Numerical Simulation of Contaminant Transport in Porous Soil

Li Lulu, Zhao Wen, Wang yilin, Meng Fanbo, Ao Hongyan , Wang Chang College of Life Science and Biotechnology,

Dalian Fisheries University Dalian, China, 116024

Email: zhaowen@dlfu.edu.cn

Abstract—Solute transport in porous soils has been the topic of experimental, theoretical research and numerical simulation aspects. The complexity of the phenomenon of transport of pollutants in porous soil has to be faced in the most complete way. The contaminant transport processes in porous soils are simulated numerically based on overlap principle for a transient contaminant resource. The influences of duration and concentration of contaminant resource and dispersion coefficient of contaminant on contaminant transport processes are investigated numerically. The computation results show that the duration and concentration of contaminant resource can distinctly affect contaminant distribution and dispersion coefficient of contaminant has a small contribution.

Keywords- contaminant transport; porous soil; water pollution; numerical simulation

I. INTRODUCTION In recent years, interest in understanding the mechanisms

and prediction of contaminant transport through soils has dramatically increased because of growing evidence and public concern that the quality of the subsurface environment is being adversely affected by industrial, municipal and agricultural activities. Transport phenomena are encountered in almost every aspect of environmental engineering science. In assessing the environmental impacts of waste discharges it is important to predicate the impact of emission on contaminant concentration in nearby air and water [2] Groundwater is one of the most important sources of water, and because of its extensive use, groundwater contamination has become a major environmental concern. The quality of groundwater has become a significant concern in all over world. Agricultural production has come under greater scrutiny for its potential role in the degradation of water resources [1]. Contamination of groundwater is an issue of major concern in residential areas which may occur as a result of spillages of hazardous chemicals, dumping of toxic waste, landfills, waste water, or industrial discharges.

In the last 20 years, groundwater research has been focused in developing quantitative models to predict contaminant transport in aquifers. These predictive tools are very important in the investigation and cleanup of contaminated subsurface systems. It is also known that the transport and fate of contaminants are greatly affected by the

heterogenity of aquifer properties [1]. Massoudieh developed a one-dimensional model for colloid-facilitated transport of chemicals in unsaturated porous media. The model has parts for simulating coupled flow, and colloid transport and dissolved and colloidal contaminant transport. Richards' equation was solved to model unsaturated flow, and the effect of colloid entrapment and release on porosity and hydraulic conductivity of the porous media is incorporated into the model. Both random sequential adsorption and Langmuir approaches have been implemented in the model in order to incorporate the effect of surface jamming [3]. Rubin concerned contaminant transport in aquifers comprising fractured porous formations. Simulations of various possible scenarios were carried out by solving the basic dimensionless equations developed in the study. The solutions were obtained by a combination of analytical and numerical solutions. The effect of contaminant diffusion into the microblocks can be approximated as a retardation phenomenon, similar to contaminant adsorption. An increase of the fracture density reduces that retardation effect [4].Parker presented a methodology for dating releases of light nonaqueous phase liquids using an inverse modeling approach with simple analytical models. Models for plume migration were presented to predict plume velocity in the unsaturated and saturated zones as a function of basic soil and fluid properties [7]. Li presented a new approach to estimate model parameter in groundwater hydrology by using hybrid ant colony system with simulated annealing. Based on the information from the observed water heads and calculated waterheads, an objective function for inverse problem is proposed. The inverse problem of parameter identification is formulated as an optimization problem[8]. Li proposed a parameter identification approach and to determine hydraulic parameters using inverse modeling. The inverse problem of parameter identification is formulated as an optimization problem. In order to identify hydraulic parameters of soils efficiently and in a robust manner, the genetic algorithm is presented for the parameter identification of the fractal models[9].

As the world’s population continues to grow, the demand for fresh water will continue to increase. Seventy-five percent of the Earth’s surface is covered with water. Of this almost 97% of the world’s water is salty and not readily drinkable. The other 2% is locked as solids, in the form of ice caps and

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glaciers, leaving us with about 1% of freshwater that is available for all of humanity’s needs. This small amount of freshwater can be found in the form of surface water and groundwater. However, quantity is not the only problem, the quality of drinking water is also a concern since this vital resource is vulnerable to contamination. With the advances of technology, more and more human activities are polluting the water system[5]. The aim of the paper is to propose a numerical algorithm to simulate contaminant transport processes in porous soils for a transient contaminant resource and investigate influences of duration and concentration of contaminant resource and dispersion coefficient of contaminant on contaminant transport processes.

II. NUMERICAL SIMULATION OF POLLUTION SOLUTE TRANSPORT IN POROUS SOIL

Contaminants that are dissolved in the subsurface environment are transported by the following three processes: advection, mechanical dispersion, and molecular diffusion. Advection refers to the contaminant being carried along with the flow of subsurface water. This process is a result of the large-scale gradients in fluid energy (head) and it is the most significant mass transport process. The velocity of the water is described by the average speed of the water movement through the pores of the soil. Mechanical dispersion and molecular diffusion collectively are referred to as hydrodynamic dispersion. Mechanical dispersion is the main process that causes the contaminant to spread out and become diluted. The contaminant spreads due to the spatial variation of flow paths and the variation of velocity in the groundwater movement. The amount of mechanical dispersion increases with the heterogeneity of the aquifer and the scales involved [5].

