METHOD AND MEASURING DEVICE FOR DETERMINING THE COMPRESSIBILITY OF A FLOWING FLUID
Patent Information
- Application Number
- DE502016016848
- Authority / Receiving Office
- DE · DE
- Patent Type
- Patents
- Current Assignee / Owner
- Priority Date
- 2015-09-15
- Filing Date
- 2016-08-24
- Publication Date
- 2025-01-09
- Estimated Expiration
- 2036-08-24
AI Technical Summary
Current methods for determining the compressibility of fluids, particularly for calculating density at reference pressure, are not reliable due to limitations in measuring accuracy and precision, especially in gas-laden mixtures.
A method and device that utilize a vibronic density meter with a throttle to maintain different pressures, allowing for precise density and pressure measurements, which are used to calculate compressibility and correct for viscosity, enabling accurate determination of fluid compressibility and density under varying conditions.
This approach allows for reliable and precise determination of fluid compressibility and density at reference pressures, improving measurement accuracy and enabling calculation of speed of sound and reference density values.
Description
[0001] The present invention relates to a method for determining the compressibility of a flowing fluid.
[0002] The density of a fluid at reference conditions, especially at a reference pressure of 1013 MPa, is of interest for fluid evaluation. However, it is not directly available in many applications. One solution is to calculate the density at reference pressure from a density measurement taken at a higher pressure. To perform this calculation reliably, the most accurate knowledge of the compressibility is required.
[0003] In US2008 / 053220 A1, the density of the incompressible phase of a mixture of a gas-laden slurry is to be determined according to: Dabs = D1 / 1 − D1 / D2 − 1 / P1 / P2 − 1
[0004] Here, Dabs is the desired density of the incompressible phase, while D1 and D2 are density measurements for the mixture at corresponding pressure measurements P1 and P2. The slurry is pumped through two densimeters connected in series, with the pressure drop across the first densimeter resulting in a lower static pressure in the second densimeter.
[0005] According to CA 2 622 602 A1, a medium, possibly containing gas, flows through a Coriolis mass flowmeter arranged in series between two pressure sensors. If the Coriolis mass flowmeter can no longer measure the flow accurately enough due to excessive gas loading, the flow is determined based on a differential pressure measurement between the two pressure sensors. If the Coriolis mass flowmeter can measure accurately enough, the transfer functions of the differential pressure measurement and the Coriolis mass flowmeter are adjusted.
[0006] The measuring system according to US 2011 / 0161018 A1 comprises a vibration-type measuring transducer with an inlet-side pressure sensor for predicting a critically low pressure at the outlet of the measuring transducer due to the flow-dependent pressure drop along the flow-through measuring tube.
[0007] US 2005 / 138993 A1 describes a density meter based on the vibration principle with pulsating pressure for measuring the density of the liquid phase of gas-laden media. The respective gas volume fraction is determined from the mixture density at different pressure values, which can then be used to calculate the density of the liquid phase. WO 2014 / 158376 A1 discloses another density meter.
[0008] It is the object of the present invention to provide a method and a measuring device which enable the compressibility of a fluid to be determined as simply and reliably as possible, in particular for determining the density of a medium at a reference pressure.
[0009] The object is achieved according to the invention by the method according to independent patent claim 1 and the device according to independent patent claim 8.
[0010] The method according to the invention for determining the compressibility of a flowing fluid comprises the following steps: Driving a volume flow of the fluid by means of a pump through at least one measuring tube of a vibronic densimeter at a first pressure maintained by a throttle; determining a first density measurement value of the flowing fluid at the first pressure; determining a first pressure measurement value of the flowing fluid at the first pressure; driving a volume flow of the flowing fluid by means of a pump through a densimeter at a second pressure maintained by a throttle; determining a second density measurement value of the fluid at the second pressure, which differs from the first pressure; determining a second pressure measurement value of the flowing fluid at the second pressure;Determining the compressibility of the fluid based on the first density measurement value, the second density measurement value, the first pressure measurement value and the second pressure measurement value, assuming that the composition of the fluid is unchanged between the recording of the first density measurement value and the second density measurement value, wherein the volume flow is a defined volume flow driven by a metering pump with a delivery accuracy of better than 1%, in particular better than 0.5%, the pressure drop across the densitometer (220) is calculated by forming the difference between the pressure measurements of the first pressure sensor (230a) and the second pressure sensor (230b), and a viscosity of the fluid is determined based on the volume flow and the pressure drop, wherein the density measurement value of the vibronic densitometer is corrected for cross-sensitivity to the viscosity of the fluid.
