DE102016005547B4 - Method for determining a physical parameter of a gas-laden liquid - Google Patents

Abstract

Method (100) for determining a physical parameter of a liquid which has a gas load, the gas being present in the liquid in particular in the form of suspended bubbles, by means of a sensor having at least one measuring tube for guiding the medium, the at least one measuring tube having an inlet-side end section and an outlet-side end section,wherein the measuring sensor has at least one inlet-side fixing device and one outlet-side fixing device, with which the measuring tube is fixed in one of the end sections, wherein the measuring tube can be excited between the two fixing devices to flexural vibrations of different modes with different natural frequencies, from in which an f1 mode has no node between the fixation devices, and wherein an f3 mode has two vibration nodes between the fixation devices,the method (100) comprising the steps of:exciting the f1 mode and the f3 mode;checking whether the f1 mode or the f3 mode is suppressed (110);when either the f1 mode or the f3 mode is suppressed due to resonance vibration of the gas-laden liquid with respect to the measuring tube, using an expected value for the natural frequency of the suppressed bending vibration mode as Value for a resonant frequency of the gas-laden liquid;determining a density correction term (130) as a function of resonance frequency to correct a preliminary density reading ρi and/or a mass flow correction term as a function of resonance frequency to correct a preliminary mass flow reading, and/or determining the speed of sound of the gas-laden Liquid in the measuring tube as a function of the resonance frequency.

Description

The present invention relates to a method for determining a physical parameter of a gas-laden liquid using a sensor with at least one measuring tube for guiding the gas-laden liquid, the measuring tube having an inlet-side end section and an outlet-side end section, the sensor having at least one inlet-side fixing device and an outlet-side fixing device, with which the measuring tube is fixed in one of the end sections, wherein the measuring tube can be excited to oscillate between the two fixing devices, wherein the mass flow rate and density of the gas-laden liquid can be determined from the vibration behavior of the measuring tube. However, the measured values for mass flow and density show cross-sensitivities to the speed of sound or compressibility of the gas-laden liquid, which increase with increasing gas loading. Compensation for these cross-sensitivities is therefore desirable.

The publication EP 2 026 042 A1 discloses a method for detecting the density of a multi-phase medium, for example a gas-laden liquid, the above cross-sensitivities due to resonance vibrations of the medium being evaluated and compensated for in different vibration modes.

The disclosure document DE 196 52 002 A1 discloses a sensor for measuring the density of a medium guided in a measuring tube on the basis of vibration frequencies of the vibrating measuring tube, the influence of axial forces on the measurement being discussed.

From the publication WO 01/01086 A1 discloses a method for compressibility compensation in mass flow measurement in a Coriolis mass flowmeter, in which case a mass flow measurement is carried out in two different modes, one of which is a flexural mode and the other is a radial mode. From the comparison of the mass flow values that are determined using these two modes. However, this is a problematic approach in that the radial mode vibrations have significant dependence on the airfoil and static pressure, and more sensors than the usual two are required to be able to detect both bending vibrations and radial mode vibrations. Likewise, a more complex exciter structure is required.

wobei c_0i, c_1i, und c_2i, modenabhängige Koeffizienten sind.In a first approximation, the relationship between a provisional measured density value ρ _i of a gas-laden liquid based on the natural frequency f _i of an fi mode can be described as: $${\rho }_i=c_{0i}+c_{1i}\frac{1}{f_l^2}+c_{2i}\frac{1}{f_l^4},$$

where c _0i , c _1i , and c _2i , are mode dependent coefficients.

However, the above approximation does not take into account the influences of the oscillating gas-laden liquid in the measuring tube. The closer the resonant frequency of the oscillating gas-laden liquid is to the natural frequency of a bending vibration mode, the stronger the influence on the natural frequency. Since the resonant frequency is usually above the natural frequencies of the measuring tubes, the influence on the f3 bending vibration mode is greater than the influence on the f1 bending vibration mode. This leads to different preliminary mode-specific density readings, the ratio between the preliminary density readings opening up the possibility of determining and correcting for the influence of the oscillating gas-laden liquid. This is in the post-published reference DE 10 2015 122 661 A1 described.

