DE102017131267A1 - Method for determining a gas volume fraction of a gas-laden medium - Google Patents

Abstract

The invention discloses a method for determining a gas volume fraction α of a medium which comprises a liquid laden with gas, by means of a vibration sensor, which has at least one oscillator with at least one oscillatable measuring tube, in which the medium is guided, wherein the oscillator Bieschwungungsmoden with different Owning frequencies, the method comprising the steps of: determining the values of media-dependent natural frequencies f, f of two of the flexural vibration modes having different natural frequencies; determining a pressure p of the medium; determining two preliminary density values ρ and ρ based on f f, determining the current sound velocity cdes On the basis of at least one of the preliminary density values, the associated natural frequency and the sound velocity, determining the gas volume fraction α on the basis of the actual The speed of sound c, the pressure p and the mixture density value ρ.

Description

The present invention relates to a method for determining a gas volume fraction of a gas-laden medium by means of a vibration-type transducer, which comprises at least one oscillator with at least one oscillatable measuring tube, in which the medium is guided. Such sensors determine measured values for the density of the medium based on natural frequencies of bending vibration modes of the measuring tube and measured mass flow values based on the phase angle between vibration of the measuring tube in the so-called Coriolis mode and vibration of the measuring tube in the fundamental mode. Measuring sensors according to this measuring principle are manufactured, for example, by the applicant under the name Promass.

The above-described relationship between the natural frequency of the measuring tube and the density or the phase angle of the Coriolis mode is ideally only for homogeneous, incompressible media. When a liquid medium carried in the measuring tube is loaded with gas, relative oscillations occur between the medium and the measuring tube or between the liquid phase and the gas phase in the oscillating measuring tube. Therefore, corrections correction algorithms are required to obtain even more accurate readings.

In the resonator effect, the liquid which has become compressible due to the gas loading oscillates in relation to the measuring tube. The closer the resonance frequency of the liquid vibration approaches the natural frequency of a bending vibration mode of the measuring tube, the more the bending vibration mode is influenced. From the ratio of the natural frequencies of two bending modes, the speed of sound of the gas-laden medium can be determined, which then correction factors for the density measurement and flow measurement can be determined. This is described in the patent applications with the file reference DE 10 20015.122661.8 . DE 10 2016 005 547.2 and DE 10 2016 112002.2 ,

This allows sufficiently accurate values for the mixture density and the mixture mass flow to be determined. However, a value for the density of the liquid phase in the gas-laden mixture is not yet obtained. It is the object of the present invention to provide a method for determining such a density reading for the liquid phase.

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

• Ermitteln der Werte von medienabhängigen Eigenfrequenzen f_a, f_b von zwei der Biegeschwingungsmoden mit unterschiedlichen Eigenfrequenzen;
• Ermitteln eines Drucks p des Mediums;
• Ermitteln zweier vorläufiger Dichtewerte ρ_a und ρ_b auf Basis von f_a und f_b,
• Ermitteln der aktuellen Schallgeschwindigkeit c_mix des Mediums anhand von ρ_a, ρ_b, f_a und f_b,
• Ermitteln eines Mischungsdichtewerts ρ_mix auf Basis mindestens eines der vorläufigen Dichtewerte, der zugehörigen Eigenfrequenz und der Schallgeschwindigkeit,
• Ermitteln des Gasvolumenanteils α auf Basis der aktuellen Schallgeschwindigkeit c, des Drucks und des Mischungsdichtewerts.

The inventive method is used to determine a gas volume fraction α of a gas-laden liquid by means of a vibration sensor having at least one oscillator with at least one oscillatable measuring tube in which the medium is guided, wherein the oscillator Biegeschwingungsmoden having different natural frequencies, the method following steps include:

• Determining the values of media-dependent eigenfrequencies f _a , f _b of two of the flexural vibration modes having different natural frequencies;
• Determining a pressure p of the medium;
• Determining two preliminary density values ρ _a and ρ _b on the basis of f _a and f _b ,
• Determining the current speed of sound c _{mix of} the medium on the basis of ρ _a , ρ _b , f _a and f _b ,
• Determining a mixture density _value ρ _mix on the basis of at least one of the preliminary density values, the associated natural frequency and the speed of sound,
• Determining the gas volume fraction α on the basis of the current sound velocity c, the pressure and the mixture density value.