[0011] In a further development of the invention, the method further comprises calculating a third density value at a third pressure based on the determined compressibility and on at least one of the first and second density measured values, wherein the third pressure differs from the first pressure and the second pressure, wherein the third pressure lies in particular outside an interval delimited by the first pressure and the second pressure.
[0012] In a further development of the invention, the method further comprises calculating a sound speed value based on the compressibility and at least one of the density measurements.
[0013] In a further development of the invention, the determination of the compressibility is carried out under the assumption of a constant temperature of the fluid at the first pressure measurement value and the second pressure measurement value.
[0014] In a further development of the invention, a first temperature of the fluid in the measuring tube when detecting the first density measurement value differs from a second temperature of the fluid in the measuring tube when detecting the second density measurement value by not more than 5 °C, in particular not more than 2 °C and preferably not more than 1 °C.
[0015] In a further development of the invention, the determination of the first density measurement value and the determination of the second density measurement value each comprise the detection of a natural frequency value of at least one bending vibration mode of the measuring tube.
[0016] In a further development of the invention, the natural frequency of the at least one bending vibration mode depends on a bending stiffness of the measuring tube, which has a cross-sensitivity to the pressure of the fluid in the measuring tube, wherein the pressure-dependent bending stiffness of the measuring tube is included in the determination of the density measurement value on the basis of the detected natural frequencies, wherein at least one of the detected pressure measurement values is used to determine the pressure-dependent bending stiffness.
[0017] The measuring arrangement according to the invention for determining the compressibility of a flowing fluid and / or a variable dependent on the compressibility comprises: a fluid path for guiding a medium; a pump, which is arranged in the fluid path, for driving a volume flow of the medium in the fluid path; a density meter with at least one oscillator, which has at least one oscillatable measuring tube, for guiding the medium, with at least one excitation arrangement for exciting oscillations of the measuring tube, and with at least one sensor arrangement for detecting at least one oscillation property of the oscillator, wherein the measuring tube or the measuring tubes of the at least one oscillator is or are arranged in the fluid path.are; a throttle arrangement with a variable flow resistance, wherein the density meter is arranged between the pump and the throttle arrangement in the fluid path, wherein the throttle arrangement serves to bring about different static pressure values in the density meter at a constant volume flow due to different flow resistances; at least one pressure sensor for detecting a pressure measurement value in the fluid path, wherein the pressure sensor is arranged between the pump and the throttle arrangement in the fluid path; an operating and evaluation unit which is set up to determine a value for the compressibility of the fluid on the basis of at least two density measurement values and the associated pressure measurement values which were detected at different flow resistances of the throttle arrangement. wherein the measuring arrangement further comprises a second pressure sensor, wherein the density meter is arranged between the first pressure sensor and the second pressure sensor, wherein the second pressure sensor is arranged between the density meter and the throttle arrangement, the pump is a metering pump with a delivery accuracy of better than 1%, in particular better than 0.5%, and the operating and evaluation unit is configured to determine a viscosity measurement value for the fluid based on the volume flow and a difference between essentially simultaneously recorded pressure measurement values of the first pressure sensor and the second pressure sensor, and to determine the density measurement value based on the oscillation property of the oscillator and the viscosity measurement value.
[0018] In a further development of the invention, the throttle arrangement has two check valves connected in parallel, of which a first check valve has a lower operating point than a second check valve, and a check valve shut-off valve is connected upstream of the first check valve, which is in particular automatically controllable.
[0019] In an alternative development of the invention, the throttle arrangement has an aperture with an adjustable aperture.
[0020] In a further development of the invention, the operating and evaluation unit is configured to determine a pressure measurement value for the fluid, which is associated with a density measurement value, as an average value of pressure measurement values recorded essentially simultaneously by the first pressure sensor and the second pressure sensor.
[0021] In a further development of the invention, the operating and evaluation unit is designed to determine a density value under reference conditions, for example 1013 mbar, based on the density measurement value, the associated pressure measurement value and the determined value for the compressibility.
