Mobile, Immobile, and Multiflow Domain Approaches - Transport and Fate of Chemicals in Soils: Principles and Applications - page 275

proposed second-order mechanism. Specifically, the influence of κ 1 and κ 2 ,
and ω on solute retention were examined. Other parameters such as D and v
have been rigorously examined in earlier studies (Coats and Smith, 1964; van
Genuchten and Wierenga, 1976).
For the simulations shown in Figures 8.2 to 8.6, initial conditions, volume
of input pulse, and model parameters were identical to those used previ-
ously for the second-order two-site model, where C i = S i = 0 within the mobile
and immobile regions. Specifically, the parameters chosen were: L = 10 cm, D
= 1 cm 2 h -1 , ρ = 1.2 g cm -3 , f = 0.50, Θ = 0.40 cm 3 cm -3 , μ = Θ m /Θ = 0.5, C o = 100
mg L -1 , and a Peclet number P = 25. Moreover, unless otherwise stated, the
values selected for the dimensionless parameters κ 1 , κ 2 , κ s , Ω, were 1, 1, 0, 5,
and 1, respectively. It is assumed a solute pulse was applied to a fully water-
saturated soil column initially devoid of a particular heavy metal of interest.
In addition, a steady water flow velocity ( v ) was maintained constant with a
Peclet number P of 25. The length of the pulse was assumed to be three pore
volumes, which was then followed by several pore volumes of metal-free
solution.
The influence of the reaction rate coefficients on the shape of the BTCs
is illustrated in Figure 8.9. Here the values of κ 1 and κ 2 were varied simul-
taneously provided that κ 1 /κ 2 (and ω 1 and ω 2 ) remained invariant. For the
nonreactive case (κ 1 = κ 2 = 0), the highest effluent peak concentration and
least tailing was observed. As the rate of reactions increased simultaneously,
solute peak concentrations decreased and excessive tailing of the BTCs was
observed. However, the arrival time or the location of peak concentration
was not influenced by increasing the rates of reactions.
The effect of increasing values of the equilibrium constant ω, which rep-
resents the ratio κ 1 /κ 2 , on the shape of BTCs is shown in Figure 8.3. Here a
constant value for κ 2 of 1 was chosen, whereas κ 1 was allowed to vary. For
all BTCs shown in Figure 8.10, the values of ω 1 and ω 2 were equal (since μ =
0.5). As a result we refer to simply ω rather than ω 1 and ω 2 . The results indi-
cate that as the forward rate of reaction (κ 1 ) increased, an increase in solute
retardation or a right shift of the BTCs was observed. This shift of the BTCs
was accompanied by an increase in solute retention (i.e., a decrease of the
amount of solute in the effluent, based on the area under the curve) and a
lowering of peak concentrations. Similar behavior was observed for the influ-
ence of the dimensionless transfer coefficient ω on the shape of the BTCs as
may be seen from the BTCs in Figure 8.4. For exceedingly large values (>2),
the diffusion between the mobile and immobile phases became more rapid.
Therefore, equilibrium condition between the two phases is nearly attained
(Valocchi, 1985).
Figure 8.12 shows BTCs of a reactive solute for several values of Ω. The
figure indicates that the shape of the BTCs is influenced drastically by the
value of Ω. This is largely due to the nonlinearity of the proposed second-
order retention mechanism. As given by Equation 8.25, Ω represents the ratio
of total sites ( S max ) to input (pulse) solute concentration ( C o ). Therefore, for