Source: https://patents.google.com/patent/US7299705B2/en
Timestamp: 2018-10-19 03:36:00
Document Index: 37871432

Matched Legal Cases: ['Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60']

US7299705B2 - Apparatus and method for augmenting a Coriolis meter - Google Patents
Apparatus and method for augmenting a Coriolis meter Download PDF
US7299705B2
US7299705B2 US11291189 US29118905A US7299705B2 US 7299705 B2 US7299705 B2 US 7299705B2 US 11291189 US11291189 US 11291189 US 29118905 A US29118905 A US 29118905A US 7299705 B2 US7299705 B2 US 7299705B2
US11291189
US20060169058A1 (en )
The present invention claims the benefit of U.S. Provisional Patent Application No. 60/631,793 filed Nov. 30, 2005; and is a continuation-in-part of U.S. patent application Ser. No. 10/892,886 filed Jul. 15, 2004 now U.S. Pat. No. 7,152,460, which claimed the benefit of U.S. Provisional Patent Application No. 60/579,448 filed Jun. 14, 2004, U.S. Provisional Patent Application No. 60/570,321 filed May 12, 2004, U.S. Provisional Patent Application No. 60/539,640 filed Jan. 28, 2004, U.S. Provisional Patent Application No. 60/524,964 filed Nov. 25, 2003, U.S. Provisional Patent Application No. 60/512,794 filed Oct. 20, 2003, U.S. Provisional Patent Application No. 60/510,302 filed Oct. 10, 2003, U.S. Provisional Patent Application No. 60/504,785 filed Sep. 22, 2003, U.S. Provisional Patent Application No. 60/503,334 filed Sep. 16, 2003, U.S. Provisional Patent Application No. 60/491,860 filed Aug. 1, 2003, and U.S. Provisional Patent Application No. 60/487,832 filed Jul. 15, 2003, which are all incorporated herein by reference.
According to the present invention, a flow measuring system for measuring the mass flow rate of an aerated fluid flowing in a pipe is provided. The flow measuring system includes a meter having a pair of vibrating tubes wherein fluid flows therethrough. The meter provides a phase signal indicative of a phase difference between the pair of tubes. The tubes have an inward flow portion and an outward flow portion. A flow measuring device measuring the speed of sound propagating through the fluid at the inward flow portion and outward flow portion of a tube is provided. The measuring device provides at least one of an SOS signal indicative of the speed of sound propagating through the fluid, a GVF signal indicative of the gas volume fraction of the fluid and a reduced frequency indicative of the reduced frequency of the fluid. A processing unit determines a compensated mass flow rate measurement in response to at least one of the SOS signal, the GVF signal and the reduced frequency signal and the phase signal.
According to another embodiment of the present invention, a method for measuring the mass flow rate of an aerated fluid flowing in a pipe is provided. The method includes a vibrating pair of tubes having the fluid flowing therethrough. The tubes have an inward flow portion and an outward flow portion. The method includes measuring a phase signal indicative of a phase difference between a pair of tubes, and measuring the speed of sound propagating through the fluid at the inward flow portion and outward flow portion of a tube. The method further includes providing at least one of a SOS signal indicative of the speed of sound propagating through the fluid, a GVF signal indicative of the gas volume fraction of the fluid, and a reduced frequency indicative of the reduced frequency of the fluid. The method includes determining a compensated mass flow rate measurement in response to at least one of the SOS signal, the GVF signal and the reduced frequency signal and the phase signal.
ρ mix = ∑ i = 1 N ⁢ ϕ i ⁢ ρ i
∑ i = 1 N ⁢ ϕ i = 1
The present invention presents an approach in which a speed-of-sound measurement of the process fluid is integrated with a coriolis meter to form a system with an enhanced ability to operate accurately on aerated fluids. A schematic of a speed-of-sound augmented coriolis system is shown in FIG. 3. Introducing a real time, speed-of-sound measurement address the effects of aeration on multiple levels with the intent to enable coriolis meters to maintain mass flow and liquid density measurements in the presence of entrained air with accuracy approaching that for non-aerated liquids. Firstly, by measuring the process sound speed with process pressure, the aeration level of the process fluid can be determined with high accuracy on a real time basis. Secondly, the real time measurements of sound speed and the derived measurement of gas volume fraction are then utilized with analytically or empirically derived correction factors to improve the interpretation of the measured phase difference and natural frequency of the vibrating tubes in terms of the density of the aerated fluid.
