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Modeling Biodegradation

Three main methods for modeling biodegradation

Monod kinetics

First-order decay

Instantaneous reaction

Methods can be used where appropriate for aerobic,

anaerobic, hydrocarbon, or chlorinated

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Microbial Growth Region 1:Lag phase

microbes are adjusting to thenew substrate (food source)

Region 2Exponential growth phase,

microbes have acclimated to

the conditions

Region 3Stationary phase,

limiting substrate or electron

acceptor limits the growth rate

Region 4

Decay phase, substrate supply has been

exhausted

Time

log [X]32 41

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Monod Kinetics

The rate of biodegradation or biotransformation is

generally the focus of environmental studies

Microbial growth and substrate consumption rates

have often been described using Monod kinetics

Cis the substrate concentration [mg/L]

Mtis the biomass concentration [mg/ L]

maxis the maximum substrate utilization rate [sec-1]

KCis the half-saturation coefficient [mg/L]

dC

dt=

max

CMt

KC +C

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Monod Kinetics

First-order region,

C> KC, the equation

can be approximated by

linear decay

(C= C0 kt)

dCdt

C

First-orderregion

Zero-orderregion

dC

dt=

kCMt

KC

dC

dt = maxMt

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Modeling Monod Kinetics

Reduction of concentration expressed as:

Mt = total microbial concentration

max = maximum contaminant utilization rate per mass

of microorganisms

KC = contaminant half-saturation constant

t = model time step size

C = concentration of contaminant

C= MtmaxC

Kc + C

t

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Bioplume II Equation - Monod

Including the previous equation for reaction

results in this advection-dispersion-reaction

equation:

C

t

=Dx2C

x2 v

C

x

MtmaxC

Kc +

C

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Multi-Species Monod Kinetics

For multiple species, one must track the species

together, and the rate is dependent on the

concentrations of both species

C=Mtmax

C

Kc+C

O

Ko+O

t

O =MtmaxFC

Kc +C

O

Ko +O

t

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Multi-Species

Adding these equations to the advection-dispersion

equation results in one equation for each component

(including microbes)

BIOPLUME III doesnt model microbes

Ct

=1

Rc

(DC vC) Mt

max

Rc

C

Kc+ C

O

Ko+ O

O

t= (DO vO) MtmaxF

C

Kc + C

O

Ko + O

Mst

=1

Rm

(DMs - vMs ) + MsmaxYC

Kc + C

O

Ko + O

+

kcY(OC)

Rm

bMs

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Modeling First-Order Decay

Cn+1= Cn ekt

Generally assumes nothing about limiting substrates

or electron acceptors

Degradation rate is proportional to the concentration

Generally used as a fitting parameter, encompassing

a number of uncertain parameters

BIOPLUME III can limit first-order decay to the

available electron acceptors (this option has bugs)

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Modeling

Instantaneous Biodegradation Excess Hydrocarbon: Hn> On/F

On+1= 0 Hn+1=Hn- On/F

Excess Oxygen: Hn< On/F

On+1= On-HnF Hn+1= 0

All available substrate is biodegraded, limited only by theavailability of terminal electron acceptors

First used in BIOPLUME II - 1987

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Sequential Electron Acceptor

Models Newer models, such as BIOPLUME III, RT3D,

and SEAM3D allow a sequential process - 1998

After O2is depleted, begin using NO3

Continue down the list in this order

O2 > NO3 > Fe3+ > SO42> CO2

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Superposition of Components

Electron donor and acceptor are each modeled

separately (advection/dispersion/sorption)

The reaction step is performed on the resulting

plumes

Each cell is treated independently

Technique is called Operator Splitting

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Principle of Superposition

Background D.O.

Initial HydrocarbonConcentration

Reduced OxygenConcentration

OxygenDepletion

Reduced HydrocarbonConcentration

+ =

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Oxygen Utilization of Substrates

Benzene: C6H6+ 7.5O2> 6CO2+ 3H2O

Stoichiometric ratio (F) of oxygen to benzene

Each mg/L of benzene consumes 3.07 mg/L of O2

F= 7.5 molO21 molC6H6

32 mgO21 molO2

1 molC6H6

(12 6 +16) mgC6H6

F= 3.07 mgO2 mgC6H6

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Biodegradation in BIOPLUME II

A A'

B B'

Zone of TreatmentZone of ReducedHydrocarbon Concentrations

Background D.O.

Zone of ReducedOxygen Concentration

Zone of OxygenDepletion

A A'

H

Without Oxygen

B B'

D.O.

Background D.O.

DepletedOxygen

With

Oxygen

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Initial Contaminant Plume

x x

o o

Concentration

x

8.89e + 2 oProduction Well7.78e + 26.67e + 22.22e + 21.11e + 2

1.00e + 3

0.00e + 0o

x

Values represent upper limitsfor corresponding color.

