Enhanced supercritical fluid measurement with vibratory sensors

Abstract

To correct speed of sound effects in mass flow rate by using mass flow rate equations and relationships that account for speed of sound.SOLUTION: A method for inferring an inferred speed of sound of a flow fluid is disclosed. The method is conducted by a computer system (200) having a processor (210) and a memory (220), the processor (210) configured to execute instructions from the memory (220) and store data in the memory (220), the memory (220) having a SoS inference module (202). The method includes inferring, by the SoS inference module (202), the inferred speed of sound of the flow fluid based on an inferential relationship between an inferred density of the flow fluid and the inferred speed of sound of the flow fluid.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The embodiments described below relate to mass flow sensors, and more particularly, to modified mass flow sensors. [Background technology]

[0002] There are several substances that are best transported under high temperature and / or pressure conditions in the critical and / or supercritical phase (hereafter referred to as "supercritical"). Ethylene is one example of a substance. For example, when ethylene is used as a raw material in plastics manufacturing processes, ethylene in the critical phase is often pumped under high pressure conditions. Ethylene in the supercritical phase is denser than gaseous ethylene, so the cost of pumping it is usually relatively low. Determining the flow rate measurement of ethylene is typically determining the mass flow rate.

[0003] In particular, supercritical ethylene is non-ideal; small variations in temperature and / or pressure cause significant changes in its density and sound speed characteristics, making its flow measurement extremely challenging by any technique, including Coriolis flow sensors. Supercritical ethylene is often transported at pressures of 50 bar or more. The temperature is typically ambient, e.g., around 20°C, but as the pipelines are often underground, the temperature can vary depending on ground conditions.

[0004] Within the supercritical range, the density of ethylene (and other substances) varies greatly with changes in pressure and / or temperature. For example, a pressure change of 1 pound per square inch (hereafter "psi") causes a density change of 2 kilograms per cubic meter (hereafter "kg / m 3 ") density change may occur. For an ideal gas, the change is not so significant; for example, the density change for a 1 psi pressure change is 0.1 kg / m 3It is for this reason that Coriolis flow sensors are generally preferred. It is difficult to combine a density sensor with a volumetric flow sensor to determine mass flow rate, because small pressure and / or temperature changes cause large changes in density.

[0005] In addition to the density of ethylene (and other substances) changing with pressure and / or temperature, its speed of sound (SoS) also changes significantly. For example, a pressure change of 1 psi The resulting change in SoS is 5 meters per second (hereafter referred to as "m / s"), but for an ideal gas, the SoS Some Coriolis flow sensors, for example large ones, are susceptible to the SoS effect. Some large Coriolis flow sensors may produce false positives. The difference can become so large that it becomes unreasonable to use it in applications with fluids in critical phase. Errors resulting from sound velocity effects are more pronounced in sensors with large flow tube inner diameters and in sensors operating at high frequencies. The lower the sound velocity of the flowing fluid, the larger the sound velocity error in the determined mass flow rate. For example, a 1 psi change, which can cause a 5 m / s change in SoS, can result in a 0.03% change in the Coriolis flow sensor measurement. Typical Pressure fluctuations in a large pipeline can be as much as 100 psi, potentially causing a 3% error in the flow measurement obtained from a Coriolis sensor. The requirement for measurement error is less than 0.5%. Many specifications state that the error must be less than 0.35%. exist.

[0006] The effect of sound speed on mass flow can be corrected using mass flow equations and relationships that take the sound speed into account. There are many equations and relationships in the prior art for correcting mass flow using the sound speed of the flowing fluid. One example is described in U.S. Pat. No. 6,412,355. The mass flow rate correction method according to that patent is discussed herein and incorporated by reference. It is to be understood, however, that the mass flow correction method is merely exemplary, and that other embodiments of mass flow correction algorithms that account for the speed of sound exist and may be used with the features of the present disclosure. Such equations and relationships may enhance the usefulness of large Coriolis flow sensors for applications where speed of sound effects are important.

[0007] Therefore, a need exists for a method to correct for speed of sound effects in Coriolis flow sensors. [Prior art documents] [Patent documents]

[0008] [Patent Document 1] U.S. Patent No. 6,412,355 Summary of the Invention

[0009] An embodiment of a method for estimating an estimated speed of sound in a flowing fluid is disclosed. The method is performed by a computer system (200) having a processor (210) and a memory (220). The processor (210) executes instructions from the memory (220) and The memory (220) is configured to store data and comprises an SoS estimation module (202). The method includes estimating, by an SoS estimation module (202), an estimated speed of sound in the flowing fluid based on an inferential relationship between the measured density of the flowing fluid and an estimated speed of sound in the flowing fluid.

[0010] An embodiment of an apparatus for estimating an estimated speed of sound in a flowing fluid is disclosed. The apparatus includes a computer system (200) including a processor (210). and a memory (220), the processor (210) executes instructions from the memory (220), The memory (220) is configured to store data, and the memory (220) includes an SoS estimation module. The SoS estimation module (202) is configured to estimate the measured density of the flowing fluid and the estimated density of the flowing fluid. An SoS estimation module (202) is configured to estimate an estimated speed of sound in the flowing fluid based on an inferential relationship with the speed of sound.

[0011] [Aspects] According to one aspect, a method for estimating an estimated speed of sound in a flowing fluid is disclosed. The method is performed by a computer system (200) having a processor (210) and a memory (220). The method includes estimating, by the SoS estimation module (202), an estimated speed of sound in the flowing fluid based on an inferential relationship between the estimated density of the flowing fluid and an estimated speed of sound in the flowing fluid. Preferably, the inferential relationship between the estimated speed of sound of the flowing fluid and the density of the flowing fluid is a relationship between the estimated speed of sound of the flowing fluid and the inverse proportion of the square root of the measured density of the flowing fluid.

[0012] Preferably, the inferential relationship between the estimated sound speed of the flowing fluid and the density of the flowing fluid further takes into account the pressure of the flowing fluid, and the pressure of the flowing fluid is either a measured pressure measured by the pressure sensor (20) or a pressure estimated from the determined stiffness of the density sensor (10). One or more.

[0013] Preferably, the inferential relationship is further based on a relationship between an estimated speed of sound in the flowing fluid and a heat capacity ratio of the flowing fluid, the inferential relationship being based on a relationship between the estimated speed of sound in the flowing fluid and a square root term obtained by dividing the square root of the product of the heat capacity ratio and the pressure by the square root of the measured density.

[0014] Preferably, the heat capacity ratio is associated with the flowing fluid and any one or more of the flowing fluid classes from which the flowing fluid originates, and the heat capacity ratio is either temperature dependent or pressure dependent. and the heat capacity ratio is a function of one or more of the measured temperature and pressure and the heat capacity The ratio is determined based on a corresponding predetermined relationship.

[0015] Preferably, the computer system (200) is adapted to perform density sensor electronic measurements of the density sensor (10). The method includes measuring a density by a density sensor and and transmitting the estimated sound speed of the fluid to the vibration sensor (5) by the sensor (10). .

[0016] Preferably, the method includes determining an estimated pressure of the flowing fluid by the density sensor electronics (120) based on a measured stiffness of an element of the density sensor (10) determined by the density sensor (10) when the pressure of the flowing fluid is factored into an inferential relationship between the measured density of the flowing fluid and the estimated sound speed of the flowing fluid. Further comprising estimating the force.

[0017] Preferably, the computer system (200) is a vibrating flow sensor electronic instrument (110) of the vibrating flow sensor (5), and the method includes receiving a density measurement from the density sensor (10) by the computer system (200); receiving the pressure and calculating by the computer system (200) the estimated sound speed of the flowing fluid; and determining a corrected mass flow rate based on the calculated mass flow rate.

[0018] Preferably, the vibration sensor (5) vibrates at a frequency of 300 Hertz or more. and having an inner diameter of 2 inches or more, and the density sensor (10) vibrates the density sensor (10) vibrating element at a frequency of less than 300 Hertz. and an inner diameter of less than 2 inches.

[0019] Preferably, the flowing fluid is in a supercritical state and comprises any one or more of ethylene, ethane, carbon dioxide, and argon.

[0020] According to one aspect, an apparatus for estimating an estimated speed of sound in a flowing fluid is disclosed, the apparatus comprising a computer system (200), the computer system (200) comprising a processor (210) and a memory (220), the processor (210) configured to execute instructions from and store data in the memory (220), the memory (220) comprising an SoS estimation module (220). The computer system (200) is configured to estimate, via the SoS estimation module (202), an estimated speed of sound in the flowing fluid based on an inferential relationship between the measured density of the flowing fluid and the estimated speed of sound in the flowing fluid.

[0021] Preferably, the inferential relationship between the estimated speed of sound of the flowing fluid and the density of the flowing fluid is a relationship between the estimated speed of sound of the flowing fluid and the inverse proportion of the square root of the measured density of the flowing fluid.

[0022] Preferably, the inferential relationship between the estimated sound speed of the flowing fluid and the density of the flowing fluid further takes into account the pressure of the flowing fluid, and the pressure of the flowing fluid is either a measured pressure measured by the pressure sensor (20) or a pressure estimated from the determined stiffness of the density sensor (10). One or more.

[0023] Preferably, the inferential relationship is further based on a relationship between an estimated speed of sound in the flowing fluid and a heat capacity ratio of the flowing fluid, the inferential relationship being based on a relationship between the estimated speed of sound in the flowing fluid and a square root term obtained by dividing the square root of the product of the heat capacity ratio and the pressure by the square root of the measured density.

