MANUFACTURING ACCURACY A KEY FACTOR FOR OVERALL PERFORMANCE ON AN ULTRASONIC GAS FLOW METER

Transcription

1 MANUFACTURING ACCURACY A KEY FACTOR FOR OVERALL PERFORMANCE ON AN ULTRASONIC GAS FLOW METER Mr. Volker Herrmann, SICK Engineering GmbH Mr. Andreas Ehrlich, SICK Engineering GmbH Mr. Toralf Dietz, SICK Engineering GmbH 1 INTRODUCTION Ultrasonic gas meters have been available commercially since the 1980s for a range of measuring tasks. Numerous developments have seen their application range increase enormously. Modern meters have found their niche particularly in applications that require official calibration and where accuracy is of paramount importance. Even after more than 20 years of development, new advances are still being made for ultrasonic meters and there is still room for improvement. One indication of this is that all high-pressure meters for custody transfer applications still have to undergo high-pressure calibration. The purpose of these investigations is not to replace this high-pressure calibration but rather to show that accurately setting the characteristic curve of the meter in the factory (dry calibration) is proof that the physical principle of the device is understood and the manufacturing processes are controlled. As a result, users can rest assured that they will not be confronted with any unexpected results in practice. During the initial development stage of a new ultrasonic gas meter designed to meet the most stringent accuracy requirements, all the design and technology principles had to be defined. These were based on many years of experience with ultrasonic flow measurements. Developing a suitable system concept and analyzing all the potential sources of errors are aimed at eliminating or minimizing as many uncertainty factors as possible. Factors that result in significant measurement uncertainty must be identified and appropriate manufacturing technologies, procedures, and test strategies developed. This presentation looks at the measurement uncertainty budget of an ultrasonic gas meter and, using the FLOWSIC 600 as an example, highlights typical orders of magnitude of influencing variables. Selected practical results demonstrate the relevance of the considerations and the current state of the art. 1

2 2 FLOWSIC 600 HOW CAN THE DESIGN HELP REDUCE UNCERTAINTY? 2.1 Operation Principle The FLOWSIC 600 meter operates according to the tried-and-tested transit time principle. Ultrasonic transducers, which define a measuring path at a certain angle to the gas flow (Fig.1), are installed in the meter body. Ultrasonic Transducer A Flow t r D L t f Ultrasonic Transducer B Fig. 1 Transit time measurement principle Fig. 2 FLOWSIC 600, 8 Both transducers work as transmitters and receivers. They transmit ultrasonic pulses through the gas at regular intervals: once in the direction of flow from transducer A to transducer B, and once against the direction of flow from transducer B to transducer A. The pulses transmitted in the flow direction are accelerated, while the pulses transmitted in the opposite direction are decelerated. The velocity along the measuring path is calculated from the two measured time values and geometrical constants. v p L 1 = 2 cosα t f 1 t r (1) To obtain a high degree of accuracy under different installation conditions, a multi-path arrangement is used and the volume flow is calculated as the weighted sum of the path velocities: π Q = Di 4 2 i w v i pi (2) 2.2 Path Configuration The path configuration has a significant effect on the uncertainty budget and, therefore, on the meter performance. To reduce potential uncertainty factors caused by bouncing, the 4- path configuration, which is very similar to that proposed by Whyler [1], was chosen for the FLOWSIC 600 meter (see Fig. 3). Fig. 3 FLOWSIC 600 path configuration 2