[0022] The invention will now be explained in more detail with reference to the exemplary embodiments illustrated in the drawings. It shows: Fig. 1 : a flowchart of an embodiment of the method according to the invention; Fig. 2a : a schematic representation of a measuring arrangement; Fig. 2b : a schematic representation of a detailed variant of the measuring arrangement from Fig. 2a ; and Fig. 3 : a schematic representation of an embodiment of a measuring arrangement according to the invention.
[0023] The Fig. 1 The illustrated embodiment of a method 1 according to the invention comprises, in a first step 10, the detection of a first density measurement value ρ 1 and an associated first pressure measurement value p 1 of a flowing fluid, wherein the first pressure of the flowing fluid is generated by pumping the fluid against a first flow resistance R 1 of a throttle arrangement with a variable flow resistance.
[0024] After recording the first density measurement value ρ 1 and the associated first pressure measurement value p 1 , in a second step 20, at a second flow resistance R 2 of the throttle arrangement, a second density measurement value ρ 2 and an associated second pressure measurement value p 2 of a flowing fluid are recorded, wherein the first flow resistance differs from the second flow resistance. With a substantially constant volume flow of the fluid through the throttle arrangement, this leads to correspondingly different values for the first static pressure and the second static pressure of the flowing medium. For example, the first pressure can be approximately 0.5 to 1 bar, while the second pressure can be 5 to 10 bar.
[0025] The density measurement can be carried out, for example, by measuring a density-dependent resonance frequency of an oscillating measuring tube through which the fluid flows.
[0026] Finally, in a third step 30, the compressibility β of the fluid is calculated based on the two density measurements ρ 1 , ρ 2 and the corresponding pressure measurements p 1 , p 2 according to: β = ρ 1 − ρ 2 1 2 ρ 1 + ρ 2 ⋅ p 1 − p 2
[0027] Following the determination of the compressibility of the fluid, the speed of sound c of the fluid can be calculated in a step 40a on the basis of a density value ρ and a compressibility value β determined therefrom according to: c = 1 ρ ⋅ β
[0028] The density value can, for example, be the arithmetic mean of the two density measurements ρ 1 , ρ 2 on the basis of which the compressibility β was calculated.
[0029] Alternatively or additionally, following the determination of the compressibility of the fluid in a step 40b, a reference density ρ ref can be calculated at a reference pressure p ref of, for example, 1013 mbar. The reference density depends on the reference pressure p ref , at least one pair of values of a pressure measurement value pi with its associated density measurement value ρ i , and the correspondingly determined value for the compressibility β of the fluid.
[0030] The Fig. 2a The measuring arrangement 101 shown comprises a sampling line 102, which is run parallel to a pipeline 104 between a first connection point 106 and a second connection point 108. The measuring arrangement 101 further comprises, in the sampling line 102, a micro annular gear pump 114, such as that available from HNP, or another metering pump with a delivery accuracy of better than 1%, in particular better than 0.5%, for driving a defined volume flow through the fluid path 116 formed by the sampling line 102 and the components arranged therein. The sampling line has, for example, an inner diameter of 4 mm. In the extraction line 102, a filter element 115 is arranged upstream of the gear pump 114, which filter element has, for example, a maximum pore size of not more than 20 µm, in particular not more than 10 µm and preferably not more than 5 µm, in order to ensure that subsequent components do not become clogged.
[0031] A density meter 120 with an oscillating measuring tube 122 is arranged in the sampling line 102. The measuring tube can be excited by an exciter to flexural vibrations whose resonant frequency depends on the density of a medium contained in the measuring tube 122. The measuring tube has a diameter of, for example, 160 µm and is prepared in silicon using MEMS technology. The resonant frequency for a low-viscosity fluid with a density of approximately 10 6 g / m 3 is, for example, in the order of 20 kHz.