However, if the resonant frequency of the gas-laden liquid coincides with a natural frequency of a flexural vibration mode, it is completely suppressed. In this situation, the approach described above cannot be used. It is therefore the object of the present invention to provide a solution for this situation.

The object is achieved according to the invention by the method according to independent patent claim 1.

• Anregen des f1-Modes und des f3-Modes;
• Prüfen ob der f1-Mode oder der f3-Mode unterdrückt sind;

wenn entweder der f1-Mode oder der f3-Mode aufgrund einer Resonanzschwingung der mit Gas beladenen Flüssigkeit bezüglich des Messrohrs unterdrückt wird, Verwenden eines Erwartungswerts für die Eigenfrequenz des unterdrückten Biegeschwingungsmodes als Wert für die Resonanzfrequenz der mit Gas beladenen Flüssigkeit;The method according to the invention is used to determine a physical parameter of a liquid which has a gas load, the gas being present in the liquid in particular in the form of suspended bubbles, by means of a measuring sensor with at least one measuring tube for guiding the medium,
wherein the at least one measuring tube has an inlet-side end section and an outlet-side end section,
wherein the sensor has at least one inlet-side fixing device and one outlet-side fixing device, with which the measuring tube is fixed in one of the end sections, wherein the measuring tube can be excited between the two fixing devices to flexural vibrations of different modes with different natural frequencies, of which an f1 mode has no vibration node between the fixing devices, and where an f3 mode has two vibration nodes between the fixation devices,
the method (100) comprising the steps of:

• exciting the f1 mode and the f3 mode;
• Check whether f1 mode or f3 mode is suppressed;

when either the f1 mode or the f3 mode is suppressed due to resonance vibration of the gas-laden liquid with respect to the measuring tube, using an expected value for the natural frequency of the suppressed flexural vibration mode as a value for the resonance frequency of the gas-laden liquid;

Determining a density correction term as a function of resonance frequency to correct a preliminary density reading and/or a mass flow correction term as a function of resonance frequency to correct a preliminary mass flow measurement, and/or determining the sound velocity of the gas-laden liquid in the measuring tube as a function of resonance frequency.

Suspended bubbles are, in particular, those bubbles whose size is no more than three times the penetration depth, which depends on the kinematic viscosity of the liquid and the natural frequency of the f1 mode.

In a development of the invention, the expected value of the natural frequency of the suppressed flexural vibration mode is determined as a function of the natural frequency of at least one non-suppressed flexural vibration mode.

In one development of the invention, the expected value for the natural frequency of the suppressed flexural vibration mode is determined by multiplying the natural frequency of a non-suppressed flexural vibration mode by a factor.

The appropriate factor can be determined experimentally, for example, by varying the gas loading of a liquid until a flexural vibration mode is suppressed. The factor can be determined from the ratio of the last measured natural frequency of the flexural vibration mode before it was suppressed and the natural frequency of the unsuppressed flexural vibration mode under these conditions.

In a development of the invention, the factor is stored as a constant parameter.

In a development of the invention, the factor is continuously updated during operation by regularly determining and recording the ratio of the natural frequencies of two bending vibration modes.

In most cases the f3 mode will be suppressed, so that an expected value for the f3 mode has to be calculated on the basis of the f1 mode. However, the opposite case is expressly covered by the invention.