3 There are several reasons why a non-bounce multi-path configuration was chosen: When bounced path technology is not used, the reflector inside the pipe becomes superfluous. This may change its characteristics due to contamination or a change in wall roughness, thereby causing additional uncertainty. Eliminating reflection saves acoustic energy, which can help reduce the electrical power input (intrinsically safe operation Ex ia) and allows even large meters to be operated under any operating conditions, including atmospheric pressure and gases of low density (H 2 ) or high acoustic attenuation (CO 2 ). Although this special path configuration does not actually measure non-axial flow components arising from swirl effects, it does compensate for them very well. This has been proven in numerous tests in high and ambient pressure facilities. Investigations have shown that four paths are sufficient for providing highly accurate results in practical installation technology. A paper [2] was recently published in which different path configurations were investigated by CFD. The results showed that, of the four configurations analyzed, the path configuration in which all the paths were at one level (similar to the one outlined here) was the least sensitive to the different installation effects. 2.3 Transducer Technology The transducers form the heart of the technology and, as we will see later, uncertainties in the time measurement can be the main contributor to the uncertainty budget. Today, natural gas meters are normally operated between 100 and 300 khz. Using frequencies as high as 200 khz gives a better resistance to ambient noise emitted by some pressure regulators and valves. This means that it would be best to use the highest possible frequency to achieve a maximum frequency and amplitude gap between the noise spectrum and the desired signal. The attenuation in the gas rises, however, as the frequency increases. This can be a particular problem when meters are operated at ambient pressure or even smaller pressure, where the attenuation is high, or when highly attenuating gases, such as CO 2, H 2 S, or Cl 2, are measured. To fulfill a greater range of requirements, therefore, the transducer frequency must be selected for the application. Fig. 4 Transducer Much effort has gone into miniaturization of the transducers. The result can be seen in Fig 4. By making them as small as possible, highly compact meters can be constructed and flow disturbance caused by the cavities is reduced. Modern transducers are made of metal with no matching layers. The impedance is matched using specially designed metal acoustic transformers, which ensures that the matching layer is no longer a potential source of uncertainty or drift. The driving force of the transducers is generated by piezoceramics. These, and all the contacts, are hermetically sealed and covered by the external metal shell of the transducers. Titanium is used as standard. In particularly corrosive environments, stainless steel or Hastelloy can be used. The transducers can be implemented in pressures of up to 250 bar (or pressures below the ambient pressure) and in temperatures of up to 220 C. The time delay behavior of the transducer has also proven to be extremely constant irrespective of the time, pressure, and temperature. The transducers are virtually drift free. The acoustic signal transmitted and received (see Fig. 5) by the transducers has a high signal noise ratio, even at ambient conditions. 3

4 Fig. 5 Received ultrasonic signal 2.4 Meter Construction The meter construction (patent pending) has been made in a way not only to avoid sources of uncertainty, but also to prevent external factors (mechanical damages, climatic influence) from influence the meter. Typical characteristics are: Minimization of potential sources of damage, long term drift, or uncertainty. Easy to use and calibrate. Robust design and no external transducer cabling. Same footprint and interfacing as other metering technologies (e.g. turbine meters). The meter body is made of cast steel, which helps reduce manufacturing and test costs. Precision machining results in high reproducibility. Shrinking or other warping effects caused by welding, which would be another source of uncertainty, are completely eliminated. The meter body is constructed in such a way that it completely encapsulates all transducers and cabling, thereby shielding the transducers from ambient influences and protecting the cables from damage that may arise during transportation, installation, or maintenance. Fig. 6 Side view of 4 transducers a cables (without cover) The transducers are extremely robust, but since no technical system is 100% failsafe, an extraction tool is provided that allows transducers to be replaced without depressurizing the pipeline. The footprint for all meter body sizes is 3D down to 2 pipe diameter. This is compatible with turbine meters, for example, which means that the meter can be used in the same installations or even can replace metering equipment where turbine-type meters were used previously. All the electronic components required for operating 4 paths, signal calculation, and interfacing with the meter are enclosed in a small, top-mounted Ex-d enclosure. The interface is compatible with turbine meters on one side (dual pulse outputs) and with modern systems on the other (RS485, Modbus, HART, Profibus, FF). Field bus interfaces are currently being developed (HART, Profibus). 4

