10_biodegradation_models

8/7/2019 10_BIodegradation_models

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Numerical Modeling of

Biodegradation

Analytical and Numerical Methods

ByPhilip B. Bedient


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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

the new substrate (food

source)

Region 2Exponential growth phase,

microbes have acclimated

to the conditions

Region 3Stationary phase,

limiting substrate or

electron acceptor limits thegrowth rate

Region 4Decay 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]

max is the maximum substrate utilization rate [sec-1]

KCis the half-saturation coefficient [mg/L]

dC

dt!Qmax

CMt

KC

C


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Monod Kinetics

First-order region,

C> KC, the equationcan be approximated by

linear decay

(C= C0 kt)

dC

dt

C

First-orderregion

Zero-orderregion

dC

dt!kCM

t

KC

dCdt

! QmaxMt


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Modeling Monod Kinetics

Reduction of concentration expressed as:

Mt = total microbial concentration

max = maximum contaminant utilization rate per massof microorganisms

KC = contaminant half-saturation constant

t = model time step size

C = concentration of contaminant

(C! MtQ

max

C

Kc C

(t


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Bioplume II Equation - Monod

Including the previous equation for reaction

results in this advection-dispersion-reaction

equation:

xC

xt! Dx

x2C

xx

2 v

xC

xx tQmax

C

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! Mt max

C

Kc C

O

Ko O

(t

(O ! Mt maxFC

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

xC

xt=

1

Rc

(DC C) Mt

Qmax

Rc

C

Kc C

O

Ko O

xO

xt

= (DO O) MtQmax

FC

Kc C

O

Ko O

xMs

xt=

1

Rm

(DMs - vMs ) MsQmaxYC

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 O2 is depleted, begin using NO3

Continue down the list in this order

O2

> NO3

> Fe3+ > SO4

2> 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 molC 6H6

(12 y6 1y6) mgC6H6

F! 3.07 mgO2 mgC6H6


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Biodegradation in BIOPLUME II

A A'

B B'

Zoneof reatmentZoneofReducedHydrocar on Concentrations

BackgroundD.O.

ZoneofReducedOxygen Concentration

ZoneofOxygenDepletion

A A'

H

WithoutOxygen

B B'

D.O.

BackgroundD.O.

DepletedOxygen

WithOxygen


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Initial Contaminant Plume

x x

o o

Con ce n tra tion

x

8.8 9e + 2 o Production ell7 .78e + 26.67e + 22.22e + 21.11e + 2

1.00e + 3

0.00e + 0o

x

Values representupper li itsfor corresponding color.

Injection ell


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Model Parameters

Grid Size 20 x 20 cells

Cell Size 50 ft x 50 ft

Transmissivity 0.002 ft2

/sec

Thickness 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 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0

0 0 0 1 11 1 0 0 0

0 0 0 6 123 6 0 0 0

0 0 1 38 1000 38 1 0 0

0 0 4 71 831 71 4 0 0

0 0 7 97 710 97 7 0 0

0 1 9 104 600 104 9 1 0

0 0 9 90 449 90 9 0 0

0 0 5 54 285 54 5 0 0

0 0 2 19 109 19 2 0 0

0 0 0 4 24 4 0 0 0

0 0 0 1 4 1 0 0 0

0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 1 1 1 1 1 0 0

0 0 2 3 4 3 2 0 0

0 0 3 7 12 8 3 1 0

0 0 4 11 20 13 5 0 0

0 0 2 8 11 8 2 0 0

0 0 0 2 4 2 0 0 0

0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 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 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 2 6 2 0 0 0 0 0 3 7 15 8 3 0 0

0 0 2 6 10 7 1 0 0 0 0 0 1 3 1 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Plume Concentrations

Plume after two years Plume after two years

O2 Injected at 20 mg/L O2 Injected at 40 mg/L

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 1 2 9 3 1 0 0

0 0 1 5 8 5 1 0 0 0 0 0 1 3 1 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 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 D im ension D escription Author

X 1 aer ob ic, microcolon

, M onod M olz, e tal. ( 19 86 )

BI O

L UM E 1 aer ob ic, Mo nod Borden, et al. (1 98 6)

X 1 anal

tical first-order D omen ico ( 19 8 7)

BI O ID 1 aer ob ic and ana erobic, M onod Srinivasan and M ercer (1 98 8)

X 1 com e tabolic, Monod Se m prini a nd McCarty(1991)

X 1aer obic, an ae robic, n utrient

limitations, microcolony, MonodWiddowson, et al. ( 19 88)

X 1aerobic, cometa bolic, m u ltiple

sub strates, fermenta tive, MonodC elia, et a l. (1 98 9)

BI OSCR EEN 1 anal ytical first-order, ins tantaneou s Newell, e tal. (1996)

BI OCH LO R 1 anal ytical Aziz, et a l. (1 99 9)

BI O

L UM E II 2 aer ob ic, instantaneo us R ifa i, e ta l. (19 88 )

X 2 M onod MacQuarrie, et a l. (1 99 0)

X 2 de nitrification Kinze lba c h , et al. (1 99 1)

X 2 M onod, biofilm O dencrantz , et al. ( 19 90)

BI O L UM E III 2 aer ob ic and an aerobic R ifa i, e ta l. (19 97 )

R T3 D 3 aer ob ic and an aerobic C le me n t(19 98 )

Biodegradation Models


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Dehalogenation of PCE

PCE (perchloroethylene

or tetrachloroethylene)

TCE (trichloroethylene)

DCE (cis-, trans-,

and1,1-dichloroethylene

VC (vinyl chloride)

C C

Cl Cl

Cl Cl

C C

Cl

Cl

C C

Cl

Cl Cl

C C

Cl

C CCl Cl

C C

Cl

Cl

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

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