[0032] The total length of a fluid path section through the measuring tube 122 and surrounding MEMS components with an inner diameter of 200 µm is approximately 1 cm. This fluid path section has a comparatively high flow resistance, making it impractical to guide the entire volume flow through the sampling line 102 via this fluid path section. The expected volume flows at pressure drops of a few bar across the fluid path section through the measuring tube 122 would be so low that the medium in the sampling line 102 would not be reliably representative, particularly given changing properties of the medium in the pipe 104. Therefore, the fluid path section through the MEMS components is routed as a bypass 126 parallel to an orifice 124, wherein the bypass 126 has a bypass path length of less than 20 mm, in particular less than 15 mm, for example 10 mm.The aperture 124 has a diameter of 0.5 to 2 mm, which is dimensioned such that, due to the volume flow in the sampling line 102, a pressure gradient is generated, which drives a portion of the volume flow of, for example, 0.1% to 5% through the bypass 126. The MEMS components further comprise a temperature sensor 127, for example a semiconductor resistance element or a Pt resistance element, which in particular detects a temperature of the measuring tube 122 or near the measuring tube, which is representative of the temperature of the medium.
[0033] The measuring arrangement 101 further comprises a pressure sensor 130 for detecting a pressure measurement value at a pressure tapping point 132, which is arranged on the fluid path 116 between the gerotor pump 140 and a throttle arrangement 160a. More precisely, the pressure tapping point is arranged below the density meter in the flow direction.
[0034] However, since a pressure drop occurs across the orifice 124 or the measuring tube 122, which is essentially proportional to the volume flow, the pressure at the pressure tapping point 132 is definitely lower than the average pressure in the measuring tube 122. In this respect, it is advantageous to provide an additional pressure sensor between the pump and the measuring tube and to calculate an average pressure for the fluid in the measuring tube from the measured values of the two pressure sensors below and above the measuring tube. This is particularly advantageous if the actual pressure of the fluid in the measuring tube is of interest, for example, in order to calculate a density value at a reference pressure. However, a second pressure sensor is expressly not required to determine the compressibility because, at a constant volume flow, the pressure drop across the measuring tube is constant, so that it does not contribute to the pressure difference in equation (1).
[0035] The throttle arrangement 160a comprises two parallel-connected check valves, of which a first check valve 162a has a lower operating point than a second check valve 164a. The first operating point of the first check valve 162a is, for example, 0.5–1 bar, while the second operating point of the second check valve 164a is 5–10 bar. An automatically controllable check valve shutoff valve 166a is connected upstream of the first check valve 162a. When the check valve shutoff valve 166a is open, the volume flow driven by the gerotor pump 114 can flow through the first check valve 162a, so that the static pressure of the flowing fluid is determined by the operating point of the first check valve 162a.If, however, the check valve 166a is closed, the volume flow flows through the second check valve 164a, so that the static pressure is determined via the second operating point and thus has a significantly higher value. Thus, with a constant volume flow, the static pressure can be determined by means of the shut-off valve 166a, alternating between the first operating point and the second operating point. The value of the static pressure of the fluid can be determined using the pressure sensor 130, subject to the limitations explained above.
[0036] The measuring arrangement 101 further comprises an operating and evaluation unit 140, which is set up to determine the compressibility of the fluid on the basis of the value tuples for various static pressure measured values, with the respectively associated density and, if applicable, temperature measured values of the flowing fluid, and thus to determine a density value under reference conditions, for example 1013 mbar. Likewise, the operating and evaluation unit controls the check valve shut-off valve 166a to block the first check valve 162a.
[0037] The electrical circuits of the differential pressure measuring system, the density meter 120, and the operating and evaluation unit are preferably designed with Exi (intrinsically safe) protection type. The electronic circuit of the gerotor pump 114 is preferably also implemented with an ignition protection type, for example, in a flameproof enclosure according to class Ex-d.
[0038] In Fig. 2b a throttle arrangement 160b is shown, which is an alternative to the Fig. 2a illustrated throttle arrangement 160a in the embodiment according to Fig. 2a can be used. The throttle arrangement 160b has an orifice 166b with a variable flow cross-section, wherein the flow cross-section can be adjusted by an actuator controlled by the operating and evaluation unit 140. By varying the flow cross-section, the pressure drop across the orifice can be varied, for example, between 0.1 and 10 bar while maintaining a constant volume flow rate.
[0039] The Fig. 3 The illustrated embodiment of a measuring arrangement 201 according to the invention comprises all components of the first embodiment. Detailed explanations of the components of the first embodiment apply accordingly to the second embodiment. The second embodiment also contains further components that enable the viscosity of the fluid to be determined and thus allow viscosity-dependent errors in the density measurement to be corrected. Together with the inventive determination of compressibility, an even more precise value for the density under reference conditions can be specified even for media with higher viscosity.
