Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Online Calibration Method for Electrical Capacitance Tomography in pneumatic conveyor
D Y Yang and S MWangf
College of Automation & electrical engineering, Nanjing University of Technology, Jiangsu, 211816, China
Jf School of Energy and Environment, Southeast University, Jiangsu, 210096, China
yangdaoye6 163.com and smwang~seu.edu.cn
Keywords: online calibration; electrical capacitance tomograplw; pneumatic conveying; capacitance model: finite element
method
Abstract
Electrical capacitance tomography is a robust method for process monitoring of pneumatic conveying. For the variation of
material category or property, the commix permittivity of twophase flow changes, which results in the measurement error, so
that the new measured material need to be recalibrated. Normally, in calibration, it is necessary to remove the ECT sensor from
the transportation pipeline and measure the capacitances when filled with a low permittivity material and a high permittivity
material. A new calibration method of ECT system used in pneumatic conveying was introduced. The model of ECT sensor
was built, and the relative error of the capacitance model was analyzed in the method of FEM simulation. The permittivity of
conveyed material was obtained by sampling the monitored object so that the capacitances of ECT sensor can be calculated
according to the precalibrated relationship between capacitance and permittivity. This calibration method needn't dismantle
ECT sensor, which doesn't disturb the process of pneumatic conveying.
Introduction
Pneumatic conveying of powder is one of the ancient and
effective technologies to transport particle with the help of
gas energy, which is widely used in chemical engineering,
power generation, pharmacy and food. From the aspect of
saving energy, the purpose of pneumatic conveying is to
improve the mass flux of particle at the given gas volume,
that is to improve the solidgas ratio. So the researchers
show great interest in densephase pneumatic conveying
[13], which has the characters such as low energy
consumption, high solidgas ratio, and great transport
capability. Many new method and technology [47] is
applied to the research of this highperformance pneumatic
conveying.
Electrical capacitance tomography (ECT) is one of the most
mature and promising PT methods, which measures the
capacitance change of multielectrode sensor due to the
change of dielectric permittivity being imaged, and then
reconstructs the crosssection images using the measured
raw data with a suitable algorithm [8]. It has the
characteristics such as low cost, fast response, nonintrusive
method, broad application, safety. Electrical capacitance
tomography is widely applied in visualization of industry
process, such as gas/1iquid flow in pipeline transportation of
petroleum [9], pneumatic conveying of granular flow [10],
gas/solid flow of material distribution in circulating
fluidized bed [11], and flame in porous media [12].
Currently, there are several kinds of calibration methods,
which are applied in Electrical Capacitance Tomograplw.
Boltony [13] proposed the improved method to decease the
error existed in twopoint calibration of oil/water flow.
Dong [14] studied the threepoint calibration method for
combustion visualization in porous media the permittivity
of the porous media, in which the relationship between the
measured capacitances and the relative permittivity of the
porous media was derived by an appropriate simplification.
Gareth [15] introduced a dynamic calibration method based
on moisture for the ECT imaging of a bed of drying
pharmaceutical granule. Bashar [16] presented a new
technique designed to accurately calibrate the traditional
ECT system using several liquid mixtures instead of the
conventional packed bed of particles, in which an
innovative immersion method is used to accurately estimate
the relative permittivity of solids.
Normally, in ECT calibration, it is necessary to dismantle
the sensor and fill with the measured medium, so that the
capacitances of empty pipe and full pipe can be measured.
Then the normal capacitance can be gotten. This process is
called calibration. However, the capacitance error of full
pipe will produce if the permittivity of measured medium
change. Obviously, the error will affect the accurate of
imaging, so it is necessary to dismantle the sensor and
recalibrate the changed permittivity.
