A high frequency electronic transducer for multiphase flow measurements

A High Frequency Electronic Transducer for Multiphase Flow Measurements

Francisco Antônio Belo

Departamento de Engenharia Mecânica

Centro de Tecnologia

Universidade Federal da Paraíba

58059-900 João Pessoa, PB Brazil

[e-mail]

Luiz Felipe Mendes de Moura

Departamento de Engenharia Térmica e de Fluidos

Faculdade de Engenharia Mecânica

Universidade Estadual de Campinas

13083-970 Campinas, SP Brazil

[e-mail]

Abstract

This paper describes an electronic transducer for multiphase flow measurement. Its high sensitivity, good signal to noise ratio and accuracy are achieved through an electrical impedance sensor with a special guard technique. The transducer consists of a wide bandwidth and high slew rate differentiator where the lead inductance and stray capacitance effects are compensated. The sensor edge effect is eliminated by using a guard electrode based on the virtual ground potential of the operational amplifier. A theoretical modeling and a calibration method are also presented. The results obtained seem to confirm the validity of the proposed technique.

Keywords: Multiphase Flow, Measurements, Tomography.

Introduction

The measurement of multiphase flows is important for research as well as industrial application. The determination of the effective transport properties of multiphase systems has attracted the attention of many researchers. There are no exact analytical predictions of the effective properties of random multiphase systems for given phase properties and volume fractions, even for some simple problems (Kin and Torquato, 1990). The description of the interfacial structure and its time evolution, as well as the gradients which control the mass, momentum, and energy transfer at these phase boundaries, is the most important challenge in two-phase flow analysis, with application in power plants and in chemical or petroleum processes.

Electrical and optical sensors are the most adequate devices to investigate multiphase flows because they can be accurate and are neither intrusive nor invasive. The electrical sensor may present a faster time response than the optical (Huang et al., 1992). The electrical capacitance sensor is based on the measurement of polarization (permittivity) without direct interaction with the flow (uninvasive). Generally, the permittivity sensitivity to temperature is negligible compared to that of conductivity. Moreover, the relative permittivity is not affected by changes in the ionic concentration (Geraets and Borst, 1988), which makes the capacitance sensor more adequate than the conductance sensor for multiphase flow measurements.

The real part of the complex electrical impedance related to a multiphase flow corresponds to very low values (capacitance from about 0.01 to 20 pF), such that the stray capacitance is the principal problem when working with transducers in multiphase flow measurement. Depending on the sensor arrangement and on the electronic transducer, in many applications the stray capacitance may be larger than the unknown capacitance and its value may fluctuate. Stray-immune transducers can be implemented by using an intrinsically stray-immune circuit configuration, with both sensor electrodes floating, or by using an active guard where one of the two sensor electrodes is grounded, as described by Huang et al. (1988). The thermal parameter and the electronic frequency are important for the measurement system output quality (Belo and Leite, 1992). High sensitivity is also necessary for high spatial resolution in the flow pattern investigation.

Kanno (1980) arranged capacitance measuring methods into four main categories: resonance, oscillation, bridge and charge/discharge. According to Huang et al. (1988), although some new transducers have been developed since then, their principles can still be allocated into one of the four groups above.

The resonance method is able to measure both the unknown capacitance and its parallel loss over a wide frequency range. A typical measuring device in the range of 0.1 to 300 MHz is described by Bennada et al. (1982). The operating steps are often done manually; therefore, the method is not suitable for continuous monitoring of physical variables, and hence is not currently used in on-line capacitance transducers.

The RC oscillation methods are more frequently used in general purpose capacitance meters (Kraus, 1980). Generally, these circuits are not accurate and present some drawbacks such as oscillation frequency influenced by the shutting conductance, poor sensitivity to small capacitance changes and poor frequency stability. The LC oscillation methods can work with a frequency as high as 200 MHz. The baseline drift of this circuit is mainly due to the stray capacitance influence. Green and Cunlife (1981) applied feedback from the output to minimize this drift. Their circuit will not measure steady-state capacitance but will measure fluctuations in the frequency range of 1 to 1000 Hz, with a resolution of 0.1 fF. A circuit design suitable for steady-state measurement uses a reference oscillator (Floyed et al., 1985). Walz (1995) developed a current-controlled LC oscillator (a combination of the resonance and LC methods), utilizing thermistor feedback in order to establish definite resonance conditions, applied to the measurement of the magnetic aftereffect.

