Speed of sound measurements in liquid Methane at cryogenic temperature and for pressure up to 10 MPa

Transcription

1 LNGII - raining Day Delft, August 07 Seed of sound measurements in liquid Methane at cryogenic temerature and for ressure u to 0 MPa Simona Lago*, P. Alberto Giuliano Albo INRiM Istituto Nazionale di Ricerca Metrologica, urin (IALY) * s.lago@inrim.it National Metrology Institute

2 LNG on-line calibration instruments LNG trading needs accurate and reliable measurements together with calibrated instrumentations. INRiM is develoing a system for the simultaneous measurement of seed of sound and density in LNG. he sensor is suitable to be mounted on existing roduction facilities, and the results are traceable to the standards of length and time. In articular, the SoS device will be useful to calibrate the commercial on-line ultrasonic flowmeters and the density sensor will be useful to monitor on-line density, that is needed for an accurate determination of LNG samle mass flow rate. Before testing the new sensor on flow-metering facilities, it has to be accurately characterized in laboratory conditions with controlled temerature, ressure and samle comosition. For this reasons, reliminary SoS measurements cycles have been carried out in ure methane (>99.999%) in the temerature range of (03 and 53) K and for ressure u to 0 MPa. National Metrology Institute LNGII - raining Day - Delft, nd of August 07

3 National Metrology Institute In a fluid, there are quantities that are very useful for imlementing and for checking the redictions of its equation of state (EoS). In articular, aside from density and vaor ressure, seed of sound is the next most imortant roerty to develo excellent equations of state. = density c = isobaric secific heat caacity = thermal exansion coeff. Initial conditions: 0 0 (, ); (, ) c w c w c c c (, ) entroy w Why measure Seed of Sound in fluids? Advantage: accurate SoS measurements in articular binary mixtures can be used to develo reliable and stable fundamental EoS, like GERG, useful for industrial and scientific aims. LNGII - raining Day - Delft, nd of August 07

4 Ultrasonic flow-meters calibration National Metrology Institute LNGII - raining Day - Delft, nd of August 07 Calibration facilities use tanks of known volume V, and samle mass m, while the time t, needed to discharge the tank, is measured. If the density of the fluid is known, the mass rate can be calculated by: Φ = = Calibration is imroved using water and, at cryogenic temerature, liquid nitrogen as reference fluids. he accuracy of ultrasonic flow-meters is about 0.5%, when calibrated with liquid nitrogen, but, when calibrated with LNG, the accuracy could reach 0.%. Moreover, if ultrasonic flow-meter is also calibrated in terms of absolute seed of sound, by comarison with a reference sensor, it would be ossible to determine the flow rate by: Φ = ( ) he novel INRiM sensor will be able to measure not only SoS but also, simultaneously, the in-situ LNG density (indeendently from the LNG comosition), allowing the calibration of the flow-meters even considering fluid velocity rofile in real working conditions.

5 Double Pulse-Echo method he limited dimensions and the simlicity of the tyical exerimental aaratus makes double ulse-echo technique suitable for oeration u to very high ressure over an extended temerature range L L FUNCION GENERAOR (sinusoidal burst) 4 MHz t t PZ 0 t t t t OSCILLOSCOPE eco eco 3 eco 4 eco First Echo L = wt L = w(t -t ) L = wt L Second Echo L = wt L = w(t -t ) L = wt w ex ( L L ) t t L t w ex = exerimental seed of sound t = delay between the two echoes L = difference between the acoustic ath-lengths National Metrology Institute LNGII - raining Day - Delft, nd of August 07

