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208 Chapter Six

which reduces to: where R is known as the retardation factor, K is the
d d
partition or distribution coefficient with units of mL
−1
⎡ 019 ⎤ g (the reciprocal of density), ρ is the solid mass dens-
s
.
=
062. erfc ⎢ ⎥ eq. 6.11 ity of the sorbing material and θ is the moisture con-
⎢ 2 α ⎥ tent of the unsaturated or saturated porous material.
.
⎣ l 0 21 ⎦
Below the water table, θ equates to the porosity and
recognizing that (1 − n) ρ equates to the bulk density,
From Appendix 8, a value of β = 0.35 produces a s
ρ , equation 6.13 can be written as:
erfc[β] = 0.62, hence: b
ρ

1
⎡ ⎤ R =+ K d b eq. 6.14
d
.
035. ⎢ 019 ⎥ eq. 6.12 n
=
⎢ 2 α ⎥
.
⎣ l 0 21 ⎦ Bouwer (1991) presented a simple derivation of the
retardation equation and also demonstrated applica-
Rearranging and solving for the longitudinal dispersiv- tions describing preferential contaminant movement
ity results in a calculated value for α = 0.35 m or 35 cm. through macropores (see Section 5.4.3) and the shape
1
of the concentration breakthrough curve for macro-
dispersion caused by layered heterogeneity (Box 6.2).
6.3.2 Transport of reactive dissolved Limitations of the equation are that it assumes ideal,
contaminants instantaneous sorption and equilibrium between the
chemical sorbed and that remaining in solution.
Reactive substances behave similarly to conservative The dimensionless retardation factor, R , is a meas-
d
solute species, but can also undergo a change in con- ure of the attenuated transport of a reactive contam-
centration resulting from chemical reactions that inant species compared to the advective behaviour
take place either in the aqueous phase or as a result of groundwater. As such, the retardation factor can
of adsorption of the solute to the solid matrix of soil, be expressed in three ways as follows:
sediment or rock. The chemical and biochemical
reactions that can alter contaminant concentrations V w l w t c
R = = = eq. 6.15
in groundwater are acid–base reactions, solution– d V l t
c c w
precipitation reactions, oxidation–reduction reactions,
ion pairing or complexation, microbiological processes where the subscripts and indicate the water and
w c
and radioactive decay. Discussion of a number of these dissolved contaminant species, respectively, V is the
processes is included in Chapter 3 in relation to natu- average linear velocity, l is the distance travelled by
ral groundwater chemistry and can be equally applied the water or the central mass of a contaminant plume
to the fate of dissolved contaminants. and t is the arrival time of the water or the midpoint
One important type of process affecting the trans- of a contaminant breakthrough curve.
port of reactive dissolved contaminants is sorption. With knowledge of the rate of movement of a non-
Sorption processes such as adsorption and the parti- reactive tracer such as chloride representing the unat-
tioning of contaminants between aqueous and solid tenuated flow of water by advection and dispersion,
phases attenuate, or retard, dissolved solutes in the time axis of a contaminant breakthrough curve
groundwater and are of special relevance to the trans- can be transformed to a dimensionless time, t/t ,
tracer
port of organic contaminants, particularly hydro- where t is the breakthrough time of the tracer.
tracer
phobic compounds. Alternatively, the time axis can be written as the
Attenuation due to sorption can be described by number of pore water flushes (V/V , the ratio of feed
P
the retardation equation, as follows: volume, V, to pore volume, V ). In doing so, the retar-
P
dation factor can be read directly from the dimension-
−
( n)ρ less breakthrough time of contaminant at C/C = 0.5.
1
1

R =+ K d s eq. 6.13 0
d
θ Examples of laboratory column breakthrough curves