[0040] The measuring arrangement 201 comprises a sampling line 202, which is run parallel to a pipeline 204 between a first connection point 206 and a second connection point 208. The measuring arrangement 201 further comprises a micro gear pump 214 in the sampling line 202 for driving a defined volume flow through the fluid path 216 formed by the sampling line 202 and the components arranged therein. A filter element 215 is arranged in the sampling line 202 upstream of the gear pump 114 to ensure that downstream components do not become clogged.
[0041] A density meter 220 with an oscillating measuring tube 222 is arranged in the sampling line 202. The measuring tube 222 can be excited by an exciter to flexural vibrations whose resonant frequency depends on the density of a medium contained in the measuring tube 222. The fluid path section through the measuring tube 222 and the subsequent MEMS components is guided as a bypass 226 parallel to an orifice 224. The orifice 224 has a diameter of 0.5 to 2 mm and is dimensioned such that, due to the volume flow in the sampling line 202, a pressure gradient is generated which drives a portion of the volume flow of, for example, 0.1% to 5% through the bypass 226. The MEMS components further comprise a temperature sensor 227, for example a semiconductor resistance element or a Pt resistance element, which in particular detects a temperature of the measuring tube 222 or near the measuring tube, which is representative of the temperature of the medium.
[0042] The measuring arrangement 201 further comprises a first pressure sensor 230a for detecting a pressure measurement value at a first pressure tapping point 232a, which is arranged on the fluid path 216 between the gear pump 240 and the density meter 220, and a second pressure sensor 230b for detecting a pressure measurement value at a second pressure tapping point 232b, which is arranged on the fluid path 116 between the density meter 220 and a throttle arrangement 160a.
[0043] The purpose of the two pressure sensors 230a and 230b is twofold. First, the weaknesses of pressure measurement with only one pressure sensor discussed in the context of the first embodiment are overcome by averaging the pressure measurements from the first and second pressure sensors.
[0044] Furthermore, by forming the difference between the pressure measured values of the first pressure sensor 230a and the second pressure sensor 230b, the pressure drop across the density meter 220 can be calculated, from which the viscosity of the fluid can be determined for a given volume flow.
[0045] The throttle arrangement 260 comprises two check valves connected in parallel, of which a first check valve 262 has a lower operating point than a second check valve 264. The first operating point of the first check valve 262 is, for example, 0.5 - 1 bar, while the second operating point of the second check valve 264 is 5 - 10 bar. An automatically controllable check valve shutoff valve 266 is connected upstream of the first check valve 262. When the check valve shutoff valve 266 is open, the volume flow driven by the gerotor pump 214 can flow through the first check valve 262, so that the static pressure of the flowing fluid is determined by the operating point of the first check valve 262. If, on the other hand, the shut-off valve 266 is closed, the volume flow flows via the second check valve 264, so that the static pressure is determined via the second operating point and thus has a significantly higher value.By means of the shut-off valve 266, the static pressure can thus be determined at a constant volume flow rate alternately through the first operating point and the second operating point. The value of the static pressure of the fluid in the measuring tube 222 can be determined by averaging the pressure measurements of the first pressure sensor 230a and the second pressure sensor 230b.
[0046] The measuring arrangement 201 further comprises an operating and evaluation unit 240, which is configured to determine a current viscosity measurement value of the fluid based on the values for the volume flow and the associated pressure difference, and to calculate a density measurement value corrected for viscosity influences based on a measured resonance frequency of the measuring tube or a density measurement value derived therefrom. Furthermore, the operating and evaluation unit 240 is suitable for determining the compressibility of the fluid based on value tuples for various averaged static pressure measurements in the measuring tube, with the respective associated density measurements corrected for viscosity influences, and optionally temperature measurements of the flowing fluid. Based on these values, a density of the fluid at a reference pressure, for example, 1013 mbar, can be calculated.
[0047] Likewise, the operating and evaluation unit controls the check valve shutoff valve 266 to block the first check valve 262a.
