# Numerical Modeling of Biodegradation Analytical and Numerical Methods By Philip B. Bedient.

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Numerical Modeling of Biodegradation Analytical and Numerical Methods By Philip B. Bedient

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

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

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]

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

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

Bioplume II Equation - Monod Including the previous equation for reaction results in this advection-dispersion-reaction equation:

Multi-Species Monod Kinetics For multiple species, one must track the species together, and the rate is dependent on the concentrations of both species

Multi-Species Adding these equations to the advection- dispersion equation results in one equation for each component (including microbes) BIOPLUME III doesnt model microbes

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)

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

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

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

Principle of Superposition

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

Initial Contaminant Plume

Model Parameters

Biodegrading Plume Original Plume ConcentrationPlume after two years Extraction Only - No Added O 2

Plume Concentrations Plume after two years O 2 Injected at 20 mg/L O 2 Injected at 40 mg/L

Biodegradation Models Bioscreen -GSI Biochlor - GSI BIOPLUME II and III - Bedient & Rifai RT3D - Clement MT3D MS SEAM 3D

Dehalogenation of PCE PCE (perchloroethylene or tetrachloroethylene) TCE (trichloroethylene) DCE (cis-, trans-, and 1,1-dichloroethylene VC (vinyl chloride)

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

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

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

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