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Modeling the Migration of Soluble Methanol in Unsaturated Soil Zone1
Pedosphere 17(3): 366-372, 2007 ISSN 1002-0160/CN 32-1315/P @ 2007 Soil Science Society of China Published by Elsevier Limited and Science Press
PEDOSPHERE www elsevier com/locate/pedosphere
Modeling the Migration of Soluble Methanol in Unsaturated Soil Zone*l LI Hongl, LI Xin-Gangl>', HUANG Guo-Qiang1)2i*2and JIANG Bin' 'School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072 (China). E-mail: lihong.tjuQ163.com National Engineering Research Center for Distillation Technology, Tianjin 300072 (China) (Received October 23, 2006; revised February 28, 2007)
ABSTRACT A combined model of solute transport and water flow was developed to simulate the migration of methanol, a soluble organic chemical, in unsaturated soil zone. The solute transport equation considered convective-dispersive transport in the liquid phase as well as diffusion in the gas phase. The effect of rainfall and evapotranspiration on transport was considered at the boundary conditions of the governing equations. Data on the characteristics of a loam soil and the climatic conditions in southern California were also introduced to compare the results with those from a study in the USA in which the profiles of methanol distribution and water content in the soil zone at different times had been depicted. This comparison showed that there was good agreement between the two studies. The results showed that methanol contamination reached a depth of about 250 cm after 8760 h. In contrast, if rainfall and evapotranspiration were not considered, the depth was only about 140 cm. The model therefore confirmed that rainfall strongly affected solute transport. Key Words:
evapotranspiration, methanol, rainfall, solute transport model
Citation: Li, H., Li, X. G., Huang, G. Q. and Jiang, B. 2007. Modeling the migration of soluble methanol in unsaturated soil zone. Pedosphere. 17(3): 366-372.
INTRODUCTION Soils can be contaminated by a variety of pollutants (Chen et al., 2003). During the past decade, the widespread production and use of industrial solvents and liquid petroleum products have provided the ample opportunity for subsurface contamination (Liu et at., 2005). The impetus to understand and manage the unsaturated zone stems from its recognition as a key factor in the improvement and protection of the quality of groundwater supplies. The unsaturated zone links surface water and groundwater; therefore, investigation of the migration of contaminants in the unsaturated zone is very important. Some soluble organic chemicals such as methyl tert-butyl ether (MTBE), methanol, and phenol have been increasingly contributing to groundwater contamination. Direct exposure of human and ecological receptors to contaminants present in the soil may also occur via inhalation of toxic solutes as they volatilize from the soil, through dermal absorption due to contact the soil, and from ingestion of soil particles. Methanol is a clear, colorless, volatile liquid with a weak odor and is slightly sweeter than ethanol. It is used in the industrial production of many synthetic organic compounds and is a constituent of a large number of commercially available solvents. Methanol is soluble in water, and this characteristic makes it highly mobile in a groundwater system. Methanol is also a toxic liquid and has been shown to cause headache, vomiting, nausea, dyspnea, and poor eyesight following contact the vapor or liquid. Accidental or suicidal ingestion can cause severe metabolic acidosis and clinical disturbances, such as blindness, permanent neurological dysfunction, and even death (Kuteifan et al., 1998). 'lProject supported by the National Natural Science Foundation of China (No. 20276048). *2Corresponding author. E-mail: hgqQtju,edu.cn.
MIGRATION OF METHANOL IN SOIL
367
Given the growing concern over the environmental impacts of contaminants in the soil, a number of different, deterministic transport models have been proposed over the last several decades to describe the movement of chemical contaminants in the vadose zone. Most of these models were used to describe the transport of soluble solutes (Bresler, 1973; Nielsen et al., 1986), and some models were developed for the transport of pesticides (Ren and Mao, 2003; Mao and Ren, 2005). Warrick et al. (1971), Kirda et al. (1973), Kelleners et al. (1999) and Li and Hu (2004) investigated the interactions between solute and water movement. The purpose of the present study was to present a model to simulate the transport of soluble organic chemicals (using methanol) and water flow in the unsaturated soil zone. As climatic conditions are very important factors in the movement of soil water, the effects of rainfall and evapotranspiration on transport were also considered.