An online calibration method of electrical capacitance
tomography in pneumatic conveying is introduced to work
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
relationship between measured capacitance Cm and internal
capacitance Cx can be carried out. Based on Equation (1),
the capacitance of empty pipe is
c cxo
cmo (3)
And the sensor capacitance filled with a material of known
relative permittivitvs is
C w r(4)
The internal capacitance Cx is proportional to the inner
permittivity. When the pipe is full with a material of known
relative permittivitve, the relationship between Cxr and Cxo
cx, = "rc, (5)
Solving the equations from (3) to (5), the following
expression can obtain,
( G )mom (6)
ec,Cm cmr
cxo= m (7)
Gr(Cmr Cm,>
On the basis of equations (4) and (5), the common form of
the model capacitance can be drawn.
mx, w+, xx (8)
If the permittivity of measured medium is known, the model
capacitance Cmx can be calculated based on equation (8).
Therefore, in sensor calculation, the medium permittivity a
can get by sampling the measured medium, and then the
fullpipe capacitance can be calculated by equation (8).
2 Model Simulation
For the purpose of validating the feasibility of above model
and the online calibration method of ECT for pneumatic
conveying, FEM analysis method [19] is adopted to build
the FEM model of 12electrode ECT sensor with external
electrode, calculate the relationship between inner relative
permittivity and electrodes capacitance, and compare the
simulation capacitance C, with the model capacitance Cmx.
Paper No
out the above problem. In the process of pneumatic
conveying, the permittivity of current measured medium
can be gotten by sampling the measured medium with a
capacitance sensor. Combined with the sensor model of
electrical capacitance tomograplw, the fullpipe capacitance
of current permittivity can be calculated. So this method can
online calibrate the ECT system and have no effect on the
flow process. ~
1 Sensor model of ECT
ECT sensor in pipeline conveying consists of several
electrodes symmetrically mounted outside or inside the
insulating pipeline. The sensors can be categorised into four
groups according to their physical structure [17]: (1)
External electrodes with radial screens: (2) Intemnal
electrodes without radial screens: (3) Extemnal electrodes
without radial screens: (4) Intemnal electrodes with radial
screens. In the gas/solid flow of pneumatic conveying, the
solid particle will generate charge in the process of particle
collision, which will disturb the capacitance measurement
of ECT sensor with internal electrodes. Moreover, the
sensor with internal electrodes is easy to be abraded. So the
sensor structure of external electrode is normally adopted in
pneumatic conveying. The radial screens can force the
power line of adjacent electrodes to pass through the inner
pipeline, so that the sensitivity of sensor to inner measured
medium can be improved. Moreover, the capacitance of
adjacent electrodes can be reduced, which can decrease the
difference between the adjacent electrodes and the others
and make the capacitance easy. However, the radial screens
make the sensor processing more difficult.
Cw Cwa
(a)model of capacitance sensor (b)equivalent capacitance
Figure 1: Model of ECT sensor with external electrodes and
radial screens
According to the modeling of Yang [18], the measuring
capacitance Cm of external electrodes with radial screen
between a pair of electrodes can be represented by the
internal capacitance Cx and two pipe wall capacitances Cwl
and Cw2, as shown in Fig.1(a). If combine the two pipe wall
capacitance, the measured capacitance Cm can be equivalent
to be Cx and Cw in series, as shown in Fig.1(b). So the
measured capacitance Cm can be expressed as
So, the internal capacitance Cx can be expressed by Cm and
It is necessary to know the value of C, so that the
Figure 2: FEM simulation model of l2electrode ECT sensor
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
capacitances in empty pipe, q=3.5 and 7.5 are calculated by
FEM method. According to Equation (6) and (7), the pipe
wall capacitance Cw and inner capacitance Cxo is easy gotten.
The model capacitance Cmx when & is from 1 to 15 is
calculated based on Equation (8). And the simulation
capacitance Cex can be calculated by FEM method. The
relative error of model capacitance Cmx and simulation
capacitance Cexis shown in Fig. 4, the relative error can be
expressed as:
Cm C
6c = xC ex (10)
And the relative error curve in the condition of q=3.5 and
7.5 are shown Fig. 4(a) and Fig. 4(b) respectively. As can be
shown from the two figures, the consistency of model
capacitance Cmx and simulation capacitance Cexis best at
the calibration point 4.