• Ermitteln eines vorläufigen Dichtemesswerts und/oder eines vorläufigen Massedurchflussmesswerts bei einer Eigenfrequenz des nicht unterdrückten Biegeschwingungsmodes, und Ermitteln eines korrigierten Dichtemesswerts und/oder eines korrigierten Massedurchflussmesswerts unter verwendung des Dichtekorrekturterms und/oder des Massedurchflusskorrekurterms, wobei

der Dichtekorrekturterm und/oder der Massedurchflusskorrekurterm eine Funktion der Resonanzfrequenz und Eigenfrequenz des nicht unterdrückten Biegeschwingungsmodes sind bzw. ist, bei welcher der vorläufige Dichtemesswert und/oder der vorläufige Massedurchflussmesswert ermittelt wurden bzw. wurde.In a development of the invention, the method also includes:

• determining a preliminary density reading and/or a preliminary mass flow reading at a natural frequency of the unsuppressed flexural mode, and determining a corrected density reading and/or a corrected mass flow reading using the density correction term and/or the mass flow correction term, wherein

the density correction term and/or the mass flow correction term is a function of the resonant frequency and natural frequency of the unsuppressed flexural mode at which the preliminary density reading and/or the preliminary mass flow reading was determined.

In a further development of the invention, the density correction term K _i for a preliminary measured density value and/or the mass flow correction term are or is a function of a quotient of the resonant frequency of the gas-laden liquid and the natural frequency of the unsuppressed flexural vibration mode, in which the preliminary density reading and/or mass flow reading have been determined.

wobei $${\rho }_{corr}\cdot =\frac{{\rho }_i}{K_i}$$

wobei reine medienunabhängige Konstante ist, f_res die Resonanzfrequenz der mit Gas beladenen Flüssigkeit ist, f_i die Eigenfrequenz des nicht unterdrückten Biegeschwingungsmodes ist, ρ_corr, ρ_i der für die Einflüsse der schwingenden mit Gas beladenen Flüssigkeit im Messrohr korrigierte und der vorläufige Dichtemesswert sind, und b eine Skalierungskonstante ist.In a development of the invention, the density correction term K _i for the provisional measured density values ρ _i based on the natural frequency of the f _i mode has the following form: $$K_i:=\left(1+\frac{\mathrm{right}}{\left(\frac{f_{\mathrm{right}es}}{f_i}\right)-b}\right),$$

whereby $${\rho }_{cO\mathrm{right}\mathrm{right}}\cdot =\frac{{\rho }_i}{K_i}$$

where is pure media-independent constant, f _res is the resonant frequency of the gas-laden liquid, f _{i is} the natural frequency of the non-suppressing th flexural mode, ρ _corr , ρ _i are those corrected for the effects of the vibrating gas-laden liquid in the measuring tube and are the preliminary density reading, and b is a scaling constant.

In a development of the invention, the following applies: $$\text{right}/\text{b}<\mathrm{1,}\text{especially r}/\text{b}<0.9$$

In a development of the invention, b=1.

In a further development of the invention, g is a proportionality factor, dependent on the diameter of the measuring tube, between a resonance frequency f _re s of the gas-laden liquid and the speed of sound of the gas-laden liquid, where the equation c = f _res / g applies, and a Equation determined value of the speed of sound c is output.

In a development of the invention, the provisional measured density value is determined on the basis of the natural frequency of the f _i mode using a polynomial in 1/f _i , in particular in (1/f _i ) ² , the coefficients of the polynomial being mode-dependent.

wobei ein Massedurchflussfehler E_m eines vorläufigen Massedurchflusswerts proportional zu dem Dichtefehler E_ρ1 des ersten vorläufigen Dichtemesswerts ist, also: $$E_m:=k\cdot E_{\rho 1},$$

wobei der Proportionalitätsfaktor k nicht weniger als 1,5, beispielsweise nicht weniger als 1,8 und insbesondere nicht weniger als 1,9 beträgt,
wobei der Proportionalitätsfaktor k nicht mehr als 3, beispielsweise nicht mehr als 2,25 und insbesondere nicht mehr als 2,1 beträgt,
wobei für den Massedurchflusskorrekturterm K_m für den Massendurchfluss gilt: $$K_m:=1+E_m,$$

wobei der korrigierte Massendurchfluss ṁ_corr ermittelt wird als $${\dot{m}}_{corr}\cdot =\frac{{\dot{m}}_v}{K_m},$$

