It is necessary to select the length of individual sections and the corresponding
flow rate of the suspension before constructing the cascade column. If the transport
velocity in the homogeneous isotropic environment decreases with the inverted
value of the diameter, then we can use a relationship for the velocity v, at a distance
r from the injection well axis, where v p is the velocity on the well surface and r p is the
well diameter (Eq. 30.7):
v ¼
v p Á r p
r
ð30:7Þ
Since the flow rate is constant throughout each section of the column, it is
necessary to choose the method of calculating this velocity for the most appropriate
approximation of the real curve. To accurately define the flow rate of the suspension
through the calculated section of the column that corresponds to a real section of the
collector, the velocity in a given section of the column (v 1,2 ) is defined by the
velocity at the beginning (v 1 ) and at the end (v 2 ) of each section (Eq. 30.8):
v 1, 2 ¼
2
1
v 1
þ
1
v 2
ð30:8Þ
Equation 30.8 corresponds to the equation for the harmonic average.
The fundamental part of the cascade column consists of a selected poly(methyl
methacrylate) column having an outer diameter of 70 mm and a wall thickness of
4 mm (Fig. 30.6). The actual measurement of the nZVI content is performed by the
device described in the previous section with an internal diameter of the detector
corresponding to the diameter of the cascade column. An inner tube (d ¼ 20 mm)
serves as a technical channel for the inlet and outlet of the suspension that is pumped
into the column through a series of thin tubes (Fig. 30.6a). Importantly, the nZVI in
the suspension flowing through the thin tubes may contribute to the overall signal.
However, this can be ignored because (i) the diameter of the tubes is considerably
smaller than the diameter of the column, (ii) the concentration of nZVI in the
suspension at a specific site is always lower than its concentration in the porous
water, and (iii) the tubes are near the detector axis and the sensitivity of the detector
around the axis is considerably smaller than near the coil.
Mobility of nZVI particles (type NANOFER 25) can serve as an example
experiment (Fig. 30.6b). The column was filled with quartz sand with a grain size
of 1 mm. The suspension of nZVI particles NANOFER 25 (20 g/L) with carboxymethylcellulose (10 g/L) was dosed for more than 8 h using a pressure pump. As a
starting point, the migration rate in the theoretical well was presumed to be 100 m/
24 h and the diameter of the well was 10 cm. The boundaries of the column sections
were set to 21.3 cm, 31.3 cm, 67.2 cm, and 185 cm from the beginning of the
column, these values correspond to a flow rate of 32 m/24 h, 16 m/24 h, 9.22 m/24 h,
and 3.89 m/24 h.
614
P. Parma et al.
flow rate of the suspension before constructing the cascade column. If the transport
velocity in the homogeneous isotropic environment decreases with the inverted
value of the diameter, then we can use a relationship for the velocity v, at a distance
r from the injection well axis, where v p is the velocity on the well surface and r p is the
well diameter (Eq. 30.7):
v ¼
v p Á r p
r
ð30:7Þ
Since the flow rate is constant throughout each section of the column, it is
necessary to choose the method of calculating this velocity for the most appropriate
approximation of the real curve. To accurately define the flow rate of the suspension
through the calculated section of the column that corresponds to a real section of the
collector, the velocity in a given section of the column (v 1,2 ) is defined by the
velocity at the beginning (v 1 ) and at the end (v 2 ) of each section (Eq. 30.8):
v 1, 2 ¼
2
1
v 1
þ
1
v 2
ð30:8Þ
Equation 30.8 corresponds to the equation for the harmonic average.
The fundamental part of the cascade column consists of a selected poly(methyl
methacrylate) column having an outer diameter of 70 mm and a wall thickness of
4 mm (Fig. 30.6). The actual measurement of the nZVI content is performed by the
device described in the previous section with an internal diameter of the detector
corresponding to the diameter of the cascade column. An inner tube (d ¼ 20 mm)
serves as a technical channel for the inlet and outlet of the suspension that is pumped
into the column through a series of thin tubes (Fig. 30.6a). Importantly, the nZVI in
the suspension flowing through the thin tubes may contribute to the overall signal.
However, this can be ignored because (i) the diameter of the tubes is considerably
smaller than the diameter of the column, (ii) the concentration of nZVI in the
suspension at a specific site is always lower than its concentration in the porous
water, and (iii) the tubes are near the detector axis and the sensitivity of the detector
around the axis is considerably smaller than near the coil.
Mobility of nZVI particles (type NANOFER 25) can serve as an example
experiment (Fig. 30.6b). The column was filled with quartz sand with a grain size
of 1 mm. The suspension of nZVI particles NANOFER 25 (20 g/L) with carboxymethylcellulose (10 g/L) was dosed for more than 8 h using a pressure pump. As a
starting point, the migration rate in the theoretical well was presumed to be 100 m/
24 h and the diameter of the well was 10 cm. The boundaries of the column sections
were set to 21.3 cm, 31.3 cm, 67.2 cm, and 185 cm from the beginning of the
column, these values correspond to a flow rate of 32 m/24 h, 16 m/24 h, 9.22 m/24 h,
and 3.89 m/24 h.
614
P. Parma et al.