Paper No
Fig. 2 is the structure of sensor. Pipeline inner diameter is
30mm, pipeline thickness is 2.5mm, electrode thread angle
is 240, the screen radius is 35mm, and the relative
permittivity of filling layer and pipeline material is 2.
There are six typical electrode structures in 12electrode
ECT sensor. Fig.3 is the relationship of inner medium
permittivity 4 and sensor simulation capacitance Cexin the
six different electrode structures. The capacitance of
adjacent electrodes is larger than the other ones. The
capacitance of adjacent electrodes reach the maximum at
a=15, while the capacitances of other ones increase with
the increase of relative permittivity, and the increase extent
decrease. According to the analysis of Jaworski [20], the
capacitance maximum point 4, is related to the pipeline
thickness in the condition of same inner diameter. With the
increase of pipeline thickness, the relative permittivity of
capacitance maximum point decrease.
m C12
2~~ C14
7 C15
1 P C16
0~~ C17
010 20 30 40 50 60 70 80
relative permittivity
Figure 3: Curve of simulation capacitance
Equation (8) is the relation between relative permittivity 4
and model capacitance. The derivation of Equation (8) gives
the curve slope of relative permittivity and model
capacitance.
dCmx CC,Cx
(9)
dex (C, + eCxo)2
As known from Equation (9), with the increase of 4, the
curve slope decrease, which is consist with the vary
tendency of permittivity and capacitance of nonadjacent
electrodes in Fig.3. Moreover, for the particularity of
adjacent electrodes, part of the power line only passes
through the pipeline wall area, so their capacitance model
can't express as the internal capacitance Cx in series with
two pipe wall capacitance C,,, Cw2, RS shown in Fig. 1. The
model error increases with the increase of the relative
permittivity difference between pipeline wall and imaging
area. When the relative permittivity of imaging area is larger
than G,, the relationship between relative permittivity and
capacitance is no longer monotonous. So this calibration
method isn't suitable for the condition that relative
permittivity of measured medium is larger than 4,.
However, when it is less than s,, the capacitance model is
satisfactory.
To validate the accuracy of the calibration model, the typical
1 3 41 5 6 7 8 9b10111111
relative permittivity
(a)sr= 3.5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
relative permittivity
(b)s,= 7.5
Figure 4: Error curve of model capacitance and simulation
capacitance
For the particularity of adjacent electrodes, its error curve is
different from nonadjacent ones obviously. The error of
nonadjacent electrodes is positive in the left of calibration
point 4, and negative in the right. The more the relative
permittivity is far from the calibration point, the larger the
model error is. The error curve of adjacent electrodes has
different tendency at different 4, which is 3.5 and 7.5
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
the sampling sensor is full, the sampling program controlled
by computer acquires the capacitance of sampling sensor.
Thus, the relative permittivity of current sampled particle
can be calculated. Because the sampling sensor is only used
in calibration process and not easily abraded, so the internal
electrodes stmecture [21] is adopted to improve the linearity
between relative permittivity and capacitance. According to
the Equation (8), the fullpipe capacitance Cmx of current
particle can be calculated. Therefore, the program of online
calibration is finished.
Paper No
respectively. However, the above mule is still right near the
calibration point.
The relative error curve of capacitance against electrode pair
is shown in Fig. 5. There are three different 4, which is 2.8,
4.2 and 10, and the relative permittivity of calibration point
is 3.5. The figure demonstrates that the difference of model
error in different & is obvious. The capacitance error in
different electrode stmecture is different, and it complies
with some laws. The difference of 4 and 2.8 is the same as
the one of 4 and 4.2, which is 0.7. The simulation result
shown that the two curves have the same error, but they
have the different polarities, the error curves are
symmetrical about the Xaxis. Comparing with the error
curves of a =4.2 and a =10, they have the similar shape,
and the point which is far away from calibration point, has
larger model error.
 2.8
* 4.2
12~ 110 1
pipeline of pneumatic conveying
12electrode
ECT sensor
Figure 6: Online calibration ECT system
After the calibration, it is necessary to close the valve 1 and
open the valve 2 to evacuate the sampled section. Then
close the valve 2 to keep the sampling section dry, which
can avoid the erosion of measured particle and effect the
measurement accurate.
