Download Numerical Simulation Analysis of the Effect of Microbiological

Numerical Simulation Analysis of the Effect of Microbiological
Degradation on Organic Contaminant Distribution in Groundwater
ZHAO Ying1, 2, LIANG Bing1, XUE Qiang2
1.Department of Mechanics and Engineering Sciences, Liaoning Technical University, Fuxin 123000,
China;
2. Institute of Rock and Soil Mechanics, The Chinese Academy of Sciences, Wuhan 430071, China
：
Abstract Considering convection, dispersion and adsorption-desorption, the kinetic model of the
transportation and transformation of organic contaminant, electrical accepter and bacteria in the
groundwater system was established by using double Monod microbiological degradation based on the
principle of mass conservation. Taking benzene and dissolved oxygen for example, the numerical
simulation analysis of contaminant and bacteria in the groundwater system was performed, and the
result shows that the bacteria concentration accumulates in the zone which the concentrations of
contaminant and dissolved oxygen are both relatively higher; the concentrations of bacteria in aqueous
phase and soil phase increase first and then reduce along the main direction of contaminant
transportation; the maximum value of bacteria concentration appears in the upstream zone near the
pollution source.
Key words: groundwater; organic contaminant; microbiological degradation; kinetic model; numerical
simulation
1. Introduction
With the fast development of economy and the rapid increase of population, the quantity of sewage
in industry, agriculture and daily life is gradually increasing. For the requirement of constructing and
living, the organic contaminants, such as pesticide, chemical fertilizer and landfill leachate, are leaked
out to environment. The organic contamination events of underground water were repeatedly reported,
and it is intimidating people’s health and safety.
Underground water system is a hidden environment, and the transportation and transformation of
contaminant in it is very hard to known. With the development of computer science and numerical
calculation method, the numerical simulation, with which the news of contaminant transportation and
transformation can be forecasted, is becoming to a significant method. Recently, many researchers
developed many researches, and established a series of mathematical models. But most of them
emphasize particularly on the description of physical transport process, the study on the microbiological
degradation was not deep.
In this paper, based on the environmental microbiology, the seepage mechanics and the theory of
solute transport, the model for describing the interaction, transportation and transformation of organic
contaminant, electron acceptor (oxygen) and bacteria in underground water was established by using
double-Monod microbiological degradation model. The numerical simulation analysis was performed
taking benzene for example. It provides theory basis for preventing and administering contamination of
underground water
2. Model description
2.1 Model of underground water flow
The governing equation for underground water flow can be written as (Freeze and Cherry, 1979)
Ss
∂h
∂ 
∂h 
=
 K ii

∂t ∂xi  ∂xi 
(1)
where t is time [T], xi are Cartesian coordinates [L], h is the hydraulic head [L], Kij is the
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hydraulic conductivity tensor [LT-1], S s is the coefficient of specific storativity [L-1].
Based on the Darcy’s Law the Darcy velocity is
qi = − Kij
∂h
∂xi
(2)
2.2 Model of solute transport and biodegradation processes
The kinetic models that include convection, dispersion, sorption, nonlinear biodegradation
(Double- Monod kinetics), biomass growth, decay, and electron acceptor availability are used for this
study.
For organic contaminant the governing model can be written as
∂C ρ ∂SＣ ∂ 
∂C  ∂vi C
+
=
 Dij
−
∂t n ∂t
∂xi  ∂x j  ∂xi
(7)
ρ  C  O 

− µm  X + X%  

 + qC
n   KC + C   KO + O 

where C , O and X are the aqueous phase concentrations of contaminant, electron acceptor
(oxygen) and bacterial cell respectively [ML-3]; SC and X% are the solid-phase concentrations of
contaminant and bacterial cell respectively [MM-1] ; KC is the half saturation coefficient for the
contaminant [ML-3]; n is the porosity of soil; ρ is bulk density of the soil[ML-3]; vi is the average pore
fluid velocity [LT-1[; Dij is the hydrodynamic dispersion coefficient [L2T-1] ; K O is the half saturation
coefficient for oxygen [ML-3], and µm is the contaminant utilization rate[T-1].
：
For the electron acceptor in aqueous phase, the governing model can be similarly written as
∂O ρ ∂SO ∂  ∂O  ∂viO
+
=  Dij
−
∂t n ∂t ∂xi  ∂x j  ∂xi
ρ   C  O 

−YO / C µm  X + X%  

 + qO
n   KC + C  KO + O 

(8)
where YO / C is the stoichiometric yield coefficient (oxygen used per unit amount of contaminant
utilized) qO is the source or sink of electron acceptor[ML-3].
Based on the double Monod theory and considering the transport, attachment, detachment, growth and
decay , the governing model of bacteria in aqueous phase and soilid phase can be written as
 C  O 
∂X ∂  ∂X  ∂vi X
=  Dij
− YX / C µm X 
−