wobei ṁ_v der vorläufige Massedurchflusswert ist.In a development of the invention, the following applies to a density error E _ρi of a provisional measured density value based on the natural frequency of the fi mode: $$E_{\rho i}:=K_i-\mathrm{1,}$$

where a mass flow error E _m of a preliminary mass flow value is proportional to the density error E _ρ1 of the first preliminary density reading, i.e.: $$E_m:=k\cdot E_{\rho 1},$$

where the proportionality factor k is not less than 1.5, for example not less than 1.8 and in particular not less than 1.9,
where the proportionality factor k is not more than 3, for example not more than 2.25 and in particular not more than 2.1,
where the mass flow correction term K _m for the mass flow is: $$K_m:=1+E_m,$$

where the corrected mass flow ṁ _corr is determined as $${\dot{m}}_{cO\mathrm{right}\mathrm{right}}\cdot =\frac{{\dot{m}}_v}{K_m},$$

where ṁ _v is the preliminary mass flow value.

• Ermitteln der Eigenfrequenz des f1-Modes und des f3-Modes;
• Ermitteln eines ersten vorläufigen Dichtemesswerts für die im Messrohr geführte gasbeladene Flüssigkeit auf Basis der Eigenfrequenz des f1-Modes;
• Ermitteln eines zweiten vorläufigen Dichtemesswerts für die im Messrohr geführte gasbeladene Flüssigkeit auf Basis der Eigenfrequenz des f3-Modes;
• Ermitteln eines Werts für die Schallgeschwindigkeit der im Messrohr geführten Flüssigkeit, und/oder zumindest eines von der Schallgeschwindigkeit und der Eigenfrequenz eines Modes abhängigen Korrekturterms und/oder Dichtefehlers für den vorläufigen Dichtemesswert, der auf Basis der Eigenfrequenz des Modes ermittelt wurde, zum Bestimmen eines korrigierten Dichtemesswerts; und/oder eines Korrekturterms für einen vorläufigen Massedurchflusswert zum Bestimmen eines korrigierten Massedurchflussmesswerts auf Basis des ersten vorläufigen Dichtemesswerts, des zweiten vorläufigen Dichtemesswerts, der Eigenfrequenz des f1-Modes und der Eigenfrequenz des f3-Modes.

In a development of the invention, the method also includes, if neither the f1 mode nor the f3 mode are suppressed:

• determining the natural frequency of the f1 mode and the f3 mode;
• Determination of a first provisional measured density value for the gas-laden liquid guided in the measuring tube on the basis of the natural frequency of the f1 mode;
• Determination of a second provisional measured density value for the gas-laden liquid guided in the measuring tube on the basis of the natural frequency of the f3 mode;
• Determination of a value for the speed of sound of the liquid carried in the measuring tube, and/or at least one correction term dependent on the speed of sound and the natural frequency of a mode and/or density error for the provisional measured density value, which was determined on the basis of the natural frequency of the mode, in order to determine a corrected one density reading; and/or a preliminary mass flow rate correction term for determining a corrected mass flow rate measurement based on the first preliminary density measurement, the second preliminary density measurement, the natural frequency of the f1 mode, and the natural frequency of the f3 mode.

In a development of the invention, the correction term K _i for a provisional measured density value is a function of a quotient of the speed of sound of the gas-laden liquid and the natural frequency of the mode with which the provisional measured density value was determined.

In a further development of the invention, the speed of sound c of the gas-laden liquid is determined by looking for the speed of sound value at which the quotient of the first correction term for the first provisional measured density value divided by the second correction term for the second provisional measured density value, the quotient of the first provisional density reading divided by the second preliminary density reading.