5 2.5. System Uncertainty The meter is designed to be operated in measurement systems containing p-,tmeasurement, flow computer, and BTU. Due to its low energy consumption, the whole system can be operated with a solar panel (Fig. 7). It is well known that the actual installation and the measurements of p, T, and BTU contribute substantially to the overall uncertainty picture. This calculation is normally made on the basis of a given, concrete installation situation. Note that all calculations given in Chapter 3 only take into account the uncertainty of the meter and not of the system. Fig. 7 - Typical solar powered field system Installation with flow computer 3 MANUFACTURING UNCERTAINTY A FACTOR IN THE MEASUREMENT UNCERTAINTY OF ULTRASONIC GAS METERS The following section only looks at measurement uncertainty factors that affect manufacturing. It does not examine factors that can be attributed to installation or test laboratory activities. The procedure described in the GUM ("Guide to the Expression of Uncertainty in Measurement" [5]) is used to determine further uncertainty. To implement this procedure, two items of information are required. First, a mathematical correlation (measurement model) describing the measurement must be established. For multi-path ultrasonic meters, this is determined by the measuring principle (see Section 2). The combined value for the operational volumetric flow (measurand) is: π Q = f ( xi ) = Di 4 2 n i= 1 L tr t i f w i 2cosα i tr t f Second, knowledge and experience of the measurands (measurement parameter x i ) used in the measurement model and their uncertainties u(x i ) must be available. The total expanded uncertainty for the measurement process can then be determined from the uncertainties of the influencing variables and the relevant sensitivity coefficients (partial derivations of the measurement model according to the influencing parameters): k P = 2 for a coverage probability of f ( x i ) 2 U( Q) = kp u( xi ) (4) i xi (3) 3.1 Manufacturing Uncertainty To calculate the uncertainty budget, all the geometrical and time variables incorporated in the conditional equation of the operational volumetric flow (equation (4)) are taken into account. All concrete data is based on the FLOWSIC

6 A) Geometric measurands The following geometric variables are required for the uncertainty budget: Internal diameter of the measured body Path length Path position Path angle All of these variables are determined using 3D coordinate measuring machines. Internal diameter of the measured body The internal diameter of the measured body is determined by scanning the contour at twelve separate points and fitting a circle to them. In addition to the best circle fit value ("true value"), the form deviation acts as a maximum value for the deviation from the circle. The uncertainty involved in determining the internal diameter is u Ddi =58 µm, irrespective of the nominal size. Path length To determine the path length, the distance between two opposing probe mounts in the transducer (uncertainty: u 3D ) must be measured using the coordinate measuring machine. To determine the real acoustic path length, the relevant probe length (uncertainty: u Lprobe ) must then be subtracted. This is determined with a differentiation measurement using a depth measurement screw. The uncertainty of the path length (u Li ) is the result of a geometric median of these measurements: u Li ul + u Pr obe 3D = (5) Path position The path position is defined as the distance between the path level and cylinder axis. Therefore, both the path level and the cylinder axis must be measured. The uncertainty of the path position (u PL ) is the geometric median of both individual uncertainties. Since the uncertainty of the measurement is dominated by the determination of the cylinder axis (see "internal diameter"), the nominal-size-dependent result is u PL =50 µm. The path position, however, is not directly incorporated in the measurement model. For the purposes of the uncertainty analysis, therefore, it is assumed that the weights may be erroneous. This procedure is justified because the path position and weight are related. The conversion is carried so that the measurement results in the transit times for the assumed uncertainty of the weights (<<0,1%) are the same as those for path positions with uncertainties. Path angle The path angle specifies the angle of the acoustic path to the projected flow axis at path level. It can be calculated by applying the angle determination equation for the analytical geometry from two points on the path axis (established when the path length is determined) and the cylinder axis. The resulting uncertainty of the path angle determination is degrees, irrespective of the nominal size. B) Time measurands To determine the mean path velocity, the absolute transit time and transit time difference on each path must be determined. The measured signal transit time for one measurement path is: L t + t = m + toffset = t f r c ± vp cos(α) / offset (6) The gas transit time t v or t r has to be calculated from the time measurement made by the meter t t + t + t + t m = / (7) f r ec tr diff 6

