Download Numerical Simulation Analysis of the Effect of Distribution in Groundwater

Physical and Numerical Simulation of Geotechnical Engineering
16th Issue, Sep. 2014
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, P.R.China
2. Institute of Rock and Soil Mechanics, The Chinese Academy of Sciences, Wuhan 430071, P.R.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.
KEYWORDS: Groundwater, Organic contaminant, Microbiological degradation, Kinetic model,
Numerical simulation
1 INTRODUCTION
2 MODEL DESCRIPTIONS
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 leach ate, 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.
2.1 Model of underground water flow
© ST. PLUM-BLOSSOM PRESS PTY LTD
The governing equation for underground water flow
can be written as (Freeze and Cherry, 1979):
Ss
h
 
h 

 Kii

t xi  xi 
(1)
Where t is time [T], xi are Cartesian coordinates
[L], h is the hydraulic head [L], Kij is the hydraulic
conductivity tensor [LT-1], Ss 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  SＣ  
C  vi C


 Dij

t n t
xi  x j  xi
(3)
  C  O 

 m  X  X  

  qC
n   K C  C   KO  O 

Where C , O and X are the aqueous phase
concentrations of contaminant, electron acceptor (oxygen)
Numerical Simulation Analysis of the Effect of Microbiological Degradation on Organic Contaminant Distribution in
Groundwater
DOI:10.5503/J.PNSGE.2014.16.012
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;  is bulk density of the soil [ML-3];
conditions of underground water flow include all points
within the considered domain  , that is:
h0  h0 ( x, y , z,0)
(8 )
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:
-1
vi is the average pore fluid velocity [LT ]; Dij is the
hydrodynamic dispersion coefficient [L2T-1]; K O is the
half saturation coefficient for oxygen [ML-3], and  m is
the contaminant utilization rate [T-1].
For the electron acceptor in aqueous phase, the
governing model can be similarly written as:
h( x, y, z, t ) h  h1 ( x, y, z, t ) , o n 1h
(9)
1
Nermann boundary condition:
O  SO   O  viO


 Dij

t n t xi  x j  xi
(4)
   C  O 

YO / C m  X  X  

  qO
n   KC  C   KO  O 

K
h( x, y, z, t )
 q1 ( x, y, z, t ) , on  h2
n
1h
(10)
Cauchy boundary condition:
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].
h( x, y, z, t )
 f1h  f 2 , o n  3h
n
1h
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:
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 C
(12)
And the boundary conditions are:
Dirichlet boundary condition:
 C  O 
X
  X  vi X

 YX / C  m X 
 Dij



t xi  x j  xi
 K C  C   K O  O  (5)
K  X
 K att X  det
 Ke X
n
A( x, y, z, t ) h  A1 ( x, y, z, t )
A=
1
C , O , S C , SO , X ,
 C   O  K att nX
X
 YX / C m X 
 Kdet X  K e X (6)


t

 K C  C   KO  O 
X
on 1C
(13)
Nermann boundary condition:
n    D  A  qnA ( x, y , z, t )
Where YX / C and YX / C are the stoichiometric yield
A ＝C ,O , X
on C2
(14)
coefficients (biomass produced per unit amount of
electron donor utilized) of aqueous phase and solid-phase
respectively; K att is the bacterial attachment coefficient
Cauchy boundary condition:
n   vA  D  A  q A ( x, y , z, t )
[T-1], K det is the bacterial detachment coefficient [T -1],
A ＝ C , O , X on C3
(15)
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:
SC
S
＝kC ( K SC C  SC ) , O ＝kO ( K sOO  SO )
t
t
(11)
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  500m and
Y  300m . 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 were plotted in Figure 1-8.
(7)
Where kC and kＯ are the first order adsorption/
desorption rate constant of contaminant and electron
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
54
Physical and Numerical Simulation of Geotechnical Engineering
16th Issue, Sep. 2014
Table 1 The values of parameters in the model
Parameters
Kij / m d
-1
Parameters
Values
2 .0
m / d
0.15
n /%
0.40
YO / C
3.08
1.85
YX / C
0.001 5
vy / m d-1
0.082
Katt / d -1
-1
L / m  d
-1
0.085
K det / d
0.042 5
K e / d -1
0.001 5
KC / mg L
K O / mg L
0 .125
kde / d -1
0.075
300
250
200
200
Y/m
150
150
100
100
50
50
50
0
100 150 200 250 300 350 400 450 500
0
50
X/m
300
250
250
200
200
Y/m
Y/m
Figure 2 The distribution of dissolved oxygen
concentration after 1 year (mg/L)
300
150
150
100
100
50
50
0
50
0
100 150 200 250 300 350 400 450 500
0
50
Figure 4 The distribution of bacteria
concentration in soil phase after 1 year
(10-10mg/L)
300
300
250
250
200
200
Y/m
Y/m
Figure 3 The distribution of bacteria
concentration in aqueous phase after 1 year
(10-5mg/L)
150
100
100
50
50
0
0
50
100 150 200 250 300 350 400 450 500
X/m
X/m
150
100 150 200 250 300 350 400 450 500
X/m
Figure 1 The distribution of pollution
concentration after 1 year (mg/L)
0
1.0
0 .115
250
0
85.0
T / m2  d-1
300
0
-1
 / g cm -3
2
Y/m
Values
100 150 200 250 300 350 400 450 500
0
0
50
100 150 200 250 300 350 400 450 500
X/m
X/m
Figure 5 The distribution of pollution
concentration after 2 years (mg/L)
Figure 6 The distribution of dissolved oxygen
concentration after 2 years (mg/L)
55
Numerical Simulation Analysis of the Effect of Microbiological Degradation on Organic Contaminant Distribution in
Groundwater
DOI:10.5503/J.PNSGE.2014.16.012
300
300
250
250
200
150
Y/m
Y/m
200
150
100
100
50
50
0
0
50
0
100 150 200 250 300 350 400 450 500
0
50
100 150 200 250 300 350 400 450 500
X/m
X/m
Figure 7 The distribution of bacteria concentration
in aqueous phase after 2 years (10-5mg/L)
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
bilateral is, 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.
Figure 8 The distribution of bacteria concentration
in soil phase after 2 years (10-10mg/L)
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.
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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4 CONCLUSIONS
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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.
56
Physical and Numerical Simulation of Geotechnical Engineering
16th Issue, Sep. 2014
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for Mixing-controlled
Bio-reactive Transport in Steady State [J]. Advances in
Water Resources. 2007, 30 (6-7): 1668-1679
57