[0024] Preferably, the heat capacity ratio is associated with the flowing fluid and any one or more of the flowing fluid classes from which the flowing fluid originates, and the heat capacity ratio is either temperature dependent or pressure dependent. and the heat capacity ratio is determined based on a corresponding predetermined relationship between any one or more of the measured temperature and pressure and the heat capacity ratio.

[0025] Preferably, the computer system (200) is adapted to measure the density sensor electronics of the density sensor (10). The density sensor (10) measures the density and calculates the estimated sound speed of the fluid using a vibration The sensor (5) is configured to transmit the

[0026] Preferably, when the pressure of the flowing fluid is factored into the inferential relationship between the measured density of the flowing fluid and the estimated sound speed of the flowing fluid, the density sensor electronics (120) determines whether the density sensor (10) is The method is configured to estimate an estimated pressure of the flowing fluid based on the determined measured stiffness of the elements of the density sensor (10).

[0027] Preferably, the device is a vibrating flow sensor (5) and the computer system (200) is a vibrating flow sensor electronic instrument (110) for the vibrating flow sensor (5). The computer system (200) receives the measured density from the density sensor (10), receives the pressure of the flowing fluid, The system is further configured to determine a corrected mass flow rate based on an estimated speed of sound of the flowing fluid. Preferably, the vibration sensor (5) vibrates at a frequency of 300 Hertz or more. and having an inner diameter of 2 inches or more, and the density sensor (10) vibrates the density sensor (10) vibrating element at a frequency of less than 300 Hertz. and an inner diameter of less than 2 inches.

[0028] Preferably, the flowing fluid is in a supercritical state and comprises any one or more of ethylene, ethane, carbon dioxide, and argon. [Brief description of the drawings]

[0029] In all the drawings, the same reference numbers indicate multiple embodiments of the same element. It should be understood that the drawings are not necessarily to scale. [Figure 1] 1 shows a system 100 that provides accurate flow sensor measurements. [Diagram 2] 2 shows a block diagram of one embodiment of a computer system 200 for estimating and / or applying the speed of sound. [Diagram 3] 3 shows a flow chart according to one embodiment of a method 300 for estimating an estimated speed of sound in a flowing fluid. [Figure 4] 4 illustrates a flow chart of an embodiment of a method 400 for estimating an estimated speed of sound in a flowing fluid. [Diagram 5] 5 shows a flow chart of one embodiment of a method 500 for estimating an estimated speed of sound of a flowing fluid within a density sensor 10. [Figure 6] 6 shows a flow chart of one embodiment of a method 600 for estimating an estimated speed of sound of a flowing fluid in a vibrating flow sensor 5. [Figure 7] 7 illustrates a flow chart of one embodiment of a method 700 for correcting flow measurements using an estimated speed of sound. [Figure 8] 8 shows a graph 800 illustrating one embodiment of the heat capacity ratio of ethylene versus both pressure and temperature. [Figure 9] The density sensor electronics shows a graph 900 of the percentage error in mass flow rate caused by speed of sound effects versus both pressure and temperature for ethylene flowing through a CMF400 mass flow meter according to one embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0030] 1-9 and the following description provide specific examples to teach one of ordinary skill in the art how to make and use the best mode of embodiments of the improved system and method for measuring supercritical fluids using a vibrating sensor. For the purpose of teaching inventive principles, conventional aspects may be simplified or omitted, and one of ordinary skill in the art will recognize variations of these examples that are within the scope of this description. One of ordinary skill in the art will recognize how the features described below can be implemented in various ways. It will be appreciated that multiple variations of the systems and methods for improving the measurement of supercritical fluids by vibratory sensors can be combined to form a number of variations of the systems and methods. As a result, the embodiments described below are not limited to the specific examples described below.

[0031] FIG. 1 illustrates a system 100 for providing accurate flow sensor measurements. The system 100 includes It is recommended to correct the flow rate measured by Coriolis flow meters that may be affected by the SoS effect. It should be understood that when the term "estimate" or "estimate" is used as a verb, it means to determine using an inferential association, e.g., an inferential relationship. In one embodiment, the system 100 may estimate the SoS of the fluid. The SoS of the flowing fluid is calculated from one or more measurements of the pressure, density, and / or temperature of the flowing fluid. The SoS can be estimated by using a relational expression between the specific heat ratio of the flowing fluid and one or more of the temperature and pressure (hereinafter referred to as "temperature- and / or pressure-dependent heat capacity ratio"). In this specification, the heat capacity ratio represented by the symbol "k" is the specific heat (Typically C p ) at constant volume (typically C v This is the ratio of the

[0032] The hardware used in system 100 may vary between embodiments. The mass flow rate determined by the Coriolis flow sensor can be determined using methods known in the art. Coriolis flow sensors can be susceptible to SoS effects, especially if the Coriolis flow sensor is large. The SoS effects can cause errors in the mass flow rate determined by the Coriolis flow sensor. If the SoS of the flowing fluid is known, the determined SoS can be easily determined. However, the SoS effect can be taken into account in the mass flow rate of the Coriolis flow sensor. Since the sensor is sensitive to SoS effects, the measurement or measurements used to estimate the SoS of the flowing fluid It is not reliable for obtaining a fixed value.

[0033] Contemplated flow fluids may generally be transported or used in a supercritical fluid state. Examples of flow fluids contemplated herein include, for example, any one or more of ethylene, ethane, carbon dioxide, and argon.

[0034] In one embodiment, the mass flow measured using a Coriolis flow sensor is analyzed for the SoS effect. Another sensor may be used to obtain flowing fluid measurements that can be used to correct for the SoS of the flowing fluid. For example, a density meter or viscometer may be used to determine the measurements used to estimate the SoS of the flowing fluid. In one embodiment, a pressure sensor may be used to measure the SoS of the flowing fluid. A constant pressure can be determined. In other embodiments, the pressure may be estimated from other measurements. For example, the density sensor 10 may measure the stiffness of the density sensor 10 and estimate the pressure of the flowing fluid from the measured stiffness. In one embodiment, the stiffness may be related to the estimated pressure by a linear relationship with a simple slope and intercept. In one embodiment, the estimated pressure may be estimated using the relationship shown in equation (13).

[0035] In one embodiment, the SoS of a flowing fluid is determined by a measured density, a measured temperature, a measured or estimated pressure, and The specific heat ratio may be determined from any one or more of the temperature and / or pressure dependent specific heat ratios. The relationship may be derived from the ideal gas equation of state modified to take into account hypercompressibility. P×V = z×R×T (1) Rearranged:

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[0036] In equations (1) and (2), P is the pressure of the flowing fluid, V is the volume of the flowing fluid, and z is the pressure of the flowing fluid. where R is the universal gas constant (as a function of molecular weight (MW)), and T is the absolute temperature of the flowing fluid. Because the gas constant is a function of MW, the density equation in equation (2) can be rewritten as follows:

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[0037] Equation (3) can be further rearranged to give (4), which will be used later.

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[0038] The SoS of a fluid, “a”, is a function of pressure change and density change, as shown in equation (5).

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[0039] Assuming that the SoS is isentropic in the system, we can expand equation (5) to equation (6). It is possible.

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[0040] In equation (6), k is the specific heat ratio of the gas, which is a function of temperature and / or pressure. As we did for , we can rearrange equation (6) to account for the effects of non-ideal gas behavior: Equation (7) can be obtained.

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[0041] By combining equations (4) and (7), we obtain equation (8).

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[0042] In one embodiment, k is a function of temperature and / or pressure and can be expressed as k(T,P) (or alternatively k(P) or k(T)). To show this, equation (8) can be rewritten as the following equation (9):

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[0043] Equations (5) to (9) are expressed by using one or more values ​​of the pressure, density, and temperature of the flowing fluid. The inferential relationship is used to estimate the SoS from the The method can use measurements that are typically taken on existing systems for storing water, making SoS estimates more practical.

[0044] The relationships in Equation (8) and / or Equation (9) have specific relationships between parameters that distinguish the inferential determination of Equation (8) and / or (9) from existing SoS determination methods. For example, the SoS can be estimated based on an inverse relationship between the SoS and density of the flowing fluid. Additionally, the SoS can be estimated based on a direct relationship between the SoS and pressure of the flowing fluid. The SoS can be estimated based on a direct relationship between the SoS and the square root of the pressure of the flowing fluid. The SoS can be estimated based on the SoS of the flowing fluid. The SoS can be estimated based on the inverse proportional relationship between the flow rate and the square root of the density of the flowing fluid. The SoS can be estimated based on a direct relationship between the product of the heat capacity ratio (k) of the moving fluid and the pressure. The SoS can be estimated based on a direct relationship between the product of the temperature and / or pressure dependent heat capacity ratio (k(T), k(P), and / or k(T,P)) and the pressure of the moving fluid. The SoS can be estimated based on a direct relationship between the SoS and the ratio of pressure to density of the moving fluid. The SoS can be estimated based on a direct relationship between the SoS and the square root of the ratio of the pressure to the density of the flowing fluid. The SoS can be calculated by the heat capacity ratio (e.g., temperature and / or pressure dependent heat capacity ratio) and the flow Estimated based on a direct relationship between the square root of the product of the ratio of pressure to density of the moving fluid and the SoS It is possible.