In a further development of the invention, the method further comprises determining a value for the density ρ _{l of} the liquid phase as a function of the gas volume fraction α and the mixture density value ρ _mix .

In one development of the invention, an adiabatic coefficient γ for the gas contained in the medium continues to be determined in the determination of the gas volume fraction α.

In a further development of the invention, a value, in particular a reference value, for the speed of sound c _g of the gas contained in the fluid continues to be determined in the determination of the gas volume fraction α.

In a further development of the invention, a value, in particular a reference value, for the speed of sound in the pure liquid c ₁ without gas loading continues to be determined in the determination of the gas volume fraction α.

In a further development of the invention, the determination of the gas volume fraction α takes place according to: $$\boxed{\alpha =\frac{\frac{1}{c_{mix}{}^2}-\frac{1}{c_l^2}}{\frac{1}{c_G^2}-\frac{2}{c_l^2}+\frac{{\rho }_{mix}}{\gamma p}}}$$

In a further development of the invention, the determination of the gas volume fraction α takes place according to: $$\boxed{\alpha =\frac{\gamma p}{c_{mix}{}^2{\rho }_{mix}}}$$

In a development of the invention, the two determined natural frequencies f _a , f _b include the natural frequency f _{1 of} the first mirror-symmetrical bending mode and the natural frequency of the second mirror-symmetrical bending mode f ₃ .

The invention will now be explained in more detail with reference to an embodiment shown in the drawings. It shows.

1 : A flow chart of an embodiment of the method according to the invention.

This in 1 illustrated embodiment of a method according to the invention 100 for determining the gas volume fraction α of a gas-laden liquid begins in one step 110 with the determination of the natural frequencies of the f ₁ bending mode and the f ₃ bending mode of a Coriolis mass flowmeter. For this purpose, the f ₁ bending mode and the f ₃ bending mode can be excited in particular simultaneously. By maximizing the ratio of the vibration amplitude to the mode-specific excitation power by varying the excitation frequencies, the sought natural frequencies can be determined.

wobei c₀₁, c_1i, und c_2i, modenabhängige Koeffizienten sind.Based on the determined natural frequencies fi are in one step 120 preliminary density values ρ ₁ and ρ _{3 are} determined as: $${\rho }_i=c_{0i}+c_{1i}\frac{1}{f_i^2}+c_{2i}\frac{1}{f_i^4}.$$

where c ₀₁ , c _1i , and c _{2i are} mode dependent coefficients.

In one step 130 , which will be explained in more detail below, the determination of the speed of sound of the gas-laden liquid and a correction term for the density measurement.

Subsequently, in one step 140 By means of the speed of sound c _mix, a mixture density _value ρ _mix for the gas-laden liquid is determined.

With the aid of a current pressure reading p for the gas-laden liquid, its speed of sound c _mix and the mixture density _value ρ _mix , in one step 150 the gas volume fraction α determined.

The knowledge of the gas volume fraction α and the mixture density _value ρ _mix , finally allows in step 160 the determination of a value for the density ρ _{l of} the liquid phase.

