2.5 Cross-Correlation Flow Metering

Transcription

1 2.5 Cross-Correlation Flow Metering Receiver B. G. LIPTÁK (1982, 1995) H. M. HASHEMIAN (23) FT Correlation Flow Sheet Symbol Current Applications Sizes Pumped paper pulp, pneumatically conveyed coal dust, cement, grain, plastic granules, chalk, water flow in nuclear and industrial plants, and animal foodstuffs Practically unlimited Cost A 4-in 15 # mass flowmeter with epoxy-resin-lined, enameled steel pipe costs $6. If the sensor costs are not considered, the electronic detector alone is around $2. Nuclear power plant flow metering installations range from $25, to $5,. Partial List of Suppliers Analysis and Measurement Services Corp. ( Endress+Hauser Inc. ( Kajaani Electronics Ltd. (Finland) The oldest and simplest methods of flow measurement are the various tagging techniques. Here, a portion of the flowstream is tagged at some upstream point, and the flow rate is determined as a measurement of transit time. Variations of this technique include particle tracking, pulse tracking, and dye or chemical tracing, including radioactive types. The advantages of tagging techniques include the ability to measure the velocity of only one component in a multicomponent flowstream without requiring calibration or pipeline penetration. For example, electromagnetic tagging of gas-entrained particles allows for the determination of their speed through the detection of their time of passage between two points that are a fixed distance from each other. Flow metering based on correlation techniques 1,2 is similar in concept to the tagging or tracing techniques, because it also detects transit time. As illustrated in Figure 2.5a, any measurable process variable that is noisy (displays localized variations in its value) can be used to build a correlation flowmeter. The only requirement is that the noise pattern must persist long enough to be seen by both detectors A and B as the flowing stream travels down the pipe. Flow velocity is obtained by dividing the distance (between the identical pair of detectors) by the transit time. In recent years, the required electronic computing hardware, with fast pattern recognition capability, has become available. Consequently, it is feasible to build on-line flowmeters using this technique. 3 The following process variables display persistent enough noise patterns (or local fluctuations) that correlation flowmeters can be built by using an identical pair of these sensors: Density Pressure Temperature Ultrasonics Gamma radiation Capacitive density Conductivity Flow m(t) n(t) Position A m(t) FIG. 2.5a Cross-correlation flow metering. Position B Delay A Transit τ B n(t) Transport Pipe Upstream Transducer Signal t Downstream Transducer Signal t 183

2 184 Flow Measurement Several of the above process variables (such as temperature, 4,5 gamma radiation, and capacitive density 6 ) have been investigated as potential sensors for correlation flowmeters. One instrument has been developed that uses the principle of ultrasonic cross-correlation to measure heavywater flow. 3 Others are available for paper pulp applications using photometric sensors and for solids flow measurement utilizing capacitance detectors (Figure 2.23v). For crosscorrelation flowmeters applied in solids flow applications, refer to Section When fully developed, correlation flow metering can extend the ability to measure flow not only into the most hostile process environments but also into areas of multiphase flow and into three-dimensional flow vectoring. NUCLEAR POWER PLANT APPLICATIONS Most process variables fluctuate, so the outputs of most process sensors undergo variations in their output. These variations can also be exploited to obtain cross-correlation flow sensors. More specifically, process sensors that normally measure temperature, pressure, radiation, or other process variables can also be used to determine the velocity of fluid flow. This can be done passively by recording the sensor output for a period of time and extracting the fluctuating component of the output (called the AC signal). If a pair of sensors are installed in the same pipe at a known distance from each other, flow velocity can be obtained by crosscorrelating the two AC signals from these two sensors. Once the fluid flow velocity is determined, the volumetric or mass flow rate can be calculated on the basis of the physical dimensions of the process piping and the properties of the fluid. Flow Direction Sensor Y Output Sensor X Output T 1 x(t) Transit Upstream Sensor Signal Downstream Sensor Signal FIG. 2.5b Illustration of principle of cross-correlation flow monitoring. T 2 y(t) T 1 T 2 τ = Transit Pipe Determining the Transit The principle of cross-correlation flow measurement is illustrated in Figure 2.5b, where a pipe is shown with two sensors installed some distance apart. Also shown in Figure 2.5b are the AC outputs of these two sensors. The output of one sensor is represented by x(t), and the output of the other sensor is represented by y(t). These output signals may be crosscorrelated to identify the transit time between the two sensors. The transit time is the time required for the process fluid to travel between the two sensors. To obtain the fluid flow velocity, the transit time has to be divided by the distance between the two sensors. To cross-correlate the outputs of two sensors, first the two output signals are multiplied by each other, after which the second signal is slowly shifted, a little bit at a time, toward the first signal until the two signals are superimposed. The averaged product of the two signals is then plotted as a function of the time shift. This plot will normally peak at a R xy (t) τ Shift (t) FIG. 2.5c Cross-correlation plot and illustration of transit time. time that is equal to the transit time, as illustrated in Figure 2.5c. The cross-correlation function (R xy ) for the signals x(t) and y(t) is given by the following equation: R () t = x ( z ) xy y ( t + z ) dz 2.5(1)