wobei $${\rho }_{corr}\cdot =\frac{{\rho }_i}{K_i}$$

wobei rund g gasunabängige Konstanten sind, c die Schallgeschwindigkeit der mit Gas beladenen Flüssigkeit ist, f_i die Eigenfrequenz des f_i-Modes ist, ρ_corr die korrigierte Dichte ist, und b eine Skalierungskonstante ist.In a development of the invention, the correction term K _i for the provisional measured density values ρ _i based on the natural frequency of the f _i mode has the following form: $$K_i:=\left(1+\frac{\mathrm{right}}{\left(\frac{G\cdot c}{f_i}\right)-b}\right),$$

whereby $${\rho }_{cO\mathrm{right}\mathrm{right}}\cdot =\frac{{\rho }_i}{K_i}$$

where around g are gas-independent constants, c is the speed of sound of the gas-laden liquid, f _i is the natural frequency of the f _i mode, ρ _corr is the corrected density, and b is a scaling constant.

wobei v die kinematische Viskosität der Flüssigkeit und f₁ die Eigenfrequenz des f1-Modes ist.In a development of the invention, the method is used when the suspended bubbles have a radius r that is no more than five times, in particular no more than three times, a penetration depth δ, which is given as $$\mathrm{\delta }={(v/\left({\pi }^{\ast }{\text{f}}_1\right))}^{1/2},$$

where v is the kinematic viscosity of the liquid and f ₁ is the natural frequency of the f1 mode.

The penetration depth δ describes the range of a flow field due to movements of a suspended bubble relative to the liquid surrounding it. In the case of small radii, suspended bubbles essentially affect the compressibility, while in the case of radii which clearly exceed the penetration depth, additional effects occur which impair the accuracy of the corrections according to the invention.

The invention will now be explained in more detail with reference to the exemplary embodiment described in the drawings.

• 1: Ein Flussdiagramm für ein Ausführungsbeispiel der ersten Alternative des erfindungsgemäßen Verfahrens;
• 2: Ein Flussdiagramm für ein Detail des Ausführungsbeispiels der ersten Alternative des erfindungsgemäßen Verfahrens;
• 3: Ein Flussdiagramm für ein Ausführungsbeispiel der zweiten Alternative des erfindungsgemäßen Verfahrens; und
• 4: Ein Flussdiagramm für ein Detail des Ausführungsbeispiels der zweiten Alternative des erfindungsgemäßen Verfahrens.

It shows:

• 1 : A flowchart for an embodiment of the first alternative of the method according to the invention;
• 2 : A flow chart for a detail of the embodiment of the first alternative of the method according to the invention;
• 3 : A flowchart for an embodiment of the second alternative of the method according to the invention; and
• 4 : A flow chart for a detail of the embodiment of the second alternative of the method according to the invention.

This in 1 The illustrated exemplary embodiment of a method 100 according to the invention for determining a measured density value begins in a step 110 with the determination that a flexural vibration mode is suppressed, for example the f3 mode.

Then the natural frequency of the unsuppressed flexural vibration mode, for example the f1 mode, is determined. The desired natural frequencies can be determined, for example, by maximizing the ratio of the oscillation amplitude to the mode-specific excitation power by varying the excitation frequencies.

wobei c_0i, c_1i, und c_2i, modenabhängige Koeffizienten sind.Based on the determined natural frequency fi, a provisional measured density value ρ ₁ is then determined in a step 120 as: $${\rho }_i=c_{0i}+c_{1i}\frac{1}{f_l^2}+c_{2i}\frac{1}{f_l^4},$$

where c _0i , c _{1i ,} and c _2i , are mode dependent coefficients.

In a step 130, which is described below with reference to FIG 2 is explained in more detail, a density correction term for the density measurement is determined.

Finally, in a step 140, a corrected measured density value is determined using the correction term.

As in 2 shown, the step 130 for determining the density correction term comprises first in a step 132 calculating an expected value of the natural frequency of the suppressed flexural mode on the basis of the natural frequency of the non-suppressed flexural mode, for example by multiplying by a factor.

With a flow meter used in the investigations for the present invention, good results have been obtained with a constant factor of 5.5 between the natural frequency of the f1 mode and the natural frequency of the f3 mode. If you want to work with a constant factor, this must certainly be determined in a type or routine test.