Most coriolis meters rely on quasi-steady models of the interaction between the structural and fluid dynamics within the meter to determine both mass flow and density. In a quasi steady model, the fluid within the flow tubes is assumed to be incompressible and homogenous. The fluid essentially adds inertial terms associated with translation, centrifuigal and coriolis acceleration to the vibrational dynamics of the flow tubes.
( M struct + M fluid ) ⁢ ⅆ 2 ⁢ x 1 ⅆ t 2 + 2 ⁢ M fluid ⁢ U R ⁢ ⅆ x 1 ⅆ t + K struct ⁢ x 1 + K torsion L ⁢ ( x 1 - x 2 ) = 0 ( M struct + M fluid ) ⁢ ⅆ 2 ⁢ x 2 ⅆ t 2 - 2 ⁢ M fluid ⁢ U R ⁢ ⅆ x 2 ⅆ t + K struct ⁢ x 2 + K torsion L ⁢ ( x 2 - x 1 ) = 0
[ - 2 ⁢ α 1 + α ⁢ U nd - s - 1 + Γ 1 + α 0 Γ 1 + α 1 - s 0 0 0 Γ 1 + α 2 ⁢ α 1 + α ⁢ U nd - s - 1 + Γ 1 + α 0 0 1 - s ] ⁢ { y 1 x 1 y 2 x 2 } = 0
The parameters governing the dynamic response of the model are defined in Table 1.
the Equation of Motion for the Lumped
Parameter Quasi-Steady Coriolis Meter
Γ Torsinal Spring Parameter Ktorsion/KstructL
Und Radial Flow Velocity U/ωstructR
FIG. 8 shows the eigenvalues for the quasi-steady model for a coriolis meter with the parameters given in Table 2. The dimensional parameters for the representative coriolis meter are given in Table 3. As shown, the quasi-steady model has two, lightly damped modes of oscillation. The location of the eigenvalues do not change significantly with mass flow. The lower frequency mode is primarily associated with bending, and the higher frequency mode in which the tubes are predominately out-of-phase torsional mode.
Parameter QuasiSteady Coriolis Meter
α Mass ratio 1.0
Γ Torsional Spring Parameter 1.0
Und Radial Flow Velocity 0-.015
Dimensional Parameters Defining the
Baseline Vibrating Tube Density Meter
D Tube diameter 2.0 inches
R Radial Position of Typical 20 inches
t Wall thickness 0.060 inches
ρfluid Liquid Density 1000 kg/m{circumflex over ( )}3
ρstruct Tube Density 8000 kg/m{circumflex over ( )}3
mdot Mass flow 0-10 kg/sec
U Fluid Velocity 0-5 m/sec
κ mix = 1 ρ mix ⁢ a mix ∞ ⁢ 2 = ∑ i = 1 N ⁢ ϕ i ρ i ⁢ a i 2
ρ mix = ∑ i = 1 N ⁢ ρ i ⁢ ϕ i
f = 1.84 π ⁢ ⁢ D ⁢ a mix = 1 2 ⁢ π ⁢ K fluid m fluid
Note that this frequency corresponds to a wavelength of an acoustic oscillation of approximately two diameters, i.e., this transverse mode is closely related to a “half wavelength” acoustic resonance of the tube.
Where fstruct is the natural frequency of the tubes in vacuum, D is the diameter of the tubes, and amix is the sound speed of the process fluid. Strictly speaking, quasi-steady models are valid for systems in which the reduced frequency is small, i.e. negligible compared to unity. In these cases, models which neglect the compressibility of the fluid are likely to be sufficient. However, the effects of unsteadiness increase with increasing reduced frequency. FIG. 12 shows the reduced frequency as a function of fluid sound speed for three representative coriolis meters.