Injection Well

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Model Parameters

Grid Size 20 x 20 cells

Cell Size 50 ft x 50 ft

Transmissivity 0.002 ft

2

/secThickness 10 ft

Hydraulic Gradient .001 ft/ft

Longitudinal Dispersivity 10 ft

Transverse Dispersivity 3 ft

Effective Porosity 0.3

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Biodegrading Plume

0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 1 0 0 0 00 0 0 1 11 1 0 0 00 0 0 6 123 6 0 0 00 0 1 38 1000 38 1 0 0

0 0 4 71 831 71 4 0 00 0 7 97 710 97 7 0 00 1 9 104 600 104 9 1 00 0 9 90 449 90 9 0 00 0 5 54 285 54 5 0 00 0 2 19 109 19 2 0 00 0 0 4 24 4 0 0 00 0 0 1 4 1 0 0 00 0 0 0 1 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

0 0 1 1 1 1 1 0 00 0 2 3 4 3 2 0 00 0 3 7 12 8 3 1 00 0 4 11 20 13 5 0 00 0 2 8 11 8 2 0 00 0 0 2 4 2 0 0 00 0 0 0 1 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

Original Plume Concentration Plume after two years

Extraction Only - No Added O2

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0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 00 0 0 2 6 2 0 0 00 0 3 7 15 8 3 0 00 0 2 6 10 7 1 0 00 0 0 1 3 1 0 0 00 0 0 0 1 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

Plume Concentrations

Plume after two years Plume after two years

O2Injected at 20 mg/L O

2Injected at 40 mg/L

0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 1 2 9 3 1 0 00 0 1 5 8 5 1 0 00 0 0 1 3 1 0 0 00 0 0 0 1 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

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Biodegradation Models

Bioscreen -GSI

Biochlor - GSI

BIOPLUME II and III - Bedient & Rifai RT3D - Clement

MT3D MS

SEAM 3D

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Name Dimension Description Author X 1 aerobic, microcolony, Monod Molz, et al. (1986)

BIOPLUME 1 aerobic, Monod Borden, et al. (1986)

X 1 analytical first-order Domenico (1987)

BIOID 1 aerobic and anaerobic, Monod Srinivasan and Mercer (1988)

X 1 cometabolic, Monod Semprini and McCarty (1991)

X 1aerobic, anaerobic, nutrient

limitations, microcolony, MonodWiddowson, et al. (1988)

X 1aerobic, cometabolic, multiple

substrates, fermentative, MonodCelia, et al. (1989)

BIOSCREEN 1 analytical first-order, instantaneous Newell, et al. (1996)

BIOCHLOR 1 analytical Aziz, et al. (1999)

BIOPLUME II 2 aerobic, instantaneous Rifai, et al. (1988)

X 2 Monod MacQuarrie, et al. (1990)

X 2 denitrification Kinzelbach, et al. (1991)

X 2 Monod, biofilm Odencrantz, et al. (1990)

BIOPLUME III 2 aerobic and anaerobic Rifai, et al. (1997)

RT3D 3 aerobic and anaerobic Clement (1998)

Biodegradation Models

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Dehalogenation of PCE

PCE (perchloroethylene or

tetrachloroethylene)

TCE (trichloroethylene)

DCE (cis-, trans-,

and

1,1-dichloroethylene

VC (vinyl chloride)

C C

Cl Cl

Cl Cl

C C

Cl H

H Cl

C C

Cl H

Cl Cl

C C

H H

Cl H

C C

H H

Cl ClC C

Cl H

Cl H

PCE

TCE

DCE's

VC

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Dehalogenation

Dehalogenation refers to the process of stripping

halogens (generally Chlorine) from an organic

molecule

Dehalogenation is generally an anaerobic process,and is often referred to as reductive dechlorination

RCl + 2e+ H+> RH + Cl

Can occur via dehalorespiration or cometabolism Some rare cases show cometabolic dechlorination

in an aerobic environment

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Chlorinated Hydrocarbons

Multiple pathways

Electron donor similar to hydrocarbons

Electron acceptor depends on human-added electron

donor Cometabolic

Mechanisms hard to define

First-order decay often used due to uncertainties inmechanism

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Modeling Dechlorination

Few models specifically designed to simulate

dechlorination

Some general models can accommodate

dechlorination

Dechlorination is generally modeled as a first-

order biodegradation process

Often, the first dechlorination step results in asecond compound that must also be dechlorinated

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Sequential Dechlorination

Models the series of dechlorination steps between

a parent compound and a non-hazardous product

Each compound will have a unique decay constant

For example, the reductive dechlorination of PCE

requires at least four constants

PCE k 1> TCE

TCE k 2> DCE DCE k 3> VC

VC k4> Ethene