Numerical Modeling of Biodegradation

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Numerical Modeling of Biodegradation

• Analytical and Numerical Methods
• By
• Philip 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 2 Exponential growth phase,
• microbes have acclimated to the conditions
• Region 3 Stationary phase,
• limiting substrate or electron acceptor limits
  the growth rate
• Region 4 Decay phase,
• substrate supply has been exhausted

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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
• C is the substrate concentration mg/L
• Mt is the biomass concentration mg/ L
• µmax is the maximum substrate utilization rate
  sec-1
• KC is the half-saturation coefficient mg/L

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Monod Kinetics

• First-order region, C ltlt KC the equation can be
  approximated by exponential decay (C C0ekt)
• Center region, Monod kinetics must be used
• Zero-order region, C gtgt KC, the equation can be
  approximated by linear decay (C C0 kt)

Zero-order
region

dC
dt
First-
order
region
C
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Modeling Monod Kinetics

• Reduction of concentration expressed as
• Mt total microbial concentration
• µmax maximum contaminant utilization rate per
  mass of microorganisms
• KC contaminant half-saturation constant
• ?t model time step size
• C concentration of contaminant

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Bioplume II Equation - Monod

• Including the previous equation for reaction
  results in this advection-dispersion-reaction
  equation

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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

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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

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Modeling First-Order Decay

• Cn1 Cn ek?t
• 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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ModelingInstantaneous Biodegradation

• Excess Hydrocarbon Hn gt On/F
• On1 0 Hn1 Hn - On/F
• Excess Oxygen Hn lt On/F
• On1 On - HnF Hn1 0
• All available substrate is biodegraded, limited
  only by the availability 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 gt NO3 gt Fe3 gt SO42 gt 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
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Oxygen Utilization of Substrates

• Benzene C6H6 7.5O2 gt 6CO2 3H2O
• Stoichiometric ratio (F) of oxygen to benzene
• Each mg/L of benzene consumes 3.07 mg/L of O2

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Biodegradation in BIOPLUME II
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Initial Contaminant Plume
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Model Parameters
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Biodegrading Plume
Original Plume Concentration Plume after two
years Extraction Only - No Added O2
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Plume Concentrations
Plume after two years Plume after two years O2
Injected at 20 mg/L O2 Injected at 40 mg/L
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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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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)

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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 gt 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
  in mechanism

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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 a
  second 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 k1gt TCE
• TCE k2gt DCE
• DCE k3gt VC
• VC k4gt Ethene