MODEL DEVELOPMENT AND APPLICATION The theory developed in this study described the one-dimensional simultaneous transport of water and methanol in the unsaturated soil zone. Some general assumptions in the study were: the soil domain was considered to be isothermal; the soil media were rigid; hysteresis of the retention curve or the water transport coefficients was neglected; the transfer of mass occurred only in one-dimension vertically; no free-phase of solution was present in the soil; the solute was not completely restricted by the soil matrix; and the degradation of methanol in soil was not considered.
Solute transport The governing solute transport in gas, liquid, and solid phases are described, respectively, by the following equations (Huang et at., 2004; Liu and Li, 2004):
where G, C, and S are solute concentrations in the gas, liquid, and solid phases, respectively; eg is the air content; Dg is the diffusion coefficient tensor for the gas phase; z is the vertical coordinate with the origin at the soil surface (positive downward); I is the mass transport between two different phases with Igw I,, ISw Isg I,, I, = 0; the subscripts g, w, and s correspond with the gas, liquid, and solid phases, respectively; Ow is the volumetric water content; D, is the dispersion coefficient tensor for the liquid phase; q is the volumetric flux density; and Pb is the soil bulk density. Combining Eqs. I, 2 , and 3 yields the overall flux equation for methanol in the soil:
+ +
+ +
+
Mass partitioning occurs between two individual phases, named liquid/solid, vapor/liquid, and vapor/solid. A thin film of water covering soil grains is assumed (Silka, 1988), so the solute transport between vapor and solid phases can be omitted. Chemical equilibriums between the vapor/liquid and liquid/solid phases are linear and described, respectively, as follows:
where H is Henry’s law constant, and Kd is the linear adsorption coefficient between the solid and liquid
H. LI
368
phases. Assuming that soil porosity, pi, is time-invariant and that pi = Ow
et al.
+ O,, it then follows that
og = 9 - ow
(7)
Substituting the partitioning coefficients and Eq. 7 into Eq. 4, the following is obtained:
The law of Darcy describes the transport of liquid water through a porous medium in the vertical direction as: 4 = - q
d(h- z ) dz
]
(9)
where K is hydraulic conductivity, h is the pressure head, and z is the vertical coordinate. In the present study, the chemical surface volatilization flux was neglected, so the boundary conditions of solute transport at the soil surface were given by:
In all the simulations, an adequate depth of soil was selected to ensure that the chemical concentration front did not reach the lower boundary (I), which was conveniently set as:
dC -=Oatz=l
at
Accordingly, the initial conditions of moisture and solute distribution were set as:
C(t = 0 , z ) = Co(z)at z # 0
(12)
ew(t= 0,
(13)
= ew,o(z)
Water flow The isothermal Darcian flow of water in a variably saturated porous medium is described with the continuity equation:
Substituting Eq. 9 into Eq. 14, one-dimensional, vertical, transient, and unsaturated flow is described with Richard's equation (Bear, 1972): -=--
dt
a dt
k K az "'1
(15)
-
In this study, the soil hydraulic properties were described with the Mualem-van Genuchten model (Mualem, 1976; van Genuchten, 1980):
K ( O ) = K,@V[l- (1 - 01/"1
1'
(17)
where 0 = (6, - O w , ) / ( ~ w , - Owr) (Ow, is the residual volumetric water content, Ow, is the saturated volumetric water content); m = 1- l / n ; a , n, and 7 are empirical parameters, and K, is the saturated hydraulic conductivity.
369
MIGRATION OF METHANOL IN SOIL
On the soil surface, in the absence of surface ponding, the absolute value of the flux q should satisfy the following two conditions:
1
dh
IQI = - K (-a2
- 2)
IL
hA 5 h 5 h, where E is the maximum potential rate of infiltration or evapotranspiration under the current atmospheric conditions; h is the pressure head at the soil surface; and hA and h, are, respectively, minimum and maximum pressure heads allowed under the prevailing soil conditions. The value for h~ is determined from the equilibrium conditions between soil water and atmospheric water vapor, whereas h, is usually set equal to zero. When one of the end points of Eq. 19 is reached, the prescribed head boundary condition will be used to calculate the actual surface flux. At the soil surface, the water velocity can be set equal to rainfall infiltration velocity under nonponding conditions, and it is set equal to unsaturated hydraulic conductivity when ponding conditions are reached. However, during periods without rainfall, the water velocity at the soil surface is set equal to the evapotranspiration velocity.