[0045] To estimate the heat capacity ratio based on temperature and / or pressure, the inferential decision making computer system 200 may use a predefined set of parameters, e.g., material specific constants, for determining the heat capacity ratio. In an alternative embodiment, the computer system 200 may store the relation: The material-specific table includes a heat capacity ratio table indicating the heat capacity ratio at specific temperature and / or pressure values, and the computer system 200 can select the heat capacity ratio value that matches the relevant temperature and / or pressure value. is not stored, the heat capacity ratio may be, for example, interpolated or extrapolated from the table values, or the closest heat capacity value in the table may be taken.

[0046] The system 100 may include a vibrating flow sensor 5, a density sensor 10, an optional pressure sensor 20, a conduit 160, and a side stream 170. In one embodiment, the vibrating flow sensor 5, the density sensor 10, and the optional pressure sensor 20 may include a conduit 160 and a side stream 170. One or more of the sensor 10 and the optional pressure sensor 20 may be, for example, Each may be communicatively coupled to a corresponding computer and / or electronic instrument. The vibratory flow sensor 5 may be configured to receive various flowing fluids and / or fluid flow measurements, such as mass flow rate, , density, and viscosity. .

[0047] The vibrating flow sensor 5 is a vibrating flow sensor that detects the flow of a fluid and / or the characteristics of a flowing fluid. In one embodiment, the vibrating flow sensor 5 is a Coriolis flow sensor. Vibration sensors, such as orifice mass flow meters, vibrational densitometers, and vibrational viscometers, typically operate by detecting the motion of a vibrating conduit containing a flowing material or a vibrating element immersed in the fluid. Properties associated with the material in the conduit, such as mass flow rate and density, can be determined by receiving and processing measurement signals from a motion transducer associated with the conduit. The vibration modes of a vibrating material-filled system are generally influenced by the mass, stiffness, and damping characteristics of the fluid-filled conduit and the material contained within the conduit.

[0048] A typical Coriolis mass flowmeter includes one or more conduits or flow tubes connected in series in a pipeline (e.g., conduit 160 or side stream 170) or other transport system for transporting a material, e.g., a fluid, slurry, emulsion, or the like, through the system 100. Each conduit can be considered to have a set of natural vibration modes, including, e.g., simple bending, torsional, radial, and coupled modes. In a typical Coriolis mass flowmeter application, the conduit is excited in vibrational modes as material flows through it, and the motion of the conduit is measured at multiple points spaced apart along the conduit. The conduit is typically excited by an actuator, such as an electromechanical device that periodically perturbs the conduit, examples of which include magnet-type and coil-type actuators. The mass flow rate can be determined by measuring the time delay or phase difference between the motions at the transducer locations. Typically, two such transducers (or pick-off sensors) are used to measure the vibrational response of one or more flow tubes, typically located upstream and downstream of the actuator. The pick-off sensors may output signals that are out of phase with each other, and the phase difference or time delay between the signals may represent the Coriolis forces that have affected the vibration of the conduit. The pick-off sensors are connected to electronics. The instrumentation receives signals from the two pick-off sensors. The instrument receives a signal from the vibrating flow sensor and processes the signal to derive a mass flow measurement or a density measurement, etc. For purposes of this specification, the instrumentation described herein will be referred to as a vibrating flow sensor electronics 110. Other flow meter configurations, such as systems using only one pickoff, or Systems are also possible in which the drivers have a pick-off mode such that only a single driver is used to determine the phase difference.

[0049] The mass flow rate generated by the flow meter using the vibrating flow sensor electronic measurement device 110

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[0050] Vibratory flow sensor electronic measurement can be used to correct the mass flow rate for sonic effects. Relationships that can be used to correct the mass flow rate for the speed of sound can be found, for example, in Equations (11) and (12).

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[0051] In equation (11), xerror is a mass flow error coefficient that depends on a relationship to the speed of sound "a." In various embodiments, the relationship may be a polynomial of the speed of sound. For each power of the speed of sound, there is a corresponding coefficient (e.g., b, c, d, e, and f), and such corresponding The coefficients are associated with a fluid (e.g., by associating them with the k value, for example, of a particular fluid, so that the electronics can perform mass flow compensation, store these coefficients, and use them in the mass flow compensation of that particular fluid). In some embodiments, there may be coefficients that are dependent on the flow sensor used, rather than on the fluid. In such cases, there is only one set of coefficients for all types of flow fluids. Combinations of embodiments are also contemplated, for example, embodiments in which both the coefficients and the flowing fluid and the coefficients and the fluid sensor are related. Other relationships involving different polynomials are contemplated. Other orders of polynomials may be used, for example, linear, quadratic, cubic, quintic, septilinear, etc. In equation (12),

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[0052] The sonic effect is most pronounced in large vibratory sensors, e.g., sensors with inner diameters of 2 inches or more. The sonic effect is believed to be significant at higher frequencies, e.g., frequencies above 300 Hz. It is believed to be also significant in vibration sensors that vibrate at wavenumbers.

[0053] In one embodiment, the vibrating flow sensor 5 is configured to reduce the susceptibility of the vibrating flow sensor 5 to the SoS effect. The vibrating flow sensor 5 may have an inner diameter large enough to easily detect the mass flow rate and / or vibrate at a frequency high enough so that the measurements made by the vibrating flow sensor 5 may have SoS related errors associated therewith. The SoS effect on the mass flow measurement produced by the sensor 5 can be determined.

[0054] The vibrating flow sensor 5 may be coupled to and / or in fluid communication with the conduit 160. The conduit is, for example, a generally cylindrical hollow member through which a flowing fluid flows. The vibrating flow sensor 5 may be embedded in the conduit 160 and / or may detect the flow of fluid from the conduit 160. It may be fluidly coupled to it in series.

[0055] If the vibrating flow sensor 5 is of a type that is susceptible to SoS effects, the density sensor 10 can also be used to determine measurements that are less susceptible to SoS effects and to determine or estimate the SoS for correcting the mass flow measured by the vibrating flow sensor 5. The resonator flow sensor 5 is a sensor for determining the density of a flowing fluid. and / or their vibrational frequencies are high, they are considered to be susceptible to SoS effects. For example, the vibrating flow sensor 5 may have an inner diameter of 2 inches or greater and / or the vibrating flow sensor 5 may vibrate a vibrating element at a frequency of 300 Hertz or greater. The density sensor 10 may make determinations and estimates that may be stored in the density sensor electronics 120. The density sensor 10 may also be a Coriolis flow sensor, e.g., vibrating at a lower frequency than the vibrating flow sensor 5, and / or Insofar as the density sensor 10 is a vibrating flow sensor different from the vibrating flow sensor 5, the density sensor 10 may be a flow sensor having a smaller inner diameter of the flow tube. The density sensor may be one of a Coriolis densitometer and a Coriolis flow meter. Although embodiments are contemplated in which the density sensor 10 is a fork densitometer or viscometer, such sensors have significant SoS effects and are subject to the associated errors that propagate to subsequent decisions. Note that this is a high frequency meter that uses empirical corrections to compensate for SoS effects. In some embodiments, the density sensor 10 is a gas density meter (GDM). Operates at high frequencies and has associated SoS effect errors, requiring in-situ calibration Note that this makes, for example, density and other determinations more prone to error and therefore more difficult to address.

[0056] In one embodiment, the density sensor 10 has a smaller diameter than the vibrating flow sensor 5 and / or For example, the inner diameter of the density sensor 10 may be less than 2 inches. , and / or the density sensor may vibrate at a frequency of less than 300 Hertz. The density sensor 10 can measure density that is substantially unaffected by the sound velocity effect, for example, within a predetermined tolerance range. Measurement of density by the density sensor 10 can be performed using a method well established in the art, for example, a relationship based on the vibration frequency of the density sensor 10 and the density of the material flowing through the density sensor 10. The density sensor 10 can measure density by detecting the vibration frequency of the vibrating flow sensor 5 (in the direction of the fluid flow). In another embodiment, if the density sensor 10 has a smaller diameter than the vibrating flow sensor 5, the density sensor 10 may be located upstream or downstream of the side stream 170 (as shown in FIG. 1 ). ) in fluid communication with the vibrating flow sensor 5. The substream 170 is in fluid communication with the conduit 160, but is, for example, a branch stream from the conduit 160 having a different internal diameter (effective diameter and / or effective cross-sectional area through which the fluid flows) than the conduit 160. Alternatively, the density sensor 10 may be in direct fluid communication with the conduit 160. The vibrating flow sensor 5 and the density sensor 10 may be arranged such that the measurements of the vibrating flow sensor 5 and the density sensor 10 correspond closely to each other and are indicative of the same flowing fluid. It may be preferable for the flow sensor 5 to be within a certain distance threshold of the density sensor 10. The density sensor 10 is connected to a computer, e.g., a density sensor electronics, in electronic communication with the vibratory flow sensor 5. A measuring instrument 120 may be included.

[0057] In embodiments where estimated pressure is used (as opposed to measured pressure), one of the density sensor 10 and the vibratory flow sensor 5 determines the pressure of the flowing fluid from the relationship between pressure and stiffness of the density sensor 10. In one embodiment, the density sensor 10 can estimate the pressure using the density sensor electronics 120 of the density sensor 10. In another embodiment, the vibrating flow sensor The stiffness of the density sensor 10 is then used to estimate the pressure of the flowing fluid. The relationship is transmitted from the density sensor 10 to the vibratory flow sensor electronics 110. The measured density, measured stiffness, and mass flow rate are then calculated for use in estimating the SoS and / or for determining the SoS corrected mass flow rate. Any measured or estimated value, including, for example, any one or more of the pressure, the pressure, the temperature, and the estimated pressure, may be secretly recorded. The density sensor 10 may transmit the flow rate to an electronic measuring device of the vibrating flow sensor 5. One or more of the pressure and sound speed of the moving fluid are estimated, and among those estimated quantities, Any one or more may be sent to the vibrating flow sensor electronics 110.