The main disadvantage of the above circuits is that the stray capacitance is included in the measurement. The AC bridge method is still recognized as the most accurate and stable method for capacitance measurement (Heerens, 1986). For measurements using frequency below 100 kHz, the AC bridge with feedback (transformer-ratio bridge transducer) is recommended. The charge/discharge method is described by a patent held by Endress and Hausser Ltd. (1984), but it is not immune to stray capacitance. A stray immune charge/discharge technique, operating up to 5 MHz, is presented by Huang et al. (1989), with experimental verification up to 2 MHz (Huang et al, 1992).

The two principal approaches to a multiphase system are the effective medium and the rigorous boundary equation solutions. A comparison of the effective medium approach (Bruggeman, 1935) with the first complete solution of the film flow (Coney, 1973) was made by Andreussi et al. (1988). Albouelwafa and Kendal (1979) adapted the microwaves guide formula to calculate the capacitance of a multiphase flow. Geraets and Borst (1988) developed a sensor with helical electrodes mounted on a dielectric pipe surface to measure the time-average void fraction in two-phase annular flows. The principal problem with the impedance sensors is the nonhomogeneous distribution of the electrical field inside the pipe. Auracher and Daubert (1985) overcame this problem by using an inner electrode. However, this is an intrusive technique.

A new technique for spatial phase distribution measurement, using several electrodes, is the phase tomography image system. Tomography is normally known as a radiological technique to obtain clear X-ray images of deep internal structures by focusing on a specific plane within a body. Some studies involving tomography applied to multiphase flows (MacCuaig et al., 1985) used gamma-ray beams to generate three-dimensional density maps of laboratory-scale fluidized beds. The X-ray computed tomography techniques were applied to multiphase flows by Vinegar and Wellington (1986). Hussein and Meneley (1986) applied neutron tomography to two-phase flows. Plaskowski et al. (1987) described the application of ultrasound to multiphase imaging flows. Process engineering studies involving impedance tomography include capacitive transducer imaging of oil-gas flows (Huang et al., 1992) and fluidized beds (Fasching and Smith, 1991), and capacitive and resistive imaging of dense-phase pneumatic conveying (McKee, 1993). In the high-energy tomography systems, the ray paths are independent of the medium present in the sensor. On the other hand, the sensitivity of each electrode pair in an electrical impedance tomography system is a function of the unknown phase distribution (Xie et al., 1989a).

The two-phase flow impedance tomography methods are sequential hardware processes that utilize the charge/discharge technique (Dickin et al., 1992) or the LC oscillation technique with signal feedback (Fasching and Smith, 1991). In a parallel tomography system (Belo, 1995), each electrode has its own demodulator and an intrinsically stray-immune transducer. The parallel system, associated with the electronic transducer, offers the possibility of a faster data capture, better imaging resolution and sensitivity due to its better signal to noise relation and high frequency response.

System description

A practical impedance transducer always has metallic elements (screen, plates, film and ground plan), whether grounded or not, to protect the electrodes from interference by the external fields and to improve the behavior of the electronic circuit. These elements are associated with leads, as shown in Fig. 1, where:

C_x is the capacitance value of the multiphase mixture;

C_s is the stray capacitance of the screen or plates and the electrode;

C_p is the stray capacitance of the measuring circuit connected to the sensor;

I_L is the stray inductance of the measuring circuit connected to the sensor.

Fig. 1 Elements of an electronic impedance transducer.

The measurement system developed to compensate for the stray effects described above is shown in Fig. 2. The electronic transducer is an intrinsically stray immune capacitance measurement circuit that provides the impedance between the emitter and receiver electrodes as a function of the input and output voltage signals and the amplifier parameters. The input signal (coming from a remote oscillator) is measured at the emitter electrode. The operational amplifier input is directly connected to the receiver electrode that acts as a virtual ground and avoids any capacitance with other grounded elements. The output signal is measured directly at the operational amplifier output.

