- Email: [email protected]
A novel tomographic sensing system for high electrically conductive multiphase flow measurement
Flow Measurement and Instrumentation 21 (2010) 184–190
Contents lists available at ScienceDirect
Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
A novel tomographic sensing system for high electrically conductive multiphase flow measurement Jiabin Jia ∗ , Mi Wang, H. Inaki Schlaberg, Hua Li Institute of Particle Science and Engineering, University of Leeds, Leeds, LS2 9JT, UK
article
info
Article history: Received 4 August 2009 Received in revised form 25 November 2009 Accepted 14 December 2009 Keywords: Electrical resistance tomography High-conductivity multiphase flow Voltage-applied system
abstract Electrical resistance tomography (ERT) has been widely applied in order to extract flow information from various multiphase flows, e.g. the concentration and velocity distributions of the gas phase in gas–water two phase flows. However, the quality of measurement may become very poor from a multiphase flow whose continuous phase has a considerably high electrical conductivity, e.g. seawater (5.0 S/m), using a conventional current-injected ERT system. It is known that a large current excitation is necessary in order to enhance the measurement sensitivity. In practice, it will be very challenging to build a current source with a large amplitude (more than 75 mA) and a high output impedance at a high excitation frequency. This paper presents an implementation of an ERT system with a voltage source and current sensing to overcome the limits of the current source. The amplitude of the current output can reach more than 300 mA. A logarithmic amplifier is used to compress the signal’s dynamic ranges from 18.32 dB to 1.66 dB. The structure and features of this system are presented in this paper and the performances of key circuits are reported. Finally the experimental results from a highly conductive flow (1.06 S/m) are analysed and compared with the measurements obtained from a low conductive flow. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Electrical resistance tomography (ERT) has been proven to be able to measure the spatial distributions of conductivity or volumetric fraction of a two-phase multiphase flow whose continuous phase is electrically conductive. Although it has been developed for almost two decades [1,2], a number of technical issues have not yet been fully solved, such as the measurement accuracy and the immunity of ERT hardware systems to various noises, particularly, the high common mode voltage. ERT measurements can be operated by applying a current through the electrodes and measuring the voltages between the electrodes, or in turn, by applying a voltage and measuring the current [3]. The current-injected method is used in most ERT systems due to its simplicity and good performance over a low conductive range. However, such a system has difficulties obtaining measurements from a high conductivity fluid, e.g. the seawater (5 S/m), with a good measurement precision. Compared with other tomography modalities, the relatively low-cost as well as being compact and simple are the inherent advantages of ERT. Furthermore it is able to collect concise and useful data without distorting the flow field, as well as identify flow regimes and estimate the void fraction of a two-phase flow quickly.
∗
Corresponding author. Tel.: +44 1133432357. E-mail address: [email protected] (J. Jia).
0955-5986/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.flowmeasinst.2009.12.002
Even so, there is still additional potential that can be further exploited to adapt to the requests from industrial applications, including simplifying the system’s structure and enhancing its performance. To date, in the majority of cases, an electrical current source is used as excitation in ERT [4,5]. The continuous aqueous phase in most tests and applications has a limited conductivity range, normally from 0.01 to 0.1 S/m, e.g. tap water. However, the process fluids in some industrial interests are highly conductive, which generally consists of ionic compounds dissolved in water [6]. These fluids have conductivities approximately midway between insulators and metallic conductors. A conductivity range of common solutions is summarized in Table 1. For a flow whose continuous phase has a high conductivity, a larger current excitation is normally required in order to enhance the measurement sensitivity. As shown in Fig. 1, three groups of cross-section images were reconstructed by a conventional ERT system using the same agar-gel and measurement configuration but different continuous phase conductivity and injection currents ranging from 0.037 S/m to 0.637 S/m and 15 mA to 60 mA, respectively. For a fixed injection current, as the conductivity of the continuous phase increases from 0.037 S/m to 0.637 S/m, the crosssectional images become more and more blurred. However when comparing those images with a fixed back ground conductivity (shown in a vertical column of images in Fig. 1), it can be observed that the larger injection current gives rise to a better image. In practice, it is very difficult to build a large current source with the requested performance, such as the high output impedance
J. Jia et al. / Flow Measurement and Instrumentation 21 (2010) 184–190
185
Fig. 1. Cross-sectional images from different continuous phase conductivity and injection current. Table 1 Conductivity ranges of common solutions. Liquid
Conductivity
Tap water Polluted water Sea water 5% Sodium chloride solution 10% Sulphuric acid solution
0.01 to 0.1 S/m 0.1 to 1.0 S/m 3.0 to 5.3 S/m 7.0 S/m 14.0 S/m
(greater than 1 M) at a high output frequency, the large commonmode voltage rejection ratio and the consistent performance over the required frequency range. Conventionally, the output amplitude of a current source is limited to 75 mA at an output frequency of less than 300 kHz [7,8]. Therefore, the voltage source was employed to generate the desired current pattern with the adjustment algorithm [9], which ensures accurate current output, but also makes the systems more complex and has the possibility of diverging the adjustment algorithm. Saulnier [3] introduced a voltage source for electrical impedance tomography, in which a complicated calibration circuit and algorithm were involved. A sense resistor was used to value the applied current in both systems. This additional resistor will produce an additional common mode voltage and increase the output impedance, therefore it may generate new error sources. The aim of this research was to widen the applications of ERT to process mediums with a conductivity dynamic range up to 14.0 S/m. In this paper an innovative voltage drive strategy is presented. The maximum current output can be more than 300 mA. The new circuitry also employs a logarithmic amplifier to compress signals, which produces a good performance for ERT signals with a large dynamic range. Both static and dynamic tests are conducted in order to prove the performance of the system. Results are reported in this paper. 2. Hardware structure 2.1. System diagram Fig. 2 shows the general block diagram of the system: the excitation block is made of a voltage source and a current sensor
Fig. 2. The voltage-applied ERT system diagram.
measuring the current through the target where the voltage source is applied to a pair of electrodes by a multiplexer; the auxiliary sensors interface to simultaneously capture the temperature and pressure of flow in the vessel which is used for the calibration of conductivity measurements; the differential voltage signals are firstly conditioned to make them suitable for the subsequent circuits; and the data acquisition system (DAS) that carries on the analogue-to-digital conversion and transmits the data to a PC via a USB 2.0 communication interface for image reconstruction and data analysis. 2.2. Excitation source As mentioned above, due to the strict requirements implementing a high specification current source, particularly with a large current amplitude, is complicated and difficult in practice. In contrast, a precise voltage source is generally easier and less costly to implement. When using a voltage source in ERT, it is necessary to maintain both the applied voltage and the resulting current with a high degree of precision in order to obtain absolute bulk resistance measurements. The applied voltage remains unchanged over a wide range of load impedances and measurement periods, and therefore the voltage source must have a low output impedance. An ideal voltage source with the following properties is desirable:
186
J. Jia et al. / Flow Measurement and Instrumentation 21 (2010) 184–190
Fig. 3. Diagram of the voltage source.
