1)

= 0.0003

s

Comparison with experimental data (cont.)

• Inlet air– ug = 23.7 m.hr-1

– CEtOH = 11 000 ppm

• Solid medium buffered to pH 7.5 with 0.0251 mol.L-1 total carbonate

Air phase ethanol concentration

0

2000

4000

6000

8000

10000

12000

0 100 200 300 400 500

TIME (hours)

ET

HA

NO

L C

ON

CE

NT

RA

TIO

N (

pp

m)

Inlet ethanol concentration

Ethanol concentration at 20 % oflength

Ethanol concentration at 40 % oflength

Ethanol concentration at 60 % oflength

Ethanol concentration at 80 % oflength

Outlet ethanol concentration

Simulation

Carbon dioxide concentration profile

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100

HEIGHT (cm)

NO

RM

AL

ISE

D C

O2

CO

NC

EN

TR

AT

ION

Model

Hodge & Devinny

Aqueous phase pH

6

6.2

6.4

6.6

6.8

7

7.2

7.4

7.6

0 100 200 300 400 500 600

TIME (hours)

pH

pH at entrance to column

pH at 20 % of column height

pH at 40 % of column height

pH at 60 % of column height

pH at 80 % of column height

pH at exit from column

Tuning the model

Requires knowledge of:• microbiological constants

– kinetic

– stoichiometric

• thermodynamic equilibrium constants– physical

– chemical

• rheological properties

Design variables

• Choice of solid medium

• Column dimensions– diameter– height

• boundary conditions

• initial conditions

s dry jW a, , , ,

Reaction vs diffusion limitation

• Reaction limitation:– low Thiele number, – high solubility, C*– low half-saturation constant, K

• Diffusion limitation– high Thiele number,– low solubility, C*– high half-saturation constant, K

Thiele numberIndication of relative rates of biological

degradation and diffusion through the

biofilm

= aqueous film characteristic dimension (m)

x = biomass concentration (g.m-3)

= biomass growth rate (hr-1)

Y = biomass yield from substrate (g.g-1)

D = diffusion coefficient (m2hr-1)

2xYD

In conclusion ...

• Numerical model successfully predicts VOC removal via biofiltration

• Model reveals information useful for optimising microbial activity

• Model may be tuned for a particular application