Coupled solute transfer and water flow Two partial differential equations (Eqs. 8 and 15) have been introduced. The two equations describe simultaneous water and solute concentration distribution in the unsaturated soil zone. The Galerkin finite element method with linear basis functions was used to obtain a solution of the two flow equations subjected to the imposed initial and boundary conditions. The HYDRUS-2D software developed by the International Ground Water Modeling Center was applied here to help with the calculation of the results.
Application of the model In this study, an unsaturated modeling soil zone was introduced. In the simulation, methanol was chosen as the solute, and the results were compared with those obtained by Grifoll and Cohen (1996). The depth of the modeling domain was 250 cm, and the total modeling time was 365 days. The soil selected for this simulation was a loam soil, and the hydraulic parameters required in modeling are given in Table I (Grifoll and Cohen, 1996). The pertinent physicochemical properties at 20 " C for methanol (Grifoll and Cohen, 1996) are given in Table 11. TABLE I Water flow-soil hydraulic parametersa) required in the methanol transfer and water flow model
ews
n
a
owr
1.43
cm-l 0.043
__ ~ r n 3 c m - ~ __ 0.022 0.35
K S
?)
Pb
cm h-l 0.75
0.5
g cm-3 1.27
a)Cited from Grifoll and Cohen (1996). n, a, and 11 are empirical parameters; Ow, is the residual volumetric water content; Ow, is the saturated volumetric water content; K8 is the saturated hydraulic conductivity; and Pb is the soil bulk density.
TABLE I1 Physicochemical properties") of methanol a t 20 "C Dair
Kd
H
Dwater cm2 h-l
5.76 x 10'
5.04 x
lo-'
1.8 x 1 0 - ~
1.9 x 1 0 - ~ ~
~~
~
~
~~~~
")Cited from Grifoll and Cohen (1996). D,,, is the molecular diffusion in air; Dwateris the molecular diffusion in water; H is dimensionless Henry's law coefficient; and Kd is solid/water partition coefficient.
H. LI et al.
3 70
To illustrate the effects of rainfall and evapotranspiration on pollutant transport in the vadose zone, a pattern mimicking the distribution of rainfall and evapotranspiration in southern California, USA (Fig. 1) was selected (Ruffner and Bair, 1987; Grifoll and Cohen, 1996). 6.0
a,
I
0
1
2
3
4
+-
m
L
C
.o_ 7 VJ
4.0
.L E Q..
20
r
Ix 2.0
4
-
v
0 Q
m >
w 5
6
7
8
o
0 Time (x 1O'h)
1
2
3
4
5
6
7
8
Fig. 1 Precipitation rates and evapotranspiration rates data set in southern California, USA (Grifoll and Cohen, 1996).
RESULTS AND DISCUSSION The soil zone was initially contaminated to a depth of 50 cm, and the values of concentration were assumed to be the same. The beginning of the simulation was set at t = 0 h. Comparing the simulation results of methanol dimensionless concentration, which represented the ratio of the calculated methanol concentration to the initial concentration, at t = 500 h with those of Grifoll and Cohen (1996), the modeling was satisfactory and reliable, as shown in Fig. 2.
0.2 0
0
20
40 60 80 Depth (cm)
100
120
Fig. 2 Comparison of the methanol dimensionless Concentration (MDC) profile of the simulation by the methanol transfer and water flow model at t = 500 h with the results of Grifoll and Cohen (1996). MDC is the ratio of the calculated methanol concentration to the initial concentration.