Output current (A)
0.6 0.5 0.4 0.3 0.2 0.1 Fig. 5. Minimum response voltage changes with solution conductivity.
0 0
0.05 0.1 0.15 0.2 Conductance (siemens)
0.25
Fig. 4. Output current vs conductance.
(a) The output impedance is infinitely low so as to stay constant no matter how the load varies; (b) The ability to supply current should be as high as possible; (c) The frequency and amplitude of the voltage applied can be controlled for different flow regimes; (d) Over-voltage and over-current should be detected swiftly to prevent components and the voltage source from being damaged. As shown in Fig. 3, firstly, a digital sine wave is converted into an analogue signal by a digital to analogue converter (DAC). The high frequency harmonic components created by the staircase sine wave are filtered with a low pass filter. After that, a power amplifier (OPA549) delivers a stable voltage supply. At this stage a digital synchronous signal is generated for use during the later data acquisition step. The voltage source has the following characteristics: the large adjustable output current up to 8 A [10]; the gain bandwidth is 0.9 MHz and can be operated from either single or dual supplies for design flexibility. In addition, the voltage source has two unique features. Firstly, its output can be disabled with a digital control signal. Secondly, when the temperature of the voltage source reaches approximately 160 ◦ C due to an overload event, an internal thermal shutdown circuit will disable the output automatically and provide an indicative signal. Fig. 4 illustrates the approximately linear relationship that was measured between the output current and conductive load. For an ERT system with a current source, the response voltage shrinks dramatically when the conductivity of the solution rises. For example, using the adjacent measurement strategy [11], the minimum value of the voltage measurement in the projection profile is from the electrode pair opposite to the excitation, which reduces from 74.2 mV to 0.2 mV with a conductivity increase of the solution from 0.081 S/m to 14.860 S/m (−25.7 dB) (the dashed curve in Fig. 5). Meanwhile, for the voltage-applied ERT, the voltage measurement attenuates only from 43.5 mV to 4.7 mV (−9.7 dB) (the solid curve in Fig. 5). Fig. 6 shows the measured relationship between the current output of the voltage source and the fluid’s conductivity. It demonstrates that the ERT system with a voltage source is able to supply up to 320 mA current to the vessel in which the electrical conductivity of fluid increases.
Fig. 6. Current output changes with solution conductivity.
voltage from electrodes to calculate the transimpedance across the whole vessel. In this system, a current sensing transformer is used to measure the current. The current sensing transformer provides a non-destructive (non-contact) current measurement. According to the operation principle of the transformer described in Eqs. (1) and (2), the relationship between the primary and secondary parameters are denoted in Eq. (1), the output voltage (Vout ) is an accurate voltage waveform representation of the sensed current (Iin ) flowing into the primary side, where N is the turn ratio of the primary coil Npri and secondary coil Nsec . N = Npri /Nsec = Iin /Iout = Vout /Vin
(1)
Vout = RT × Iin /N .
(2)
2.4. Multiplexer The multiplexer is used to channel the excitation source to each electrode. An ideal multiplexer should have a small onresistance and be able to switch off a large current. Its operation frequency should be as high as possible. The multiplexer is selected to allow a ±200 mA continuous current or ±300 mA peak current (pulsed at 1 ms 10% duty cycle max) to go through the electrodes. Its on-resistance is only 1.25 and its operation bandwidth is 12.5 MHz. This is the commercially available multiplexer with one of the biggest operational currents at the required operational bandwidth. Even though, it is still the bottleneck of the high current application of this ERT system. Using two or more multiplexers in parallel may be the solution for this problem in the future. 2.5. Signal conditioning
2.3. Current sensing At the time of applying the voltage source, it is indispensable to simultaneously measure the current and differential response
The signal conditioning circuit converts the output signals of ERT sensors into a suitable form for the ADC and maintains their essential characteristics. The conditioning entails processes such
J. Jia et al. / Flow Measurement and Instrumentation 21 (2010) 184–190
187
Fig. 7. Structure of the signal conditioner.
as isolating the ERT sensor from the conditioner, modifying the dynamic range to maximise the accuracy of the DAS, removing unwanted signals and limiting the signal’s spectrum. The structure of the signal conditioner is shown in Fig. 7. Each electrode is followed by an AC coupling buffer, which decreases the impedance seen by the subsequent circuit. A high pass filter prevents DC components flowing through. Then, multiplexers route one pair of differential analog input signals, at one time, to the programmable gain instrumentation amplifier (PGIA), which is controlled by input range selection to amplify or attenuate the input signals. A logarithmic amplifier is employed to adjust the dynamic range of signals and to scale the input signal to match the maximum input range of the ADC. More detailed information on this process is explained in the next section. A low pass filter rejects the ripples of the demodulated output of the logarithmic amplifier. The remaining frequency components are converted by a logarithmic amplifier before the analogue to digital conversion. A sampling signal synchronized with the voltage source, controls the timing of analogue to digital conversion. A large first-infirst-out (FIFO) buffer stores data during data acquisition. These conditioning steps modify the dynamic range to maximize the accuracy of DAS, remove the unwanted frequency components and limit the signal’s spectrum. 3. Logarithmic amplifier In the conventional process tomographic measurement, voltage measurements are taken as a reference from a homogeneous sample. Among 16 electrodes, one pair of adjacent electrodes was excited and 13 differential voltages were measured from the remaining pairs of adjacent electrodes. These measured differential voltages were as small as 0.0894 V and as large as 0.7373 V in the same voltage profile (black dashed curve in Fig. 8), which had a dynamic range of 18.33 dB. This large difference may present difficulties for the ADC reaching accurate conversion values. Therefore, a programmable gain amplifier (PGA) is normally required to enhance the measurement dynamics range. Fig. 8 also gives a voltage change after a plastic rod was inserted the vessel (the blue solid curve). It indicates the large changes are around the measurements with the small amplitudes. Based on the amplitudes of input signals, the external control signals provide different gains with the PGA [7]. Eq. (3) denotes a classic relationship between the input and output of the PGA.