The expected value determined for the natural frequency of the suppressed flexural vibration mode is of interest insofar as an excitation of the flexural vibration mode should preferably be tried at this frequency in order to make it oscillate again when the resonant frequency moves away again.

wobei f₁ die Eigenfrequenz des nicht unterdrückten Biegeschwingungsmodes ist, mit welcher der vorläufige ρ_i Dichtemesswert bestimmt wurde. Und wobei r eine Konstante ist, die hier den Wert 0,84 aufweist.According to step 132, the expected value determined for the natural frequency of the suppressed flexural vibration mode is used as the value for the resonant frequency f _res . In a step 133, a density correction term K _i is calculated according to: $$K_i:=\left(1+\frac{\mathrm{right}}{\left(\frac{f_{\mathrm{right}es}}{f_i}\right)-1}\right),$$

where f ₁ is the natural frequency of the unsuppressed flexural vibration mode with which the preliminary ρ _i density reading was determined. And where r is a constant, which here has the value 0.84.

Finally, the corrected density reading ρ _corr is calculated in step 140 of the method in FIG 1 calculated according to: $${\rho }_{cO\mathrm{right}\mathrm{right}}=\frac{{\rho }_i}{K_i}$$

The provisional density reading ρ _i is thus divided by the correction term K _i to obtain the corrected density reading ρ _corr .

This in 3 The illustrated exemplary embodiment of a method 200 according to the invention for determining a measured density value begins in a step 210 with the determination of the natural frequencies f ₁ , f ₃ of the f1 flexural vibration mode and the f3 flexural vibration mode. For this purpose, the f1 flexural vibration mode and the f3 flexural vibration mode can in particular be excited simultaneously. The desired natural frequencies can be determined by maximizing the ratio of the vibration amplitude to the mode-specific excitation power by varying the excitation frequencies.

wobei c_0i, c_1i und c_2i, modenabhängige Koeffizienten sind.In a step 220, provisional measured density values ρ ₁ and ρ ₃ are determined as: $${\rho }_i=c_{0i}+c_{1i}\frac{1}{f_l^2}+c_{2i}\frac{1}{f_l^4},$$

where c _0i , c _1i and c _2i are mode dependent coefficients.

In a step 230, which is described below with reference to FIG 4 is explained in more detail, a correction term for the density measurement is determined.

Finally, in a step 240, a corrected measured density value is determined using the correction term.

As in 4 shown, the step 230 for determining the correction term firstly includes in a step 231 the calculation of the ratio V of the provisional measured density values, ie for example the division of the provisional measured density values ρ ₁ and ρ ₃ to V:=ρ ₁ /ρ ₃ .

wobei r etwa 0,84, b=1 und g ein messrohrabhängiger Proportionalitätsfaktor zwischen Schallgeschwindigkeit und Resonanzfrequenz ist, der beispielsweise einen Wert von 10/m annehmen kann.Then, in a step 232, the speed of sound c is determined, which leads to the calculated ratio V of the provisional measured density values at the measured natural frequencies f ₁ , f ₃ of the bending vibration modes: $$\frac{\left(1+\frac{\mathrm{right}}{{\left(\frac{G\cdot c}{{ƒ}_1}\right)}^2-b}\right)}{\left(1+\frac{\mathrm{right}}{{\left(\frac{G\cdot c}{{ƒ}_3}\right)}^2-b}\right)}=V$$

where r is about 0.84, b=1 and g is a measuring tube-dependent proportionality factor between the speed of sound and the resonance frequency, which can assume a value of 10/m, for example.

Based on the determined speed of sound, in step 233 of the method in 4 a mode-specific correction term K _i calculated according to: $$K_i=\left(1+\frac{\mathrm{right}}{{\left(\frac{G\cdot c}{{ƒ}_i}\right)}^2-1}\right).$$

Finally, the corrected density reading ρ _corr is calculated in step 240 of the method in FIG 1 calculated according to: $${\rho }_{cO\mathrm{right}\mathrm{right}}\cdot =\frac{{\rho }_i}{K_i}$$

The provisional density reading ρ _i is thus divided by the correction term K _i to obtain the corrected density reading ρ _corr .