Based on the simulation results, water content (Fig. 3a) and the dimensionless concentrations of methanol (Fig.3b) considering the effects of rainfall and evapotranspiration in the soil at t = 0, 500, 2 000, 4 000, and 8 760 h were depicted. To determine the effects of rainfall and evapotranspiration on methanol solute transport in the soil, a contrast simulation was made, where the rate of rainfall and evapotranspiration was set to zero. The results of this scenario are shown in Fig. 3c. Soil moisture played an important role in solute transport in soil. As shown in Fig. 3a, the water content profile varied at different times under the rainfall and evapotranspiration conditions. The simulation results showed that the water content of the soil near the surface fluctuated considerably. When it was rainy, the water content increased quickly, then the water content fell gradually because of both water infiltration and evapotranspiration. From the comparisons of Figs. 3b and 3c, the effects of rainfall and evapotranspiration on methanol transport in unsaturated zone were notable. As shown in Fig. 3b, after 4000 h the depth of methanol
371
MIGRAT’ION OF METHANOL IN SOIL
1 .o
70.30
0.8
0.8
’ n
D
a,
2
0.4
0.12
t=Qh t=500h t = 2000 h f = 4000 h t = 8760 h
0 0.6
0 0.6
0.18 c 0
0.4
0
0.2
0.2
$ 0.06 Y
$
n
0
0
0
0
50 100 150 200 250
50 100 150 200 250 Depth (cm)
0
50
100 150 200 250
Fig. 3 Water content profiles considering the effects of rainfall and evapotranspiration (a) and methanol dimensionless concentration (MDC) profiles with (b) and without (c) considering the effects of rainfall and evapotranspiration. MDC is the ratio of the calculated methanol concentration to the initial concentration.
contamination reached about 220 cm, whereas if rainfall and evapotranspiration were not considered, the depth was only about 120 cm (Fig. 3c). Because of its solubility, methanol traveled quickly down the soil profile along with water infiltration, especially during the rainy season. Under rainy conditions, the water content in the unsaturated soil zone increased and accordingly the liquid convection of the solute was prominent due to the infiltration of rainwater, However, in the dry season, methanol transport in soil depended mainly on diffusion. This was shown from a comparison of the methanol dimensionless concentration profiles at a depth of 25 cm under different simulation conditions (Fig. 4).
0
2
4 6 Time (x 10’ h)
8
0
Considering the effect of rainfall and evapotranspiration
*
Without considering the effect of rainfall and evapotranspiration
10
Fig. 4 Methanol dimensionless concentration (MDC) profiles a t a depth of 25 cm with/without considering the effects of rainfall and evapotranspiration. MDC is the ratio of the calculated methanol concentration to the initial concentration.
CONCLUSIONS A combined model of solute transport and water flow was developed to investigate soluble organic chemical (methanol) transport in the unsaturated soil zone. The potential effects of rainfall and evapotranspiration on contaminant migration were studied by considering the boundary conditions of the governing equations. The results proved t o be consistent with those of earlier studies, so in the future this model could be used t o analyze the results from field investigations.
REFERENCES Bear, J. 1972. Dynamics of Fluids in Porous Media. Elsevier, New York. 764pp. Bresler, E. 1973. Simultaneous transport of solute and water under transient unsaturated flow conditions. Water Resour. Res. 9(4): 975-986. Chen, 3 . Z., Chen, J., Xie, X. J. and Zhang, X. L. 2003. Soil pollution and its environmental impact. Sods (in Chinese). 35(4): 298-303.
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H. LI et al.