6 Cell calibration As shown before, in order to obtain the seed of sound, it is necessary to know the difference of the acoustic ath lengths. his determination can be carried out by means of a reference liquid at a fixed thermodynamic state ( 0, 0 ), using the equation L w t ( 0, 0 ) calibr calibr w calibr = known seed of sound of the reference fluid t calibr = measured delay time between echoes in the same fluid at 0 and 0 he difference of ath lengths L can be calculated at a different state (,) as L( L,(,) ) L ( L (, ) ( ) ( ) i 0,93K) ( 0 0 0) i i = thermal exansion coefficient = comressibility coefficient ( RatioPoiss on) = ModYoung L(, ) w calibr t calibr 4 i National Metrology Institute LNGII - raining Day - Delft, nd of August 07 i ( ) 0 i 0 3 i from NIS Cryogenic Database

7 Delay determination rocedure Echoes (Amlitude = ) P ( t) P ( t t ) τ Amlitude / u.a. t t Amlitude / u.a Correlation Function C(t) t C F[C] = F[P ] F[P ] ime / μs t P t P t t dt Samling Rate = 4 GS/s Samling Interval = 0.5 ns c( t) F F[ P( t)] F[ P ( t)] ime / s S N 0 est with synthetic data: => t = samling interval National Metrology Institute LNGII - raining Day - Delft, nd of August 07

8 ime-of-flight measurement ime-of-flight direct measurements, usually, does not reresent the main source of uncertainty. Exected uncertainty ~ between % (0 GS/s) and 0.00% (4 GS/s) (or 3-0 m), using correlation method However, the obtained results have to be corrected for effects that are difficult to model (both the effects are modeled aroximating exerimental conditions). t Corrections of ime-of-flight: diffraction effects ime correction for DIFFRACION EFFECS are due to a finite dimensions of the ultrasonic source wt meas L L, L ex0 t t where t L 0 = delay between lane and curved wave = hase shift = angular frequency of the carrier L, L = distances between the source and the reflectors Exected correction ~ between 0.000% and 0.03% (or m) National Metrology Institute LNGII - raining Day - Delft, nd of August 07

9 Corrections of ime-of-flight Near-field effects: Methane case he near-field limit (NFL): 4 NFL r 4 where r is the source radius is the wavelength calculated considering that the signal is described as a continuous wave and not as a burst near-field region - lane wave roagation - high erturbed ressure distribution far-field region - sherical wave roagation - regular acoustic ressure rofile For examle, the seed of sound measured at = 53 K and = 4 MPa is about equal to 90 m/s. Using a cell with sacers equal to L = 30 mm and L = 45 mm and with source diameter equal to 7 mm, the seed of sound cannot be measured accurately at any carrier frequency: At signal frequency of 5.5 MHz, the wavelength is aroximately 0. mm and NFL 73. mm. hus the first echo (travelling L = 60 mm) is in near-field condition, while the other echo (travelling L = 90 mm) is in far-field conditions. Reducing the frequency near to 4.5 MHz or at 4 MHz, the near-field limit becomes 59.9 > NFL > 53. mm, that (remembering that this theory considers the signal not described by a burst, but as a continuous wave) moves both echoes in far-field region. Although the signal-to-noise ratio at 4 MHz is about 0 times worst (it revealed a more comlex harmonic decomosition), anyway, nodes and eaks of the signals have a better overlaing than in the case of 5.5 MHz burst, where the shaes of the received echoes become different. Because of the low signal-to-noise ratio, we have chosen 4.5 MHz. National Metrology Institute LNGII - raining Day - Delft, nd of August 07

10 Near-field effects: Methane case For examle, in conditions of = 53 K, = 4 MPa at 5.5 MHz (7 mm of source diameter) w ex = m/s.07 % at 4.5 MHz (7 mm of source diameter) w ex = m/s at 4 MHz (7 mm of source diameter) w ex = m/s % Considering diffraction corrections (less than 0.03 %) calculated by he relative deviation at 5.5 MHz can rise u 0 times worst than the declared uncertainty (u to % or worst). => near-field he agreement between measurements at 4.5 MHz and 4 MHz, in this case, better than 0.0% (within the declared uncertainty). It roves that seed of sound has to be indeendent from the frequency, at least in this interval of frequencies => far-field => the geometry of the ultrasonic sensor is really imortant and may limit the seed of sound measuring range. t L L 0 % National Metrology Institute LNGII - raining Day - Delft, nd of August 07 he Asian hermohysical Proerties Conference