[0048] The measuring arrangement 201 can further comprise a storage container 250 and a waste container 252 for an auxiliary medium. The auxiliary medium can be a cleaning fluid, for example gasoline, or a reference medium with a defined viscosity or density for calibrating the measuring arrangement 201. To prevent the auxiliary medium from entering the pipeline 204 in an uncontrolled manner, a first and a second check valve 210, 212 are provided in the extraction line 202 near the first and second connection points 206, 208. The storage container 250 is connected to the extraction line between the first check valve 210 and the filter 215 by means of a branch line, with a check valve 254 being arranged in the branch line. The waste container 252 is connected to the extraction line between the second pressure sensor 230b and the throttle arrangement 260 by means of a branch line, with a check valve 256 being arranged in the branch line. Bezugszeichenliste
[0049] 1 Compressibility Determination 10 First Density and Pressure Measurement 20 Second Density and Pressure Measurement 30 Calculating Compressibility 40a Calculating the Speed of Sound 40b Calculating a Reference Density 101 Measuring Arrangement 102 Sampling Line 104 Pipeline 106 Connection Point 108 Connection Point 114 Pump 115 Filter Element 116 Fluid Path 120 Density Meter 122 Measuring Tube 124 Orifice Plate 126 Bypass 127 Temperature Sensor 130 Pressure Sensor 132 Pressure Tapping Point 140 Evaluation Unit 160a Throttle Arrangement 162a Check Valve with Lower Threshold 164a Check Valve with Higher Threshold 166a Check Valve-Shut-Off Valve 160b Throttle Arrangement 166b Throttle with Continuously Adjustable Flow Cross-Section 201Measuring arrangement 202Sampling line 204Pipe 206Connection point 208Connection point 210Shut-off valve 214Pump 215Filter element 216Fluid path 220Density meter 222Measuring tube 224Orifice plate 226Bypass 227Temperature sensor 230aFirst pressure sensor 230bSecond pressure sensor 232aFirst pressure tap point 232bSecondPressure tapping point 240 Evaluation unit 250 Storage container 252 Waste container 254 Check valve 256 Shut-off valve 262 Lower threshold check valve 264 Higher threshold check valve 266 Check valve-shut-off valve
Claims
1. A method (1) for determining the compressibility of a flowing fluid, the method comprising the following steps: Driving a volumetric flow of the fluid by means of a pump, through at least one measuring tube of a vibronic density meter at a first pressure maintained by means of a throttle, a first pressure sensor and a second pressure sensor being arranged between the pump and the throttle, the density meter being arranged between the first pressure sensor and the second pressure sensor; Determining a first density measurement of the flowing fluid at the first pressure (10); Determining a first measured pressure value of the flowing fluid at the first pressure (10); Driving a volume flow of the flowing fluid by means of a pump, through a density meter at a second pressure which is maintained by means of a throttle; Determining a second density reading of the fluid at the second pressure, which is different from the first pressure (20); Determining a second measured pressure value of the flowing fluid at the second pressure (20); Determining the compressibility of the fluid, using the first density measurement value, the second density measurement value, the first pressure measurement value and the second pressure measurement value, assuming that the composition of the fluid is unchanged between the detection of the first density measurement value and the second density measurement value (30), characterized in that the volume flow is a defined volume flow which is driven by a dosing pump with a delivery accuracy of better than 1%, in particular better than 0.5%, the pressure drop across the density meter (220) is calculated by forming a difference between the measured pressure values of the first pressure sen sensor (230a) and the second pressure sensor (230b), and a viscosity of the fluid is determined on the basis of the volume flow and the pressure drop, whereby the measured density value of the vibro nical density meter is corrected with regard to a cross-sensitivity to the viscosity of the fluid.
2. The method (1) according to claim 1, further comprising: calculating a third density value (40b) at a third pressure using the determined compressibility and using at least one of the first and second density measured values, wherein the third pressure differs from the first pressure and the second pressure, wherein the third pressure lies in particular outside an interval delimited by the first pressure and the second pressure.
3. Method according to claim 1 or 2, further comprising: calculating a sound velocity value (40a) based on the compressibility lity and at least one of the measured density values.
4. Method according to one of the preceding claims, wherein the compressibility is determined assuming a constant temperature of the fluid at the first pressure measurement value and the second pressure measurement value.