[0058] In embodiments where the density sensor 10 estimates pressure (as opposed to measuring it), the density sensor 10 may, by the density sensor electronics 120, calculate, for example, the estimated density and the measured density. Density and measurement temperature (temperature and / or pressure used to determine heat capacity ratio k) One or more of these may be used to estimate an estimated speed of sound, for example, by evaluating one of the relationships in equation (8) or equation (9).

[0059] In embodiments that use measured pressure (as opposed to estimated pressure), the system 100 further The flow control system may include an optional pressure sensor 20 that measures the pressure of the flowing fluid. The optional pressure sensor 20 may be any pressure sensor known in the art. The pressure sensor 20 may be in fluid communication with the conduit 160 to determine the pressure of the flowing fluid passing through any one or more of the conduit 160, the side stream 170, the vibrating flow sensor 5, and / or the density sensor 10 ... The pressure data can be transmitted to the vibratory flow sensor electronics 110 and / or the density sensor electronics 120 for use in estimating the speed of sound of the flowing fluid from the measured pressure. In one embodiment, the pressure sensor 20 may be integrated into one or more of the vibratory flow sensor 5 and the density sensor 10.

[0060] In some embodiments, the density sensor 10 itself estimates the SoS of the fluid. The density sensor electronics can measure the density of the flowing fluid and estimate the pressure of the flowing fluid from the stiffness of the measuring density sensor 10. In this embodiment, the density sensor 10 can send an estimated SoS to the vibrating flow sensor electronics 110. The estimated SoS is This is used to correct the measured mass flow rate of sensor 5.

[0061] FIG. 2 illustrates a block diagram of one embodiment of a computer system 200 for estimating and / or applying the speed of sound. In one embodiment, the computer system 200 is an electronic measuring instrument. or associated with multiple computer systems or electronic instruments, such as the vibrating flow sensor electronic instrument 110, the density sensor electronic instrument 120, and / or any pressure sensor 20. Either or both of the vibrating flow sensor electronics 110 and / or the density sensor electronics 120 may perform a number of operations, each of which is illustrated in conjunction with the computer system 200. It should be understood that there may be separate embodiments of computer system 200 having one or more embodiments with the various modules or functionality.

[0062] In various embodiments, computer system 200 may be implemented as an application specific integrated circuit. The computer system 200 may be configured as a separate processor element, a virtual machine, and / or a cloud computing system, or may have separate processor elements and memory elements for processing commands from and storing data in the memory elements. The computer system 200 may be implemented in a computing environment. The present invention may be configured to accomplish any step of the method.

[0063] The computer system includes a processor 210, a memory 220, an interface 230, and a communication The memory 220 may include, for example, an SoS estimation module 202, a pressure estimation module 204, a measurement module 206, and / or a compensation module 208. In various embodiments, computer system 200 may include an integrated circuit that: The components may include other computer elements integrated into them, or in addition to them, or in communication with them, e.g., via a bus, other communication protocol, etc.

[0064] Processor 210 is a data processing element. Processor 210 may be any element used for processing, such as a central processing unit, an application specific integrated circuit, another integrated circuit, an analog controller, a graphics processing unit, a field programmable gate array, any combination of these, or any combination of other general processing elements. Processor 210 may also have a cache memory for storing processed data. Processor 210 can benefit from the methods herein because the methods are computationally This is because the resolution can be improved and the calculation errors can be reduced using the presented structure of the present invention.

[0065] Memory 220 is an electronic storage device. Memory 220 may be any non-transitory storage medium and may include one, more, or all of the following: a hard drive, a solid state drive, a volatile memory, an integrated circuit, a field programmable gate array, a random access memory, a read-only memory, a dynamic random access memory, an erasable programmable read-only memory, an electrically erasable programmable read-only memory, cloud storage, cache memory, etc. Processor 210 may access memory 220 from the The device may execute commands from the device and utilize data stored in the memory.

[0066] The computer system 200 may also include any data used by one or more of the SoS estimation module 202, the pressure estimation module 204, the measurement module 206, and / or the compensation module 208. The SoS estimation module 202, the pressure estimation module 204, the measurement The signal is received or used by one or more of the determination module 206 and / or the correction module 208. Historical data representing any parameter may be stored in memory 220 for any period of time, possibly with timestamps indicating when the data was measured and / or determined. The computer system 200 may also store any data representing any intermediate decisions in the memory 220. One or more of the SoS estimation module 202, the pressure estimation module 204, the measurement module 206, and / or the compensation module 208 may be implemented as four separate and distinct modules. Although depicted as a single block, the present specification may refer to any number of various modules (whether one or four as specified) that cooperate to accomplish the methods described herein. We are also taking this into consideration.

[0067] The SoS estimation module 202 is a module that estimates the speed of sound of a flowing fluid. The SoS estimation module 202 may use one or more of the relationships expressed in Equations (1)-(9) to estimate the speed of sound of the flowing fluid. an inverse relationship between the SoS of a body and its density; a direct relationship between the SoS of a flowing fluid and its pressure; a direct relationship between the square root of the pressure of a flowing fluid and its SoS; an inverse relationship between the SoS of a flowing fluid and its square root of its density; a direct relationship between the SoS of a flowing fluid and the product of the heat capacity ratio (k) and pressure; and a direct relationship between the SoS of a flowing fluid and the temperature and / or pressure. a direct relationship between the product of the heat capacity ratio (k(T,P)) and the pressures, a direct relationship between the SoS of the flowing fluid and the ratio of pressure to density, a direct relationship between the SoS of the flowing fluid and the square root of the ratio of pressure to density, and / or The speed of sound in the flowing fluid is estimated using one or more of the heat capacity ratio (e.g., temperature and / or dependent heat capacity ratio), the square root of the product of the pressure to density ratio, and a direct relationship with the SoS of the flowing fluid.

[0068] If the heat capacity ratio is temperature and / or pressure dependent, the relationship of the heat capacity ratio depending on temperature and / or pressure may be pre-stored in the SoS estimation module 202. The measured temperature that can be used is measured by any of the vibrating flow sensor 5, the density sensor 10, and / or the pressure sensor 20. Again, the pressure may be measured by the density sensor 10 stored in the density sensor electronics 120. The density sensor 10 may be estimated from its stiffness using the pressure estimation module 204. Alternatively, the pressure may be measured by a measurement module 206 housed in the optional pressure sensor 20. In an alternative embodiment, density and stiffness measurements may be determined and / or transmitted as raw data signals for interpretation by the SoS estimation module 202.

[0069] In an embodiment in which the sound speed estimation is performed by the vibrating flow sensor 5, the computer system The system 200 may be an embodiment of the vibrating flow sensor electronics 110 and includes an SoS estimation module. The SoS estimation module 202 may be stored in the vibrating flow sensor electronics 110. In this embodiment, the SoS estimation module 202 may receive density measurements from the density sensor 10 and pressure. The pressure may be a measured pressure, and the vibrating flow sensor electronics 110 may store the SoS estimation module 202 in an optional The pressure may be received from a pressure sensor 20. Alternatively, the pressure may be determined using a pressure estimation module 204. Alternatively, the pressure may be an estimated pressure estimated from the stiffness measurement value of the density sensor 10.

[0070] In an embodiment in which the sound speed estimation is performed by the density sensor 10, the computer system 200 may be an embodiment of the density sensor electronics 120, and the SoS estimation module 202 The SoS estimation module 202 may be stored in the sensor electronics 120. The density sensor electronics 120 may receive density measurements from the density sensor 10 and may receive or estimate pressure values. The pressure may be a measured pressure and may be optionally measured by the density sensor electronics 120. The pressure may be received from a local pressure sensor 20. Alternatively, the pressure may be an estimated pressure estimated from the stiffness measurements of the density sensor 10 using the pressure estimation module 204.

[0071] In another embodiment, a stand-alone computer system 200 may receive measurements from one or more of the vibrating flow sensor 5, the density sensor 10, and the optional pressure sensor 20. The stand-alone computer system 200 may receive a constant value and / or a pressure estimate. The stand-alone computer system 200 may store an SoS estimation module 202 such that the speed of sound of the flowing fluid is estimated on the stand-alone computer system 200.

[0072] The pressure estimation module 204 estimates the pressure value of the flowing fluid from the stiffness measurement of the density sensor 10. In one embodiment, the pressure estimation module 204 is a programming module that The density sensor 10 may be housed in the pressure sensor electronics 120, so that the density sensor 10 is The pressure estimation module 204 may be used to estimate the fluid pressure from the stiffness measurement of the density sensor 10 measured by the density sensor electronics 120. The pressure estimation module 204 may estimate the fluid pressure from the stiffness measurement of the density sensor 10 measured by the density sensor electronics 120. A simple empirically derived relationship between the constant stiffness and the load may be used. The relationship may be a linear relationship, such as a linear relationship with a simple slope and intercept. For example, the pressure estimation module 204 may use a relationship of the type represented by equation (13). P = A × τ + B (13) In equation (13), P is the estimated pressure, and A and B are coefficients (constants or temperature-dependent coefficients). and τ is the measurement stiffness of the density sensor 10.