VOUT
1000 × VIN , (0 < |VIN | ≤ 0.01) 100 × VIN , (0.01 < |VIN | ≤ 0.1) = 10 × VIN , (0.1 < |VIN | ≤ 1) 1 × VIN , (1 < |VIN | ≤ 10).
(3)
However, the use of PGA usually only regulates the amplitude of the analog signal in discrete gains steps (the derivative of Eq. (3) is shown in the Eq. (4)), which may cause a mismatch between
Fig. 8. Voltage profiles obtained with a linear PGA for the homogeneous and heterogeneous set-ups.
different voltage amplitudes and between different channels due to gain error and the individual difference of PGAs. dVOUT dVIN
1000, (0 < |VIN | ≤ 0.01) 100, (0.01 < |VIN | ≤ 0.1) = 10, (0.1 < |VIN | ≤ 1) 1, (1 < |VIN | ≤ 10).
(4)
Usually, a larger closed-loop gain leads to a larger gain error. For example, the gain error of a commercial programmable gain amplifier (PGA202) is 6% when its gain is 1000 at 100 kHz. In addition, the larger gain also results in a longer settling time to respond to the step change of input. The typical settling time is 10 µs at a gain of 1000 for the PGA202, which is one fifth of the period of the signal frequency 20 kHz. This rather slows the speed of the ERT system and complicates the operations. On the other hand, the settling time introduced by a logarithmic amplifier is 40 ns. An offset adjustment and full-range calibration is normally required for a PGA after the change of its gain in order to eliminate the side effects of the PGA. Therefore this work utilises a demodulating Log Amp to compress and demodulate AC input signals, yielding the logarithm of the rectified signal’s envelope. The combination of a Log Amp and a conventional ADC can reduce the problems caused by the PGA as discussed above, as well as simplifying the circuitry. The logarithmic amplifiers perform a more complex operation than classical linear amplifiers, and their circuits are significantly different. Although amplification is embedded inside the chip, the essential purpose of a Log Amp is not to amplify but to compress a signal of wide dynamic range to its decibel equivalent. The basic function is conversion of a signal from one domain of representation to another, via a precise non-linear transformation (Eq. (5)). VOUT = VY log(VIN /VX )
(5)
where: VOUT is the demodulated and filtered output voltage; VY is the voltage slope. The logarithm is usually taken to base ten, in which case VY is also the volts-per-decade; VIN and VX are the input voltage and the intercept voltage respectively.
188
J. Jia et al. / Flow Measurement and Instrumentation 21 (2010) 184–190
Fig. 9. Input level vs output of Log Amp by adjusting the logarithmic slope. Fig. 11. Voltage profiles obtained with a Log Amp for the homogeneous and heterogeneous set-ups.
Fig. 10. Input level vs gain. Fig. 12. Relative change of voltage profiles.
Transfer the Eq. (5) in terms of power [12] as Eq. (6) below. VOUT = VSLOPE (PIN − PO )
(6)
where: VOUT is the demodulated and filtered baseband output (V ); VSLOPE is the logarithmic slope; PIN is the input power (dBV), defined as decibels with respect to a 1 V rms sine wave (Vo ); PO is the logarithmic intercept (dBV). The Eq. (7) illustrates the calculation between dBV and V. dBV = 20 log (VIN /V0 ) .
(7)
Now, the output voltage is proportional to the Log of the input power, with an adjustable slope and intercept by external resistors configuration to suit the different input range. In Fig. 9, the default relation between the input and output of the logarithmic amplifier is shown in the black dotted line; the blue solid line indicates the adjusted relation. So, the minimum working input range can be changed from 0.01 mV to 0.3 mV. The Log Amp function described by Eq. (5) differs from the Eq. (3) of a linear PGA. Comparing with the incremental gain described in Eq. (4), Eq. (8) is a very strong non-linear function of the instantaneous value of VIN by calculating the derivative of Eq. (5). dVOUT dVIN
=
VY VIN · ln(10)
.
(8)
As shown in Fig. 10, the incremental gain of the logarithmic amplifier (blue solid line) is inversely proportional to the instantaneous value of the input level, which means the signals dropped in the lower part of the dynamic range will automatically get a larger gain; the signals at the higher part of the dynamic range will get a smaller gain, or even an attenuation when the input is more than 9.35 dBV (2.934 V). The incremental gain of the PGA is also given in Fig. 10 (black dashed line), which is inversely proportional to the total input level but in a discrete stepped way. By using the Log Amp to process the same data in Fig. 8, the voltage profile (black dashed curve in Fig. 11) varies from 2.0885 V to 2.5285 V; therefore the dynamic range is compressed
dramatically from 18.32 dB to 1.66 dB, which is very helpful for the accuracy improvement of the ADC. The black dashed curve and the blue solid curve in Fig. 12 are the relative changes corresponding to Figs. 8 and 11. Large changes mainly occur over small voltage measurement values. The logarithmic amplifier not only compresses the dynamic range of the signal but also reduces the relative change, which is a drawback of Log Amp usage. A test was conducted to compare the measurement precision without and with a Log Amp. The measurements were obtained from a signal source with a fixed amplitude of 25 mV. The histograms graphically summarize the signal amplitude distributions after a large number of repeated measurements. The more constricted the distribution, the more precise the measurement. The histogram after the Log Amp (Fig. 13(b)) is better than that without the Log Amp (Fig. 13(a)). In order to compare the statistical variation of voltage-applied ERT system with current-injected ERT system, one thousand differential voltage values from a pair of electrodes opposite the excitation source were recorded for both systems with the same vessel and highly conductive solution (5.46 S/m). The coefficient of variation (CV) is the ratio of the standard deviation to the mean. The CV of the current-injected ERT is 7.35 × 10−3 . In contrast, the CV of voltage-applied ERT is 9.93 × 10−4 . This means in multiphase flow, voltage-applied ERT is able to present more precise measurements than the current ERT when the conductivity of the continuous phase is extremely high. 4. Experiments 4.1. Stationary test The diameter of the test vessel was 14.8 mm and the diameter of agar-gel in it was 2.3 mm. Throughout the whole experiment the object was kept in the same position of the vessel. The conductivity
J. Jia et al. / Flow Measurement and Instrumentation 21 (2010) 184–190
10.00
Frequency
Frequency
8.00 6.00 4.00 2.00 0.00 0.23
0.24 0.25 Amplitude (mV)
0.26
0.27
(a) No logarithmic amplifier.