7 For the uncertainty budget, only t tr is taken into account because this is main contributor. t ec can be maintained at a constant level and its variation is at least one order of magnitude below that of the transducers. The diffraction constant is time, which represents acoustic diffraction effects that lead to a time delay in a given meter configuration. Since it only depends on a given geometrical configuration, it is constant with a given meter (see detailed description in [3]). Absolute transit time The absolute transit time for a path is determined by measuring the probes by electronic means under defined conditions. It is extremely difficult, however, to determine the uncertainty of the time measurements due to a number of factors (temperature, air humidity, gas movement). To compensate the distance-dependent diffraction effect, these times are corrected using an empirically determined parameter set. The uncertainty of the absolute transit time determination corresponds to a transit time difference of approx. 100 ns once the distance effects have been corrected. The time variables are measured in two stages. The transit time differences of the probe pairs ( t tr ) are measured with respect to a "master" electronics system, and the transit time influences of the electronics ( t ec ) are measured with respect to a "master" probe pair. The differentiation procedure chosen when the probe pairs are characterized largely isolates the absolute variables of transducer distance, gas composition, and gas temperature. The standard uncertainty of the transit time differentiation measurement is less than 4 ns. 3.2 Results Using the calculated expanded uncertainties for the individual influencing variables, the expected expanded uncertainty of the operational volumetric flow measurement, without influences from the installation, can be determined using the procedure described in the GUM. 2,5% DN80 DN150 DN400 Total Manufactoring Uncertainty 2,0% 1,5% 1,0% 0,5% 0,0% Velocity [m/s] Fig. 8 Manufacturing uncertainty for 4-path meters with different nominal sizes Fig. 8 shows that the influence of the manufacturing uncertainty on the measurement result decreases as the flow velocity increases, and converges towards a constant value. This limit value is less than 0.3% for smaller meters too (DN80, DN100). Taking a nominal size of DN150 as an example, the components of the total manufacturing uncertainty are outlined below. 7

8 0,30% 1 ms-1 10 ms-1 0,25% Manufactoring Uncertainty 0,20% 0,15% 0,10% 0,05% 0,00% Travel time absolute inner path Travel time absolute outer path Travel time difference inner path Travel time difference outer path weight inner path weight outer path Path angle inner path Path angle outer path Path length inner path Path length outer path Inside diameter Fig. 9 Uncertainty factors (FLOWSIC 600, DN150) It is clear that the transit time differentiation measurement dominates the uncertainty budget at low gas velocities. For high gas velocities, the uncertainty of the internal diameter measurement governs the budget. It is also clear that only the transit time differences provide a significant velocity-dependent contribution to the total uncertainty. 3.3 Influence Of Temperature And Pressure To ensure a high degree of accuracy even under changeable conditions, the behavior of the modules in the measuring device that affect uncertainty must be examined and, if necessary, corrected at different temperatures and pressures Influences On The Meter Body The FLOWSIC 600 meter body has a reinforced zone containing ports for mounting ultrasonic transducers. This section is always identical within a nominal size. Thermal effects For geometry changes, unobstructed expansion in all directions is assumed. This assumption is also valid for the axial direction considering that pipes are normally equipped with suitable expansion joints. This means that all lengths in all directions expand uniformly with the material-specific linear thermal extension coefficients. The uniform expansion in all directions does not affect the path angle and path position. Only changes to the internal diameter and path length need to be taken into account. Changes in length as a result of thermal effects can be described as follows: l = l α th T 0 (8) The expansion coefficients of steel result in the correction factor, which is independent of the nominal meter size, for the temperature with 5 1 K T K =. 8