V sphere = 3 ⁢ ρ ρ + 2 ⁢ ρ 0 ⁢ V fluid
In the inviscid limit, the compensating mass of fluid (2φ) does not participate in the oscillation of remaining fluid, and the velocity of the mass-less gas bubble approaches three times the velocity of the remaining fluid. The velocity ratio between the bubble and the remaining fluid is shown in FIG. 14 as a function of gas damping ratio defined in Table 4. The effect of this relative motion is to reduce the effective inertia of the fluid inside the tube to (1-3φ times that presented by a homogeneous fluid-filled the tube. In the limit of high viscosity, the increased damping constant minimizes the relative motion between the gas bubble and the liquid, and the effective inertia of the aerated fluid approaches 1-φ.
The effective inertia an aerated, but incompressible, fluid oscillating within a tube predicted by this model is consistent with known potential theory models in the limits of high and low viscosities.
of Motion for the Aeroelastic, Lumped Parameter Model of a
Coriolis Meter with a Compressible, Aerated Fluid
φ Gas Volume Fraction
ζg Critical Damping Ratio of Structural bgas/(2(2φ)mfluidωstruct)
Models were presented for the effects of aeration on vibrating tube density meters in which the effects of compressibility and inhomogeniety were addressed independently. FIG. 16 shows a schematic of a lumped parameter model that incorporates the effects of compressibility and inhomogeniety using the mechanism-specific models developed above. The purpose of this model is to illustrate trends and parametric dependencies associated with aeration, it is not intended as a quantitative predictive tool.
[ A 11 A 12 A 21 A 22 ] ⁢ { y 1 x 1 y 2 x 2 y 3 x 3 q 1 z 1 q 2 z 2 q 3 z 3 } = { 0 } where ⁢ : A 11 ≡ [ s + 2 ⁢ ζ f ⁢ αQ + 2 ⁢ ζ s 1 + αQ 2 + Γ - 2 ⁢ ζ f ⁢ αQ - αQ 2 0 0 - 1 s 0 0 0 0 - 2 ⁢ ζ f ⁢ Q 1 - 3 ⁢ φ - Q 2 1 - 3 ⁢ φ s + 2 ⁢ ζ f ⁢ Q 1 - 3 ⁢ φ + 2 ⁢ ζ g ⁡ ( 2 ⁢ φ ) 1 - 3 ⁢ φ + 2 ⁢ U ND Q 2 1 - 3 ⁢ φ - 2 ⁢ ζ s ⁡ ( 2 ⁢ φ ) 1 - 3 ⁢ φ 0 0 0 - 1 s 0 0 0 0 0 - 2 ⁢ ζ g 2 ⁢ φ s + 2 ⁢ ζ g 2 ⁢ φ + 2 ⁢ U ND 0 0 0 0 0 - 1 s ] A 22 ≡ [ s + 2 ⁢ ζ f ⁢ αQ + 2 ⁢ ζ s 1 + αQ 2 + Γ - 2 ⁢ ζ f ⁢ αQ - αQ 2 0 0 - 1 s 0 0 0 0 - 2 ⁢ ζ f ⁢ Q 1 - 3 ⁢ φ - Q 2 1 - 3 ⁢ φ s + 2 ⁢ ζ f ⁢ Q 1 - 3 ⁢ φ + 2 ⁢ ζ g ⁡ ( 2 ⁢ φ ) 1 - 3 ⁢ φ - 2 ⁢ U ND Q 2 1 - 3 ⁢ φ - 2 ⁢ ζ s ⁡ ( 2 ⁢ φ ) 1 - 3 ⁢ φ 0 0 0 - 1 s 0 0 0 0 0 - 2 ⁢ ζ g 2 ⁢ φ s + 2 ⁢ ζ g 2 ⁢ φ - 2 ⁢ U ND 0 0 0 0 0 - 1 s ] A 12 = A 21 ≡ [ 0 - Γ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
The additional non-dimensional parameters that govern the dynamic response of the aeroelastic model compared to the quasi-steady model are defined in Table 4.