Grifoll, J. and Cohen, Y . 1996. Contaminant migration in the unsaturated soil zone: The effect of rainfall and evapotranspiration. Journal of Contaminant Hydrology. 23(3): 185-211. Huang, G. Q., Li, X. G. and Xu, S. M. 2004. Soil vapor extraction: Mechanisms and basic mathematical model. Acta Pedologica Sinica (in Chinese). 41(3): 394-400. Kelleners, T. J., Beekma, J. and Chaudhry, M. R. 1999. Spatially variable soil hydraulic properties for simulation of field-scale solute transport in the unsaturated zone. Geoderma. 92(4): 199-215. Kirda, C., Nielsen, D. R. and Biggar, J. W. 1973. Simultaneous transport of chloride and water during infiltration. Soil Sci. SOC.Am. Proc. 37(3): 339-345. Kuteifan, K., Oesterl6, H., Tajahmady, T., Gutbub, A. M. and Laplatte, G. 1998. Necrosis and haemorrhage of the putamen in methanol poisoning shown on MRI. Neuroradiology. 40(3): 158-160. Li, Y. Z. and Hu, K. L. 2004. Simulation for the effect of clay layer on the transport of soil water and solutes under evaporation. Acta Pedologica Sinica (in Chinese). 41(4): 493-502. Liu, W. B. and Li, J. H. 2004. Models of soil vapor extraction for soil contaminated by volatile organic compounds. Soils (in Chinese). 36(4): 351-358. Liu, X. Y . , Ji, X. Y., Li, X. W., Dai, C. L. and Chu, W. H. 2005. Migration of petroleum-series contaminants in the soil. Soils (in Chinese). 37(5): 482-486. Mao, M. and Ren, L. 2005. Risk assessment of atrazine leaching in soil at field scale level. Acta Pedologica Sinica (in Chinese). 42(2): 177-186. Mualem, Y . 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12(3): 593-622. Nielsen, D. R., van Genuchten, M. T. and Biggar, J . W. 1986. Water flow and solute transport processes in the unsaturated zone. Water Resour. Res. 22(9): 89-108. Ren, L. and Mao, M. 2003. Simulation of nonequilibrium transport of atrazine in saturated sandy loam under steady-state water flow condition. Acta Pedologica Sinica (in Chinese). 40(6): 829-837. Ruffner, 3. A. and Bair, F. E. (eds.). 1987. The Weather Almanac. 5th Edition. Gale Research Co., Detroit, MI. 811pp. Silka, L. R. 1988. Simulation of vapor transport through the unsaturated zone-Interpretation of soil-gas surveys. Ground Water Monitoring Review. S(2): 115-123. Van Genuchten, M. T. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. SOC.Am. J. 44(5): 892-898. Warrick, A. W., Biggar, J. W. and Nielsen, D. R. 1971. Simultaneous solute and water transfer for an unsaturated soil. Water Resour. Res. 7(5): 1216-1 225.
PEDOSPHERE www elsevier com/locate/pedosphere
Modeling the Migration of Soluble Methanol in Unsaturated Soil Zone*l LI Hongl, LI Xin-Gangl>', HUANG Guo-Qiang1)2i*2and JIANG Bin' 'School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072 (China). E-mail: lihong.tjuQ163.com National Engineering Research Center for Distillation Technology, Tianjin 300072 (China) (Received October 23, 2006; revised February 28, 2007)
ABSTRACT A combined model of solute transport and water flow was developed to simulate the migration of methanol, a soluble organic chemical, in unsaturated soil zone. The solute transport equation considered convective-dispersive transport in the liquid phase as well as diffusion in the gas phase. The effect of rainfall and evapotranspiration on transport was considered at the boundary conditions of the governing equations. Data on the characteristics of a loam soil and the climatic conditions in southern California were also introduced to compare the results with those from a study in the USA in which the profiles of methanol distribution and water content in the soil zone at different times had been depicted. This comparison showed that there was good agreement between the two studies. The results showed that methanol contamination reached a depth of about 250 cm after 8760 h. In contrast, if rainfall and evapotranspiration were not considered, the depth was only about 140 cm. The model therefore confirmed that rainfall strongly affected solute transport. Key Words:
evapotranspiration, methanol, rainfall, solute transport model
Citation: Li, H., Li, X. G., Huang, G. Q. and Jiang, B. 2007. Modeling the migration of soluble methanol in unsaturated soil zone. Pedosphere. 17(3): 366-372.