[0073] In an alternative embodiment, the pressure estimation module 204 may be stored in the vibrating flow sensor electronics 110. In this embodiment, the pressure estimation module 204 uses the In order to measure the stiffness of the density sensor 10, the density sensor electronics 120 can receive the measured stiffness. In other embodiments, the pressure estimation module 204 can determine pressure from raw measured or transmitted data representing stiffness measurements of the density sensor 10 for use in estimating pressure. In embodiments where the optional pressure sensor 20 is used to measure pressure for estimating the speed of sound of the flowing fluid, the pressure estimation module 204 is not required and may not be present in the computer system 200, the vibrating flow sensor electronics 110, or the density sensor electronics 120.

[0074] The measurement module 206 is a module that determines the measurement value. The measuring device 110, the density sensor electronics 120, and the pressure sensor 20 may each have a different variation of the measuring module 206. For example, in one embodiment, a vibrating flow sensor electronics The measurement module 206 of the slave meter 110 may be configured to obtain a measurement of mass flow rate. The density sensor electronics 120 may measure the density of the flowing fluid and the stiffness of the density sensor 10. The density sensor 10 may have a measurement module 206 that measures one or more of the pressures, i.e., the density sensor 10 may have a measurement module 206 that measures one or more of the pressures, i.e., the density sensor 10 may have a measurement module 206 that measures one or more of the pressures, i.e., the density sensor 10 may have a measurement module 206 that is stored in electronics that is configured to measure the pressure value of the flowing fluid, to the exclusion of other measurements, if the pressure used in the inferential relationship for the speed of sound is an estimated pressure.

[0043]

[0075] The compensation module 208 is a programming module that compensates the measurements of the vibrating flow sensor 5 for errors due to sound speed effects in the flowing fluid. In one embodiment, the compensation module 208 is stored in the vibrating flow sensor electronics 110. The compensation module 208 calculates the estimated sound speed by: The mass flow rate measured by the vibrating flow sensor 5 can be corrected using the sound velocity. As a term, an example of a mass flow correction formula for correcting the sonic effect can be expressed as an equation of the type shown in equations (10) to (12). Alternatively, the correction module 208 may , an existing mass flow rate relationship may be used. In an embodiment in which the estimation of the estimated sound speed of the flowing fluid is performed by the vibrating flow sensor electronics 110, the correction module 208 may receive the estimated sound speed of the flowing fluid from the vibrating flow sensor electronics 110 itself. In embodiments where the estimation is performed by the density sensor electronics 120 , the compensation module 208 may receive the estimated speed of sound of the flowing fluid from the density sensor electronics 120 via the vibrating flow sensor electronics 110 .

[0076] In embodiments where the vibrating flow sensor electronics 110 estimates the speed of sound, the vibrating flow sensor The electronic measuring instrument 110 may include an SoS estimation module 202, which may measure the measured temperature of the flowing fluid, the flow rate of the flowing fluid, and the like. Any one of the measured pressure of the fluid, the measured density of the flowing fluid, and the stiffness of the density sensor 10. may receive multiple measurements and / or estimates. In these embodiments, the flow sensor electronics 110 may determine a compensated mass flow rate based on one or more of the phase difference, time delay, and / or temperature measurements obtained by the measurement module 206 stored in the vibrating flow sensor electronics 110, or the temperature measurements may be measured by the measurement module 206 or the pressure sensor 20 (using the respective temperature sensors) in the density sensor electronics 120. In this embodiment, the density sensor 10 may have a measurement module 206 configured to measure the density of the flowing fluid. In this embodiment, the compensation module 206 may be configured to measure the density of the flowing fluid. The flow sensor electronics 110 determines the estimated sound speed of the flowing fluid. In this embodiment, if the pressure used to determine the estimated sound speed of the flowing fluid is an estimated pressure, the estimated pressure may be estimated by the pressure estimation module 204 of the density sensor 10. In an alternative embodiment using an estimated pressure, The measurement module 206 of the density sensor 10 measures the stiffness of the density sensor 10 and converts the stiffness value into a vibration flow rate. The measured pressure may be transmitted to the flow sensor electronics 110, which may determine an estimated pressure using a pressure estimation module 204 stored in the flow sensor electronics 110. In embodiments using measured pressure, an estimated pressure may not be necessary since the stiffness of the density sensor 10 prevents any estimation of pressure.

[0077] In an alternative embodiment in which the density sensor 10 estimates the speed of sound of the flowing fluid, the SoS estimation module 202 may be stored in the density sensor electronics 120. The SoS may be stored in the density sensor electronics 120. The density sensor electronics 120 may transmit the mass flow rate data to the vibrating flow sensor electronics 110 in a compensation module 208 stored in the vibrating flow sensor electronics 110 and used by the vibrating flow sensor electronics 110 to compensate the mass flow rate measurement. The compensated mass flow measurement may also be based on the phase difference or time delay data determined by the measurement module 206 of the vibrating flow sensor electronics 110. In this embodiment, the density sensor electronics 120 is a measurement module that measures the measured density of the flowing fluid. The density sensor electronics 120 may include a pressure estimation module 204. The temperature measurements may be provided by a measurement module housed in one of the density sensor electronics 120, the vibrating flow sensor electronics 110, and the optional pressure sensor 20. The pressure used to estimate the speed of sound of the flowing fluid may be estimated by the density sensor electronics 120 using the pressure estimation module 204. In an alternative embodiment, the pressure used is the measured pressure provided to the density sensor electronics 120 by the optional pressure sensor 20.

[0078] The functions of the SoS estimation module 202, the pressure estimation module 204, the measurement module 206, and / or the correction module 208 may be considered and compared to the methods performed in the illustrated flowcharts. All methods herein are contemplated with respect to each flowchart and noting the order specified, other possible orders, or flowcharts where specified that the order is not important, but include the SoS estimation module 202, the pressure estimation module 204, and the like. All methods and functions of the measurement module 206 and / or the compensation module 208 are contemplated for purposes of any method and / or apparatus claims herein. It is also understood that the systems and methods herein may include multiple sensors (e.g., vibrating flow sensors 5, dense and optionally one or more of the temperature sensor 10 and the pressure sensor 20. Considering that each sensor may have its own unique Each sensor may have an embodiment as an SoS estimation module, if desired. The system may have an embodiment as any one or more of the pressure estimation module 202, the pressure estimation module 204, the measurement module 206, and / or the correction module 208. The sensors may all have an embodiment as the SoS estimation module 202. If the pressure used in the inferential relationship for determining the speed of sound is an estimated pressure, the vibration sensor 5 and Any one or more of the density sensors 10 may themselves have an embodiment as a pressure estimation module 204. Each of the measurement making sensors may itself have an embodiment as a measurement module 206 (capable of making the measurements made by each corresponding sensor). The compensation module 208 is most likely housed in the vibratory sensor 5, but individual embodiments of the compensation module 208 may be housed in other sensors. There are also embodiments.

[0079] Various embodiments of the computer system 200 are contemplated. Particular elements of system 200 may belong to different hardware elements, such as any one or more of vibrating flow sensor electronics 110, density sensor electronics 120, and optional pressure sensor 20. In the example where the measured pressure is used to estimate the speed of sound of the flowing fluid, optional pressure sensor 20 is a computer that measures the pressure of the flowing fluid and performs the sound speed estimation of the flowing fluid. The measured pressure is transmitted to a computer system (e.g., a vibrating flow sensor electronic measurement device 110 and a The pressure sensor may include a measurement module 206 that transmits pressure to one or both of the pressure sensors and electronic gauges 120.

[0080] Also, in embodiments in which the computer system 200 is the electronic measuring instrument 110, the electronic measuring instrument 110 The electronic measuring instrument 110 may include several communicatively coupled elements. The hardware that interacts to form the mid-size computer system 200 may be of different configurations. The electronic meter 110 may be part of a component, such as a conventional electronic meter array communicatively coupled to a corresponding and / or compatible transmitter. In one embodiment, the electronic meter 110 may include the processor 210 as an integral electronic meter element of the meter, and may include at least some elements of the memory 220 within the transmitter.

[0081] The order in which a particular module performs steps will depend largely on the relationships required, as disclosed herein. For example, an inferential relationship to estimate the speed of sound in a fluid may require measurement and / or inference of any one or more of density, pressure, sensor stiffness, and temperature. In order to estimate the speed of sound, quantities must be measured or estimated before they can be used to estimate the speed of sound. Also, if the mass flow rate is to be corrected by an estimated speed of sound, the speed of sound must first be estimated before the mass flow rate can be corrected based on the estimated speed of sound. Thus, in basic procedures, unless a step must occur before the next step, mandatory steps are not required. There is no required order of steps or modules that must be used. For example, measurements can be taken in almost any order. Estimations must be made in sequence only to the extent that their values ​​are needed as input to the next step.

[0082] The interface 230 is an input / output device that is used to communicatively couple the data computer system 200 to external computing elements. The interface 230 may be, for example, a universal Serial Bus, Prolink, Serial Communications, Serial Advanced Technology Attachment Using well-known technologies such as WAN, HPC-style connections, Gigabit Ethernet, and InfiniBand 2, the computer system 200 can be connected to an external element. The interface 230 may include a communication coupler 240. The communication coupler 240 may couple the computer system 200 to an external element. The computer system 200 may be coupled to any one or more of external components, such as an external computing device, a vibrating flow sensor 5, a density sensor 10, and an optional pressure sensor 20. It is used to

[0083] [flowchart] 3-7 show flow charts of embodiments of methods for estimating the speed of sound and methods of correcting flow measurements using the estimated speed of sound. The methods disclosed in the flow charts are not exhaustive but merely represent possible embodiments of steps and sequences. The methods may include any of the elements disclosed in the description of FIG. 1 and FIG. 2, one or more components disclosed in FIG. In the context of this specification, including the computer system 200 and / or the SoS estimation module 202, It must be interpreted.