Fig. 2 Measurement system for multiphase flow.

With an operational amplifier of wide bandwidth and high slew rate, the capacitance of the sensor is given by Eq. (1). The operational amplifier used in this work was the OPA 621.

(1)

where C_x is the sensor impedance;

f is the signal frequency

R_f is the feedback resistance;

V_i is the input signal;

V_o is the output signal;

The electronic circuit and the guard electrodes used to avoid the sensor edge effect are shown in Fig. 3. The receiver electrode is a virtual ground and the longitudinal guard electrodes are grounded. Consequently, the electrical field near the receiver electrode is uniform and the edge effect remains outside the sensor volume.

Fig. 3 The guard and the electronic arrangement used to avoid the edge effect.

A capacitance tomography system for two-phase flow pattern visualization (bubbly, slug, annular, stratified or droplet) was built with eight electrodes around a glass tube, as shown in Fig. 4. In this system, when an electrode is an emitter, the seven other electrodes are receivers, leading to a parallel reading tomography type. Using this technique, only n electrodes must be scanned, while with a sequential technique n(n-1)/2 electrodes must be scanned. For both techniques, the number of independent readings are n(n-1)/2. A very important feature of this technique is that its frequency response may be greater than that of other tomography systems.

Fig. 4 Arrangement of eight electrodes around a glass tube.

A linear back projection algorithm based on the finite element method was developed for a capacitance tomography system applied to two-phase flows (Moura and Belo, 1996).

In order to validate experimentally the prototype of the tomography system described above, the analytical solution of the electrical potencial equation for two electrodes making any angle is used (see Fig. 5). The capacitance between the two electrodes is given by Eq. (2), according to Belo (1995).

(2)

where:

e₁ is the electric permittivity of phase 1;

e₂ is the electric permittivity of phase 2;

e₃ is the electric permittivity of the insulator (pipe);

f_i is the electrode angle;

R₁ is the radius of the annular flow;

R₂ is the internal radius of the insulator;

R₃ is the external radius of the insulator.

Fig. 5 Two electrodes around a glass tube.

Experimental results

Experimental and theoretical analyses of the electronic transducer were done for different sensor geometries. Performance measurements of the integrated system (electronic transducer and sensor) with and without guard electrodes were done and a calibration method to compensate for the sensor fabrication errors was proposed.

A first capacitance sensor prototype was made with two electrodes with a 179° angle, fixed around a glass tube. Table 1 shows the sensor parameters.

Table 1 Parameters of the two-electrode sensor.

All measurements were performed with a HP 34401A multimeter. The uncertainty associated wit the voltage, feedback resistance and signal frequency measurements were 0.5 mV, 10 W and 1 kHz , respectively.

The response of the sensor with longitudinal guard electrodes is presented in Fig. 6. Water was continuously added to the sensor and the transducer output signal recorded. The uncertainty associated to the water volume measurement was 0.5 ml. A comparison between the response of the sensor with and without guard electrodes is shown in Fig. 7. It should be observed that without guard electrodes the output signal did not monitor the volume of water inside the sensor. The relative error was of about 7 %.

Fig. 6

Response of the sensor with guard electrodes when increasing the water volume.

Fig. 7 Response of the sensor with the guard electrodes on and off.

Figure 8 shows the response of the sensor containing air, with and without guard electrodes (2 MHz). Here the transducer output signal is shown as a function of the input signal. From Eq. (1) it is clear that the data slope is proportional to the sensor impedance. The results of the fit (C=0.711 without guard and C=0.925 with guard) give a relative error of about 30% due to the absence of guard electrodes.

Fig. 8 Response of the sensor containing air, with and without guard electrodes.

The sensor calibration was made with chemical substances characterized by a high degree of purity (carbon tetrachloride, distilled water, ethyl alcohol) and with ambient air.