3 2.5 Cross-Correlation Flow Metering 185 In this equation, t is the time interval that one signal is shifted toward the other, and z is the integration variable. The cross-correlation function, R xy, will normally have values between +1. and 1., provided that x and y are constructed from mean-removed raw signals divided by their standard deviations. Values close to +1. indicate a good direct correlation between two signals, and values close to 1. indicate a good inverse correlation. Conversely, when there is little or no correlation between the two signals, the value of R xy, will approach zero. The transit time can also be obtained from plotting the phase between the two signals as a function of frequency. For this, the slope of the phase as a function of frequency is used to calculate the transit time as follows: 2π Fτ = φ φ slope ( Degrees/ Hz) τ = = 2π F 36 ( Degrees) 2.5(2) Phase (Degrees) FIG. 2.5d Phase plot and calculation of transit time. 8 2 Slope = 16.2 /Hz Transit Estimate = 44.4 msec 4 6 Frequency (Hz) 8 1 where τ = transit time (sec) ϕ = change in FFT phase (degrees) F = frequency band of highest coherence (Hz or sec 1 ) over which φ occurs 2π (radians) = 36 To eliminate the effects of process variations that are not related to flow, the slope is calculated over the region of the phase spectrum where the two signals are most coherent. Figure 2.5d shows a phase vs. frequency plot and the calculation of the transit time. As shown by Equation 2.5(2) and Figure 2.5d, the transit time is calculated by dividing the slope of the phase plot by 36. Reliability and Accuracy The reliability of cross-correlation flow metering is improved if 1. The response times of the two sensors are similar and fast compared to the spectrum of the process and the transit time that must be resolved. 2. The correlation between the data does not occur at or after the break frequency of the sensor and/or the data acquisition system. 3. The information being correlated can be resolved from the effects of other process perturbations and noise. In theory, any two sensors can be used to provide signals for cross-correlation flow measurements as long as the two sensors can register a process parameter that affects the output of both sensors. For example, signals from two temperature sensors (thermocouples, RTDs, and so forth) or two pressure sensors can be cross-correlated to determine fluid flow rate. Figure 2.5e shows a phase plot for two RTDs. This Phase (Degrees) Frequency (Hz) FIG. 2.5e Cross-correlation phase plot for a pair of RTDs. information was generated in a laboratory test loop where cross-correlation flow equipment and techniques were developed and validated. The plot shows the experimental data as well as the least-squares fit to the data. The least-squares fit provides the slope of the line that is then divided by 36 to obtain the transit time. Based on these laboratory experiments, it has been determined that the error in cross-correlationbased flow measurement is less than 3%. Even dissimilar sensors, such as a temperature and a pressure detector, can be used for cross-correlation flow measurement if the temperature and pressure measurements are related. Nuclear Power Applications Phase Data Linear Fit The cross-correlation technique of flow metering has been used successfully in nuclear power plants by using the thermal hydraulic fluctuations within the reactor coolant system, which are detectable by temperature, pressure, and radiation sensors. For example, the signals from temperature and neutron detectors have been cross-correlated to monitor the

4 186 Flow Measurement 1. Illustration of Correlation Function 8 Correlation Function.5. Correlation Function Peak at 6 msec Detector Output (millivolts) A 44C (msec) FIG. 2.5f Plot of correlation function for a pair of signals from a thermocouple and a neutron detector (sec) FIG. 2.5g Examples of raw data for a pair of sensors used for cross-correlation flow measurements. flow through the core. Figure 2.5f shows a cross-correlation plot for a thermocouple that is installed on top of the reactor core inside a pressurized water reactor (PWR) and a neutron detector located outside the reactor at a lower elevation than the thermocouple. This method is not normally used for flow measurements in nuclear power plants. Rather, it is used for monitoring flow rate changes and for detecting flow blockages within the reactor coolant system. A more direct means of flow measurements in PWR plants is to cross-correlate the signals from a pair of nitrogen 16 (N-16) radiation detectors that are installed on the reactor coolant pipes. The N-16 detectors measure the gamma radiation produced in the reactor water by the neutron bombardment of oxygen-16. When oxygen-16 is bombarded by fast neutrons, an unstable isotope of nitrogen is produced, which is N-16. It decays rapidly while emitting gamma radiation. Even though it decays rapidly, N-16 activity lasts long enough to measure the gamma radiation as the water circulates in the reactor coolant loop. This method of flow measurement is often referred to as transit-time flow measurement (TTFM). Figure 2.5g shows two raw data records for a pair of N-16 detectors in a PWR plant. Data accumulated for a period of only one second is shown, although data can be collected for periods of 1 or 2 h if high measurement accuracy is desired. If the purpose of the measurement is only to detect sudden flow changes or blockages, then shorter data recording periods are adequate. The TTFM System The TTFM system (Figure 2.5h) includes a signal conditioning circuit shown in Figure 2.5h. This circuitry is used to extract the AC signals that are cross-correlated for flow measurement. The raw signal typically contains a DC component on which the AC signal of interest is superimposed. FIG. 2.5h Photograph of TTFM system. (Courtesy of Analysis and Measurement Services Corp. [AMS].) As shown in Figure 2.5i, the DC component of each signal is removed by a highpass filter or by a bias that is added to or subtracted from the signal. The remaining component (the AC signal) is then amplified and sent through a lowpass filter to remove the extraneous noise and to provide for anti-aliasing. A computer with a built-in analogto-digital converter (A/D) then samples the signals and performs the cross-correlation to identify the transit time and calculate the flow. Typically, the cross-correlation analysis is performed in both the time domain, using the crosscorrelation plot, and in the frequency domain, using the phase plot, and the results are averaged to provide the fluid flow velocity. The TTFM software not only collects the data, it performs data qualification and statistical analysis to ensure that the signals are suitable for analysis, the sensors have comparable response times, and the cross-correlated AC signals have the required statistical and spectral properties. Figure 2.5j shows a block diagram of the entire TTFM system.