[0084] 3 illustrates a flow chart of an embodiment of a method 300 for estimating an estimated speed of sound in a flowing fluid. The method 300 includes references to the vibrating flow sensor 5, density sensor 10, optional pressure sensor 20, computer system 200, vibrating flow sensor electronics 110, density sensor electronics 120, SoS estimation module 202, pressure estimation module 204, measurement module 206, and The compensation module 208 includes a vibrating flow sensor 5, a density sensor 10, an optional pressure sensor 20, a computer system 200, a vibrating flow sensor electronics, and a A measuring instrument 110, a density sensor electronic measuring instrument 120, a SoS estimation module 202, a pressure estimation module 204, The measurement module 206 and the correction module 208 may be, but in alternative embodiments The present invention includes any suitable vibrating flow sensor 5, a density sensor 10, an optional pressure sensor 20, The present invention may employ a computer system 200, a vibrating flow sensor electronics 110, a density sensor electronics 120, an SoS estimation module 202, a pressure estimation module 204, a measurement module 206, and a compensation module 208. Any method for accomplishing these steps as disclosed herein is contemplated. Also, the vibrating flow sensor 5, the density sensor 10, and the optional pressure sensor 120 may be used. It is assumed that all of the force sensors 20 (if applicable) are in fluid flow communication with each other and receive the flowing fluid, and the estimated sound speed referenced in the method 300 is the estimated sound speed of the flowing fluid.

[0085] Step 302 measures input parameters using one or more measurement modules 206. The measurement input parameters may include, for example, any one or more of density, temperature, stiffness of the density sensor 10, and pressure. It is not necessary that all of the measured input parameters be included. For example, in an embodiment in which the pressure used to estimate the speed of sound is a measured pressure, the pressure is a measured input parameter (e.g., obtained by any pressure sensor 20) and the stiffness of the density sensor 10 is not necessary to estimate the SoS. In some embodiments where pressure is estimated, the pressure can be estimated by measuring the stiffness of the density sensor 10, and pressure measurement may not be necessary (in some cases eliminating the need for the optional pressure sensor 20). Also, temperature measurements may be performed using the vibration flow sensor 5, the density sensor 10, and the This may be done by any of the measurement modules 206 of the optional pressure sensor 20. All of the functions of the different embodiments of the measurement module 206 disclosed herein are implemented in accordance with this scheme. It is expected that the company will achieve this step.

[0086] Step 304 is optionally a step of estimating the estimated pressure by the pressure estimation module 204. As mentioned above, the estimated pressure can be used instead of the measured pressure to estimate the estimated sound speed of the flowing fluid. The density sensor 10 may measure the stiffness of the density sensor 10. One of the density sensor 10 and the vibratory sensor 5 (the one having the pressure estimation module 204 in its electronic instrumentation) may estimate the estimated pressure using the measured stiffness. The functionality of the different embodiments of the pressure estimation module 204 disclosed herein all contribute to accomplishing this step. It is expected that this will happen.

[0087] Step 306 includes estimating, by the SoS estimation module 202, an estimated speed of sound in the flowing fluid. The SoS estimation module may estimate an estimated sound speed from any one or more of the measured input parameters and the estimated pressure. The SoS estimation module 202 may use any of the functions and any of the described relationships. For example, the relationship between the estimated sound speed and the measured input parameters (and, in related embodiments, the estimated pressure) and the relationships represented by equations (1)-(9) may be used. As disclosed herein, the SoS estimation module 202 may estimate an estimated sound speed from any one or more of the measured input parameters and the estimated pressure. Any electronic measuring instrument element of the measuring instrument 120 that is expected to estimate the estimated sound speed. In an alternative embodiment, the SoS estimation module 202 may include a standalone computer system 200 that receives relevant measurements and / or estimates to estimate the speed of sound. The SoS promotion method disclosed herein may be stored in a stand-alone computer system. The functions of the different embodiments of the determination module 202 all contribute to accomplishing this step. It is assumed that:

[0088] In one embodiment, each step of the method illustrated in FIG. In this embodiment, steps 302 to 306 may be treated as separate steps even though they are shown as separate steps in FIG. In other embodiments, the method shown in FIG. 3 may include all of the above steps. The method may not include, and / or may comprise other steps in addition to or instead of those listed above. The steps of the method shown in FIG. As part of the method illustrated in FIG. 3, a subset of the steps listed above may be included as a method in their own right. The steps of method 300 may be used in any combination and order. , may be repeated any number of times, for example, in a continuous loop to provide a consistent and / or continuous sound speed estimate for the flowing fluid.

[0089] 4 illustrates a flow chart of one embodiment of a method 400 for estimating an estimated speed of sound in a flowing fluid. The method 400 references the vibrating flow sensor 5, density sensor 10, optional pressure sensor 20, computer system 200, vibrating flow sensor electronics 110, density sensor electronics 120, SoS estimation module 202, pressure estimation module 204, measurement module 206, and correction The module 208 may be the vibrating flow sensor 5, density sensor 10, optional pressure sensor 20, computer system 200, vibrating flow sensor electronics 110, density sensor electronics 120, SoS estimation module 202, pressure estimation module 204, measurement module 206, and compensation module 208 as disclosed in FIGS. 1 and 2, although in alternative embodiments any suitable vibrating flow sensor 5, density sensor 10, optional pressure sensor 20, computer system 200, vibrating flow sensor electronics 110, density sensor electronics 120, SoS estimation module 202, pressure estimation module 204, measurement module 206, and compensation module 208 may be used. The present invention may employ a flow sensor system 200, a vibrating flow sensor electronics 110, a density sensor electronics 120, an SoS estimation module 202, a pressure estimation module 204, a measurement module 206, and a compensation module 208. Any method for accomplishing these steps as disclosed herein is contemplated. Also, the vibrating flow sensor 5, the density sensor 10, and the optional pressure sensor 120 may be used. All of the sensors 20 (if applicable) are assumed to be in fluid communication with each other and to receive a flowing fluid, and the estimated sound speed is the estimated sound speed of the flowing fluid.

[0090] Step 402 involves the SoS estimation module 202 computing the measured density of the flowing fluid and the propulsion of the flowing fluid. and estimating an estimated speed of sound of the flowing fluid based on an inferential relationship between the constant speed of sound and the measured input parameters. The SoS estimation module may receive any one or more of the measured input parameters and the estimated pressure and determine the estimated speed of sound from the any one or more. The SoS estimation module 202 may use any of the functions and may use any of the relationships described. For example, the relationships described above between the estimated sound speed and the measured input parameters (and, in related embodiments, the estimated pressure) and the relationships represented by equations (1)-(9) may be used. As disclosed herein, the SoS estimation module 202 may be an element of either the vibrating flow sensor electronics 110 or the density sensor electronics 120 that is expected to estimate the estimated sound speed. In alternative embodiments, the SoS estimation module 202 may be stored in the computer system 200, which is a stand-alone computer system that receives the relevant measurements and / or estimates and estimates the sound speed on the stand-alone computer system. Different implementations of the SoS estimation module 202 disclosed herein may be used. All of the functions according to the embodiments described above are intended to accomplish this step. Step 402 may be an embodiment of step 306.

[0091] In one embodiment, as part of the method illustrated in FIG. 4, substeps of the steps listed above may be performed. The steps of method 400 may be optionally a number of times, for example, looped continuously to provide a consistent and / or continuous sound speed estimate for the flowing fluid.

[0092] 5 illustrates a flow chart of one embodiment of a method 500 for estimating an estimated speed of sound of a flowing fluid in a density sensor 10. The vibrating flow sensor 5, density sensor 10, optional pressure sensor 20, computer system 200, vibrating flow sensor electronics 110, density sensor electronics 120, SoS estimation module 202, pressure estimation module 204, measurement module 206, and compensation module 208 referenced in method 500 may be the vibrating flow sensor 5, density sensor 10, optional pressure sensor 20, computer system 200, vibrating flow sensor electronics 110, density sensor electronics 120, SoS estimation module 202, pressure estimation module 204, measurement module 206, and compensation module 208 as disclosed in FIGS. 1 and 2, although alternative implementations may be used. In this embodiment, any suitable vibrating flow sensor 5, density sensor 10, and optional pressure sensor 20, computer system 200, vibration type flow sensor electronic measurement instrument 110, density sensor electronic measurement 120, an SoS estimation module 202, a pressure estimation module 204, a measurement module 206, and a correction Module 208 may be employed to accomplish these steps disclosed herein. In addition, the vibrating flow sensor 5, the density sensor 10, and the It is assumed that all of the pressure sensors 20 (if applicable) in the system are in fluid communication with one another and receive the flowing fluid, and the estimated sound speed is the estimated sound speed of the flowing fluid.