9 Pressure effects Internal pressure primarily results in only a change in a radial direction. In the axial direction, the dimensions are modified in accordance with Poisson's number. The expansion joints enable the calculation to be carried out under plane stress conditions (no stress in the axial direction). Due to the geometry of the measuring cell, different effects must be taken into account in the radial, axial, and circumferential directions because the effective wall thickness changes. Pressure effects, therefore, influence all geometric influencing variables. Due to the design of the probe mount zone, the meter body geometry here possesses excellent form stability. The correction factor for a steel probe, which is independent of the nominal meter size, 6 1 has been calculated analytically for the pressure with K p = bar In this way, thermal and pressure effects on the measurement result can be expressed as follows: Q Q 0 = (9) ( 1+ KT ( T1 T0 ) + K p ( p1 0)) 1 p Fig. 10 shows the influence of pressure and temperature on the measurement error around one reference point for a range of between ±50K and ±50 bar. 0,25% 0,20% 0,15% pressure temperature 0,10% Deviation [%] 0,05% 0,00% -0,05% -0,10% -0,15% -0,20% -0,25% Difference to reference point [bar], [K] Fig. 10 Influence of the meter body dimension changes It is evident that the proportion of the temperature-related measurement error is significantly greater, reaching as much as 0.1 % at gas temperatures deviating by 25K Influence On The Transit Time Of The Ultrasonic Probes In addition to the influence on the geometric variables, the time measurands must be analyzed as a function of pressure and temperature. To this end, a comprehensive series of measurements was carried out in pressure and temperature measuring chambers. These meteorological tests show a systematic gradient for transducer transit times of 6ns/K for the temperature and 1ns/bar for the pressure. The transducer transit time difference, however, is practically independent of pressure and temperature. The temperature dependence is again the most dominant influence here. 9

10 0,0% Deviation [%] -0,1% pressure temperature -0,2% -0,3% 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 path length L [m] Fig. 11 Relative measurement error for T = 50K, p = 50bar, c = 400m/s (natural gas) 4 PRACTICAL MEASUREMENT RESULTS The measurement results below, which were determined during the final device inspection and meter tests on flow test laboratories, show how measurement uncertainty is currently controlled. 4.1 Zero-Point Check The zero-point check is used for gauging the measurement uncertainty and accuracy of a meter at the zero point. As its name suggests, checks cannot be carried out at other meter operating points. It is, however, invaluable for evaluating meters without using a high-pressure test laboratory. Ultrasonic gas meters allow the measured signal transit times to be compared with theoretical setpoints. A theoretical sound velocity can be calculated using the gas composition and condition, which means the theoretical ultrasonic signal transit times are also defined with regard to the measuring path lengths. All components that affect the transit time (electronics, ultrasonic transducers, transit time correction parameters) are determined independently of each other during the initial stage of meter production. The zero-point check is an integrated test for determining the overall influence. When the gas meter is checked, it is sealed at both ends using a blind flange. It is then filled with a gas of known composition. Since the sound velocity is highly sensitive to temperature changes, its stability can be used to indicate thermal compensation. As soon as thermal equilibrium has been reached after the gas meter has been filled, the transit time difference of the ultrasonic paths and, therefore, the zero-point precision is checked. At the same time, the precision of the absolute signal transit time measurement and the geometry parameters are checked using the difference between the measured and theoretical sound velocity. International recommendations (such as AGA 9 [4]) require zero-point stability values of at least 6mm/s and a sound velocity measurement accuracy of at least 0.2%. Optimized electronics, ultrasonic transducer, and signal processing parameters ensure that these requirements regarding the industrial series manufacture of modern ultrasonic gas meters are reliably fulfilled for all nominal meter sizes down to DN80. More stringent pre-selection criteria for components ensure that these requirements can even be applied to smaller nominal sizes. 10