I I I I 'I 'I I I I I I I I I I I'I I I I I I 'I 'I
electrode pair
Figure 5: Contrast of model capacitances
3 Experimental Facility of online calibration ECT
In the process of pneumatic conveying, if the relative
permittivity of transported medium changes, the actual
capacitance of full pipe will departure from the calibration
value, so the measurement error will cause. In the coal
powder transportation, several factors can induce the
variation of integrate relative permittivity, such as difference
of coal type, the variation of moisture content and the
change of particle size distribution. For the purpose of
decreasing the measurement error and simplifying the
calibration process, a set of ECT online calibration
equipment is built based on the above capacitance model, as
shown in Fig.6. This equipment is different with other
normal ECT system. A sampling capacitance sensor is
installed in the downstream of ECT sensor, which is used to
sample the transported medium, so the relative permittivity
of measured medium can be calculated based on the
measurement capacitance of the sampling sensor.
In the beginning of calibration, the valve 1 is open and the
valve 2 is close, so that the accumulated particle above the
valve 1 can be swept off by gas. Then close the valvel and
open the valve 2 to remove the moisture and residual
particle in the sampling sensor. After a while, open the valve
1 and close the valve 2 to collect the sampled particle. When
00 00
electrode pair
Figure 7: Measured error curve of online calibration ECT system
To validate the feasibility of this online calibration method,
a selfresearch online calibration ECT system [22] is
applied to calibrate the pneumatic conveying process. The
relative permittivity 4 of calibration particle is 3.1, and the
permittivity of measured particle is 3.5. Fig. 7 is the relative
curve error between model capacitance and measured
capacitance of experiment when & is equal to 3.5. When
comparing Fig.5 with Fig. 7, a conclusion can be drawn that
the experimental error is larger than the simulation one. In
the actual measurement process, several factors can induce
error, such as ECT capacitance measurement, physical
property of measured particle and measured permittivity of
sampling sensor. In addition, the capacitance error of
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
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Paper No
adjacent electrodes has some difference with the simulation
ones for the effect of sensor machining precision.
4 Conclusion
An online calibration method for ECT system is introduced.
The inner capacitance Cxo and pipe wall capacitance C, are
calculated by means of precalibration. If the relative
permittivity of measured particle changed, the new
permittivity can be obtained by sampling the measured
particle. The fullpipe capacitance of new particle can be
calculated according to the expression of relative
permittivity and capacitance. Thus, the new measured
particle can be online calibrated. This method needn't
dismantle the sensor, and the calibration process doesn't
disturb the running of ECT system.
Because of the effect of the pipe wall capacitance and sensor
structure electrodes capacitance, the relation between
permittivity and capacitance is not linear. The online
calibration range is related to the relative permittivity a of
precalibration particle. The more the relative permittivity of
calibrated particle is near to 4, the less the calibration error
For the effect of practice factor, the calibration accurate iS
not satisfactory, and it should be further improved. There
are some improvement methods such as decreasing the
sampling error, improving the accurate of capacitance
measurement and capacitance model of ECT.
NOmenclature
Cm measuring capacitance (pF)
Cx internal capacitance (pF)
Cxo internal capacitance (pF) of empty pipe
C, sensor capacitance (pF) when inner relative
permittivity is 4
C capacitances of pipe wall 1
C capacitances of pipe wall 2
Pipe wall capacitances
C, simulation capacitance
Cmx model capacitance
Greek letters
Relative permittivity of calibration point
Relative permittivity of measured medium
6c relative error of capacitance model
Acknowledgements
This research was supported by National Natural Science
Foundation of China (50836003, 50906012, and 50906013),
Major State Basic Research Projects (2010CB22~'lr'' and
Subject Fund of Nanjing University of Technology
(39710003). The authors wish to express their gratitude.
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ICMF 2010, Tampa, FL USA, May 30June 4, 2010
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