Method for characterizing the gas load of a medium and densimeter therefor

Abstract

A method (100) for characterizing a gas load of a medium comprising a liquid loaded with gas by means of a measuring sensor guiding the medium in at least one vibrating measuring tube, wherein the method comprises determining a sound speed value (130) and a resonant cavity density value (140) of the medium based on the natural frequencies of at least two different vibration modes of the measuring tube, determining a measured pressure value (110) of the medium guided in the measuring tube, determining a gas volume content of the suspended gas bubbles in the medium (150) based on the resonant cavity density value, the sound speed value and the measured pressure value, determining a value of the gas volume content of the free gas bubbles (170) based on the resonant cavity density value of the medium and the gas volume content of the suspended gas bubbles.

Description

Technical Field

[0001] The invention relates to a method for characterizing the gas loading of a medium comprising a liquid loaded with gas, and to a densitometer configured to perform the method. Background Art

[0002] The published patent application DE 10 2017 131 267 A1 discloses the determination of the gas loading of a liquid based on the resonant cavity effect and the Sorokine equation. However, the gas loading determined in this way has some disadvantages, since suspended gas bubbles, on the one hand, and free gas bubbles, on the other hand, occur in the liquid and have different effects on the measurement of parameters of the medium, such as its density or flow rate. Therefore, the object of the present invention is to provide a method and a densitometer for carrying out the method, which enable a more differentiated characterization of the gas loading of a medium. Summary of the Invention

[0003] According to the invention, this object is achieved by a method according to independent claim 1 and a densitometer according to independent claim 13 .

[0004] The method according to the invention serves to characterize the gas loading of a medium comprising a gas-laden liquid by means of a measuring sensor which guides the medium in at least one vibrating measuring tube, wherein the method comprises:

[0005] determining a value for the sound velocity of the medium and a value for the resonance cavity density based on the natural frequencies of at least two different vibration modes of the measuring tube;

[0006] determining a measured pressure value of a medium conducted in the measuring tube and the natural frequencies of at least two different vibration modes of the measuring tube;

[0007] determining a value for the speed of sound and a value for the resonance cavity density of the medium based on the natural frequencies of at least two different vibration modes of the at least one measuring tube;

[0008] The value of the gas volume content of the free bubbles is determined as a function of the value of the resonance cavity density of the medium and the gas volume content of the suspended bubbles.

[0009] In a development of the invention, the value of the gas volume content of the free bubbles is proportional to the difference between an expected value of the medium density and an expected value of the resonance cavity density, the expected value of the medium density being based on a reference density value of the liquid and the gas volume content of the suspended bubbles.

[0010] In a development of the invention, in order to determine the value of the gas volume content of free bubbles, the difference is divided by the product of an expected value of the medium density and a correction factor, the expected value of the medium density being based on a reference density value of the liquid and the gas volume content of suspended bubbles, wherein the correction factor is not less than 1 and not greater than 4, and in particular not greater than 3.

[0011] In a development of the invention, the correction factor depends on the expected mobility of the free gas bubbles in the liquid and / or the Stokes number.

[0012] In a development of the invention, the correction factor has the value 2.

[0013] In a development of the invention, the gas volume content of the suspended bubbles is determined based on the Sorokin equation.

[0014] In a development of the invention, the value of the resonance cavity density is determined based on the natural frequencies of the F1 bending vibration mode and the F2 bending vibration mode or the F3 bending vibration mode.

[0015] In a development of the invention, the measuring sensor has at least two different measuring tubes, in which similar bending vibration modes have different natural frequencies, wherein the resonance cavity density value is determined based on the different natural frequencies of two similar bending vibration modes, in particular two F1 bending vibration modes of the different measuring tubes.

[0016] In a development of the invention, the value of the mixed phase density of the medium is determined as a function of the gas volume content of the suspended bubbles and the gas volume content of the free bubbles.