INTRODUCTION Soils can be contaminated by a variety of pollutants (Chen et al., 2003). During the past decade, the widespread production and use of industrial solvents and liquid petroleum products have provided the ample opportunity for subsurface contamination (Liu et at., 2005). The impetus to understand and manage the unsaturated zone stems from its recognition as a key factor in the improvement and protection of the quality of groundwater supplies. The unsaturated zone links surface water and groundwater; therefore, investigation of the migration of contaminants in the unsaturated zone is very important. Some soluble organic chemicals such as methyl tert-butyl ether (MTBE), methanol, and phenol have been increasingly contributing to groundwater contamination. Direct exposure of human and ecological receptors to contaminants present in the soil may also occur via inhalation of toxic solutes as they volatilize from the soil, through dermal absorption due to contact the soil, and from ingestion of soil particles. Methanol is a clear, colorless, volatile liquid with a weak odor and is slightly sweeter than ethanol. It is used in the industrial production of many synthetic organic compounds and is a constituent of a large number of commercially available solvents. Methanol is soluble in water, and this characteristic makes it highly mobile in a groundwater system. Methanol is also a toxic liquid and has been shown to cause headache, vomiting, nausea, dyspnea, and poor eyesight following contact the vapor or liquid. Accidental or suicidal ingestion can cause severe metabolic acidosis and clinical disturbances, such as blindness, permanent neurological dysfunction, and even death (Kuteifan et al., 1998). 'lProject supported by the National Natural Science Foundation of China (No. 20276048). *2Corresponding author. E-mail: hgqQtju,edu.cn.
MIGRATION OF METHANOL IN SOIL
367
Given the growing concern over the environmental impacts of contaminants in the soil, a number of different, deterministic transport models have been proposed over the last several decades to describe the movement of chemical contaminants in the vadose zone. Most of these models were used to describe the transport of soluble solutes (Bresler, 1973; Nielsen et al., 1986), and some models were developed for the transport of pesticides (Ren and Mao, 2003; Mao and Ren, 2005). Warrick et al. (1971), Kirda et al. (1973), Kelleners et al. (1999) and Li and Hu (2004) investigated the interactions between solute and water movement. The purpose of the present study was to present a model to simulate the transport of soluble organic chemicals (using methanol) and water flow in the unsaturated soil zone. As climatic conditions are very important factors in the movement of soil water, the effects of rainfall and evapotranspiration on transport were also considered.
MODEL DEVELOPMENT AND APPLICATION The theory developed in this study described the one-dimensional simultaneous transport of water and methanol in the unsaturated soil zone. Some general assumptions in the study were: the soil domain was considered to be isothermal; the soil media were rigid; hysteresis of the retention curve or the water transport coefficients was neglected; the transfer of mass occurred only in one-dimension vertically; no free-phase of solution was present in the soil; the solute was not completely restricted by the soil matrix; and the degradation of methanol in soil was not considered.
Solute transport The governing solute transport in gas, liquid, and solid phases are described, respectively, by the following equations (Huang et at., 2004; Liu and Li, 2004):
where G, C, and S are solute concentrations in the gas, liquid, and solid phases, respectively; eg is the air content; Dg is the diffusion coefficient tensor for the gas phase; z is the vertical coordinate with the origin at the soil surface (positive downward); I is the mass transport between two different phases with Igw I,, ISw Isg I,, I, = 0; the subscripts g, w, and s correspond with the gas, liquid, and solid phases, respectively; Ow is the volumetric water content; D, is the dispersion coefficient tensor for the liquid phase; q is the volumetric flux density; and Pb is the soil bulk density. Combining Eqs. I, 2 , and 3 yields the overall flux equation for methanol in the soil:
+ +
+ +
+
Mass partitioning occurs between two individual phases, named liquid/solid, vapor/liquid, and vapor/solid. A thin film of water covering soil grains is assumed (Silka, 1988), so the solute transport between vapor and solid phases can be omitted. Chemical equilibriums between the vapor/liquid and liquid/solid phases are linear and described, respectively, as follows:
where H is Henry’s law constant, and Kd is the linear adsorption coefficient between the solid and liquid
H. LI
368
phases. Assuming that soil porosity, pi, is time-invariant and that pi = Ow
et al.