35.00 30.00 25.00 20.00 15.00 10.00 5.00 0.00 0.23
0.24
0.25 0.26 Amplitude (mV)
189
0.27
(b) With logarithmic amplifier.
Fig. 13. Comparison of histograms without Log Amp and with Log Amp.
a
b Fig. 14. Comparison of cross-section images under different conductivities. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
of the salt solution varied from 0.081 S/m up to 14.860 S/m by changing the concentration of the salt content. The first series of cross-sectional images (a) were obtained from a conventional ERT system with a current source and the ones in the second series ones (b) were obtained from the new voltage-applied ERT system. Both of them were reconstructed using a linear back-projection algorithm (LBP). Fig. 14 indicates that for a lower conductivity solution (from 0.081 S/m to 0.610 S/m), the two ERT systems have a similar performance. The blue area always represents the lower conductivity phase, the red area represents the higher conductivity phase and the green area represents the transition area created by the LBP. When the conductivity of the solution gradually increases, the voltage-applied ERT system was capable of producing better images than the traditional ERT system. 4.2. Liquid–gas flow test The experiments were carried out in a flow loop built at the University of Leeds with a 3.0 m long, 50 mm internal diameter, transparent, vertical working section, which is shown in Fig. 15. Air was introduced into the base of the working section via a central tube inside a Y tee. A thermometer was used to provide continuous monitoring of the water temperature. Two differential pressure sensors for measuring the differential pressure drop were placed along the column at around 2.5 m above the air distributor. The water volumetric flow rate Qw , varying from 0 to 1.94 × 10−3 m3 /s and the air volumetric flow rate Qa , varying from 0 to 1.67 × 10−4 m3 /s were measured separately through a turbine flowmeter and a gas flow controller before they were mixed together. An ERT sensor with 16 electrodes was mounted in the inner wall of the column. The electrodes were made of stainless steel with a contact area of 8 mm (width) by 16 mm (height). The data collection rate was 250 frames/s with an excitation signal frequency of 10.0 kHz.
If the gas velocity and the liquid velocity are ideally identical, the void fraction of gas (α ) is defined as follows: Qa (9) Qa + Qw where Qa is the gas volumetric rate and QW is the liquid volumetric rate. This criterion is a fundamental method to validate the void fraction measurement in the liquid–gas flow. In the vertical flow pipe, the real gas void fraction should not exceed α . Because the velocity of gas bubbles is much higher than that of liquid, this will lead to a smaller void fraction than that of the ideal no slip velocity between the two phases. Tests were classified into two groups with identical flow conditions using just the current-injected ERT system and the proposed voltage-applied ERT in the earlier test. The volumetric rate of the liquid was kept stable at 9.26 × 10−4 m3 /s stable and volumetric gas rates of 4.17 × 10−5 m3 /s, 8.33 × 10−5 m3 /s and 1.67 × 10−4 m3 /s were applied. The gas void fraction should be the same even though conductivities of the liquids are different. Liquids with 0.033 S/m and the 1.060 S/m were used in the test. In Fig. 16, the red and blue curves represent the measured gas void fraction when the conductivity of the liquid is 0.033 S/m and 1.060 S/m respectively and the black curve is derived from the non-slip model in Eq. (9) based on volumetric flow meters. Fig. 16(a) is based on the results from a conventional ERT system with a current source excitation. There is a large gap between the blue and red curve, so the system is considerably affected by the conductivity of continuous phase while the voltage-applied ERT system is exempt form this influence since the blue and red curve have a good agreement (in Fig. 16(b)).
α=
5. Conclusions In order to extend the applications of ERT to the highly conductive multiphase flows, a novel ERT system was developed,
190
J. Jia et al. / Flow Measurement and Instrumentation 21 (2010) 184–190
Fig. 15. Liquid–gas flow loop.
(a) Current source ERT.
(b) Voltage source ERT.
Fig. 16. Comparison between the measurements obtained with a current source ERT and the voltage source ERT. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
which uses a voltage source with current sensing technique as excitation to enlarge the amplitude of the output current up to 320 mA. The specific logarithmic amplifier of the system naturally compresses the dynamic range of the voltage measurement from 18.32 dB to 1.66 dB. Two groups of comparative experiments of gas–water flows with low and highly conductive continuous phases were conducted separately. The results show that under highly conductive conditions, the voltage-applied ERT system can deliver more accurate measurements than the conventional current source ERT. Acknowledgement The authors gratefully acknowledge the support of the British Council in the form of an Overseas Research Students Awards Scheme (ORSAS). References [1] Wang M. Seeing a new dimension—The past decade’s developments on electrical impedance tomography. Progress in Natural Science 2005;15:1–13.
[2] Schlaberg HI, Jia J, Qiu C, Wang M, Li H. Development and application of the Fast Impedance Camera —A high performance dual-plane electrical impedance tomography system. In: 5th international symposium on process tomography in Poland, 2008. [3] Saulnier GJ, Ross AS, Liu N. A high-precision voltage source for EIT. Physiological Measurement 2006;27(5):S221–36. [4] Boone K, Barber D, Brown B. Imaging with electricity: Report of the European concerted action on impedance tomography. Journal of Medical Engineering & Technology 1997;21(6):201–32. [5] A S Ross, et al. Current source design for electrical impedance tomography. Physiological Measurement 2003;24(2):509–16. [6] Bolton GT, et al. Development of an electrical tomographic system for operation in a remote, acidic and radioactive environment. Chemical Engineering Journal 2007;130(2–3):165–9. [7] Wang M, et al. A high-performance EIT system. IEEE Sensors Journal 2005;5(2): 289–99. [8] Rafiei-Naeini M, McCann H. Low-noise current excitation sub-system for medical EIT. Physiological Measurement 2008;29(6):S173–84. [9] Hartov A, et al. Using voltage sources as current drivers for electrical impedance tomography. Measurement Science & Technology 2002;13(9): 1425–30. [10] Datasheet. Hig-voltage, high-current operational amplifier (Rev. E). BurrBrown Products from Texas Instruments, 07 Oct 2005. [11] Seagar AD, Barber DC, Brown BH. Electrical-impedance imaging. IEE proceedings A 1987;134(2):201–10. [12] Fast, voltage-out DC-440 MHz, 95 dB Logarithmic Amplifier, AD8310. Texas instruments.