11 Ultrasonic Cells -35 C +0 C 0. MPa 70 MPa 30 mm -95 C +0 C 0. MPa 400 MPa 0 mm (30+45) mm 8mm AISI-36L SS -95 C +0 C 0. MPa 400 MPa -95 C +0 C 0. MPa 400 MPa (30+45) mm 5mm (45+67) mm National Metrology Institute LNGII - raining Day - Delft, nd of August 07

12 High ressure vessel and Comonents of the heat exchanger High Pressure Vessel (0. MPa < < 50 MPa) Heat exchanger for cryogenic temeratures (77 K < < 60 K) National Metrology Institute LNGII - raining Day - Delft, nd of August 07

13 Exerimental System National Metrology Institute LNGII - raining Day - Delft, nd of August 07

14 Cryostat and temerature control In and out of liquid nitrogen P00 and heater Pressure transducer Heater P00 Heater P00 National Metrology Institute LNGII - raining Day - Delft, nd of August 07

15 Exerimental Problems: sealing and thermal shock Remounting of the High Pressure lugs High Pressure Vessel starts to lose Piezo-electric ransducer hydraulic and electric feed-through National Metrology Institute LNGII - raining Day - Delft, nd of August 07

16 Very Preliminary Exerimental Seed of Sound results in liquid Methane National Metrology Institute LNGII - raining Day - Delft, nd of August 07

17 Relative deviation of exerimental SoS results from Setzmann s EoS* he measurements will be reeated, after imroving the thermal couling between the heat exchanger and the ressure vessel, in order to guarantee the corresondence between temerature and thermodynamical state in which the SoS sensor is. * Setzmann, U. and Wagner, W., "A New Equation of State and ables of hermodynamic Proerties for Methane Covering the Range from the Melting Line to 65 K at Pressures u to 000 Ma, J. Phys. Chem. Ref. Data, 0(6):06-5, 99. National Metrology Institute LNGII - raining Day - Delft, nd of August 07

18 Combined uncertainty for SoS results in liquid Methane L(, ) w (, ) w (,, L, t) t(, ) w w w L t w w w L t ( reeatability) ex ex Uncertainty Source Relative Magnitude Determination of the acoustic ath Determination of temoral delay Pressure measurements L L t t 0.056% % Reeatability 0.000% emerature measurements u u 0.077% u u 0.034% Estimated Overall Uncertainty (k=) 0.6% National Metrology Institute LNGII - raining Day - Delft, nd of August 07

19 Conclusions In this work, high ressure seed of sound measurements (and their associated uncertainties) in ure liquid methane are reorted. he results have been obtained using the double ulse-echo technique at cryogenic temerature; in articular in the temerature range of (03 and 53) K and for ressures u to 0 MPa. heir estimated relative overall uncertainty is less than 0.% in the whole ressure and temerature range. he authors have shown the effects on the seed of sound measurement due to near-field conditions and how to get over the roblem, obtaining reliable measurements. Since the obtained deviation are bigger than the exected ones, the measurements will be reeated, after imroving the thermal couling between the heat exchanger and the ressure vessel, in order to guarantee the corresondence between temerature and thermodynamical state in which the SoS sensor is. Once solved this roblem, the accuracy will be imroved and the results will be useful to calibrate the commercial on-line ultrasonic flow-meters. he INRiM SoS sensor can be characterized using rimary measurements as a reference, and the results are traceable to the standards of length and time. Moreover, it differs from commercial ultrasonic flow-meters because the cell can be immersed directly into the LNG and can be installed on industrial roduction facilities in order to calibrate commercial sensors when they are in real working conditions. National Metrology Institute LNGII - raining Day - Delft, nd of August 07