5 2.5 Cross-Correlation Flow Metering 187 v v v v t t t t X High-Pass Filter or DC Bias Amplifier Low-Pass Filter A/D Computer Y High-Pass Filter or DC Bias Amplifier Low-Pass Filter Samples Data Performs data qualification and statistical analysis Performs Cross Correlation Remove DC Component Amplify AC Component Anti-Aliasing Filter Identifies Transit Calculates Fluid Flow Rate Prints Out Results Prints Out Raw Data Stores Results FIG. 2.5i Block diagram of data acquisition system of TTFM. Signal Pair Signal Isolators Instrumentation Amplifier with DC Offset and Anti-Aliasing Filter A/D Converter with Amplification Results Report Data Qualification Data Analysis /Frequency Domain Statistical Analysis FIG. 2.5j Block diagram of TTFM system.

6 188 Flow Measurement References 1. Porges, K. G., On-line correlation flowmetering in coal utilization plants, in Proc. 198 Symposium on Instrumentation and Control of Fossil Energy Processes, June 9 11, 198, Virginia Beach, VA. 2. Porges, K. G., Correlation flowmetering review and application, in Proc Symposium on Instrumentation and Control for Fossil Energy Processes, August 2 22, 1979, Denver, CO. 3. Flemans, R. S., A new non-intrusive flowmeter, Transactions, Flow Measurement Symposium, NBS, February 23 25, Ashton, M. W. and Bentley, P. G., Design study for on-line flow measurement by transit time analysis of temperature fluctuations, in Proc. Conference on Industrial Measurement Techniques for On-Line Computers, June 11 13, 1968, London. 5. Boonstoppel, F., Veltman, B., and Vergouwen, F., The measurement of flow by cross-correlation techniques, in Proc. Conference on Industrial Measurement Techniques for On-Line Computers, June 11 13, 1968, London. 6. O Fallon, N. M., Review of the state-of-the-art of flow and analysis instruments, in Proc Symposium on Instrumentation and Control for Fossil Demonstration Plants, July 13 15, 1977, Chicago, IL. Espina, Peter G., Ultrasonic clamp-on flowmeters have they finally arrived? Flow Control Magazine, January Estrada, H., An assessment of the integrity and accuracy of feedwater flow and temperature measurements, Electric Power Research Institute, in Proc. Nuclear Plant Performance Improvement Seminar, Asheville, NC, Hashemian, H. M. et al., Advanced Instrumentation and Maintenance Technologies for Nuclear Power Plants, U.S. Nuclear Regulatory Commission, NUREG/CR-551, August Hashemian, H. M., On-Line Testing of Calibration of Process Instrumentation Channels in Nuclear Power Plants, U.S. Nuclear Regulatory Commission, NUREG/CR-6343, November Kirimaa, J. C. J., Cross-Correlation for Pulp Flow Measurement, ISA/93 Conference, Chicago, IL, September Mersh, F., Speed and Flow Measurement by an Intelligent Correlation System, Paper #9 632, 199 ISA Conference, New Orleans. Robinson, C., Obstructionless flowmeters: smooth sailing for some, rough passage for others, InTech, 33(12), 33 36, Spitzer, D. W., Industrial Flow Measurement, ISA, Research Triangle Park, NC, Bibliography Beck, M. S., Calvert, G., Hobson, J. H., Lee, K. T., and Mendies, P. J., Flow measurement in industrial slurries and suspensions using correlation techniques, Trans. Inst., Meas. and Control, 4(8).