∂t ∂xi  ∂x j  ∂xi
 KC + C  KO + O
(9)
Kdet ρ X%
−Katt X +
− Ke X
n
；
：
 C  O  Katt nX
∂X%
= YX% / C µm X% 
− Kdet X% − Ke X%

+
ρ
∂t
 KC + C  KO + O 
(10)
where YX / C and YX% / C are the stoichiometric yield coefficients (biomass produced per unit amount of
electron donor utilized) of aqueous phase and solid-phase respectively; K att is the bacterial attachment
coefficient [T-1], K det is the bacterial detachment coefficient [T-1], and K e is the endogenous cell death or
decay coefficient[T-1].
Assuming an equilibrium sorption for contaminant and electron acceptor, the sorption model can be
written as
：
∂S C
∂t
＝k (K
C
SC
C − SC )
， ∂∂St ＝k ( K
O
O
sO
O − SO )
(11)
where kC and kＯ are the first order adsorption/desorption rate constant of contaminant and electron
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acceptor[T-1]; K SC and K SO are the distribution coefficient of contaminant and electron acceptor
between aqueous phase and soil phase[L3M-1].
2.3 Initial and boundary condition
To solve a particular problem, the governing partial differential equation has to be supplemented by
appropriate initial and boundary condition. Initial conditions of underground water flow include all
points within the considered domain Ω , that is
h0 = h0 ( x, y , z ,0)
(12)
Three boundary conditions are commonly used in the solution of solute transport problems. They
are called Dirichlet, Nermann and Cauchy boundary condition respectively.
Dirichlet boundary condition
h ( x , y, z, t ) Γ = h1 ( x , y, z, t ) , on Γ1h
(13)
：
h
1
：
Nermann boundary condition
∂h ( x , y , z, t )
−K
= q1 ( x, y , z , t ) , on Γh2
h
∂n
Γ1
(14)
：
Cauchy boundary condition
∂h ( x , y , z , t )
+ f1h = f 2 , on Γh3
∂n
Γ1h
(15)
For solute transport model the initial condition can be written as
A0 = A( x, y , z ,0) ,
A = C , O, SC , SO , X , X% in Ω C
And the boundary conditions are
Dirichlet boundary condition
A( x , y , z , t ) Γ = A1 ( x , y , z, t )
A
on Γ1C
C , O , SC , SO , X , X%
：
Nermann boundary condition：
n ⋅ ( − D ⋅ ∇A) = q
Cauchy boundary condition：
h
1
nA
( x , y , z, t )
n ⋅ ( vA − D ⋅ ∇A) = qA ( x , y , z, t )
＝
A ＝ C , O , X on Γ
A ＝ C , O , X on Γ
C
3
C
2
(16)
(17)
(18)
(19)
3 Simulation results and discussion
Benzene is common used chemical material. Its uncontrolled release to the environment will cause
the contaminant to the soil and underground water. So, taking the benzene for example, the transport and
attenuation of organic pollutants in underground water was studied. The study area is 2D plane with
X = 500 m and Y = 300 m . The pollution source is in the domain X =100m and Y =100m~200m,
with the concentration of 650 mg⋅ L . The parameter was showed in table 1, and the simulation results
was plotted in figure 1~9.
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Table 1 The values of parameters in the model
P ar a mete rs
Val ues
P ar a mete rs
Val ues
2 .0
µm / d
n /%
0.40
YO / C
3.08
ρ / g⋅ cm -3
1.85
YX / C
0.0015
v y / m⋅ d-1
0.082
K att / d -1
85.0
0.085
K det / d -1
1.0
K ij / m⋅ d
-1
αL / m ⋅ d
-1
αT / m ⋅ d
-1
2
2
-1
-1
0.0425
Ke / d
KC / mg⋅ L
0 .1 25
kde / d -1
KO / mg⋅ L
0 .11 5
300
300
250
250
m
/ 150
Y
m
/
Y 150
100
100
50
50
0
50
0
100 150 200 250 300 350 400 450 500
X/m
0
300
300
250
250
200
200
m
/
Y 150
m
/
Y 150
100
100
50
50
0
50
0
100 150 200 250 300 350 400 450 500
X/m
300
300
250
250
200
200
m
/
Y 150
m/
Y 150
100
100
50
50
0
50
50
100 150 200 250 300 350 400 450 500
X/m
0
50
100 150 200 250 300 350 400 450 500
X/m
Fig.4 The distribution of bacteria concentration in
soil phase after 1 year (10-10mg/mg)
Fig.3 The distribution of bacteria concentration in
aqueous phase after 1 year (10-5mg/L)
0
0.075
Fig.2 The distribution of dissolved oxygen
concentration after 1 year (mg/L)
Fig.1 The distribution of pollution concentration
after 1 year (mg/L)
0
0.0015
200
200
0
0.15
0
100 150 200 250 300 350 400 450 500
X/m
Fig.5 The distribution of pollution concentration
after 2 year (mg/L)
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0
50
100 150 200 250 300 350 400 450 500
X/m
Fig.6 The distribution of dissolved oxygen
concentration after 2 year (mg/L)
300
300
250
250
200
200
m
/
Y 150
m
/
Y 150
100
100
50
50
0
0
50
0
100 150 200 250 300 350 400 450 500
X/m