ζgas Critical Damping Ratio - gas 1.0
Q Frequency Ratio As determined by sound
speed of air/water at STP
FIG. 18 shows the eigenvalues for a Coriolis meter operating at significantly higher tube frequencies, all the other parameters are identical. As shown, the locations of the eigenvalues of the various modes are in much closer proximity, indicative of significantly higher level of aeroelastic interaction. Note that the higher structural frequency is reflected in the non-dimensional frequency of the “acoustic modes”, approaching 10 in the limit of no gas and decreasing to approximately 1 at 10% GVF.
As shown, the model predicts that the coriolis meter operating with the lowest frequency tubes reports a mass flow measurement that is in good agreement with the actual mass flow over the range of gas volume fraction evaluated. However, for the higher frequency tubes, aeroelastic interactions associated with the increased compressibility and the inhomogeneity of the fluid result in significant errors between the actual and the interpreted mass flow rates. The “1-GVF” and “1-3GVF” lines are shown for reference purposes.
ρ apparent = ρ liq a ⁢ ( f s 2 f observed 2 - 1 )
The effect of this imbalance can seriously degrade the performance of a coriolis meter. In one aspect of the present invention the speed of sound is measured in each leg of a coriolis meter to aid in interpreting the traditional direct measurements, ie the phase lag in the tubes and the natural frequency of the tubes, in terms of mixture mass flow and density.
FIGS. 21 and 22 shows the effect of gas volume fraction on the mass flow measurement of representative coriolis meters. The charts shows that imbalance of 10% of the GVF in the vibrating tubes has a significant impact. For this example, knowledge of the imbalance and knowledge of the average GVF in terms of measurement accuracy may be used to augment the coriolis meter.
The array of pressure sensors 118-121 comprises an array of at least two pressure sensors 118,119 spaced axially along the outer surface 122 of the pipe 14, having a process flow 112 propagating therein. The pressure sensors 118-121 may be clamped onto or generally removably mounted to the pipe by any releasable fastener, such as bolts, screws and clamps. Alternatively, the sensors may be permanently attached to, ported in or integral (e.g., embedded) with the pipe 14. The array of sensors of the sensing device 116 may include any number of pressure sensors 118-121 greater than two sensors, such as three, four, eight, sixteen or N number of sensors between two and twenty-four sensors. Generally, the accuracy of the measurement improves as the number of sensors in the array increases. The degree of accuracy provided by the greater number of sensors is offset by the increase in complexity and time for computing the desired output parameter of the flow. Therefore, the number of sensors used is dependent at least on the degree of accuracy desired and the desire update rate of the output parameter provided by the apparatus 100. The pressure sensors 118-119 measure the unsteady pressures produced by acoustic waves propagating through the flow, which are indicative of the SOS propagating through the fluid flow 12 in the pipe. The output signals (P1(t)-PN(t)) of the pressure sensors 118-121 are provided to a pre-amplifier unit 139 that amplifies the signals generated by the pressure sensors 118-121. The processing unit 124 processes the pressure measurement data P1(t)-PN N(t) and determines the desired parameters and characteristics of the flow 12, as described hereinbefore.
Similar to the apparatus 100 of FIG. 23, an apparatus 200 of FIG. 24 embodying the present invention has an array of at least two pressure sensors 118,119, located at two locations x1,x2 axially along the pipe 14 for sensing respective stochastic signals propagating between the sensors 118,119 within the pipe at their respective locations. Each sensor 118,119 provides a signal indicating an unsteady pressure at the location of each sensor, at each instant in a series of sampling instants. One will appreciate that the sensor array may include more than two pressure sensors as depicted by pressure sensor 120,121 at location x3,xN. The pressure generated by the acoustic pressure disturbances may be measured through strained-based sensors and/or pressure sensors 118-121. The pressure sensors 118-121 provide analog pressure time-varying signals P1(t),P2(t),P3(t),PN(t) to the signal processing unit 124. The processing unit 124 processes the pressure signals to first provide output signals 151,155 indicative of the speed of sound propagating through the flow 12, and subsequently, provide a GVF measurement in response to pressure disturbances generated by acoustic waves propagating through the flow 12.
