Kouli_etal_2008_Groundwater modelling_BOOK.pdf - Pantelis ...

94
Sabrina Saponaro, Sara Puricelli, Elena Sezenna et al.
k
rl
=
S
ls
1
− S
lr
Slr
Sl
−
S − S
ls
lr
(31)
k
rg
1
= 1
S − S
gs
gr
( − S )
l
Sgr
−
S − S
gs
gr
(32)
where k rl increases linearly from 0 to 1 in the range S lr ≤ S l ≤ S ls , and k rg increases linearly
from 0 to 1 in the range 1 - S ls ≤ 1 - S l ≤ 1 - S lr .
Another set of linear functions that TOUGH2 can manage is:
krl
krl
0
= S
(33)
l
k = 1
(34)
rg
where k rl0 has a constant value.
Corey’s curves
Corey’s curves can be written as follows (Corey, 1986):
k
rg
( S ) 4
krl =
el
(35)
2
( )
( − S ) 2 1−
( S )
1
el
el
= (36)
Grant’s curves
Grant (1977) reports k rl as in Corey's model, whereas k rg is calculated according to:
Functions of Fatt and Klikoff
These expressions are reported in Fatt et al. (1959):
k rg = 1 − k rl (37)
( S ) 3
krl =
el
(38)
k
rg
( − S ) 3
1
el
= (39)
where S el is calculated by Eq. (22) with S ls = 1.
van Genuchten – Mualem model
van Genuchten (1980) reported the following relationship between k rl and h:
n−1
n m
{ 1−
( αh)
[ 1+
( αh)
] }
krl
( h)
=
m
n / 2
[ 1+
( αh)
]
(40)