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Engineering, Technology & Applied Science Research Vol. 13, No. 4, 2023, 11332-11337 11332
www.etasr.com Ghaly et al.: Diagnosis of Two-Phase Oil/Gas Flow in a Closed Pipe using an 8-Electrode ECT System
Diagnosis of Two-Phase Oil/Gas Flow in a
Closed Pipe using an 8-Electrode ECT System
Sidi Mohamed Ahmed Ghaly
Electrical Engineering Department, Imam Mohammad Ibn Saud Islamic University, Saudi Arabia | Ecole
Normale Supérieure, Mauritania
smghaly@imamu.edu.sa
Mohammed Shalaby
Electrical Engineering Department, Imam Mohammad Ibn Saud Islamic University, Saudi Arabia
myshalaby@imamu.edu.sa
Mohammad Obaidullah Khan
Electrical Engineering Department, Imam Mohammad Ibn Saud Islamic University, Saudi Arabia
okkhan@imamu.edu.sa
Khaled Alsnaie
Electrical Engineering Department, Imam Mohammad Ibn Saud Islamic University, Saudi Arabia
kalsnaie@imamu.edu.sa
Asad Ali Mohammed
Electrical Engineering Department, Imam Mohammad Ibn Saud Islamic University, Saudi Arabia
asad207@imamu.edu.sa
Faisal Baloshi
Electrical Engineering Department, Imam Mohammad Ibn Saud Islamic University, Saudi Arabia
fbaloshi@imamu.edu.sa
Abdalmajid Imad
Electrical Engineering Department, Imam Mohammad Ibn Saud Islamic University, Saudi Arabia
aimad@imamu.edu.sa
Majdi Taha Oraiqat
Electrical Engineering Department, Imam Mohammad Ibn Saud Islamic University, Saudi Arabia
mtoraiqat@imamu.edu.sa
Received: 4 May 2023 | Revised: 24 May 2023 and 26 May 2023 | Accepted: 29 May 2023
Licensed under a CC-BY 4.0 license | Copyright (c) by the authors | DOI: https://doi.org/10.48084/etasr.6011
ABSTRACT
Electrical tomography techniques have been developed to monitor the internal behavior of industrial
processes. Electrical capacitance gives the best benefits over other tomography modalities, as it has no
radiation, is non-intrusive, and has a low cost. This study investigated the diagnosis of two-phase oil/gas
flow in a closed pipe, using an image data capture system for an 8 external electrode Electrical Capacitance
Tomography (ECT) sensor. The system had a high-resolution ratio, a small measurement error, and was
able to remove the effects of stray capacitance. Experimental measurements were carried out on two
different materials that filled the space inside the pipe in different proportions to determine the sensitivity
and accuracy of the measurement. The results showed that the system had fast image data capture time,
high accuracy, a very small resolution ratio, and a good signal-to-noise ratio and quality factor.
Engineering, Technology & Applied Science Research Vol. 13, No. 4, 2023, 11332-11337 11333
www.etasr.com Ghaly et al.: Diagnosis of Two-Phase Oil/Gas Flow in a Closed Pipe using an 8-Electrode ECT System
Keywords-ECT sensor; imaging; electrode; permittivity; fluid dynamics; sensitivity; accuracy
I. INTRODUCTION
Electrical Capacitance Tomography (ECT) is a widely used
imaging technique in monitoring and diagnosing the internal
dynamics of the flow mechanism of gaseous or liquid materials
in the process industry [1-5]. ECT is an economic, non-
interrupting or non-invasive, and fast-responding imaging
scheme, as it can produce real-time images with an
approximate speed of 100 fps. Different experimental studies
showed that the Water-in-Liquid Ratio (WLR) and Gas
Volume Fraction (GVF) in an oil-gas-water flow can be
roughly calculated or measured by ECT with suitable
algorithms [6-7]. Obtaining a high-speed image along with
quantitative measurements of a multiphase flow system is a
challenging demand in the petroleum industry and hydraulic
applications. ECT can also be used to detect corrosion and
leakage or monitor liquid dynamics in a petroleum/gas pipeline
network [8-10]. It can also be used to investigate the
distribution of spatial permittivity in a defined region in the
interior of a closed pipe. ECT works on the principle of
measuring capacitances between electrodes located outside the
sample portion in the region of investigation. In general, the
specimen region can be a hollow pipe carrying a liquid or gas.