5. Method according to one of the preceding claims, wherein a first temperature of the fluid in the measuring tube when detecting the first density measurement value deviates from a second temperature of the fluid in the measuring tube when detecting the second density measurement value by no more than 5 °C, in particular no more than 2 °C and preferably no more than 1 °C.
6. Method according to one of the preceding claims, wherein the determination of the first density measurement value and the determination of the second density measurement value each comprise the detection of a natural frequency value of at least one bending vibration mode of the measuring tube.
7. Method according to claim 6, wherein the natural frequency of the at least one bending vibration mode depends on a bending stiffness of the measuring tube which has a cross-sensitivity to the pressure of the fluid in the measuring tube, wherein the pressure-dependent bending stiffness of the measuring tube is included in the determination of the density measured value on the basis of the detected natural frequencies, wherein at least one of the detected pressure measured values is used to determine the pressure-dependent bending stiffness.
8. Measuring arrangement (201) for determining the compressibility of a flowing fluid and or a variable dependent on the compressibility, comprising: a fluid path (216) for guiding a medium; a pump (214) disposed in the fluid path (216) for driving a volumetric flow of the medium in the fluid path (116; 216); a density meter (220) with at least one oscillator which has at least one oscillating measuring tube (222) for guiding the medium, with at least one exciter arrangement for exciting oscillations of the measuring tube, and with at least one sensor arrangement for detecting at least one oscillation characteristic of the oscillator, the measuring tube or the measuring tubes of the at least one oscillator being arranged in the fluid path; a throttle arrangement (262, 264, 266) with a variable flow resistance, the density meter (220) being arranged between the pump (214) and the throttle arrangement (262, 264, 266) in the fluid path, the throttle arrangement serving to bring about different static pressure values in the density meter (220) at a constant volume flow due to different flow resistances; at least one pressure sensor (230a) for detecting a measured pressure value in the fluid path (216), wherein the pressure sensor is arranged between the pump (214) and the throttle arrangement (262, 264, 266) in the fluid path (116; 216); an operating and evaluation unit (240), which is set up to determine a value for the compressibility of the fluid using at least two measured density values and the associated measured pressure values, which were recorded at different flow resistances of the throttle arrangement (262, 264, 266), characterized in that the measuring arrangement further comprises a second pressure sensor (230b), wherein the density meter (220) is arranged between the first pressure sensor (230a) and the second pressure sensor (230b), wherein the second pressure sensor (230b) is arranged between the density meter (220) and the throttle arrangement (262, 264, 266), the pump (214) is a metering pump with a delivery accuracy of better than 1%, in particular better than 0.5%, and the operating and evaluation unit (240) is set up to determine a viscosity measurement value for the fluid on the basis of the volume flow and a difference between substantially simultaneously recorded pressure measurement values of the first pressure sensor and the second pressure sensor, and to determine the density measurement value on the basis of the oscillation characteristic of the oscillator and the viscosity measurement value.
9. Measuring arrangement according to claim 8, wherein the throttle arrangement (262, 264, 266) has two non-return valves connected in parallel, of which a first non-return valve (262) has a lower operating point than a second non-return valve (264), and a non-return valve shut-off valve (266) is connected upstream of the first non-return valve (262), which in particular can be controlled automatically.
10. Measuring arrangement according to claim 8, wherein the throttle arrangement (160b) has an orifice (166b) with an adjustable orifice opening.
11. Measuring arrangement (201) according to any one of claims 8 to 10, wherein the operating and evaluation unit (240) is set up to determine a measured pressure value for the fluid, which is associated with a measured density value, as an average value of pressure measured values of the first pressure sensor and the second pressure sensor recorded substantially simultaneously.
12. Measuring arrangement (201) according to any one of claims 8 to 11, wherein the operating and evaluation unit (240) is arranged to determine a viscosity measurement value for the fluid on the basis of the volume flow and a difference between substantially simultaneously recorded pressure measurement values of the first pressure sensor (230a) and the second pressure sensor (230b), and to determine the density measurement value on the basis of the oscillation characteristic of the oscillator and the viscosity measurement value.
13. Measuring arrangement according to one of claims 8 to 12, wherein the operating and evaluation unit (240) is set up to determine a density value under reference conditions, for example 1013 mbar, using the measured density value, the associated measured pressure value and the determined value for the compressibility.