[0017] In a development of the invention, the method is performed at least partially iteratively, wherein in a second iteration the determined mixed phase density value is used instead of the resonance cavity density value for determining the gas volume content of the suspended bubbles.

[0018] In a development of the invention, at least one of the following values ​​provided as measured values ​​is output: a mixed phase density value, a gas volume content of free bubbles, a gas volume content of suspended bubbles and a sum of the aforementioned gas volume contents.

[0019] The density meter according to the present invention comprises:

[0020] a measuring sensor having at least one measuring tube which can be excited to oscillate and serves to guide a flowable medium;

[0021] an exciter for exciting vibration;

[0022] at least one vibration sensor for detecting a vibration-related signal; and

[0023] A measuring and operating circuit is configured to drive the exciter, detect the vibration-related signal, and perform the method according to the invention.

[0024] In a development of the invention, the at least one measuring tube is a measuring tube of a pair of essentially identical measuring tubes which can be excited to vibrate relative to one another. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The present invention will now be described in more detail based on the exemplary embodiments illustrated in the figures. As follows:

[0026] Figure 1 : A flow chart of an exemplary embodiment of a method according to the present invention;

[0027] Figure 2a : measurement data on gas volume content obtained using the method according to the present invention; and

[0028] Figure 2b : Determination of the relative density according to the prior art and according to the method according to the invention. DETAILED DESCRIPTION

[0029] Figure 1 The illustrated exemplary embodiment of a method 100 according to the present invention for characterizing a gas-laden liquid begins with step 110, wherein the natural frequencies of the f1 and f3 bending vibration modes of a measuring tube pair of a Coriolis mass flowmeter, which is used in this case, in particular, as a density sensor, are determined. For this purpose, the f1 and f3 bending vibration modes can be excited simultaneously. By maximizing the ratio of the vibration amplitude to the mode-specific excitation power by varying the excitation frequency, the sought natural frequencies can be determined. Furthermore, the measured pressure value p, which is applicable during the frequency measurement, is detected.

[0030] Based on the determined natural frequencies fi, preliminary density values ​​ρ1 and ρ3 are determined in step 120 as follows:

[0031]

[0032] Among them, c 0i 、c 1i and c 2i is the pattern correlation coefficient.

[0033] In step 130, described in more detail below, the acoustic velocity of the gas-laden liquid and the mode-specific resonant cavity correction term K for density measurement are determined. res-i .

[0034] Then, in step 140, the speed of sound c res To determine the cavity density ρ of the gas-laden liquidres .

[0035] Use the current measured pressure value p of the liquid loaded with gas, its sound velocity c res and the resonant cavity density ρ res , in step 150, the gas volume content α of the suspended bubbles is determined susp .

[0036] Gas volume content α based on suspended bubbles susp And using the pure liquid density ρ l With knowledge of the density of the gas-laden liquid, it is possible to determine in a next step 160 the mixed phase density median value ρ l-susp .

[0037] ρ l-susp =ρ l *(1-α susp ) (ii)

[0038] Based on the median value of the mixed phase density ρ l-susp and the resonant cavity density ρ res The difference between can be calculated in the next step 170 for ρ as follows res <ρ l-susp To calculate the gas volume content of free bubbles α free :

[0039]

[0040] In this case, k gas is a correction factor with a value between 1 and 3, which depends on the Stokes number of the gas bubble and is well estimated by 2 for most cases.

[0041] For ρ res >ρ l-susp , the following applies: α free =0.

[0042] For the real mixed phase density value ρ mix , so in the subsequent step 180 the following formula is obtained:

[0043] ρ mix =ρ l *(1-α susp -α free ) (iv)

[0044] In addition to the mixed phase density value, the individual gas volume content α can also be output susp and α free and the sum as the total gas volume content α totalBased on these gas volume content and flow variables, it is possible, for example, to characterize the flow pattern in the flowing medium.