+ O,, it then follows that
og = 9 - ow
(7)
Substituting the partitioning coefficients and Eq. 7 into Eq. 4, the following is obtained:
The law of Darcy describes the transport of liquid water through a porous medium in the vertical direction as: 4 = - q
d(h- z ) dz
]
(9)
where K is hydraulic conductivity, h is the pressure head, and z is the vertical coordinate. In the present study, the chemical surface volatilization flux was neglected, so the boundary conditions of solute transport at the soil surface were given by:
In all the simulations, an adequate depth of soil was selected to ensure that the chemical concentration front did not reach the lower boundary (I), which was conveniently set as:
dC -=Oatz=l
at
Accordingly, the initial conditions of moisture and solute distribution were set as:
C(t = 0 , z ) = Co(z)at z # 0
(12)
ew(t= 0,
(13)
= ew,o(z)
Water flow The isothermal Darcian flow of water in a variably saturated porous medium is described with the continuity equation:
Substituting Eq. 9 into Eq. 14, one-dimensional, vertical, transient, and unsaturated flow is described with Richard's equation (Bear, 1972): -=--
dt
a dt
k K az "'1
(15)
-
In this study, the soil hydraulic properties were described with the Mualem-van Genuchten model (Mualem, 1976; van Genuchten, 1980):
K ( O ) = K,@V[l- (1 - 01/"1
1'
(17)
where 0 = (6, - O w , ) / ( ~ w , - Owr) (Ow, is the residual volumetric water content, Ow, is the saturated volumetric water content); m = 1- l / n ; a , n, and 7 are empirical parameters, and K, is the saturated hydraulic conductivity.
369
MIGRATION OF METHANOL IN SOIL
On the soil surface, in the absence of surface ponding, the absolute value of the flux q should satisfy the following two conditions:
1
dh
IQI = - K (-a2
- 2)
IL
hA 5 h 5 h, where E is the maximum potential rate of infiltration or evapotranspiration under the current atmospheric conditions; h is the pressure head at the soil surface; and hA and h, are, respectively, minimum and maximum pressure heads allowed under the prevailing soil conditions. The value for h~ is determined from the equilibrium conditions between soil water and atmospheric water vapor, whereas h, is usually set equal to zero. When one of the end points of Eq. 19 is reached, the prescribed head boundary condition will be used to calculate the actual surface flux. At the soil surface, the water velocity can be set equal to rainfall infiltration velocity under nonponding conditions, and it is set equal to unsaturated hydraulic conductivity when ponding conditions are reached. However, during periods without rainfall, the water velocity at the soil surface is set equal to the evapotranspiration velocity.
Coupled solute transfer and water flow Two partial differential equations (Eqs. 8 and 15) have been introduced. The two equations describe simultaneous water and solute concentration distribution in the unsaturated soil zone. The Galerkin finite element method with linear basis functions was used to obtain a solution of the two flow equations subjected to the imposed initial and boundary conditions. The HYDRUS-2D software developed by the International Ground Water Modeling Center was applied here to help with the calculation of the results.
Application of the model In this study, an unsaturated modeling soil zone was introduced. In the simulation, methanol was chosen as the solute, and the results were compared with those obtained by Grifoll and Cohen (1996). The depth of the modeling domain was 250 cm, and the total modeling time was 365 days. The soil selected for this simulation was a loam soil, and the hydraulic parameters required in modeling are given in Table I (Grifoll and Cohen, 1996). The pertinent physicochemical properties at 20 " C for methanol (Grifoll and Cohen, 1996) are given in Table 11. TABLE I Water flow-soil hydraulic parametersa) required in the methanol transfer and water flow model
ews
n
a
owr
1.43
cm-l 0.043
__ ~ r n 3 c m - ~ __ 0.022 0.35
K S
?)
Pb
cm h-l 0.75
0.5
g cm-3 1.27
a)Cited from Grifoll and Cohen (1996). n, a, and 11 are empirical parameters; Ow, is the residual volumetric water content; Ow, is the saturated volumetric water content; K8 is the saturated hydraulic conductivity; and Pb is the soil bulk density.
TABLE I1 Physicochemical properties") of methanol a t 20 "C Dair
Kd
H
Dwater cm2 h-l
5.76 x 10'
5.04 x
lo-'
1.8 x 1 0 - ~
1.9 x 1 0 - ~ ~
~~
~
~
~~~~
")Cited from Grifoll and Cohen (1996). D,,, is the molecular diffusion in air; Dwateris the molecular diffusion in water; H is dimensionless Henry's law coefficient; and Kd is solid/water partition coefficient.
