Environmental Engineering Reference
In-Depth Information
Sorption isotherms can be fitted by different formulas [DEL 99, HIL 98, MUS
91] among which the three following are the more common:
- the “GAB” formula, from the names of its inventors Guggenheim, Anderson,
Beboer, results from absorption theory:
φ
θ
=
[9.15]
2
a
φ
+
b
φ
+
c
where
a
,
b
and
c
are constants to be fitted;
- the “Brooks and Corey” relation (1964):
b
θ
−
θ
h
⎛
⎞
r
e
S
=
=
[9.16]
⎜
⎝
⎟
⎠
e
θ
−
θ
h
sat
r
where:
θ
r
: residual water content corresponding to
S
r
(see section 9.2.1.1),
θ
sat
: saturated water content, normally equal to porosity,
h
e
: air intake potential (suction scale factor), and
b
: an exponent to be fitted (shape factor);
- the “Van Genuchten” relation (1980):
−
m
⎡
n
⎤
⎛
⎞
h
⎢
⎜
⎜
⎝
⎟
⎟
⎠
⎥
S
= 1
+
[9.17]
e
⎢
⎥
h
g
⎣
⎦
where:
h
g
: suction scale factor, and
n, m
: two shape factors.
Equations [9.16] and [9.17] have no real physical significance and they were
developed to reproduce the “S-shape” that can be usually observed on the sorption
isotherms of porous media such as stone. They are also very useful for interpolating
between experimental points, always scarce, or for other calculations (see section
9.3.2).