[0045] Describe the details related to the method steps above:

[0046] In order to determine the value of ρ for calculating the resonant cavity density res The resonant cavity correction term K res-i Initially, the ratio V of the preliminary density values ​​is calculated as follows, i.e., for example, the division of the preliminary density values ​​ρ1 and ρ3:

[0047] V:=ρ1 / ρ3.

[0048] Then determine the speed of sound c res and using the measured natural frequencies f1 and f3 of the bending vibration modes, the observed ratio V of the preliminary density values ​​is produced in the following equation:

[0049]

[0050] where r is approximately 0.84, b = 1, and g is the speed of sound c res The proportionality factor between the resonance frequency and the measuring tube is dependent on the measurement tube and can assume a value of 10 / m, for example. The speed of sound c satisfies the above equation res The value of is the sought value for the speed of sound of the gas laden liquid.

[0051] Based on the determined sound velocity value c res , the mode-specific correction term K can then be calculated for the resonant cavity effect as follows res-i :

[0052]

[0053] The cavity density value ρ can be set in the next step 140 res Calculated as:

[0054]

[0055] Furthermore, according to Sorokin, the speed of sound c in a liquid loaded with gas is mix The following relationships exist with other parameters:

[0056]

[0057] In this case, α s is the gas volume content (or gas void fraction GVF), c g is the speed of sound in pure gas, c l is the speed of sound of the pure liquid, γ is the adiabatic coefficient of the gas, p is the current pressure of the liquid loaded with gas, and ρ l is the density of the pure liquid.

[0058] According to Sorokin's mixture density value ρ S-mix The following formula is used to calculate the gas volume content α and the liquid density ρ l Linked to gas density:

[0059] ρ S-mix =ρ l (1-α s )+ρ g α s (ix)

[0060] Because liquids are significantly more dense than gases, and because gas concentrations by volume are typically in the single-digit percentage range, the following approximations apply:

[0061] ρ S-mix ≈ρ l (1-α s ) (x)

[0062] Therefore, equation (viii) can be rewritten as:

[0063]

[0064] By neglecting the square term in α, we obtain the following:

[0065]

[0066] By targeting α s Solve equation xii to find the expression for calculating the gas volume content according to Sorokin:

[0067]

[0068] By neglecting the fact that the (1 / c l ) 2 and (1 / c g ) 2 The value of the gas volume fraction α is obtained with a relative accuracy in the low single-digit percentage range:

[0069]

[0070] If in equation xiii or xiv, the mixed sound velocity c S-mix Use the speed of sound c found by v according to Eq. res Replace, and according to Sorokin's mixture density value ρ S-mix The cavity density value ρ determined in equation vii is used res Replace, then according to Sorokin's gas volume content α scorresponds to the gas volume content α of the suspended bubbles used in equations ii and iv susp .

[0071] In the second iteration, the cavity density value ρ is replaced by res , the true mixed phase density value ρ found by equation iv in the first iteration mix can be used in equations xiii or xiv for the value of the mixture density ρ according to Sorokin S-mix The gas volume content α found in this way is based on Sorokin's s It is also used as the gas volume content α of the suspended bubbles in equation ii susp To determine the new intermediate value of the mixed phase density ρ l-susp , which is then used in equation iii to determine a second value for the gas volume content of the free bubbles. The value of the gas volume content iteratively determined in this way is then used in equation iv to obtain a second value for the true mixed phase density p mix If necessary, this iteration can be continued until the convergence criterion is met. However, experience has shown that one iteration is quite sufficient.

[0072] Figure 2a The graph in FIG shows measurement data of the gas volume content of gum arabic into which air has been introduced, collected using the method according to the present invention. The dotted line shows the gas volume content of the suspended bubbles α s , whereas the solid line shows the gas volume content of the free bubbles α free Depending on the type of introduction, the volume content of the various gases varies significantly. The method according to the invention is able to distinguish between the two types of gas loads and to generate accurate measured values ​​for the respective gas volume content. Figure 2b The figure in FIG shows the value of the resonant cavity density ρ generated by equation vii according to the prior art with a dashed line. res , and the solid line shows the mixed phase density value ρ according to equation iv of the present invention mix The determination of the density of the mixed phase according to the invention proves to be superior in terms of the determination of the density when given different types of gas loadings.