Claims (18)

Method (100) for determining a physical parameter of a liquid which has a gas load, the gas being present in the liquid in particular in the form of suspended bubbles, by means of a sensor having at least one measuring tube for guiding the medium, the at least one measuring tube having an inlet-side End section and an outlet side Has an end section, wherein the sensor has at least one inlet-side fixing device and one outlet-side fixing device, with which the measuring tube is fixed in one of the end sections, wherein the measuring tube can be excited between the two fixing devices to flexural vibrations of different modes with different natural frequencies, of which an f1- mode has no node between the fixation devices, and wherein an f3 mode has two vibration nodes between the fixation devices, the method (100) comprising the following steps: exciting the f1 mode and the f3 mode; checking whether f1 mode or f3 mode is suppressed (110); when either the f1 mode or the f3 mode is suppressed due to resonance vibration of the gas-laden liquid with respect to the measuring tube, using an expected value for the natural frequency of the suppressed flexural vibration mode as a value for a resonance frequency of the gas-laden liquid; Determining a density correction term (130) as a function of the resonant frequency to correct a preliminary density measurement value ρ _i and/or a mass flow correction term as a function of the resonance frequency to correct a preliminary mass flow measurement value, and/or determining the sound velocity of the gas-laden liquid in the measuring tube as a function of the resonance frequency. Method (100) according to claim 1 , wherein the expected value for the natural frequency of the suppressed flexural vibration mode is determined as a function of the natural frequency of at least one non-suppressed flexural vibration mode (131). procedure after claim 1 or 2 , wherein the expected value for the natural frequency of the suppressed flexural vibration mode is determined by multiplying the natural frequency of a non-suppressed flexural vibration mode by a factor. procedure after claim 3 , where the factor is stored as a constant parameter. procedure after claim 3 , whereby the factor is continuously updated during operation by regularly determining and recording a ratio of the natural frequencies of two bending vibration modes. The method of any preceding claim, further comprising: determining a preliminary density reading ρ _i and/or a preliminary mass flow reading at the natural frequency of the unsuppressed flexural mode, and determining a corrected density reading and/or a corrected mass flow reading using the density correction term and/or the mass flow correction term , wherein the density correction term and/or the mass flow correction term is a function of the resonant frequency and the natural frequency of the non-suppressed flexural vibration mode at which the preliminary density reading ρ _i and/or the preliminary mass flow measurement was determined. Method according to one of the preceding claims, wherein the density correction term K _i for a preliminary density measurement value ρ _i and/or the mass flow correction term is a function of a quotient of the resonant frequency of the gas-laden liquid and the natural frequency of the non-suppressed flexural vibration mode, in which the preliminary density reading and/or mass flow reading have been determined. Method according to one of the preceding claims, wherein the density correction term K _i for the preliminary density measurement values ρ _i based on the natural frequency of the f _i mode has the following form: $$K_i=\left(1+\frac{\mathrm{right}}{{\left(\frac{{ƒ}_{\mathrm{right}es}}{{ƒ}_i}\right)}^2-b}\right),$$

whereby $${\rho }_{cO\mathrm{right}\mathrm{right}}\cdot =\frac{{\rho }_i}{K_i}$$

where is pure media-independent constant, f _res is the resonant frequency of the gas-laden liquid, f _i is the natural frequency of the unsuppressed flexural vibration mode, ρ _corr , ρ _i is the density reading corrected for the effects of the oscillating gas-laden liquid in the measuring tube and the preliminary density reading and where b is a scaling constant. procedure after claim 8 , where: $$\mathrm{right}/b<\mathrm{1,}\text{in particular}\mathrm{right}/b<0.9$$