The data obtained from these electrodes are processed to
reconstruct the internal image of the pipe. The necessary
elements of a typical ECT system are a set of multi-electrode
sensors mounted equidistant around the pipe, a data retrieval or
acquisition system, and an image reconstruction block, as
shown in Figure 1 [11-12]. Using N electrodes in the sensor for
capacitance measurements, there will be M independent
capacitance measurements as expressed in:
� = � (���) (1)
In the present case, as shown in Figure 2, an 8-electrode
sensor needs 28 independent measurements of electrode pairs
as:1-2, 1-3, ..., 1-8; 2-3, 2-4, ..., 2-8; ..., up to 7-8.
Fig. 1. A typical ECT system with 8 electrodes.
Fig. 2. Cross section of a typical 8-electrode ECT system.
In general, ECT systems directly employ the "raw"
capacitance data obtained from the sensor to develop images
using Linear Back-Projection (LBP) and recursive or neural
network algorithms [10]. The LBP algorithm is one of the most
popular methods due to its simplicity and high rates of image
reconstruction. An LBP image is obtained by overlaying the
sensor sensitivity maps for all electrode pairs after weighting
by the corresponding measured changes in normalized
capacitance. This can be represented mathematically as:
(�) =
∑ ∑ �
� �
�(�)���
��
���
��
∑ ∑ ���(�)���
��
���
��
(2)
��� =
�
�
���
�
�
�
�
� ��
�
� (3)
where N represents the number of electrodes in the ECT sensor,
X(p) is the fraction of a high permittivity material in the p-th
pixel, S is the sensitivity of electrode pair i-j at the p-th pixel,
Cij represents the capacitance of the electrode pair i-j when the
sensor is filled with low and high permittivity materials,
respectively, c
m
is the raw measured capacitance of the
electrode pair i-j, and λij is the change in normalized
capacitance of the respective electrode pair.
II. ELECTRICAL MODELING OF THE ECT SENSOR
WITHOUT RADIAL SCREEN
Consider an ECT sensor with eight external electrodes
without radial screens, as shown in Figure 2. These electrodes
can be made with a flexible printed circuit board with greater
precision in size and position. Without radial screens, the
external capacitances must be considered, as they have
considerable capacitance. A model of capacitance measured Cm
with radial screens for one pair of electrodes, that is the
capacitance between two measurement electrodes through the
space outside them, can be given as the combination of an
internal capacitance Cx, two pipe wall capacitances Cw1, Cw2,
and two stray capacitances Cs1, Cs2, as demonstrated in Figure
3(a). This can be further simplified as shown in Figure 3(b)
[13]. The equivalent capacitance Cm can be calculated
mathematically as:
�� = ��� ��!�" (4)
(a) (b)
Fig. 3. Electrical Model of 8-electrode sensing system without radial
screen: (a) Model with all capacitances, (b) simplified model.
The unknown capacitances Cw and Cx can be found by
filling a material of known relative permittivity r1 into the
sensor. This process is repeated with another material of known
Engineering, Technology & Applied Science Research Vol. 13, No. 4, 2023, 11332-11337 11334
www.etasr.com Ghaly et al.: Diagnosis of Two-Phase Oil/Gas Flow in a Closed Pipe using an 8-Electrode ECT System
relative permittivity of r2 and the air. Thereafter, by finding Cx
and Cw, the internal capacitance with any fluid existing inside
the region of interest in the PVC pipe can be calculated from
the raw capacitance measured using (4). This can be rearranged
as follows:
� = �# �$ /��# & �$ � (5)
III. CALCULATION OF THE SENSITIVITY MAP OF
THE 8-ELECTRODE ECT
Consider the circular sensor filled with one-phase with air
dielectric constant and fitted with eight electrodes. The wall
permittivity is constant. Thus, the domain of the model is the
unit square Ω on the x-y plane, representing the cross-section
of the scaled sensor area. The electrodes are placed on the unit
square x
2
=1, where x is the length of the side and the boundary
of Ω. Suppose that the relative radial thickness of the wall is t0
(0<t0<1), and denotes the interior cavity by [14-15]:
'( = )(*, ,): * . (1 & 0() 1 (6)
The electric potential u(x, y) on Ω is governed by Poisson’s
equation derived for the static electric field, which is given by:
∇(3∇4) = 0' (7)
where ε = ε(x, y) > 0 is the relative permittivity distribution in
Ω. A finite difference method was employed to discretize the
differential equation for the numerical solution using
rectangular coordinates.