Contents lists available at ScienceDirect
Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
A novel tomographic sensing system for high electrically conductive multiphase flow measurement Jiabin Jia ∗ , Mi Wang, H. Inaki Schlaberg, Hua Li Institute of Particle Science and Engineering, University of Leeds, Leeds, LS2 9JT, UK
article
info
Article history: Received 4 August 2009 Received in revised form 25 November 2009 Accepted 14 December 2009 Keywords: Electrical resistance tomography High-conductivity multiphase flow Voltage-applied system
abstract Electrical resistance tomography (ERT) has been widely applied in order to extract flow information from various multiphase flows, e.g. the concentration and velocity distributions of the gas phase in gas–water two phase flows. However, the quality of measurement may become very poor from a multiphase flow whose continuous phase has a considerably high electrical conductivity, e.g. seawater (5.0 S/m), using a conventional current-injected ERT system. It is known that a large current excitation is necessary in order to enhance the measurement sensitivity. In practice, it will be very challenging to build a current source with a large amplitude (more than 75 mA) and a high output impedance at a high excitation frequency. This paper presents an implementation of an ERT system with a voltage source and current sensing to overcome the limits of the current source. The amplitude of the current output can reach more than 300 mA. A logarithmic amplifier is used to compress the signal’s dynamic ranges from 18.32 dB to 1.66 dB. The structure and features of this system are presented in this paper and the performances of key circuits are reported. Finally the experimental results from a highly conductive flow (1.06 S/m) are analysed and compared with the measurements obtained from a low conductive flow. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Electrical resistance tomography (ERT) has been proven to be able to measure the spatial distributions of conductivity or volumetric fraction of a two-phase multiphase flow whose continuous phase is electrically conductive. Although it has been developed for almost two decades [1,2], a number of technical issues have not yet been fully solved, such as the measurement accuracy and the immunity of ERT hardware systems to various noises, particularly, the high common mode voltage. ERT measurements can be operated by applying a current through the electrodes and measuring the voltages between the electrodes, or in turn, by applying a voltage and measuring the current [3]. The current-injected method is used in most ERT systems due to its simplicity and good performance over a low conductive range. However, such a system has difficulties obtaining measurements from a high conductivity fluid, e.g. the seawater (5 S/m), with a good measurement precision. Compared with other tomography modalities, the relatively low-cost as well as being compact and simple are the inherent advantages of ERT. Furthermore it is able to collect concise and useful data without distorting the flow field, as well as identify flow regimes and estimate the void fraction of a two-phase flow quickly.
∗
Corresponding author. Tel.: +44 1133432357. E-mail address: [email protected] (J. Jia).
0955-5986/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.flowmeasinst.2009.12.002
Even so, there is still additional potential that can be further exploited to adapt to the requests from industrial applications, including simplifying the system’s structure and enhancing its performance. To date, in the majority of cases, an electrical current source is used as excitation in ERT [4,5]. The continuous aqueous phase in most tests and applications has a limited conductivity range, normally from 0.01 to 0.1 S/m, e.g. tap water. However, the process fluids in some industrial interests are highly conductive, which generally consists of ionic compounds dissolved in water [6]. These fluids have conductivities approximately midway between insulators and metallic conductors. A conductivity range of common solutions is summarized in Table 1. For a flow whose continuous phase has a high conductivity, a larger current excitation is normally required in order to enhance the measurement sensitivity. As shown in Fig. 1, three groups of cross-section images were reconstructed by a conventional ERT system using the same agar-gel and measurement configuration but different continuous phase conductivity and injection currents ranging from 0.037 S/m to 0.637 S/m and 15 mA to 60 mA, respectively. For a fixed injection current, as the conductivity of the continuous phase increases from 0.037 S/m to 0.637 S/m, the crosssectional images become more and more blurred. However when comparing those images with a fixed back ground conductivity (shown in a vertical column of images in Fig. 1), it can be observed that the larger injection current gives rise to a better image. In practice, it is very difficult to build a large current source with the requested performance, such as the high output impedance
J. Jia et al. / Flow Measurement and Instrumentation 21 (2010) 184–190
185
Fig. 1. Cross-sectional images from different continuous phase conductivity and injection current. Table 1 Conductivity ranges of common solutions. Liquid
Conductivity
Tap water Polluted water Sea water 5% Sodium chloride solution 10% Sulphuric acid solution
0.01 to 0.1 S/m 0.1 to 1.0 S/m 3.0 to 5.3 S/m 7.0 S/m 14.0 S/m
(greater than 1 M) at a high output frequency, the large commonmode voltage rejection ratio and the consistent performance over the required frequency range. Conventionally, the output amplitude of a current source is limited to 75 mA at an output frequency of less than 300 kHz [7,8]. Therefore, the voltage source was employed to generate the desired current pattern with the adjustment algorithm [9], which ensures accurate current output, but also makes the systems more complex and has the possibility of diverging the adjustment algorithm. Saulnier [3] introduced a voltage source for electrical impedance tomography, in which a complicated calibration circuit and algorithm were involved. A sense resistor was used to value the applied current in both systems. This additional resistor will produce an additional common mode voltage and increase the output impedance, therefore it may generate new error sources. The aim of this research was to widen the applications of ERT to process mediums with a conductivity dynamic range up to 14.0 S/m. In this paper an innovative voltage drive strategy is presented. The maximum current output can be more than 300 mA. The new circuitry also employs a logarithmic amplifier to compress signals, which produces a good performance for ERT signals with a large dynamic range. Both static and dynamic tests are conducted in order to prove the performance of the system. Results are reported in this paper. 2. Hardware structure 2.1. System diagram Fig. 2 shows the general block diagram of the system: the excitation block is made of a voltage source and a current sensor
Fig. 2. The voltage-applied ERT system diagram.
measuring the current through the target where the voltage source is applied to a pair of electrodes by a multiplexer; the auxiliary sensors interface to simultaneously capture the temperature and pressure of flow in the vessel which is used for the calibration of conductivity measurements; the differential voltage signals are firstly conditioned to make them suitable for the subsequent circuits; and the data acquisition system (DAS) that carries on the analogue-to-digital conversion and transmits the data to a PC via a USB 2.0 communication interface for image reconstruction and data analysis. 2.2. Excitation source As mentioned above, due to the strict requirements implementing a high specification current source, particularly with a large current amplitude, is complicated and difficult in practice. In contrast, a precise voltage source is generally easier and less costly to implement. When using a voltage source in ERT, it is necessary to maintain both the applied voltage and the resulting current with a high degree of precision in order to obtain absolute bulk resistance measurements. The applied voltage remains unchanged over a wide range of load impedances and measurement periods, and therefore the voltage source must have a low output impedance. An ideal voltage source with the following properties is desirable:
186
J. Jia et al. / Flow Measurement and Instrumentation 21 (2010) 184–190
Fig. 3. Diagram of the voltage source.
