Underground Construction - January 2022 - 35

Generally, model parameters are infl uenced by the composition
of the cement and curing conditions (temperature, humidity,
stress). In the range of variables investigated in up to 24 hours
of curing, parameter q1
content, and parameter p1
by the initial resistivity ρ0
and t0
.
Th e compressive strength of the smart cement increased with
the SBR polymer addition, to 1400 psi after one day of curing.
With 1 percent SBR polymer, the strength increased 18 percent,
to 1650 psi, and with 3 percent SBR polymer, the one-day
compressive strength increased 32 percent, to 1850 psi.
It is important to characterize the sensing property, resistivity
change, of the smart cement without and with polymer. For the
smart cement slurry application, a compressive stress of 800 psi
reduced the resistivity by 14 percent, indicating even the cement
slurry is piezoresistive.
Piezoresisitive responses (stress-resistivity relationship) of the
smart cement without and with polymer are shown in FIG. 3.
As summarized in TABLE 2:
* Th e piezoresistivity of the smart cement at failure after 1 day
of curing (∆ρ /ρo
)f
)f
was 171 percent.
* Th e addition of 1 percent and 3 percent SBR polymer to the
smart cement decreased the electrical resistivity at failure
(∆ρ /ρo
to 125 percent and 104 percent, respectively.
* However, the smart cement with SBR polymer is piezoresistive
and the responses were over 500 times the compressive failure
strain (0.2 percent) of cement.
* Both parameters were sensitive to the polymer content in
the smart cement model: p2
while q2
decreased.
Th e Vipulanandan p-q piezoresistivity model, Equation (4) as
follows, was used to predict the observed trends for the smart
cement without and with SBR:
x
σ=
(
xf
q2 + 1−p2 −q2 ) x
× σf
xf
where σ is the stress (MPa); σf
(MPa); x = (∆ρ /ρo
⎛
⎝
+ p2 ⎜
x
xf
⎞
⎠
⎟
: is compressive stress at failure
resistivity due to the stress; xf = (∆ρ /ρo
and q2
) × 100 is percentage of change in electrical
)f
of change in electrical resistivity at failure; ∆ρ ισ change in
electrical resistivity; ρo
and p2
are piezoresistive model parameters.
Gas Leak
Tests were performed to investigate the sensing characteristics of
the smart cement during a gas leak.
Maximum pressure gradient of 2100 psi/ft was used in this
study. Th e pressure gradient was increased, and the discharges were
measured using the HPHT test facilities (FIG. 1). Th e resistance
changes were monitored continuously during the test.
Th e smart cement without and with 3 percent polymer was
tested for gas leaks after 1 hour and after 24 hours of curing.
× 100 is the percentage
initial electrical resistivity (σ = 0 MPa),
⎛
⎜⎝
p2
p2−q2
⎞
⎟⎠
(4)
FIGURE 4: Variation of gas discharge velocity with pressure gradient
after 1-hour curing
increased with polymer content,
were infl uenced by the polymer
was not. Parameter t0 was infl uenced
In FIGURE 4, the discharge velocity (volume discharge per
unit area) for smart cement without and with 3 percent polymer
is compared for one-hour cured specimens. Polymer addition
reduced the discharge velocity of gas at all the pressure gradients
tested, with a maximum reduction of about 18 percent. Th e velocity
of discharge and pressure gradient relationship was non-liner
and, hence, Darcy's Law cannot be used.
In FIGURE 5, the gas leak velocities with pressure gradients
are compared for 2- hour cured smart cement without and with
3 percent polymer and the relationship was non-linear. With
3 percent polymer, the maximum gas velocity reduction was
about 33 percent.
To quantify the gas leak (average discharge per unit area = V)
occurring in cement at diff erent pressure gradients (i) and curing
time, the new Vipulanandan Fluid Flow Model, Equation (5), is
represented as follows:
V = i / (M + Ni)
Model parameters M and N are summarized in TABLE 3,
with the coeffi cient of determination and root-mean square
error (RMSE). Th e Vipulanandan Fluid Flow Model predictions
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