To determine a correction term for calculating a correct mixture density value, the ratio V of the preliminary density values is first of all calculated, that is, for example, the division of the preliminary density values ρ ₁ and ρ ₃ into 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. Der Wert der Schallgeschwindigkeit c_mix, welcher die obige Gleichung erfüllt, ist der gesuchte Wert für die Schallgeschwindigkeit der mit Gas beladenen Flüssigkeit.Subsequently, a value of the sound velocity c is determined, which with the measured natural frequencies f ₁ and f _{3 of} the bending vibration modes in the following equation leads to the observed ratio V of the preliminary density values: $$\frac{\left(1+\frac{r}{{\left(\frac{G\cdot c_{mix}}{f_1}\right)}^2-b}\right)}{\left(1+\frac{r}{{\left(\frac{G\cdot c_{mix}}{f_3}\right)}^2-b}\right)}=V$$

where r is about 0.84, b = 1 and g is a meter tube dependent proportionality factor between the speed of sound and the resonant frequency, which may for example have a value of 10 / m. The value of the speed of sound c _mix , which satisfies the above equation, is the sought value for the speed of sound of the gas laden liquid.

On the basis of the determined sound velocity value, a mode-specific correction term Ki for the resonator effect can then be calculated according to: $$K_i:=\left(1+\frac{r}{{\left(\frac{G\cdot c}{f_i}\right)}^2-1}\right)$$

A mixture density value ρ _mix can finally be calculated as: $${\rho }_{mix}\cdot =\frac{{\rho }_i}{K_i}$$

A corresponding Coriolis mass flow correction term K _ṁ for calculating a mixing flow measured value ṁ _mix corrected for the influence of the resonator effect can be determined in step 134 calculated as: $$K_{\dot{m}}:=\left(1+\frac{2\cdot r}{{\left(\frac{G\cdot c}{f_1}\right)}^2-1}\right)$$

The mixture flow _measurement value ṁ _mix corrected for the influence of the resonator effect is then given as: $${\dot{m}}_{mix}\cdot =\frac{\dot{m}}{K_{\dot{m}}}$$

Here, ṁ is a preliminary mass flow measurement resulting from multiplying a sensor calibration factor to the phase angle between the first bending mode and the Coriolis mode.

The corrected density density value ρ _mix for the density is satisfactory, if only the mixture is important. If the density of the liquid phase is to be determined, then further steps are required.

According to Sorokin, the following relationship exists between the speed of sound c _{mix of} a gas-laden liquid and other parameters: $$c_{mix}={\left[\frac{\alpha }{c_G{}^2}+\frac{{\left(1-\alpha \right)}^2}{c_l{}^2}+\frac{\alpha \left(1-\alpha \right)\cdot {\rho }_l}{\gamma \cdot p}\right]}^{-\frac{1}{2}}$$

Here, α is the gas volume fraction (or the gas void fraction GVF), c _g the sound velocity of the pure gas, c _l the sound velocity of the pure liquid, γ the adiabatic coefficient for the gas, p the current pressure of the gas-laden liquid and ρ _l the Density of the gas laden liquid.

The mixture density _value ρ _mix is linked to the density of the liquid phase ρ _l and the gas density via the gas volume fraction α by: $${\rho }_{mix}={\rho }_l\left(1-\alpha \right)+{\rho }_G\alpha$$

Since the liquid density is much larger than the gas density and since the gas volume fraction is usually in the single-digit percentage range, the following approximation applies: $${\rho }_{mix}\approx {\rho }_l\left(1-\alpha \right)$$

Thus, equation (1) can be rewritten as: $$c_{mix}={\left[\frac{\alpha }{c_G^2}+\frac{{\left(1-\alpha \right)}^2}{c_l^2}+\frac{\alpha {\rho }_{mix}}{\gamma p}\right]}^{-\frac{1}{2}}$$

Neglecting quadratic terms in α yields: $$c_{mix}={\left[\frac{\alpha }{c_G^2}+\frac{1-2\alpha }{c_l^2}+\frac{\alpha {\rho }_{mix}}{\gamma p}\right]}^{-\frac{1}{2}}$$

By solving equation 10 for α, an expression for calculating the gas volume fraction is found: $$\boxed{\begin{array}{cc}\alpha =\frac{\frac{1}{c_{mix}{}^2}-\frac{1}{c_l^2}}{\frac{1}{c_G^2}-\frac{2}{c_l^2}+\frac{{\rho }_{mix}}{\gamma P}}& \left(11\right)\end{array}}$$