The simulation was assumed for a cross-sectional circular
shape, which can be a cylindrical non-metal container. ECT is
difficult to perform on metallic cylinders, as the metals leak the
charge all over their surface and make the theoretic
assumptions wrong for calculations. On a non-metallic surface,
the electrodes are attached and a voltage is applied, which
passes through the non-metallic cylinder from the inside and
through the fluid or gas. This creates a small charge that
accumulates in the fluid or gas and creates a small capacitance
since when a potential is applied to one electrode, the other 7
electrodes act as ground. The technique of 8-electrode ECT is
like 7 capacitors along the surface of the cylinder. However, as
the permittivity and voltage between the plates are very small
and the distance between the electrodes is greater, a very low
capacitance is measured. If the permittivity of the fluid or gas
and their potential breakdown are known, an increase in
voltage below the breakdown voltage can lead to better
performance of the ECT technique. The breakdown voltage is
the voltage at which an arc occurs between the electrodes.
Figure 4 shows the electric potential between the energized
electrode 1 and the grounded electrodes 2-8. The sensitivity
map Sij is obtained on a cylinder object fixed with 8 electrodes.
Figure 5 shows S12 between the first and second electrodes.
Electrode 1 is energized at a low voltage of 0.02 V and
electrode 2 is grounded, which has some stray charge on it, as
the metal electrodes cannot be charged after applying an
electric field. Similarly, electrode 1 is energized at a low
voltage of 0.02 V, and electrode 3 is grounded having some
stray charge. The potentials for electrodes 1 and 3 are
illustrated below. This can be demonstrated for all
combinations of 1-8 electrodes in the ECT sensor, as shown in
Figure 6. Figure 7 shows S13 between the first and third
electrodes.
Fig. 4. Electric Potential between Electrodes 1 and 2.
Fig. 5. Sensitivity map between electrodes 1 and 2.
Fig. 6. Electric potential between electrodes 1 and 3 at low intensity.
Fig. 7. Sensitivity map between electrodes 1 and 3.
Engineering, Technology & Applied Science Research Vol. 13, No. 4, 2023, 11332-11337 11335
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Figure 8 illustrates the potential distribution from electrode
1 to electrode 3 when a high voltage of 1000 V is applied. If
carefully analyzed, there is a continuous decrease in voltage
until the second electrode is approached. It seems as an
exponential decrease in voltage, but when applying a higher
voltage at electrode 1, a more positive expectation of
capacitance is measured. The application of higher voltage is
due to the limitation of the medium which is transmitted
through the cylindrical pipes, and its effect needs to be studied.
Fig. 8. Electric potential between electrodes 1 and 3 at high voltage.
IV. IMPLEMENTATION FOR SENSITIVITY
MEASUREMENT
The AC-ECT system includes hardware and software, in
particular software drivers and ECTGUI. As shown in Figure 9,
the hardware has a front-end unit in a 19'' Eurocase, with an
internal power supply and an NI DAQ board/card operated by a
host PC. Two NI DAQ units are supported: the NI PCI-6024E
DAQ board that works with a desktop PC and the NI PCMCIA
6062E DAQ card that works with a laptop. Both NI DAQ units
use a 68-way ribbon cable with the same female connectors
connected to the 19'' Eurocase, but a different female connector
at the other end to connect to the PC [16].
Fig. 9. Hardware blueprint.
This section presents the results of the experiments carried
out using the 8-electrode ECT sensor, with dimensions
specified in Table I, to quantify its sensitivity. The accuracy of
the sensor may also depend on physical specifications and
assumptions. If the tube wall is made up of a dielectric
material, electrodes can be installed inside or outside [17-18],
but if the wall is conductive there is only one choice to design
the electrode location (external electrode). However, as the
proposed design used dielectric material, the electrodes were
put outside the pipe because it is easier to design. The number
of electrodes depends on capacitance, circuit complexity, and
data acquisition speed. Using more electrodes provides a better
image, but they are difficult to measure. In most cases, the
number of electrodes used is 8 or 12, whereas this study used 8.
A guard electrode is required to improve measurement
sensitivity and prevent the electric field from reaching the
ground and the end of the measuring electrode [19]. They must
be used if the length of measuring electrodes is less than
approximately twice the sensor diameter. Finally, it is
important to add a discharge resistor. The resistor must be
connected between each electrode and the driven guard and
earth to avoid a static charge and damage to the measuring
sensor. Typically, the resistance value is 1 MΩ. If the
capacitance of the inter-electrodes is around 1 pF, an earthed
screen is required around the electrodes to avoid unwanted or
external signals. Figure 10 shows a photo of the typically
developed prototype.
