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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] M t is the biomass concentration [mg/ L] µ max is the maximum substrate utilization rate [sec -1 ] K C is the half-saturation coefficient [mg/L]

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Monod Kinetics First-order region, C << K C the equation can be approximated by exponential decay (C = C 0 e –kt ) Center region, Monod kinetics must be used Zero-order region, C >> K C, the equation can be approximated by linear decay (C = C 0 – kt) –dC dt C First- order region Zero-order region

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Modeling Monod Kinetics Reduction of concentration expressed as: M t = total microbial concentration µ max = maximum contaminant utilization rate per mass of microorganisms K C = 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 C n+1 = C n e –kt 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: H n > O n /F O n+1 = 0 H n+1 = H n - O n /F Excess Oxygen: H n < O n /F O n+1 = O n - H n F H n+1 = 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 O 2 is depleted, begin using NO 3 – Continue down the list in this order O 2 ––> NO 3 – ––> Fe 3+ ––> SO 4 2– ––> CO 2

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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: C 6 H 6 + 7.5O 2 ––> 6CO 2 + 3H 2 O Stoichiometric ratio (F) of oxygen to benzene Each mg/L of benzene consumes 3.07 mg/L of O 2

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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 ConcentrationPlume after two years Extraction Only - No Added O 2

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Plume Concentrations Plume after two years O 2 Injected at 20 mg/L O 2 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 R–Cl + 2e – + H + ––> R–H + 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–k 1 –>TCE TCE–k 2 –>DCE DCE–k 3 –>VC VC –k 4 –>Ethene

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