Output current (A)
0.6 0.5 0.4 0.3 0.2 0.1 Fig. 5. Minimum response voltage changes with solution conductivity.
0 0
0.05 0.1 0.15 0.2 Conductance (siemens)
0.25
Fig. 4. Output current vs conductance.
(a) The output impedance is infinitely low so as to stay constant no matter how the load varies; (b) The ability to supply current should be as high as possible; (c) The frequency and amplitude of the voltage applied can be controlled for different flow regimes; (d) Over-voltage and over-current should be detected swiftly to prevent components and the voltage source from being damaged. As shown in Fig. 3, firstly, a digital sine wave is converted into an analogue signal by a digital to analogue converter (DAC). The high frequency harmonic components created by the staircase sine wave are filtered with a low pass filter. After that, a power amplifier (OPA549) delivers a stable voltage supply. At this stage a digital synchronous signal is generated for use during the later data acquisition step. The voltage source has the following characteristics: the large adjustable output current up to 8 A [10]; the gain bandwidth is 0.9 MHz and can be operated from either single or dual supplies for design flexibility. In addition, the voltage source has two unique features. Firstly, its output can be disabled with a digital control signal. Secondly, when the temperature of the voltage source reaches approximately 160 ◦ C due to an overload event, an internal thermal shutdown circuit will disable the output automatically and provide an indicative signal. Fig. 4 illustrates the approximately linear relationship that was measured between the output current and conductive load. For an ERT system with a current source, the response voltage shrinks dramatically when the conductivity of the solution rises. For example, using the adjacent measurement strategy [11], the minimum value of the voltage measurement in the projection profile is from the electrode pair opposite to the excitation, which reduces from 74.2 mV to 0.2 mV with a conductivity increase of the solution from 0.081 S/m to 14.860 S/m (−25.7 dB) (the dashed curve in Fig. 5). Meanwhile, for the voltage-applied ERT, the voltage measurement attenuates only from 43.5 mV to 4.7 mV (−9.7 dB) (the solid curve in Fig. 5). Fig. 6 shows the measured relationship between the current output of the voltage source and the fluid’s conductivity. It demonstrates that the ERT system with a voltage source is able to supply up to 320 mA current to the vessel in which the electrical conductivity of fluid increases.
Fig. 6. Current output changes with solution conductivity.
voltage from electrodes to calculate the transimpedance across the whole vessel. In this system, a current sensing transformer is used to measure the current. The current sensing transformer provides a non-destructive (non-contact) current measurement. According to the operation principle of the transformer described in Eqs. (1) and (2), the relationship between the primary and secondary parameters are denoted in Eq. (1), the output voltage (Vout ) is an accurate voltage waveform representation of the sensed current (Iin ) flowing into the primary side, where N is the turn ratio of the primary coil Npri and secondary coil Nsec . N = Npri /Nsec = Iin /Iout = Vout /Vin
(1)
Vout = RT × Iin /N .
(2)
2.4. Multiplexer The multiplexer is used to channel the excitation source to each electrode. An ideal multiplexer should have a small onresistance and be able to switch off a large current. Its operation frequency should be as high as possible. The multiplexer is selected to allow a ±200 mA continuous current or ±300 mA peak current (pulsed at 1 ms 10% duty cycle max) to go through the electrodes. Its on-resistance is only 1.25 and its operation bandwidth is 12.5 MHz. This is the commercially available multiplexer with one of the biggest operational currents at the required operational bandwidth. Even though, it is still the bottleneck of the high current application of this ERT system. Using two or more multiplexers in parallel may be the solution for this problem in the future. 2.5. Signal conditioning
2.3. Current sensing At the time of applying the voltage source, it is indispensable to simultaneously measure the current and differential response
The signal conditioning circuit converts the output signals of ERT sensors into a suitable form for the ADC and maintains their essential characteristics. The conditioning entails processes such
J. Jia et al. / Flow Measurement and Instrumentation 21 (2010) 184–190
187
Fig. 7. Structure of the signal conditioner.
as isolating the ERT sensor from the conditioner, modifying the dynamic range to maximise the accuracy of the DAS, removing unwanted signals and limiting the signal’s spectrum. The structure of the signal conditioner is shown in Fig. 7. Each electrode is followed by an AC coupling buffer, which decreases the impedance seen by the subsequent circuit. A high pass filter prevents DC components flowing through. Then, multiplexers route one pair of differential analog input signals, at one time, to the programmable gain instrumentation amplifier (PGIA), which is controlled by input range selection to amplify or attenuate the input signals. A logarithmic amplifier is employed to adjust the dynamic range of signals and to scale the input signal to match the maximum input range of the ADC. More detailed information on this process is explained in the next section. A low pass filter rejects the ripples of the demodulated output of the logarithmic amplifier. The remaining frequency components are converted by a logarithmic amplifier before the analogue to digital conversion. A sampling signal synchronized with the voltage source, controls the timing of analogue to digital conversion. A large first-infirst-out (FIFO) buffer stores data during data acquisition. These conditioning steps modify the dynamic range to maximize the accuracy of DAS, remove the unwanted frequency components and limit the signal’s spectrum. 3. Logarithmic amplifier In the conventional process tomographic measurement, voltage measurements are taken as a reference from a homogeneous sample. Among 16 electrodes, one pair of adjacent electrodes was excited and 13 differential voltages were measured from the remaining pairs of adjacent electrodes. These measured differential voltages were as small as 0.0894 V and as large as 0.7373 V in the same voltage profile (black dashed curve in Fig. 8), which had a dynamic range of 18.33 dB. This large difference may present difficulties for the ADC reaching accurate conversion values. Therefore, a programmable gain amplifier (PGA) is normally required to enhance the measurement dynamics range. Fig. 8 also gives a voltage change after a plastic rod was inserted the vessel (the blue solid curve). It indicates the large changes are around the measurements with the small amplitudes. Based on the amplitudes of input signals, the external control signals provide different gains with the PGA [7]. Eq. (3) denotes a classic relationship between the input and output of the PGA.