In this case, only the mixture density value ρ _mix goes from variable equation 3, the pressure applied during the determination of the mixture density p and the speed of sound of the liquid loaded with gas

Neglecting the terms with (1 / c _l ) ² and (1 / c _g ) ² , which is justified for pressure values up to a few bar, one obtains a value for the gas volume fraction α with a relative accuracy in the lower single-digit percentage range: $$\boxed{\begin{array}{cc}\alpha =\frac{\gamma p}{c_{mix}{}^2{\rho }_{mix}}& \left(12\right)\end{array}}$$

By switching from Equation 8 and using the gas volume fraction α from Equation 12 or Equation 11, one thus obtains the desired value for the density of the liquid phase: $${\rho }_l=\frac{{\rho }_{mix}}{\left(1-\alpha \right)}.$$

Since the gas volume fraction α has absolute values in the single-digit percentage range in many applications, by using the value of the gas volume fraction α from Equation 12 for the density ρ _{l of} the liquid phase a relative measurement accuracy in the range of better than 0.1% results.

For more accurate values, the gas volume fraction α from Equation 11 should be used. Even approximate reference values for the sound velocities c _l and c _g in the pure liquid phase and the pure gas phase, respectively, can still increase the accuracy significantly in the determination of the gas volume fraction α by at least an order of magnitude if Equation 11 is used. The value for the density ρ _{1 of} the liquid phase according to Equation 13 is correspondingly more accurate.

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• DE 1020015122661 [0003]
• DE 102016005547 [0003]
• DE 102016112002 [0003]

Claims (8)

Method for determining a gas volume fraction α of a gas-laden liquid by means of a vibration-type transducer having at least one oscillator with at least one oscillatable measuring tube in which the medium is guided, the oscillator having bending modes having different natural frequencies, the method comprising the following steps Determining the values of media-dependent natural frequencies f _a , f _b of two of the bending modes with different natural frequencies; Determining a pressure p of the medium; Determining two preliminary density values ρ _a and ρ _b on the basis of f _a and f _b , determining the current sound velocity c _{mix of} the medium on the basis of ρ _a , ρ _b , f _a and f _b , determining a mixture density _value ρ _mix on the basis of at least one of provisional density values, the associated natural frequency and the sound velocity, determining the gas volume fraction α on the basis of the current sound velocity c, the pressure and the mixture density value. Method according to Claim 1 , further comprising: determining a value for the density ρ _{l of} the liquid phase as a function of the gas volume fraction α and the mixture density value ρ _mix . Method according to one of the preceding claims, wherein in the determination of the gas volume fraction α further adiabatic coefficient γ for the gas contained in the medium is received. Method according to one of the preceding claims, wherein in the determination of the gas volume fraction α further includes a value, in particular a reference value, for the speed of sound c _g of the gas contained in the liquid. Method according to one of the preceding claims, wherein in the determination of the gas volume fraction α continues to receive a value, in particular a reference value for the speed of sound in the pure liquid c _l without gas loading. Method according to one of the preceding claims, wherein the determination of the gas volume fraction α is carried out according to: $$\boxed{\alpha =\frac{\frac{1}{c_{mix}{}^2}-\frac{1}{c_l^2}}{\frac{1}{c_G^2}-\frac{2}{c_l^2}+\frac{{\rho }_{mix}}{\gamma p}}}$$

Method according to one of Claims 1 to 5 , wherein the determination of the gas volume fraction α is carried out according to: $$\boxed{\alpha =\frac{\gamma p}{c_{mix}{}^2{\rho }_{mix}}}$$

Method according to one of the preceding claims, wherein the two determined natural frequencies f _a , f _b include the natural frequency f _{1 of} the first mirror-symmetrical Bieschwwingungsmodes and the natural frequency of the second mirror-symmetrical Bieschwwingungsmodes f ₃ .

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