procedure after claim 8 or 9 , where b = 1. The method according to any one of the preceding claims, wherein g is a diameter of the Measuring tube-dependent proportionality factor between the resonant frequency f _res of the gas-laden liquid and the sound velocity of the gas-laden liquid, where an equation c = f _res / g applies and a value of the sound velocity c determined according to the equation is output. Method according to one of the preceding claims, wherein the preliminary density measurement values ρ _i are determined on the basis of the natural frequency f ₁ of the f _i mode by means of a polynomial in 1/f _i , in particular in (1/f _i ) ² , the coefficients of the polynomial are mode dependent. procedure after claim 4 , where the following applies to a density error E _ρi of a provisional measured density value ρ _i based on the natural frequency f _i of the fi mode: $$E_{\rho i}:=K_i-\mathrm{1,}$$

where a mass flow error E _m of a preliminary mass flow value is proportional to the density error E _ρ1 of the first preliminary density reading ρ _i , i.e.: $$E_m:=k\cdot E_{\rho 1},$$

wherein the proportionality factor k is not less than 1.5, for example not less than 1.8 and in particular not less than 1.9, wherein the proportionality factor k is not more than 3, for example not more than 2.25 and in particular not more than 2 .1, where the mass flow correction term K _m for the mass flow is: $$K_m:=1+E_m,$$

where the corrected mass flow ṁ _corr is determined as $${\dot{m}}_{cO\mathrm{right}\mathrm{right}}\cdot =\frac{{\dot{m}}_v}{K_m},$$

where ṁ _v is the preliminary mass flow value. Method according to one of the preceding claims, in which the suspended bubbles have a radius r which is no more than five times, in particular no more than three times, a penetration depth δ which is given as $$\delta ={\left(v/\left(\pi *f1\right)\right)}^{1/2},$$

where f ₁ is the natural frequency of the f1 mode and where v is the kinematic viscosity of the liquid. procedure after claim 1 , further comprising, if neither the f1 mode nor the f3 mode are suppressed: determining the natural frequencies f ₁ , f ₃ of the f1 mode and the f3 mode (110); Determination of a first provisional measured density value ρ ₁ for the gas-laden liquid guided in the measuring tube on the basis of the natural frequency f ₁ of the f1 mode (120); Determination of a second provisional measured density value ρ ₃ for the gas-laden liquid guided in the measuring tube on the basis of the natural frequency f ₃ of the f3 mode (120); Determining a value for the speed of sound c of the gas-laden liquid in the measuring tube, and/or at least one correction term K _i (130) dependent on the speed of sound c and the natural frequency f _i of a mode and/or a density error E _ρi for the provisional measured density value ρ _i , which was determined on the basis of the natural frequency f _i of the mode, for determining (140) a corrected density measurement value ρ _corr ; and/or a correction term K _m for a preliminary mass flow value ṁ _v for determining a corrected mass flow measurement value ṁ _corr on the basis of the first preliminary density measurement value ρ ₁ , the second preliminary density measurement value ρ ₃ , the natural frequency f ₁ of the f1 mode and the natural frequency f ₃ of the f3 modes. procedure after claim 15 , where the correction term K _i for a preliminary measured density value ρ _i is a function of a quotient of the speed of sound c of the gas-laden liquid and the natural frequency f _i of the mode with which the preliminary measured density value ρ _i was determined. procedure after claim 15 or 16 , where the sound velocity c of the gas-laden liquid is determined by finding the sound velocity value c where the quotient of the first correction term K ₁ for the first preliminary density reading ρ ₁ divided by the second correction term K ₂ for the second preliminary density reading ρ ₂ , equals the quotient of the first preliminary density reading ρ ₁ divided by the second preliminary density reading p ₂ . Procedure according to one of Claims 15 until 17 , where the correction term K _i for the provisional measured density values ρ _i based on the natural frequency f _i of the fi mode has the following form: $$K_1:=\left(1+\frac{\mathrm{right}}{{\left(\frac{G\cdot c}{{ƒ}_i}\right)}^2-b}\right),$$

whereby $${\rho }_{cO\mathrm{right}\mathrm{right}}\cdot =\frac{{\rho }_i}{K_i}$$

where around g are gas-independent constants, c is the speed of sound of the gas-laden liquid, f _i is the natural frequency of the fi mode, ρ _corr is the corrected density, and b is a scaling constant.

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