To calculate the power in the k-ω plane, as represented by a k-ω plot (see FIG. 25) of either the signals or the differenced signals, the array processor 160 determines the wavelength and so the (spatial) wavenumber k, and also the (temporal) frequency and so the angular frequency ω, of various of the spectral components of the stochastic parameter. There are numerous algorithms available in the public domain to perform the spatial/temporal decomposition of arrays of sensor units 118-121.
An array processor 160 uses standard so-called beam forming, array processing, or adaptive array-processing algorithms, i.e. algorithms for processing the sensor signals using various delays and weighting to create suitable phase relationships between the signals provided by the different sensors, thereby creating phased antenna array functionality. In other words, the beam forming or array processing algorithms transform the time domain signals from the sensor array into their spatial and temporal frequency components, i.e. into a set of wave numbers given by k=2π/λ where λ is the wavelength of a spectral component, and corresponding angular frequencies given by ω=2πυ.
1 ρ mix ⁢ a mix ∞ 2 ⁢ = ∑ i = 1 N ⁢ ϕ i ρ i ⁢ a i 2 ⁢ ⁢ where ⁢ ⁢ ρ mix = ∑ i = 1 N ⁢ ρ i ⁢ ϕ i
a eff = 1 1 a mix ∞ 2 + ρ mix ⁢ 2 ⁢ R E ⁢ ⁢ t ( eq ⁢ ⁢ 1 )
Referring to FIG. 27, a dual tube 302 coriolis meter 300 is provided having an array of pressure sensors 118-121,318-320 disposed on a tube 302 of the coriolis meter. In this embodiment, an array of piezoelectric material strip or sensors 118-121,318-320 are disposed on a web and clamped onto the tube 302 as a unitary wrap. This configuration is similar to that described in U.S. patent application Ser. No. 10/795,111, filed on Mar. 4, 2004, which is incorporated herein by reference. Similar to that described herein before as shown in FIGS. 23 and 24, the pressure signals are provided to a processing unit to calculate at least one of the SOS, GVF and reduced frequency. As shown, the coriolis meter 300 includes an array of sensor disposed on the outward flow portion and inward flow portion of one of the tubes 302 of the meter 300. Each array providing signals that are processed in accordance with the invention as described hereinbefore to provide at least one of the SOS, GVF and reduced frequency. Knowing these parameters at the outward and inward portions of a tube 302, the mass flow and/or density measurement of the coriolis meter may be augmented to compensated for entrained gas in the fluid flow 12.
While integrated coriolis meters 300 of FIG. 27 are U-shaped, the present invention contemplates that the sensor array may similarly disposed on a tube of a straight tube coriolis meter.
The pressure sensors 118-121 of FIG. 23 described herein may be any type of pressure sensor, capable of measuring the unsteady (or ac or dynamic ) pressures within a pipe 14, such as piezoelectric, optical, capacitive, resistive (e.g., Wheatstone bridge), accelerometers (or geophones), velocity measuring devices, displacement measuring devices, etc. If optical pressure sensors are used, the sensors 118-121 may be Bragg grating based pressure sensors, such as that described in U.S. patent application Ser. No. 08/925,598, entitled “High Sensitivity Fiber Optic Pressure Sensor For Use In Harsh Environments”, filed Sep. 8, 1997, now U.S. Pat. No. 6,016,702, and in U.S. patent application Ser. No. 10/224,821, entitled “Non-Intrusive Fiber Optic Pressure Sensor for Measuring Unsteady Pressures within a Pipe”, which are incorporated herein by reference. In an embodiment of the present invention that utilizes fiber optics as the pressure sensors 14 they may be connected individually or may be multiplexed along one or more optical fibers using wavelength division multiplexing (WDM), time division multiplexing (TDM), or any other optical multiplexing techniques.