VOUT
1000 × VIN , (0 < |VIN | ≤ 0.01) 100 × VIN , (0.01 < |VIN | ≤ 0.1) = 10 × VIN , (0.1 < |VIN | ≤ 1) 1 × VIN , (1 < |VIN | ≤ 10).
(3)
However, the use of PGA usually only regulates the amplitude of the analog signal in discrete gains steps (the derivative of Eq. (3) is shown in the Eq. (4)), which may cause a mismatch between
Fig. 8. Voltage profiles obtained with a linear PGA for the homogeneous and heterogeneous set-ups.
different voltage amplitudes and between different channels due to gain error and the individual difference of PGAs. dVOUT dVIN
1000, (0 < |VIN | ≤ 0.01) 100, (0.01 < |VIN | ≤ 0.1) = 10, (0.1 < |VIN | ≤ 1) 1, (1 < |VIN | ≤ 10).
(4)
Usually, a larger closed-loop gain leads to a larger gain error. For example, the gain error of a commercial programmable gain amplifier (PGA202) is 6% when its gain is 1000 at 100 kHz. In addition, the larger gain also results in a longer settling time to respond to the step change of input. The typical settling time is 10 µs at a gain of 1000 for the PGA202, which is one fifth of the period of the signal frequency 20 kHz. This rather slows the speed of the ERT system and complicates the operations. On the other hand, the settling time introduced by a logarithmic amplifier is 40 ns. An offset adjustment and full-range calibration is normally required for a PGA after the change of its gain in order to eliminate the side effects of the PGA. Therefore this work utilises a demodulating Log Amp to compress and demodulate AC input signals, yielding the logarithm of the rectified signal’s envelope. The combination of a Log Amp and a conventional ADC can reduce the problems caused by the PGA as discussed above, as well as simplifying the circuitry. The logarithmic amplifiers perform a more complex operation than classical linear amplifiers, and their circuits are significantly different. Although amplification is embedded inside the chip, the essential purpose of a Log Amp is not to amplify but to compress a signal of wide dynamic range to its decibel equivalent. The basic function is conversion of a signal from one domain of representation to another, via a precise non-linear transformation (Eq. (5)). VOUT = VY log(VIN /VX )
(5)
where: VOUT is the demodulated and filtered output voltage; VY is the voltage slope. The logarithm is usually taken to base ten, in which case VY is also the volts-per-decade; VIN and VX are the input voltage and the intercept voltage respectively.
188
J. Jia et al. / Flow Measurement and Instrumentation 21 (2010) 184–190
Fig. 9. Input level vs output of Log Amp by adjusting the logarithmic slope. Fig. 11. Voltage profiles obtained with a Log Amp for the homogeneous and heterogeneous set-ups.
Fig. 10. Input level vs gain. Fig. 12. Relative change of voltage profiles.
Transfer the Eq. (5) in terms of power [12] as Eq. (6) below. VOUT = VSLOPE (PIN − PO )
(6)
where: VOUT is the demodulated and filtered baseband output (V ); VSLOPE is the logarithmic slope; PIN is the input power (dBV), defined as decibels with respect to a 1 V rms sine wave (Vo ); PO is the logarithmic intercept (dBV). The Eq. (7) illustrates the calculation between dBV and V. dBV = 20 log (VIN /V0 ) .
(7)
Now, the output voltage is proportional to the Log of the input power, with an adjustable slope and intercept by external resistors configuration to suit the different input range. In Fig. 9, the default relation between the input and output of the logarithmic amplifier is shown in the black dotted line; the blue solid line indicates the adjusted relation. So, the minimum working input range can be changed from 0.01 mV to 0.3 mV. The Log Amp function described by Eq. (5) differs from the Eq. (3) of a linear PGA. Comparing with the incremental gain described in Eq. (4), Eq. (8) is a very strong non-linear function of the instantaneous value of VIN by calculating the derivative of Eq. (5). dVOUT dVIN
=
VY VIN · ln(10)
.
(8)
As shown in Fig. 10, the incremental gain of the logarithmic amplifier (blue solid line) is inversely proportional to the instantaneous value of the input level, which means the signals dropped in the lower part of the dynamic range will automatically get a larger gain; the signals at the higher part of the dynamic range will get a smaller gain, or even an attenuation when the input is more than 9.35 dBV (2.934 V). The incremental gain of the PGA is also given in Fig. 10 (black dashed line), which is inversely proportional to the total input level but in a discrete stepped way. By using the Log Amp to process the same data in Fig. 8, the voltage profile (black dashed curve in Fig. 11) varies from 2.0885 V to 2.5285 V; therefore the dynamic range is compressed
dramatically from 18.32 dB to 1.66 dB, which is very helpful for the accuracy improvement of the ADC. The black dashed curve and the blue solid curve in Fig. 12 are the relative changes corresponding to Figs. 8 and 11. Large changes mainly occur over small voltage measurement values. The logarithmic amplifier not only compresses the dynamic range of the signal but also reduces the relative change, which is a drawback of Log Amp usage. A test was conducted to compare the measurement precision without and with a Log Amp. The measurements were obtained from a signal source with a fixed amplitude of 25 mV. The histograms graphically summarize the signal amplitude distributions after a large number of repeated measurements. The more constricted the distribution, the more precise the measurement. The histogram after the Log Amp (Fig. 13(b)) is better than that without the Log Amp (Fig. 13(a)). In order to compare the statistical variation of voltage-applied ERT system with current-injected ERT system, one thousand differential voltage values from a pair of electrodes opposite the excitation source were recorded for both systems with the same vessel and highly conductive solution (5.46 S/m). The coefficient of variation (CV) is the ratio of the standard deviation to the mean. The CV of the current-injected ERT is 7.35 × 10−3 . In contrast, the CV of voltage-applied ERT is 9.93 × 10−4 . This means in multiphase flow, voltage-applied ERT is able to present more precise measurements than the current ERT when the conductivity of the continuous phase is extremely high. 4. Experiments 4.1. Stationary test The diameter of the test vessel was 14.8 mm and the diameter of agar-gel in it was 2.3 mm. Throughout the whole experiment the object was kept in the same position of the vessel. The conductivity
J. Jia et al. / Flow Measurement and Instrumentation 21 (2010) 184–190
10.00
Frequency
Frequency
8.00 6.00 4.00 2.00 0.00 0.23
0.24 0.25 Amplitude (mV)
0.26
0.27
(a) No logarithmic amplifier.