Claims

1. A method (100) for characterizing the gas loading of a medium comprising a gas-laden liquid by means of a measuring sensor which guides the medium in at least one vibrating measuring tube, wherein: The method comprises: determining a measured pressure value (110) of the medium guided in the measuring tube and the natural frequencies of at least two different vibration modes of the measuring tube; determining a sound velocity value (130) and a resonance cavity density value (140) of the medium based on the natural frequencies of the at least two different vibration modes of the at least one measuring tube; determining a gas volume content of suspended bubbles in the medium based on the resonance cavity density value, the sound velocity value, and the measured pressure value (150); determining a value (170) of the gas volume content of free bubbles as a function of the value of the resonance cavity density of the medium and the gas volume content of the suspended bubbles; wherein the value of the gas volume content of the free bubbles is proportional to a difference between an expected value of the medium density and an expected value of the resonance cavity density, the expected value of the medium density being based on a reference density value of the liquid and the gas volume content of the suspended bubbles; wherein, in order to determine the value of the gas volume content of the free bubbles, the difference is divided by the product of the expected value of the medium density and a correction factor, wherein the expected value of the medium density is based on the reference density value of the liquid and the gas volume content of the suspended bubbles, wherein the correction factor is not less than 1 and not greater than 4.

2. The method according to claim 1, wherein The correction factor is no greater than 3.

3. The method according to claim 1, wherein The correction factor depends on the expected mobility and / or Stokes number of the free gas bubbles in the liquid.

4. The method according to claim 1, wherein The correction factor has a value of 2.

5. The method according to any one of claims 1 to 4, wherein: The gas volume content of the suspended bubbles is determined based on the following equation: Among them, c res The value of is the sought value of the speed of sound of the liquid loaded with gas, ρ res is the cavity density, c g is the speed of sound in pure gas, c l is the speed of sound of the pure liquid, γ is the adiabatic coefficient of the gas, and P is the current pressure of the liquid loaded with the gas.

6. The method according to any one of claims 1 to 4, wherein: The resonance cavity density value is determined based on the natural frequencies of the F1 bending vibration mode and the F2 bending vibration mode or the F3 bending vibration mode.

7. The method according to any one of claims 1 to 4, wherein: The measuring sensor has at least two different measuring tubes, wherein similar bending vibration modes have different natural frequencies, wherein the resonance cavity density value is determined based on the two similar bending vibration modes.

8. The method according to claim 7, wherein: The resonance cavity density values ​​are determined based on the different natural frequencies of the two F1 bending vibration modes of the different measuring tubes.

9. The method according to any one of claims 1 to 4, wherein: The mixed phase density value of the medium is determined as a function of the volume content of the suspended bubbles and the gas volume content of the free bubbles.

10. The method according to claim 9, wherein: The method is at least partially performed iteratively, wherein, in a second iteration, the gas volume content of the suspended bubbles is determined using the determined mixed phase density value instead of the resonance cavity density value.

11. The method according to claim 9, wherein: At least one of the following values ​​provided as measured values ​​is output: the mixed phase density value, the gas volume content of the free bubbles, the gas volume content of the suspended bubbles, and the sum of the aforementioned gas volume contents.

12. A density meter comprising: a measuring sensor having at least one measuring tube which can be excited to oscillate and serves to guide a flowable medium; an exciter, the exciter being used to excite the vibration; at least one vibration sensor for detecting a vibration-related signal; as well as A measuring and operating circuit configured to drive the exciter, detect the vibration-related signal, and perform the method according to any one of claims 1-11.

13. The densitometer according to claim 12, wherein The at least one measuring tube is a measuring tube of a pair of substantially identical measuring tubes which can be excited to vibrate relative to each other.

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