[0093] Step 502 is a step of measuring a measurement input parameter of the density sensor 10 by the measurement module 206. The measurement input parameter of the density sensor 10 may include, for example, any one or more of density, temperature, and stiffness of the density sensor 10. In some embodiments, the measurement step need not include all of the described measurement input parameters. For example, in embodiments where the pressure used to estimate the speed of sound is the measured pressure, the stiffness of density sensor 10 is not required and may not be measured at all. In embodiments where pressure is estimated, the stiffness of density sensor 10 may be measured to estimate the pressure. Additionally, temperature measurements may be performed using any of the measurement models of vibrating flow sensor 5, density sensor 10, and optional pressure sensor 20. The measured temperature used to estimate the speed of sound can be measured by a density sensor 206. If the temperature is measured by a sensor other than density sensor 10, density sensor 10 may receive the measured temperature from a sensor other than the density sensor. All of the different embodiments of measurement module 206 associated with density sensor 10 disclosed herein are contemplated to accomplish this step. Step 502 may be an embodiment of step 302.

[0094] Step 504 is optionally a step of estimating an estimated pressure by the pressure estimation module 204. As described above, the estimated pressure can be used instead of the measured pressure to estimate the estimated speed of sound in the flowing fluid. The density sensor 10 may measure the stiffness of the density sensor 10. The density sensor 10 may use the measured stiffness to estimate the estimated pressure. The functionality of the different embodiments of the pressure estimation module 204 associated with the density sensor 10 disclosed herein is not limited to the above. It is contemplated that all of the above steps will accomplish this step. Step 504 may be one embodiment of step 304.

[0095] Step 506 is optionally a step of receiving a measured pressure from the optional pressure sensor 20 by the density sensor electronics 120. In this embodiment, the pressure is measured and not estimated. In one embodiment, steps 504 and 506 may be separate steps that use either the measured pressure or the estimated pressure to estimate the speed of sound of the flowing fluid.

[0096] Step 508 includes estimating, by the SoS estimation module 202, an estimated speed of sound in the flowing fluid. The SoS estimation module 202 may be stored in the density sensor electronics 120. The SoS estimation module may estimate an estimated speed of sound from any one or more of the measured input parameters, the estimated pressure, and any received parameters. The SoS estimation module 202 may Any of the functions described may be used, and any of the relationships described may be used. For example, the relationships described as the relationships between the estimated sound speed and the measured input parameters (and / or the estimated pressure in the relevant embodiment) and the relationships shown as equations (1)-(9) may be used. All of the functions of the different embodiments of the SoS estimation module 202 associated with the density sensor 10 disclosed herein are contemplated to accomplish this step. Step 508 is a step of calculating the speed of sound. This may be an embodiment of step 306.

[0097] In one embodiment, each step of the method illustrated in FIG. In this embodiment, steps 502-508 are shown as separate steps in FIG. In other embodiments, the method shown in FIG. 5 may include all of the steps described above. The method may not include and / or may include other steps in addition to or instead of those listed above. The steps of the method shown in FIG. 5 may be performed in other orders. As part of the method illustrated in FIG. 5, a subset of the steps listed above may be performed by themselves. The steps of method 500 may be combined in any combination and The sequence may be repeated any number of times, for example, looped continuously to provide a consistent and / or continuous sound speed estimate for the flowing fluid.

[0098] FIG. 6 illustrates one embodiment of a method 600 for estimating an estimated speed of sound of a flowing fluid in a vibratory flow sensor 5. 6 shows a flow chart of an embodiment of the present invention. The vibrating flow sensor 5, density sensor 10, optional pressure sensor 20, computer system 200, vibrating flow sensor electronics 110, density sensor electronics 120, SoS estimation module 202, pressure estimation module 204, measurement module 206, and compensation module 208 referenced in the method 600 may be the vibrating flow sensor 5, density sensor 10, optional pressure sensor 20, computer system 200, vibrating flow sensor electronics 110, density sensor electronics 120, SoS estimation module 202, pressure estimation module 204, measurement module 206, and compensation module 208 as disclosed in FIG. 1 and FIG. 2, but may be alternatively configured. In an embodiment, any suitable vibrating flow sensor 5, density sensor 10, optional pressure A force sensor 20, a computer system 200, a vibrating flow sensor electronics 110, a density sensor electronics 120, a SoS estimation module 202, a pressure estimation module 204, a measurement module 206, and A correction module 208 may be employed to accomplish these steps as disclosed herein. Any method for measuring the flow rate is envisioned. and optional pressure sensor 20 (if applicable) are all assumed to be in fluid flow communication with each other and to receive the flowing fluid, and the estimated sound speed is the estimated sound speed of the flowing fluid.

[0099] Step 602 is to measure input parameters of the vibratory flow sensor 5 by the measurement module 206. The measurement input parameters of the vibrating flow sensor 5 are, for example, density. and temperature. The density of the vibrating flow sensor 5 may be too dependent on sound speed effects to be used to estimate the speed of sound of the flowing fluid, and therefore another density measurement, such as that by density sensor 10, may be required. The functionality of the different embodiments of measurement module 206 for the vibrating flow sensor 5 disclosed herein are all intended to accomplish this step. Step 602 may be an embodiment of step 302.

[0100] Step 604 is optionally a step of estimating an estimated pressure by the pressure estimation module 204. As described above, the estimated pressure can be used instead of the measured pressure to estimate the estimated speed of sound of the flowing fluid. The density sensor 10 may measure the stiffness of the density sensor 10. In one embodiment, the density sensor 10 uses the measured stiffness to calculate the stiffness of the density sensor electronics 120. In this embodiment, the pressure estimation module 204 estimates the estimated pressure of the density The density sensor 10 is stored in the sensor electronics 120. In an alternative embodiment, the density sensor 10 is The stiffness of the density sensor 10 is measured and transmitted to the vibration type flow sensor electronic measuring instrument 110. This allows the pressure estimation module 204 stored in the vibrating flow sensor electronics 110 to estimate the pressure used to estimate the speed of sound. All of the functions of the different embodiments of the pressure estimation module 204 disclosed herein are intended to accomplish this step. Step 604 may be an embodiment of step 304.

[0101] Step 606 is optionally a step of receiving a measured pressure from optional pressure sensor 20 by vibrating flow sensor electronics 110. In this embodiment, the pressure is measured and not estimated. In one embodiment, steps 604 and 606 may be alternative steps.

[0102] Step 608 is optionally a step of receiving the density measured by the density sensor 10 by the vibrating flow sensor electronics 110. The density sensor 10 may be less susceptible to the sonic effect than the vibrating flow sensor 5. In that case, the measurement module of the density sensor 10 may be It may be better to use the density measurement of the flowing fluid provided by the flow control module 206. There is a gender.

[0103] Step 610 includes estimating, by the SoS estimation module 202, an estimated speed of sound in the flowing fluid. The SoS estimation module 202 may be stored in the vibrating flow sensor electronics 110. The SoS estimation module uses the measured input parameters, the estimated pressure, and any received measurements. The SoS estimation module 202 may estimate the estimated speed of sound from any one or more of the following: , any of its functions may be used, and any of the relationships described may be used. For example, the relationships described as the relationships between the estimated speed of sound and the measured input parameters (and / or the estimated pressure, in related embodiments), and the relationships shown as equations (1)-(9) may be used. All of the functions of the different embodiments of the SoS estimation module 202 disclosed herein are contemplated to accomplish this step. Step 610 may be an embodiment of step 306.

[0104] In one embodiment, each step of the method illustrated in FIG. In this embodiment, steps 602-610 may be separate steps, although they are shown as separate steps in FIG. In other embodiments, the method shown in FIG. 6 may include all of the above steps. The method may not include any of the steps listed above and / or may include other steps in addition to or instead of those listed above. The steps of the method shown in FIG. 6 may be performed in a different order. As part of the method illustrated in FIG. 6, a subset of the steps listed above may be performed, by themselves. The steps of method 600 may be used in any combination and order. The process may be repeated any number of times, for example in a continuous loop, to provide a consistent and / or continuous estimate of the speed of sound of the flowing fluid.

[0105] FIG. 7 shows a flow chart of one embodiment of a method 700 for correcting flow measurements using an estimated sound speed. The vibrating flow sensor 5, density sensor 10, vibrating flow sensor electronics 110, and compensation module 208 referenced in method 700 may be the vibrating flow sensor 5, density sensor 10, vibrating flow sensor electronics 110, and compensation module 208 as disclosed in FIGS. 1 and 2, although any suitable vibrating flow sensor 5, density sensor 10, vibrating flow sensor electronics 110, and compensation module 208 may be used in alternative embodiments. Any method for accomplishing these steps as disclosed herein is contemplated. Also, the vibrating flow sensor 5, density sensor 10, and optional pressure sensor 20 (if relevant) may be used in alternative embodiments. All are in fluid communication with one another to receive a flowing fluid, the estimated sound speed is an estimated sound speed of the flowing fluid, and the flow measurement is a flow measurement of the flowing fluid.

[0106] Step 702 is receiving an estimated speed of sound of the flowing fluid by the compensation module 208. In embodiments where the speed of sound estimation is performed by an SoS estimation module 202 stored in the vibrating flow sensor electronics 110, the estimated speed of sound may be received from the SoS estimation module 202 stored in the vibrating flow sensor electronics 110. The speed of sound estimation may be performed by the density sensor electronics 120. In an embodiment performed by an SoS estimation module 202 stored in the density sensor electronic gauge 120, the estimated speed of sound may be received from an SoS estimation module 202 stored in the density sensor electronic gauge 120. Step 704 is measuring the phase difference or time delay by the measurement module 206. The phase difference or time delay may be indicative of the Coriolis forces acting on the flowing fluid such that the phase difference or time delay of the vibrations of the upstream and downstream sensors is indicative of a parameter of the fluid, e.g., mass flow rate. Methods for measuring time delay and / or phase difference in vibrating flow sensors are well established in the art and will not be described for the sake of brevity.