11 Testreport - Zeroflowtest number of test name: Flowsic 600 place of test: SICK Dresden type: 12 " CL600 date: path number: 4 tester: MTR JLE prod. number: 42 file name: Logging_Zerotest_42 serial number: time: 15 min year: 2003 medium: atm. Air humidity [%] 56 temperatur [ C] 22,2 pressure [bar] 0,996 theor. vel. of sound [m/s] 345,47 ambient condition Velocity of sound check Criterion VOS Error between theor. and measuring value [m/s] 0,5 Error between max. and min. VOS [m/s] 0,5 measuring values VOS [m/s] diff. to theor. result Path 1 345,60 0,1371 ok Path 2 345,44-0,0242 ok Path 3 345,41-0,0583 ok Path 4 345,28-0,1892 ok Maximum 345,60 0,3263 ok Minimum 345,28 VOS [m/s] VOS 346,20 346,00 345,80 345,60 345,40 345,20 345,00 344, measuring values pathes theoret. VOS Velocity of gas check Criterion VOG Error VOG [m/s] 0,012 measuring values VOS [m/s] result Path 1 0,001 ok Path 2 0,007 ok Path 3-0,002 ok Path 4 0,001 ok VOG [m/s] VOG 0,020 0,010 0,000-0,010-0, pathes measuring values Fig. 12 Zero-point test report (FLOWSIC 600, nominal size DN300) Fig. 12 shows a typical test report for a zero-point check. Parameterization errors or errors in the signal transit time correction can be easily identified thanks to the tight tolerance limits. In principle, this test can also be carried out under field conditions. Due to the practical requirements regarding the underlying flow, temperature stability, and gas composition, a slight reduction in the accuracy of the absolute reference conditions is to be expected. The benefits of multi-path ultrasonic gas meters, however, can also be brought to bear here. If at least three measurement paths are available, the ratio of the differences between the sound velocity differences can be used as a quality criterion. This method is very sensitive and can also be used for flowing gas. 11

12 Fig. 13 Sound velocity differences for 4-path ultrasound gas meters, DN100, 50m³/h Fig. 13 shows the relative differences between the sound velocities of the ultrasonic paths. In a line through which gas is flowing and that is not directly exposed to sunlight, uniform temperature distribution and, therefore, uniform sound velocities at all path levels in the pipeline can be assumed. The knowledge of the absolute values for pressure, temperature, and gas composition is irrelevant because only the relative difference between the sound velocities is included. 4.2 Test Laboratory Measurements High precision during production leads to high expectations but can these be met on a certified test laboratory? In the following analysis, the uncertainty of the basic characteristic device curve as a function of different operational pressures and media (determined, for example, on a master device for each nominal size), as well as the uncertainty of the test installations used (pressure and temperature measurement, flow normal) must now also be considered. Taking into account an uncertainty of 0.3 % for the basic characteristic device curve and adding the test laboratory uncertainty by 0.2% yields an uncertainty of 0.3% % = 0.36%, which must also be taken into account. When the nominal-size-dependent manufacturing uncertainty shown above is now taken into account, values of between ±0.66% (nominal size: DN80) and ±0.46% (nominal size: DN400) can be expected. 2,5 2,0 1,5 1,0 red: NPS 4 brown: NPS 6 pink: NPS 8 green: NPS 12 Error [%] 0,5 0,0-0,5-1,0-1,5-2,0-2, Q/Qmax Air NG 16bar NG 50bar NG 70bar AGA 9 small meters custody transfer range Fig. 14 Measurement errors before FLOWSIC 600 calibration DN100 to DN300 12

13 This diagram shows the characteristic curves for gas meters of nominal sizes DN100, DN150, DN200, and DN300 determined on different test laboratories (PTB Braunschweig, Recklinghausen, Pigsar, TCC Canada, GRI San Antonio, and CEESI Iowa, USA). No calibration factors have been applied to the characteristic curves in the diagram. The tests were carried out using air and natural gas at different operational pressures. All error characteristics are within the expected range, which proves conclusively that modern ultrasonic gas meters can be produced with low manufacturing uncertainty. 1,5 1,0 # , 16bar, Pigsar, # , 50bar, Pigsar, # , Pamb, PTB Braunschweig, # , 70bar, CEESI Iowa, ,5 Error [%] 0,0-0,5-1,0-1, Flowrate [m³/h] Fig. 15 Detailed view of FLOWSIC 600, DN200 1,5 1,0 0,5 # , 70bar, SwRI, # , 16bar, SwRI, # , 16bar, Pigsar, # , 50bar, Pigsar, # , 16bar, Pigsar, # , 50bar, Pigsar, # , 25bar, HDV Lintorf, Juni 2003 Error [%] 0,0-0,5-1,0-1, Flowrate [m³/h] Fig. 16 Detailed view of FLOWSIC 600, DN300 5 SUMMARY The investigations outlined here show that factors influencing the measurement uncertainty of ultrasonic gas meters are understood and can be controlled to a considerable degree. This implies that ultrasonic meters with a level of precision such that manufacturing uncertainty lies within normal test laboratory uncertainties can be manufactured in series. Although continued research will undoubtedly lead to an improved theoretical understanding, particularly with regard to installation effects, ultrasound technology is already highly sophisticated. Series manufacture, combined with the inherent benefits of technology, ensures that multi-path ultrasound measurement is the technology of choice for a wide range of applications. 13

