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tracers were used showed the significance of diffusion during solute trans-
port in aggregated media.
The mobile-immobile approach described above, which is commonly
referred to as the two-region model, is regarded as a mechanistic approach
where physical nonequilibrium causes solute transfer between regions. Flow
interruption can be accounted for in the above formulation by simply assum-
ing the flux
v
as zero and
D
=
D
o
during interruption, where
D
o
is the effec-
tive molecular diffusion coefficient. As a result, Equation 8.1 is reduced to the
commonly known diffusion equation:
2
∂
∂
m
m
C
t
∂
∂
C
x
m
=
Θ
m
D
−α
(
mim
−
)
Θ
CC
(8.20)
o
2
Therefore, during flow interruption, we assume that transport of nonre-
active solutes can be described by molecular diffusion within the mobile
water phase. Thus, during flow interruption, the exchange of solute between
mobile and immobile phases is assumed to follow the simple mass transfer
in Equation (8.20).
The examples presented here to illustrate physical nonequilibria are those
of the work of Reedy et al. (1996) where transport of the nonreactive tracer
bromide (Br) in packed columns was investigated. Reedy et al. (1996) car-
ried out a series of experiments to examine the time dependency of the
diffusive mass transfer process by imposing flow interruptions of increas-
ing duration (0.25 to 7 d) on tracer experiments conducted at similar fluxes
(Figure 8.6). Stop flow or simply flow interruption during tracer pulse appli-
cation resulted in decreased Br concentrations, whereas flow interruption
during tracer leaching or displacement resulted in increased Br concentra-
tions when flow was reinitiated (Figure 8.6). These observed concentration
perturbations resulting from flow interruption are indicative of solute diffu-
sion between the two regions (fracture and matrix) of the porous medium.
Conditions of preferential flow create concentration gradients between
pore domains, resulting in diffusive mass transfer between the regions.
Concentration perturbations observed in Figure 8.6 were driven by solute
concentration gradients established between pore regions, that is, physical
nonequilibria. Upon stop flow, the decrease in relative concentration indi-
cates that solute diffusion is occurring from the larger, more conductive
pores, into the smaller pores. During tracer displacement or leaching, Br
concentrations within the preferred flow paths are lower than those within
the matrix. The relative concentration increase after the second interruption
indicates solute diffusion from smaller pore regions back into larger pore
regions (Figure 8.6).
The extent of concentration perturbations can be observed in the Br BTC
with increased interruption time. As the duration of stop flow increased,
the concentration perturbation increased, which suggests that the diffusive
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