Environmental Engineering Reference
In-Depth Information
the Langmuir isotherm is similar to the linear Freun-
dlich isotherm, with F linearly proportional to c aq , while
at high concentrations , when K 1 c aq ≪>> 1, F approaches
the limiting value of S . Despite the apparent advan-
tages of using the Langmuir isotherm, the linear Freun-
dlich isotherm remains the most widely used.
In applying linear isotherms such as Equation (5.44),
care should be taken since the actual isotherm is usually
piecewise linear , and therefore extrapolation beyond the
range of experimental conditions used to estimate K d
is not recommended. Values of K d in Equation (5.44)
range from near zero to 10 3 cm 3 /g or greater.
In the case of organic compounds, the mass of the
organic compound sorbed per unit mass of solid matrix
has been observed to depend primarily on the amount
of organic carbon in the solid matrix, and it is more
appropriate to deal with the organic carbon sorption
coefficient K oc , which is defined as the ratio of sorbed
mass of organic compound per unit mass of organic
carbon to the aqueous concentration. Therefore, the dis-
tribution coefficient, K d , is related to the organic carbon
sorption coefficient, K oc , by
0.1% (Banerjee et al., 1985; Schwarzenbach and Westall,
1981), and values of K oc for several organic compounds
typically found in contaminated groundwater are given
in Appendix B.2. When the organic fraction is less than
0.1%, sorption of organic compounds on nonorganic
solids can become significant, and it is not automatic
that the soil or aquifer organic carbon will be the
primary surface onto which the organic compounds will
partition. The octanol-water partition coefficient, K ow , is
a widely available and easily measured parameter that
gives the relative concentrations of various substances
between n -octanol and water in contact with each other.
The octanol-water partition coefficient is defined by
c
c
o
K
=
(5.47)
ow
w
where c o is the concentration in the octanol and c w is the
concentration in the water. Octanol serves as a general-
ized surrogate for organic media, and the reason for
using octanol is historical: During the early years of
pharmaceutical research, researchers found that octanol
served as an inexpensive surrogate for human tissue,
and, as a result, pharmaceutical studies often involved
partitioning tests using octanol as an index for drug
uptake by organisms. K ow is now commonly reported for
most synthetic organic chemicals. Studies with a variety
of organic contaminants have generally shown a linear
relationship between log K oc and log K ow , with nonlin-
earities caused by sorption to the mineral portion of
soils. Several proposed empirical relationships are
shown in Table 5.7, where K oc is in cm 3 /g and K ow is
dimensionless. Clearly, there is no universal relation
for deriving K oc from the more easily measured K ow ,
although estimates of K oc derived using equations in
Table 5.7 are likely to fall within one standard deviation
of the geometric mean of K oc estimated from the com-
bined predictions of all the equations listed in Table 5.7.
Values of log K ow for selected organic compounds are
listed in Table 5.8, and it is best to estimate K oc from
these values using an empirical relation derived for
similar chemicals. Values of K ow range over many orders
of magnitude (typically, 10 1 -10 7 ), and therefore K ow is
usually reported as log K ow (typically, 1-7). The higher
the value of K ow , the greater the tendency of the com-
pound to partition from the water into the organic
phase.
The amount of sorbed mass per unit volume of the
porous medium, c s (mL −3 ), is related to the mass of
tracer sorbed per unit mass of solid phase, F (mm −1 ), by
the expression
K
=
f K
(5.46)
d
oc
oc
where f oc is the fraction of organic carbon in the porous
medium (mm −1 ). Values of f oc are typically in the range
of 0.02-3%, and suggested values of f oc for several
soil textures are given in Table 5.6. The mass fraction
of natural organic material in soil can be represented
using two different notations: f om represents the mass
fraction of organic matter present in the soil, and f oc
represents the mass fraction of organic carbon in soil.
mass fraction f om considers the mass of the entire organic
molecule, while f oc considers only the mass of carbon
present in the organic matter. Using the rule of thumb
that the weight of organic matter is roughly double the
weight of organic carbon, a useful approximation is
f om ≈ 2 f oc .
The formulation described by Equation (5.46) is
appropriate whenever the organic fraction exceeds
TABLE 5.6.  Typical Values of Carbon Content in Soils
Soil
f oc
Silty clay
0.01-0.16
Sandy loam
0.10
Silty loam
0.01-0.02
Unstratified silts, sands, gravels
0.001-0.006
medium to fine sand
0.0002
Sand
0.0003-0.10
Sand and gravel
0.00008-0.0075
Coarse gravel
0.0011
c
= ρ
F
(5.48)
Source of data : Prakash (2004).
s
b
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