1. A flow measuring system for measuring the mass flow rate of an aerated fluid flowing in a pipe, the flow measuring system comprising:
a meter having a pair of vibrating tubes wherein fluid flows therethrough, the meter providing a phase signal indicative of a phase difference between the pair of tubes, said tubes having an inward flow portion and an outward flow portion;
a flow measuring device measuring the speed of sound propagating through the fluid at the inward flow portion and outward flow portion of a tube, the measuring device providing at least one of an SOS signal indicative of the speed of sound propagating through the fluid, a GVF signal indicative of the gas volume fraction of the fluid and a reduced frequency indicative of the reduced frequency of the fluid; and
a processing unit determining a compensated mass flow rate measurement in response to at least one of the SOS signal, the GVF signal and the reduced frequency signal and the phase signal.
3. The measuring system of claim 1, wherein the meter comprises a first speed of sound sensor arranged on the outward portion of the tube and a second speed of sound sensor arranged on the inward portion of the tube for determining the speed of sound measurement on the fluid flowing in each respective inward and outward portion of the tube.
4. The measuring system of claim 1, wherein the meter comprises a first speed of sound sensing device arranged on the pipe at the input end of the meter and a second speed of sound sensing device arranged of the pipe at the output end of the meter for performing the speed of sound measurement of the fluid flowing therethrough.
5. The measuring device of claim 1, wherein the tubes are bent or straight.
6. The measuring system meter of claim 1, wherein the meter comprises at least one tube having a first array of sensors arranged on the outward portion of the tube and a second array of sensors arranged on the inward portion of the tube for determining the speed of sound measurement on the fluid flowing in each respective inward and outward portion of the tube.
7. The measuring system of claim 6, wherein the array of sensors includes strain based sensors.
8. A method for measuring the mass flow rate of an aerated fluid flowing in a pipe, the method comprising:
vibrating a pair of tubes having the fluid flowing therethrough, said tubes having an inward flow portion and an outward flow portion;
measuring a phase signal indicative of a phase difference between a pair of tubes;
measuring the speed of sound propagating through the fluid at the inward flow portion and outward flow portion of a tube;
providing at least one of a SOS signal indicative of the speed of sound propagating through the fluid, a GVF signal indicative of the gas volume fraction of the fluid, and a reduced frequency indicative of the reduced frequency of the fluid; and
determining a compensated mass flow rate measurement in response to at least one of the SOS signal, the GVF signal and the reduced frequency signal and the phase signal.
9. The method of claim 8, further includes determining wherein a gas volumetric fraction (GVF) in the flow of the fluid in response to the SOS signal.
10. The method of claim 8, wherein the measuring the speed of sound includes providing a first speed of sound sensor arranged on the outward portion of the tube and a second speed of sound sensor arranged on the inward portion of the tube for determining the speed of sound measurement on the fluid flowing in each respective inward and outward portion of the tube.
11. The method of claim 8, wherein the measuring the speed of sound includes providing a first speed of sound sensing device arranged on the pipe at the input end of the meter and a second speed of sound sensing device arranged of the pipe at the output end of the meter for performing the speed of sound measurement of the fluid flowing therethrough.
12. The method claim 8, wherein the tubes are bent or straight.
13. The method of claim 8, wherein measuring the speed of sound includes providing at least one tube having a first array of sensors arranged on the outward portion of the tube and a second array of sensors arranged on the inward portion of the tube for determining the speed of sound measurement on the fluid flowing in each respective inward and outward portion of the tube.