Fig. 10. A typical 8-electrode ECT sensor.
TABLE I. DIMENSIONS OF THE SENSOR PARTS
Component Dimensions
Electrode dimensions= length×width 15×1.7 cm
Gap between electrodes 0.275 cm
External circumference of pipe 15.8 cm
Outer radius of pipe 2.51 cm
Inner pipe cross section area 19.86 cm2
Total volume of the ECT section (electrode region): Vtotal=
19.86×15
297.9 cm3
V. RESULT AND DISCUSSION
A. Sensitivity of Measurements
Two dielectric materials were used to calibrate the
developed sensor: oil and air. Then, different amounts of oil
were introduced into the pipe, where the air surrounded the oil.
Figure 11 shows that the smallest amount to be detected had a
cross-sectional area of 0.97 cm
2
(volume = 14.56 cm
3
and
quantity = 0.67 L). A minimum detectable value was defined as
the product of the dielectric constant to describe the POS
sensitivity of the ECT sensor. The difference between the two
dielectric materials (air and oil) was multiplied by the
minimum detectable volume of the object and divided by the
volume of the sensor section as in (6):
Engineering, Technology & Applied Science Research Vol. 13, No. 4, 2023, 11332-11337 11336
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678 = ∆3:
;�<
;=>=?�
× 100 (6)
where POS is the percentage of sensitivity [20], Δεr is the
difference between the dielectric constants of the full and
empty states, Vmd is the minimum detectable volume of the
object, and Vtotal is the total volume of the ECT Sensor. In the
present case of oil Δεr = 6. From Figure 10, the calculated
sensitivity of the POS measurements was 67.4%. Figure 11
shows the decrease in the amount of oil gradually searching for
the minimum detectable volume of the object Vmd.
(a)
(b)
Fig. 11. Sensitivity patterns with variable amounts of different materials.
B. Accuracy of the Obtained Image
The accuracy of the measurements [21] was calculated
from the images obtained. Two different dielectric materials
were considered, where the empty state was air and the full
state was lubricating oil (density = 823 kg/m
3
). An amount of
lubricating oil was introduced so that when the pipe was placed
horizontally, it was half filled with lubricating oil. Referring to
Figure 11, it was discovered that the separation line between
the lubricating oil and the air deviated from being a sharp line.
The gradual change from blue (air) to red color (lubricating oil)
indicates that the accuracy of the sensor was not high enough.
To quantify the accuracy of the ECT sensor, the percentage of
accuracy (POA) was defined as follows:
POA = D1 & EFGH IJFKLGHMMNOPQH RFPOHIHST × 100 (7)
The POA term was introduced to represent the percentage
of accuracy. In the case of Figure 12, POA was achieved to be
as high as 82%.
Fig. 12. Illustration of sensitivity pattern with two different materials when
it is placed horizontally.
Figure 12 shows the line separation between the two
different dielectric materials (lubricating oil and air) when the
pipe is placed horizontally. The results obtained with the
developed sensor with eight external electrodes show that the
larger the width of the electrodes, the more accurate the
measurements. Moreover, the shorter the electrode length, the
more sensitive the measurements. These observations were
made while keeping the same gap between the electrodes and
for the same cross-sectional area.
VI. CONCLUSION
This paper presented the modeling, simulation, and
experimental measurements of an ECT sensor having eight
external electrodes. In terms of modeling, the potential
distribution, the electric field, and the sensitivity map were
obtained to extract the dependence of the sensor characteristics
in terms of sensitivity and accuracy on the sensor parameters.
To verify the modeling results, an 8-electrode ECT sensor was
developed and implemented, and experimental measurements
were carried out on two different materials filling the pipe with
different proportions to determine the sensitivity of the
measurements and the accuracy of the probe. Furthermore,
definitions of accuracy and sensitivity were developed and
calculated for the developed sensor to validate the simulation
results.
ACKNOWLEDGEMENT
This project was funded by the National Plan for Sciences,
Technology, and Innovation (MAARIFAH), King Abdulaziz
City for Science and Technology, Kingdom of Saudi Arabia
award number (14-ELE741-08).
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