Underground Infrastructure - February 2023 - 33

cleaning effi ciency for smart spacer fl uid (Vipulanandan
Cleaning Effi ciency model) is given as follows:
CE(%)=
τmax
E + F × τmax
(7)
where CE (%) = Cleaning effi ciency in percentage, τmax
=
Maximum Shear Stress capacity of the spacer fl uid (Pa), and E
and F are the model parameters.
Piezoresistivity of the slurry is modeled using the Vipulanandan
Correlation model and the relationship is as follows:
Δρ
ρo
=
where (Δρ/ρo
p
J + K × p
applied, J and K are the model parameters.
Results and Discussion
Spacer fl uid applications require the materials to be multifunctional.
Hence, the spacer fl uid must be modifi ed or treated to
enhance the diff erent properties, such as density, rheology,
cleaning effi ciency, and sensitivity.
In this study, the water-based spacer fl uid was modifi ed with
nanoFe2O3 for insitu sensing, property modifi cations, and to
investigate the eff ect of magnetic fi eld and temperature on the
sensing property.
It is important to identify the critical electrical property that
can be used to monitor the spacer fl uids in the fi eld during various
applications. Th e electrical impedance-frequency response
using the two probes and alternative current (AC), coupled with
the Vipulanandan Impedance Model, was used to identify critical
electrical property, such as inductance, capacitance (permitt ivity),
resistance (resistivity) or a combination for the spacer fl uids.
Identifi cation of the most-appropriate equivalent circuit to
represent the two-probe contacts and the electrical properties
of the testing material, is essential to further understand
its properties. In this study, an equivalent circuit to represent
the smart spacer fl uid was required for bett er characterization
through the analyses of the Impedance Spetroscopy (IS) data.
Based on the testing results in this study, the typical impedance-frequency
response and the equivalent electrical circuit
are shown in FIGURE 1, which includes the two contacts and
the bulk material (smart space fl uid). Th is is also referenced as
CASE 2-Reisitance Only, in the following.
Th e total impedance of the equivalent circuit for CASE-2
(Z2
) is as follows:
Z2 σ( ) = Rb σ( ) +
= R2 + j X2
Th e term R2
pedance (Zreal
impedance (Z2
of Z2) and X2
2Rc σ( )
1 + ω2Rc
2Cc
2 − j
2ωRc
1 + ω2Rc
2Cc σ( )
2Cc
2
(9)
(10)
in Eqn. (3) represents the real part of the imrepresents
the imaginary part of the
). When the frequency of the applied signal was
FIGURE 1: Typical impedance-frequency response and the equivalent
electrical circuit, representing the smart spacer fluid, with two- probe
monitoring
UndergroundInfrastructure.com | FEBRUARY 2023 33
(8)
) is the change in bulk resistivity, p is the pressure
very low, ω → 0, Z2
ω → ∞, Z2
= R2
= Rb
= R2
, X2
= Rb
+ 2Rc
CIGMAT Report
, and when it was very high,
will be equal to zero.
In CASE-2, if the impedance is measured at very high frequency,
it will measure the resistance (Rb
) in the material and
eliminate the eff ects of the contacts; it is also frequency independent.
Th is becomes another unique advancement in measurement
and monitoring, since the resistance is independent
of the very high frequency of measurement.
Also, changing spacer fl uid conditions were monitored using
the LCR meter at 300 kHz frequency to eliminate the contacts
and measure the bulk spacer fl uid resistance. Th e measured
resistance was correlated to resistivity (material property), according
to the conductivity probe and digital resistivity meter.
In the fi eld, it will be easier to monitor the electrical resistance
(R), but it is not a material property. And cement is not
a conductive material, such as metals. Hence, from past studies
and theoretical understanding of electrical resistivity (ρ), the
following relationship between resistivity and resistance was
used and experimentally verifi ed:
ρ = R / K + GR
(11)
Both material parameters K and G are determined using experiments,
while ρ and R are measured independently. Several
experimental studies were performed to determine the parameters
K and G for the smart spacer fl uids.
Based on the studies, it was proven that parameter G was
zero for smart spacer fl uids. Th erefore, changes in resistivity
(dρ) can be related to the change in resistance (dR), represented
in Eqn. (11), as follows (parameter G = 0):
where ρ0
(dρ / ρ0) = (dR / R0
and R0
) (12)
are the measured initial resistivity and resistance,
respectively.
Parameter K (eff ective K), determined experimentally from
this study for the smart spacer fl uids by directly measuring the
resistivity (ρ) and resistance (R), varied between 50 m-1
, depending on the composition of the spacer fl uids.
60 m-1
to
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