Figure 1. Typical pollution source dispersion in one dimension.

One-dimensional heterogeneous, non-reactive contaminant transport in a semi-infinite domain, as shown in Fig. 1, described by the advection-dispersion equation is

2

2 .C C CD vx x t

∂ ∂ ∂− =∂ ∂ ∂

(1)

Where D is the dispersion coefficient, C is the solute concentration, v is the transport velocity. As in the case of a steady input of contaminant resources, the initial and boundary conditions are expressed as follows:

( 0, 0) 0C x t≥ = = . (2)

0 ( 0,C C x t= = > . (3)

( , 0) 0C x t= ∞ ≥ = . (4)

As in the case of a steady input of contaminant resources, the analytical solution of equation (1) can be expressed as follows:

01

0

/[ ]2 2 /

/exp( / ) [ ]2 2 /

C x vt nC erfcDt n

C x vt nvx d erfcDt n

−= +

+× ×. (5)

Where

2

0

2( ) exp( )y

erf y t dtπ

= −∫ . (6)

( ) 1erf ∞ = . (7)

2

( ) 1 ( )

2 exp( )y

erfc y erf y

t dtπ

∞

= −

= −∫ . (8)

As in the case of a rectangular input of contaminant resources, it can be obtained by assuming two Heaviside functions superimposed on each other but displaces a period tp in time, a shown in Fig. 2 and 3.

Based on the overlap principle of boundary condition of duration of contaminant resources, the variation of contaminant concentration in x depth at any time t in the case of a rectangular input of contaminant resources can be expressed as follows

1 2( , ) ( , ) ( , )C x t C x t C x τ= − . (9)

2 1( , ) ( , ) ( )C x C x Hτ τ τ= . (10) Where H is Heaviside function, τ=t-tp. tp is duration of

rectangular input of contaminant resources.

1 0( )

0 0H

ττ

τ>⎧

= ⎨ <⎩. (11)

III. CASE STUDY Many environmental problems involve diffusion and

convection processes. These problems include the dispersal of pollutions into air and water, and also the spread of species of plants, infections and animals. Each area has its own physics, chemistry, biology and ecology [6].

In order to investigate pollution solute transport in porous soil and analyze the influences of model parameters on distribution of concentration in porous soils, a numerical simulation is carried out. Table Ⅰ lists the main model parameters. The computational model is shown in Fig. 1.

Figure 2. Duration of contaminant resources.

Figure 3. Overlap principle of boundary condition of duration of

contaminant resources.

TABLE I. MAIN MODEL PARAMETERS

Parameters v/m/s D/m2/s C0/% Value 0.002 0.0001 10.0

02468

1012

400 700 1000 1300 1600 1900

Time/s

Con

tam

inan

tco

ncen

tratio

n/%

x=1.0mx=2.0m

Figure 4. Variation of contaminant concentration in different depth versus

time (C0=10.0%,tp=∞).

05

1015202530

500 800 1100 1400

Time/s

Con

tam

inan

tco

ncen

tratio

n/%

c0=10%c0=15%c0=20%c0=25%

Figure 5. Influence of contaminant source concentration on distribution of

concentration in porous soils (tp=700s).

02468

1012

500 800 1100 1400

Time/s

Con

tam

inan

tco

ncen

tratio

n/%

tp=700tp=500tp=300tp=100

Figure 6. Influence of duration of contaminant resource on distribution of

concentration in porous soils (C0=10.0%, x=1.0m).

Variation of contaminant concentration in different depth versus time in the case of a steady input of contaminant resources is depicts in Fig. 4. Fig. 5 shows the influence of contaminant source concentration on distribution of concentration in porous soils in the case of a rectangular input (tp=700s)of contaminant resources. Fig. 6 Influence of duration of contaminant resource on distribution of concentration in porous soils (C0=10.0%, x=1.0m). Fig. 7 shows influence of the dispersion coefficient on distribution of concentration in porous soils (C0=10.0%, x=1.0m).

0

2

4

6

8

10

500 800 1100 1400

Time/s

Con

tam

inan

tco

ncen

tratio

n/%

d=5e-4d=1e-3d=2e-3d=5e-3

Figure 7. Influence of the dispersion coefficient on distribution of

concentration in porous soils (C0=10.0%, x=1.0m).

tp

C0

Time

IV. CONCLUSION 1) A one-dimensional transient contaminant transport in

porous soils was solved by using overlap principle of boundary condition of duration of contaminant resources.

2) The influences of duration and concentration of contaminant resource and dispersion coefficient of contaminant on contaminant transport processes are investigated numerically.

3) The computation results show that the duration and concentration of contaminant resource can distinctly affect contaminant distribution and dispersion coefficient of contaminant has a small contribution.

ACKNOWLEDGMENT The research is funded by the National Natural Science

Foundation of China (30671625, 40776065).

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