Numerical Modeling of Biodegradation Analytical and Numerical Methods By Philip B. Bedient.
-
Upload
amanda-leavins -
Category
Documents
-
view
230 -
download
4
Transcript of Numerical Modeling of Biodegradation Analytical and Numerical Methods By Philip B. Bedient.
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
Time
log [X]32 41
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]
−dCdt
=μmaxCMt
KC +C
Monod Kinetics• First-order region,
C << KC the equation can be approximated by exponential decay (C = C0e–kt)
• Center region, Monod kinetics must be used
• Zero-order region, C >> KC, the equation can be approximated by linear decay (C = C0 – kt)
–dCdt
C
First-orderregion
Zero-orderregion
−dCdt
=kCMt
KC
−dCdt
=μmaxMt
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
ΔC=MtμmaxC
Kc +C
⎛
⎝ ⎜
⎞
⎠ ⎟ Δt
Bioplume II Equation - Monod
• Including the previous equation for reaction results in this advection-dispersion-reaction equation:
∂C∂t
=Dx∂2C
∂x2 −v∂C∂x
−MtμmaxC
Kc +C
⎛
⎝ ⎜
⎞
⎠ ⎟
Multi-Species Monod Kinetics
• For multiple species, one must track the species together, and the rate is dependent on the concentrations of both species
ΔC=MtμmaxC
Kc +C
⎛
⎝ ⎜
⎞
⎠ ⎟
OKo +O
⎛
⎝ ⎜
⎞
⎠ ⎟ Δt
ΔO=MtμmaxF C
Kc +C
⎛
⎝ ⎜
⎞
⎠ ⎟
O
Ko +O
⎛
⎝ ⎜
⎞
⎠ ⎟ Δt
Multi-Species
• Adding these equations to the advection-dispersion equation results in one equation for each component (including microbes)
• BIOPLUME III doesn’t model microbes
∂C∂t
=1Rc
∇ ⋅ (D∇C −vC) −Mtμmax
Rc
CKc +C
⎛
⎝ ⎜
⎞
⎠ ⎟
OKo +O
⎛
⎝ ⎜
⎞
⎠ ⎟
∂O∂t
=∇ ⋅(D∇O−vO) −MtμmaxF C
Kc +C
⎛
⎝ ⎜
⎞
⎠ ⎟
OKo +O
⎛
⎝ ⎜
⎞
⎠ ⎟
∂Ms
∂t=
1
Rm∇ ⋅(D∇Ms - vMs)+MsμmaxY
C
Kc +C
⎛
⎝ ⎜
⎞
⎠ ⎟
O
Ko +O
⎛
⎝ ⎜
⎞
⎠ ⎟ +
kcY(OC)
Rm−bMs
Modeling First-Order Decay
• Cn+1 = Cn e–k∆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)
ModelingInstantaneous 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 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 O2 is depleted, begin using NO3–
• Continue down the list in this order
O2 ––> NO3– ––> Fe3+ ––> SO4
2– ––> CO2
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
Background D.O.
Initial HydrocarbonConcentration
Reduced OxygenConcentration
OxygenDepletion
Reduced HydrocarbonConcentration
+ =
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 molO2
1 molC6H6
32 mgO2
1 molO2
1 molC6H6
(12•6+1•6) mgC6H6
F=3.07 mgO2 mgC6H6
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
WithOxygen
Initial Contaminant Plume
x x
o o
Concentrationx
8.89e + 2 o Production Well7.78e + 26.67e + 22.22e + 21.11e + 2
1.00e + 3
0.00e + 0o
x
Values represent upper limitsfor corresponding color.
Injection Well
Model ParametersGrid 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
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 00 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 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 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 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 00 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
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 00 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 00 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
O2 Injected at 20 mg/L O2 Injected 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 00 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 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0
Biodegradation Models
• Bioscreen -GSI
• Biochlor - GSI
• BIOPLUME II and III - Bedient & Rifai
• RT3D - Clement
• MT3D MS• SEAM 3D
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, nutrientlimitations, microcolony, Monod
Widdowson, et al. (1988)
X 1aerobic, cometabolic, multiplesubstrates, fermentative, Monod
Celia, 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
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 Cl
C C
Cl H
Cl H
PCE
TCE
DCE's
VC
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 –k1–> TCE
• TCE –k2–> DCE
• DCE –k3–> VC
• VC –k4–> Ethene