poster - International Conference of Agricultural Engineering

R
f
C
t
D
L
2
C
V
2
x
w
C
x
(9)
where
C : concentration of the dissolved chemical species (contaminant)
R : retardation factor ( ( K / ) )
f
1
d e
: bulk density of the soil,
e
: effective porosity of the soil
K : distribution coefficient of the soil ( K )
d
oc
foc
K
oc
: organic carbon partition coefficient,
oc
*
D : longitudinal dispersion coefficient ( V D / )
L
L
: longitudinal dispersivity,
c
w
f
L
V V / R ,
f : fraction of organic carbon content
c
e
*
D : diffusion coefficient
V
w
: pore water velocity in the x-direction ( ( K / e
) /( dh / dx)
)
K : hydraulic conductivity, dh / dx : hydraulic gradient
Analytical solution to the governing equation can be written as:
x V t V x x V t
c
c
c
C x t C erfc
erfc
( , ) 0.5
0
exp
t T
D t
D
, 0 (10)
L L DLt
4
4
where and T is a period of injection. In this paper, Benzene is considered as contaminant.
Model parameters of contaminant Benzene are given in Table 1 and 2.
TABLE 1: The deterministic parameters of Benzene
C
0
Chemical
*
dh / dx D
L
species (mg/L) (g/cm 3 ) (m/m) (m 2 /s) (%) (%) (m)
Benzene 100 1.8 -0.008 0 1.6 25 5.0
f
oc
e
Chemical
species
TABLE 2: The uncertainty parameters of Benzene
K
Mean (cm/s)
Standard
Mean (cm 3 /g)
deviation
Benzene 0.001 0.0002 58.9 5.0
K
oc
Standard
deviation
4. Results and Discussions
The 50 samples of random variables are generated by combining of three different
distributions (Normal, Log-Normal and Uniform). If sample size of a random variable is small,
it is impossible to estimate the exact PDF. In order to compare results from using probability
distributions by Hermite polynomials and results from using estimated well-known PDF, Chisquare
goodness-of-fit test is performed for generated samples of K and K . The results
oc