Figure 9 shows the transducer output for (a) ambient air and carbon tetrachloride at 2.63 MHz and (b) distilled water and ethyl alcohol at 500 kHz. From the transducer response (ratio between output to input signal), the sensor capacitance was calculated by using Eq. (1).An uncertainty analysis Bruns et al. (1996) applied to Eq. (1) gives a capacitance uncertainty of 0.06 pF (2.63 MHz) and 0.12 pF (500 Hz). The experimental results were compared to the analytical values of the capacitance sensor obtained from Eq. (2).

Fig. 9

Table 2 presents the relative error between the analytical and experimental sensor capacitance values. These results are good, considering the uncertainties of the sensor geometry, glass parameters and transducer electronics. From these data a calibration curve may be obtained, relating directly the analytical value of the sensor capacitance to the transducer response.

Table 2 Relative error between analytical and experimental results

An annular two-phase flow was simulated experimentally by introducing a glass rod at the center of the sensor containing water. Figure 10 shows a comparison between the sensor capacitance experimental results and the corresponding analytical results based on Eq. (2), for different glass rod diameters .

Fig. 10 Transducer output for a simulation of annular two-phase flow

The second capacitance sensor was a tomography system prototype made with eight electrodes fixed around a glass tube, such as presented in Fig. 4. Table 3 shows the geometric parameters of the sensor.

Table 3 Geometric characteristics of the tomography system

The analytical response of this capacitance sensor filled with water or ambient air was determined from Eq. (2). The measurements were done by the parallel processing technique described above, where the source electrode is represented by index "o", whereas index "i" is associated with the receiving electrode.

Figure 11 presents the experimental and analytical results of the capacitance between different electrode pairs of the tomography system containing air or water. The capacitance measurement uncertainty was the same as for the two electrodes sensor (about 0.10 pF) and the analytical results were obtained from Eq. (2). The principal systematic errors were due to the sensor's geometric imperfections, the use of a single input signal measurement and the absence of guard electrodes. The measurement error for a pair of adjacent electrodes of the sensor containing water was about 4%. The measurement error for the sensor containing air reached 25%, with about 5% due to the single input signal measurement. These results are in agreement with those reported in Figs. 7 and 8 and with the results presented by Purcell (1973) for the capacitance between parallel circular plates containing air.

Fig. 11

The measurements of capacitance C01 and C10 (a pair of adjacent electrodes) with the sensor containing water (500 kHz) are shown in Fig. 12. The variation of the angular coefficient between the curves may be related to the sensor's geometric imperfections, while the constant term may be related to the offset drift of the alternate voltage measurement technique, characteristic of each meter.

Fig. 12 Response of C01 and C10 with the sensor containing water.

Figure 13 shows the measurements of capacitance C01 and C10 with the sensor containing air (2 MHz). The measurements of capacitance C02 and C20 (a pair of electrodes separated by one electrode) with the sensor containing air (8 MHz) are shown in Fig. 14.

Fig. 13 Response of C01 and C10 with the sensor containing air.

Fig. 14 Response of C02 and C20 with the sensor containing air.

It was necessary to adjust the input signal frequency in order to achieve the desirable sensitivity and resolution. The measurement of C04 (a pair of opposite electrodes) with the sensor containing only air will require a higher frequency, while the measurement of the same electrode pair with the sensor containing only water will require a lower frequency. Presently, tests are being conducted up to 100 MHz, employing the operational amplifier OPA 621 as a differentiator and the schotty diode BAT 82 as a demodulation element.

Conclusion

The analysis of the experimental data seems to prove the viability of the proposed measurement system. The analytical model was adequate to evaluate both the hardware performance and the calibration method. The longitudinal guard electrodes, the sensor's geometric and electrical parameters, the arrangement of electronic elements, the system layout, and the input signal were the most important parameters concerning the accuracy of the measurement system. The parallel reading type of tomography was important to achieve high sensitivity and resolution. The proposed electronic circuit associated with the system layout was effectively immune to stray capacitance in all frequency ranges.

Manuscript received: October 1997, Technical Editor: Angela Ourívio Nieckele.

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Publication Dates

• Publication in this collection
  11 Oct 2001
• Date of issue
  Dec 1999

History

• Received
  Oct 1997