14. The method of claim 13, wherein the array of sensors includes strain based sensors.
US11291189 2003-07-15 2005-11-30 Apparatus and method for augmenting a Coriolis meter Active 2024-09-14 US7299705B2 (en)
US10892886 Continuation-In-Part US7152460B2 (en) 2003-07-15 2004-07-15 Apparatus and method for compensating a coriolis meter
US11872304 Continuation US7793555B2 (en) 2003-07-15 2007-10-15 Apparatus and method for augmenting a coriolis meter
US20060169058A1 true US20060169058A1 (en) 2006-08-03
US7299705B2 true US7299705B2 (en) 2007-11-27
ID=46323269
US11291189 Active 2024-09-14 US7299705B2 (en) 2003-07-15 2005-11-30 Apparatus and method for augmenting a Coriolis meter
US11872304 Active 2025-03-06 US7793555B2 (en) 2003-07-15 2007-10-15 Apparatus and method for augmenting a coriolis meter
US (2) US7299705B2 (en)
RU2502962C2 (en) * 2008-11-13 2013-12-27 Майкро Моушн, Инк. Method and device to measure fluid parameter in vibration metre
US20150068321A1 (en) * 2013-03-12 2015-03-12 Sergey V. SHUMILIN Method for measuring the flow rate of a multi-phase liquid
US9562427B2 (en) * 2012-11-19 2017-02-07 Invensys Systems, Inc. Net oil and gas well test system
JP4546926B2 (en) * 2003-09-05 2010-09-22 マイクロ・モーション・インコーポレーテッドＭｉｃｒｏ Ｍｏｔｉｏｎ Ｉｎｃｏｒｐｏｒａｔｅｄ Flow meter filter system and method
US20180120269A1 (en) * 2015-04-02 2018-05-03 Los Alamos National Security, Llc Acoustic gas volume fraction measurement in a multiphase flowing liquid
DE102016007905A1 (en) * 2016-06-30 2018-01-04 Endress+Hauser Flowtec Ag A method for operating a measurement transducer of the vibration type
DE102016112002A1 (en) * 2016-06-30 2018-01-04 Endress + Hauser Flowtec Ag A method for determining a physical parameter of a compressible medium with a vibratory transducer and the sensor for carrying out such a method
DE102016114974A1 (en) * 2016-08-11 2018-02-15 Endress+Hauser Flowtec Ag A method for determining a void fraction of a loaded with gas medium
DE102016114972A1 (en) * 2016-08-11 2018-02-15 Endress+Hauser Flowtec Ag A method for determining a void fraction of a loaded with gas liquid medium
GB2009931A (en) * 1977-12-09 1979-06-20 Solartron Electronic Group Improvements relating to the measurement of fluid density
GB1127231A (en) 1965-01-06 1968-09-18 British Aluminium Co Ltd Improvements in or relating to methods of and apparatus for testing molten metal
US4569991A (en) * 1982-01-26 1986-02-11 Mitsubishi Monsanto Chemical Company Production of thermoplastic resin
GB8525781D0 (en) 1985-10-18 1985-11-20 Schlumberger Electronics Uk Transducers
US5932793A (en) 1996-08-01 1999-08-03 Gas Research Institute Apparatus and method for determining thermophysical properties using an isochoric approach
US6636815B2 (en) 2001-08-29 2003-10-21 Micro Motion, Inc. Majority component proportion determination of a fluid using a coriolis flowmeter
EP1429119A4 (en) 2001-09-21 2006-05-17 Oval Corp Arch-shaped tube type coriolis meter and method of determining shape of the coriolis meter
GB2411476B (en) 2004-02-27 2007-01-31 Roxar Flow Measurement As Flow meter
US7013715B2 (en) * 1999-10-28 2006-03-21 Micro Motion, Inc. Multiphase flow measurement system
US20060156831A1 (en) * 2004-03-19 2006-07-20 Endress + Hauser Flowtec Ag Coriolis mass measuring device
US7793555B2 (en) * 2003-07-15 2010-09-14 Expro Meters, Inc. Apparatus and method for augmenting a coriolis meter
US9316518B2 (en) * 2013-03-12 2016-04-19 Sergey V. SHUMILIN Method for measuring the flow rate of a multi-phase liquid
US7793555B2 (en) 2010-09-14 grant
US20060169058A1 (en) 2006-08-03 application
US20090013799A1 (en) 2009-01-15 application
Cotoni et al. 2007 Numerical and experimental validation of a hybrid finite element-statistical energy analysis method
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