14 6. NOTATION v p Mean path velocity u(x i ) Standard uncertainty meas. parameter t r Transit time (upstream) c Sound velocity t f Transit time (downstream) t m Primary measured time L Measuring path length t ec Delay time of electronics α Installation angle t tr Delay time of transducer pair v pi Mean path velocity of path i t f/r Transit time w i Weight factor for path i t diff Diffraction time Q Volume flow under actual conditions l Length change D i Internal diameter l 0 Start length for reference temperature U Expected measured uncertainty result T Temperature change (max. 225K) k p Coverage factor α th Linear thermal expansion coefficient of material 6 BIBLIOGRAPHY [1] John S. Wyler; FLUID FLOW MEASUREMENT SYSTEM FOR PIPES, United States Patent 3,940,985, 1975 [2] Chris J. Duffell, Gregor J. Brown, Neil A. Barton, Dr. Brian P. Stimpson; A NEW FAMILY OF ULTRASONIC FLOWMETERS, WITH IMPROVED PERFORMANCE IN ASYMMETRIC FLOWS, PRODUCED BY USING OPTIMISATION ALGORITHMS AND CFD; International Conference on Hydrocarbon Flow Measurement ; Palakkad, Kerala, India; September 2003 [3] Per Lunde, Kjell Eivind Foysa, Remi A. Kippersrud; TRANSIENT DIFFRACTION EFFECTS IN ULTRASONIC METERS FOR VOLUMETRIC, MASS AND ENERGY FLOW MEASUREMENT OF NATURAL GAS; 21 st International North Sea Flow Measurement Workshop; Tonsberg, Norway; October 2003 [4] AGA Report No. 9; MEASUREMENT OF GAS BY MULITPATH ULTRASONIC METERS; Transmission Measurement Committee; Arlington; June 1998 [5] Guide to the Expression of Uncertainty in Measurement; ISO International Organization for Standardization, Geneva 7066/2; 1988 [6] Draft AGA Report No. 10; SPEED OF SOUND IN NATURAL GAS AND OTHER RELATED HYDROCARBON GASES; Transmission Measurement Committee; July 23, 2002 [7] B. Nath, V. Lötz-Dauer, V. Wetzel, A. Hilgenstock, S. Kolpatzik; MEASURING RESPONSE OF ULTRASONIC GAS METERS IN DEPENDENCE OF GAS TYPES; Int. Gas Research Conference IGRC, , TSP-02, San Diego, USA, 1998 [8] Volker Herrmann, Toralf Dietz, Michael Kochan; IMPROVEMENTS IN ULTRASONIC TRANSDUCER TECHNOLOGY A KEY TO THE EXTENSION OF THE APPLICATION RANGE OF GAS FLOW METERS; International Conference on Hydro Carbon Flow Measurement, Palakkad, Kerala, India; September 2003 [8] Toralf Dietz, Andreas Ehrlich, Volker Herrmann, Burger Nath, Günter Maurer,; A NEW ULTRASONIC GAS FLOW METER AS A BASE FOR A NATURAL GAS ENERGY SYSTEM; 20 st International North Sea Flow Measurement Workshop, St. Andrews Bay Resort, Scotland; October 2002 [10] Volker Herrmann, Toralf Dietz, Michael Kochan; IMPROVEMENTS IN ULTRASONIC TRANSDUCER TECHNOLOGY A KEY TO THE EXTENTION OF THE APPLICATION RANGE OF GAS FLOW METERS; Petrotech 2003 Conference in the Kingdom of Saudi Arabia; September