35.00 30.00 25.00 20.00 15.00 10.00 5.00 0.00 0.23
0.24
0.25 0.26 Amplitude (mV)
189
0.27
(b) With logarithmic amplifier.
Fig. 13. Comparison of histograms without Log Amp and with Log Amp.
a
b Fig. 14. Comparison of cross-section images under different conductivities. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
of the salt solution varied from 0.081 S/m up to 14.860 S/m by changing the concentration of the salt content. The first series of cross-sectional images (a) were obtained from a conventional ERT system with a current source and the ones in the second series ones (b) were obtained from the new voltage-applied ERT system. Both of them were reconstructed using a linear back-projection algorithm (LBP). Fig. 14 indicates that for a lower conductivity solution (from 0.081 S/m to 0.610 S/m), the two ERT systems have a similar performance. The blue area always represents the lower conductivity phase, the red area represents the higher conductivity phase and the green area represents the transition area created by the LBP. When the conductivity of the solution gradually increases, the voltage-applied ERT system was capable of producing better images than the traditional ERT system. 4.2. Liquid–gas flow test The experiments were carried out in a flow loop built at the University of Leeds with a 3.0 m long, 50 mm internal diameter, transparent, vertical working section, which is shown in Fig. 15. Air was introduced into the base of the working section via a central tube inside a Y tee. A thermometer was used to provide continuous monitoring of the water temperature. Two differential pressure sensors for measuring the differential pressure drop were placed along the column at around 2.5 m above the air distributor. The water volumetric flow rate Qw , varying from 0 to 1.94 × 10−3 m3 /s and the air volumetric flow rate Qa , varying from 0 to 1.67 × 10−4 m3 /s were measured separately through a turbine flowmeter and a gas flow controller before they were mixed together. An ERT sensor with 16 electrodes was mounted in the inner wall of the column. The electrodes were made of stainless steel with a contact area of 8 mm (width) by 16 mm (height). The data collection rate was 250 frames/s with an excitation signal frequency of 10.0 kHz.
If the gas velocity and the liquid velocity are ideally identical, the void fraction of gas (α ) is defined as follows: Qa (9) Qa + Qw where Qa is the gas volumetric rate and QW is the liquid volumetric rate. This criterion is a fundamental method to validate the void fraction measurement in the liquid–gas flow. In the vertical flow pipe, the real gas void fraction should not exceed α . Because the velocity of gas bubbles is much higher than that of liquid, this will lead to a smaller void fraction than that of the ideal no slip velocity between the two phases. Tests were classified into two groups with identical flow conditions using just the current-injected ERT system and the proposed voltage-applied ERT in the earlier test. The volumetric rate of the liquid was kept stable at 9.26 × 10−4 m3 /s stable and volumetric gas rates of 4.17 × 10−5 m3 /s, 8.33 × 10−5 m3 /s and 1.67 × 10−4 m3 /s were applied. The gas void fraction should be the same even though conductivities of the liquids are different. Liquids with 0.033 S/m and the 1.060 S/m were used in the test. In Fig. 16, the red and blue curves represent the measured gas void fraction when the conductivity of the liquid is 0.033 S/m and 1.060 S/m respectively and the black curve is derived from the non-slip model in Eq. (9) based on volumetric flow meters. Fig. 16(a) is based on the results from a conventional ERT system with a current source excitation. There is a large gap between the blue and red curve, so the system is considerably affected by the conductivity of continuous phase while the voltage-applied ERT system is exempt form this influence since the blue and red curve have a good agreement (in Fig. 16(b)).
α=
5. Conclusions In order to extend the applications of ERT to the highly conductive multiphase flows, a novel ERT system was developed,
190
J. Jia et al. / Flow Measurement and Instrumentation 21 (2010) 184–190
Fig. 15. Liquid–gas flow loop.
(a) Current source ERT.
(b) Voltage source ERT.
Fig. 16. Comparison between the measurements obtained with a current source ERT and the voltage source ERT. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
which uses a voltage source with current sensing technique as excitation to enlarge the amplitude of the output current up to 320 mA. The specific logarithmic amplifier of the system naturally compresses the dynamic range of the voltage measurement from 18.32 dB to 1.66 dB. Two groups of comparative experiments of gas–water flows with low and highly conductive continuous phases were conducted separately. The results show that under highly conductive conditions, the voltage-applied ERT system can deliver more accurate measurements than the conventional current source ERT. Acknowledgement The authors gratefully acknowledge the support of the British Council in the form of an Overseas Research Students Awards Scheme (ORSAS). References [1] Wang M. Seeing a new dimension—The past decade’s developments on electrical impedance tomography. Progress in Natural Science 2005;15:1–13.
[2] Schlaberg HI, Jia J, Qiu C, Wang M, Li H. Development and application of the Fast Impedance Camera —A high performance dual-plane electrical impedance tomography system. In: 5th international symposium on process tomography in Poland, 2008. [3] Saulnier GJ, Ross AS, Liu N. A high-precision voltage source for EIT. Physiological Measurement 2006;27(5):S221–36. [4] Boone K, Barber D, Brown B. Imaging with electricity: Report of the European concerted action on impedance tomography. Journal of Medical Engineering & Technology 1997;21(6):201–32. [5] A S Ross, et al. Current source design for electrical impedance tomography. Physiological Measurement 2003;24(2):509–16. [6] Bolton GT, et al. Development of an electrical tomographic system for operation in a remote, acidic and radioactive environment. Chemical Engineering Journal 2007;130(2–3):165–9. [7] Wang M, et al. A high-performance EIT system. IEEE Sensors Journal 2005;5(2): 289–99. [8] Rafiei-Naeini M, McCann H. Low-noise current excitation sub-system for medical EIT. Physiological Measurement 2008;29(6):S173–84. [9] Hartov A, et al. Using voltage sources as current drivers for electrical impedance tomography. Measurement Science & Technology 2002;13(9): 1425–30. [10] Datasheet. Hig-voltage, high-current operational amplifier (Rev. E). BurrBrown Products from Texas Instruments, 07 Oct 2005. [11] Seagar AD, Barber DC, Brown BH. Electrical-impedance imaging. IEE proceedings A 1987;134(2):201–10. [12] Fast, voltage-out DC-440 MHz, 95 dB Logarithmic Amplifier, AD8310. Texas instruments.