Fig.7 The distribution of bacteria concentration in
aqueous phase after 2 year (10-5mg/L)
0
50
100 150 200 250 300 350 400 450 500
X/m
Fig.8 The distribution of bacteria concentration in
soil phase after 2 year (10-10mg/mg)
～
The results plotted in figure 1 8 show that with the increasing of time, the contaminant is
gradually filtered from the source in the upper boundary to downstream with the flow of underground
water, and diffused to the bilateralis, making the contaminated area an ellipse. The oxygen concentration
presents a decreasing trend with the contaminant increasing. The bacterial concentration is restricted
both by contaminant concentration and oxygen concentration, so the change law is relatively complex.
In the main transport direction ( Y = 150m X ≥ 100m ), the bacterial concentrations both in the water and
the soil present a trend that increasing firstly and then decrease, the bacteria aggregates in the place
where both the oxygen concentration and contaminant concentration are high. Near the pollution source,
although the contaminant concentration is high and can offer the necessary nutrient for metabolism of
bacteria, the bacterial concentration is very low, because of the absence of oxygen. The bacteria
aggregate on the left of the pollution source, because the dispersion of pollution makes the sufficient
nourishment, and the flow of water takes the high concentration of oxygen.
，
4 Conclusions
The dynamic models for describing the interaction, transportation and transformation of organic
contaminant, oxygen and bacteria in underground water were established by using double-Monod
degradation model. The numerical simulation analysis was performed taking benzene for example. The
numerical simulation results show that:
1. The bacterium growing is restricted both by contaminant and oxygen. The bacteria aggregate in
the zone which the concentrations of contaminant and dissolved oxygen are both relatively higher;
2. The concentrations of bacteria in aqueous phase and soil phase increase first and then reduce
along the main direction of contaminant transportation;
3. The maximum value of bacteria concentration appears in the upstream zone near the pollution
source;
So, it can be concluded that the dissolved oxygen is important for contaminant degradation and
bacterium growing, when modeling the organic contaminant transportation and transformation in
underground water, the oxygen must be considered.
References
[1] Markus Bause, Willi Merz. Higher order regularity and approximation of solutions to the Monod
biodegradation model [J]. Applied Numerical Mathematics, 2005, (55): 154–172
[2] Xue Qiang, Liang Bing, Wang Qixin. Environmental prediction models for transport of chemicals
and pesticides in soils [J]. Journal of Experimental Botany, 2003,54 (Suppl. 1): 59-59.
[3] H. Prommer, D.A. Barry, G.B. Davis. A one-dimensional reactive multi-component transport model
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for biodegradation of petroleum hydrocarbons in groundwater [J]. Environmental Modeling &
Software, 1999:(14) 213-223.
[4] XUE Qiang, LIANG Bing, LIU Xiao-li. Progress on organic contaminant transport and transform in
soil [J]. Soil and Environmental Sciences, 2002,11(1): 90-93.
[5] LIU Ming-zhu, CHEN Hong-han, HU Li-qin. Modeling of transformation and transportation of PCE
and TCE by biodegradation in shallow groundwater [J]. Earth Science Frontiers, 2006, 13(1):
155-159.
[6] Olaf A. Cirpka and Albert J. Valocchi. Two-dimensional concentration distribution for
mixing-controlled bio-reactive transport in steady state [J]. Advances in Water Resources, 2007, 30
(6-7): 1668-1679.
Acknowledgment
This research was supported with funding from National Natural Science Foundation of
China(50874102) and a grant from Natural Science Foundation of HuBei Province for Distinguished
Young Scholars（2007ABB039）and a grant from the Key Technologies Programs of HuBei Province
（2008AC008）and Open Fund of State Key laboratory of Geohazard Prevention and Geoenvirnment
Protection（GZ2006-03）and Science and Technique Foundation from Municipal Manage Agency of
WuHan.
This research was supported with funding from National Natural Science Foundation of
China(50574048).
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