H. LI et al.
3 70
To illustrate the effects of rainfall and evapotranspiration on pollutant transport in the vadose zone, a pattern mimicking the distribution of rainfall and evapotranspiration in southern California, USA (Fig. 1) was selected (Ruffner and Bair, 1987; Grifoll and Cohen, 1996). 6.0
a,
I
0
1
2
3
4
+-
m
L
C
.o_ 7 VJ
4.0
.L E Q..
20
r
Ix 2.0
4
-
v
0 Q
m >
w 5
6
7
8
o
0 Time (x 1O'h)
1
2
3
4
5
6
7
8
Fig. 1 Precipitation rates and evapotranspiration rates data set in southern California, USA (Grifoll and Cohen, 1996).
RESULTS AND DISCUSSION The soil zone was initially contaminated to a depth of 50 cm, and the values of concentration were assumed to be the same. The beginning of the simulation was set at t = 0 h. Comparing the simulation results of methanol dimensionless concentration, which represented the ratio of the calculated methanol concentration to the initial concentration, at t = 500 h with those of Grifoll and Cohen (1996), the modeling was satisfactory and reliable, as shown in Fig. 2.
0.2 0
0
20
40 60 80 Depth (cm)
100
120
Fig. 2 Comparison of the methanol dimensionless Concentration (MDC) profile of the simulation by the methanol transfer and water flow model at t = 500 h with the results of Grifoll and Cohen (1996). MDC is the ratio of the calculated methanol concentration to the initial concentration.
Based on the simulation results, water content (Fig. 3a) and the dimensionless concentrations of methanol (Fig.3b) considering the effects of rainfall and evapotranspiration in the soil at t = 0, 500, 2 000, 4 000, and 8 760 h were depicted. To determine the effects of rainfall and evapotranspiration on methanol solute transport in the soil, a contrast simulation was made, where the rate of rainfall and evapotranspiration was set to zero. The results of this scenario are shown in Fig. 3c. Soil moisture played an important role in solute transport in soil. As shown in Fig. 3a, the water content profile varied at different times under the rainfall and evapotranspiration conditions. The simulation results showed that the water content of the soil near the surface fluctuated considerably. When it was rainy, the water content increased quickly, then the water content fell gradually because of both water infiltration and evapotranspiration. From the comparisons of Figs. 3b and 3c, the effects of rainfall and evapotranspiration on methanol transport in unsaturated zone were notable. As shown in Fig. 3b, after 4000 h the depth of methanol
371
MIGRAT’ION OF METHANOL IN SOIL
1 .o
70.30
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’ n
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t=Qh t=500h t = 2000 h f = 4000 h t = 8760 h
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$ 0.06 Y
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50 100 150 200 250
50 100 150 200 250 Depth (cm)
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Fig. 3 Water content profiles considering the effects of rainfall and evapotranspiration (a) and methanol dimensionless concentration (MDC) profiles with (b) and without (c) considering the effects of rainfall and evapotranspiration. MDC is the ratio of the calculated methanol concentration to the initial concentration.
contamination reached about 220 cm, whereas if rainfall and evapotranspiration were not considered, the depth was only about 120 cm (Fig. 3c). Because of its solubility, methanol traveled quickly down the soil profile along with water infiltration, especially during the rainy season. Under rainy conditions, the water content in the unsaturated soil zone increased and accordingly the liquid convection of the solute was prominent due to the infiltration of rainwater, However, in the dry season, methanol transport in soil depended mainly on diffusion. This was shown from a comparison of the methanol dimensionless concentration profiles at a depth of 25 cm under different simulation conditions (Fig. 4).
0
2
4 6 Time (x 10’ h)
8
0
Considering the effect of rainfall and evapotranspiration
*
Without considering the effect of rainfall and evapotranspiration
10
Fig. 4 Methanol dimensionless concentration (MDC) profiles a t a depth of 25 cm with/without considering the effects of rainfall and evapotranspiration. MDC is the ratio of the calculated methanol concentration to the initial concentration.
CONCLUSIONS A combined model of solute transport and water flow was developed to investigate soluble organic chemical (methanol) transport in the unsaturated soil zone. The potential effects of rainfall and evapotranspiration on contaminant migration were studied by considering the boundary conditions of the governing equations. The results proved t o be consistent with those of earlier studies, so in the future this model could be used t o analyze the results from field investigations.
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