[0107] Step 706 is a step of determining a corrected mass flow parameter based on the estimated sound speed of the flowing fluid by the correction module 208. The mass flow parameter may be a mass flow rate. The mass flow rate may be determined by any determination and correction relationship, such as the relationships shown as equations (10) to (12). A formula may be used to determine and correct.

[0108] In one embodiment, each step of the method illustrated in FIG. In this embodiment, steps 702-706 are separate steps, although they are shown as separate steps in FIG. In other embodiments, the method shown in FIG. 7 may include all of the above steps. The method may not include any of the steps listed above and / or may include other steps in addition to or instead of those listed above. The steps of the method shown in FIG. 7 may be performed in a different order. As part of the method illustrated in FIG. 7, a subset of the steps listed above may be performed, by themselves. The steps of method 700 may be used to form a method, for example, Or continuously, the steps may be looped and repeated any number of times in any combination and order to provide a mass flow rate that is corrected for sonic effects.

[0109] [graph] 8 and 9 show graphs illustrating the components of the sound speed estimation and subsequent estimated mass flow correction described herein.

[0110] FIG. 8 is a graph illustrating one embodiment of the heat capacity ratio of ethylene versus both pressure and temperature. Graph 800 shows a graph 800 of ethylene at 20° C., a first data series 802 representing ethylene at 40° C., an ordinate 810 representing the magnitude of the heat capacity ratio, and a pressure graph 802 representing the ethylene at 40° C. and abscissa 820 representing force. As can be seen from the graph, the force varies with temperature and / or pressure. The data shows that there is a significant difference in heat capacity associated with the temperature and / or pressure, which is why the accuracy of the estimation of the speed of sound in a flowing fluid can be greatly improved by using the temperature and / or pressure dependent heat capacity in an inferential relationship.

[0111] Figure 9 shows how the density sensor electronics measure the sound velocity of ethylene flowing through a CMF400 mass flowmeter. 9 shows a graph 900 of the percent error in mass flow caused by the effect versus both pressure and temperature, according to one embodiment. The CMF 400 was used for this particular demonstration of the inventive concept. The vibratory flow sensor 5 used is merely an exemplary embodiment, and the described features of the invention may be used in any It should be understood that the graph 900 is also applicable to a vibratory flow sensor 5 such as the one shown in FIG. 9 has a first data series 902 representing ethylene, a second data series 904 representing ethylene at 80° F., a third data series 906 representing ethylene at 90° F., an ordinate 910 representing the magnitude of the error in mass flow rate due to sonic effects in percent, and an abscissa 920 representing pressure in pounds per square inch. It can be seen that the percent error in mass flow rate due to sonic effects varies significantly with temperature and pressure. This can be accounted for by using a temperature and / or pressure dependent heat capacity ratio and / or an estimated speed of sound that is pressure dependent, greatly reducing the error in mass flow rate due to sonic effects.

[0112] The detailed description of the above embodiments is not an exhaustive description of all embodiments that the inventors consider to be within the scope of the present specification. Indeed, one of ordinary skill in the art will recognize that certain elements of the above-described embodiments can be combined or removed in various ways to create further embodiments, and such further embodiments are within the scope and teachings of the present specification. It will also be apparent to one of ordinary skill in the art that the above-described embodiments can be combined in whole or in part to create additional embodiments within the scope and teachings of the present specification. When specific numbers are specified to represent parameter values, all ranges between those numbers, as well as ranges above and below those numbers, are contemplated and disclosed.

[0113] Thus, while specific embodiments are described herein for illustrative purposes, various equivalent modifications are possible within the scope of the present disclosure, as those skilled in the art will recognize. The teachings provided herein may be used to describe not only the embodiments described above and illustrated in the accompanying drawings, but also other methods and apparatus for estimating the speed of sound, and other methods and apparatus for using the speed of sound to correct measurements of a fluid. Accordingly, the scope of the above embodiments should be determined based on the following claims.

Claims

1. 1. A method for estimating an estimated speed of sound in a flowing fluid, the method comprising: a processor (210) and a memory (220), the processor (210) executes instructions from the memory (220) and stores data in the memory (220). The memory (220) is configured to store an SoS estimation module (202), The method is as follows: estimating, by the SoS estimation module (202), the estimated speed of sound in the flowing fluid based on an inferential relationship between the measured density of the flowing fluid and the estimated speed of sound in the flowing fluid.

2. 2. The method of claim 1, wherein the inferential relationship between the estimated speed of sound in the flowing fluid and the density of the flowing fluid is an inverse relationship between the estimated speed of sound in the flowing fluid and a square root of the measured density of the flowing fluid.

3. 3. The method of claim 2, wherein the inferential relationship between the estimated sound speed of the flowing fluid and the density of the flowing fluid further takes into account a pressure of the flowing fluid, the pressure of the flowing fluid being one or more of a measured pressure measured by a pressure sensor (20) and a pressure estimated from a determined stiffness of a density sensor (10).

4. 4. The method of claim 3, wherein the inferential relationship is further based on a relationship between the estimated speed of sound in the flowing fluid and a heat capacity ratio of the flowing fluid, the inferential relationship being based on a relationship between the estimated speed of sound in the flowing fluid and a square root term of the square root of the product of the heat capacity ratio and the pressure divided by the square root of the measured density.

5. The heat capacity ratio is associated with the flowing fluid and any one or more of the flowing fluid classes from which the flowing fluid originates, and the heat capacity ratio is either temperature dependent or pressure dependent. and the heat capacity ratio is determined based on a corresponding predetermined relational expression between the heat capacity ratio and any one or more of the measured temperature and the pressure. The method described.

6. The computer system (200) is a density sensor electronic instrument (120) for a density sensor (10), and the method comprises: Measuring a measured density by the density sensor (10); The density sensor (10) transmits the estimated sound speed of the fluid to a vibration sensor (5). The method of any one of claims 1 to 5, further comprising:

7. a density sensor electronics (120) that measures the density of the flowing fluid based on a measured stiffness of an element of the density sensor (10) determined by the density sensor (10) when the pressure of the flowing fluid is factored into the inferential relationship between the measured density of the flowing fluid and the estimated sound speed of the flowing fluid; The method of claim 6 , further comprising estimating an estimated pressure of the fluid.

8. The computer system (200) is a vibratory flow sensor electronic measuring instrument (110) for a vibratory flow sensor (5), and the method comprises: receiving a density measurement from a density sensor by said computer system; And, receiving, by the computer system (200), the pressure of the flowing fluid; The computer system (200) performs a correction based on the estimated sound speed of the flowing fluid. The method of any one of claims 3 to 5, further comprising determining a corrected mass flow rate.

9. The vibration sensor (5) Vibrating the vibration element of a vibration sensor (5) at a frequency of 300 Hz or more; and The inside diameter is 2 inches or more. Any one or more of the following: The density sensor (10) vibrating a vibration element of a density sensor (10) at a frequency of less than 300 Hertz; and The inside diameter is less than 2 inches, The method according to claims 6 to 8, wherein the method is any one or more of the following:

10. The method of any one of claims 1 to 9, wherein the flowing fluid is in a supercritical state and comprises any one or more of ethylene, ethane, carbon dioxide, and argon.

11. An apparatus for estimating an estimated speed of sound in a flowing fluid, the apparatus comprising a computer system (200), the computer system (200) including a processor (210) and a memory (220). (220), the processor (210) executes instructions from the memory (220) and The memory (220) is configured to store data, and the memory (220) is configured to store a SoS estimation model. The computer system (200) includes: The apparatus, wherein the SoS estimation module (202) is configured to estimate the estimated speed of sound in the flowing fluid based on an inferential relationship between a measured density of the flowing fluid and the estimated speed of sound in the flowing fluid.

12. 12. The apparatus of claim 11, wherein the inferential relationship between the estimated speed of sound in the flowing fluid and the density of the flowing fluid is an inverse relationship between the estimated speed of sound in the flowing fluid and the square root of the measured density of the flowing fluid.

13. 13. The apparatus of claim 12, wherein the inferential relationship between the estimated sound speed of the flowing fluid and the density of the flowing fluid further takes into account a pressure of the flowing fluid, the pressure of the flowing fluid being one or more of a measured pressure measured by a pressure sensor (20) and a pressure estimated from a determined stiffness of a density sensor (10).

14. 14. The apparatus of claim 13, wherein the inferential relationship is further based on a relationship between the estimated speed of sound in the flowing fluid and a heat capacity ratio of the flowing fluid, the inferential relationship being based on a relationship between the estimated speed of sound in the flowing fluid and a square root term of the square root of the product of the heat capacity ratio and the pressure divided by the square root of the measured density.

15. The heat capacity ratio is associated with the flowing fluid and any one or more of the flowing fluid classes from which the flowing fluid originates, and the heat capacity ratio is either temperature dependent or pressure dependent.

15. The apparatus of claim 14, wherein the heat capacity ratio is determined based on a corresponding predetermined relationship between any one or more of the measured temperatures and pressures and the heat capacity ratio.

16. The computer system (200) controls the density sensor electronics of the density sensor (10). (120), and the density sensor (10) comprises: Measure the measured density; 12. The method of claim 11, further comprising the steps of: transmitting the estimated sound speed of the fluid to a vibratory sensor (5); The apparatus described in 1 to 15.

17. When the pressure of the flowing fluid is factored into the inferential relationship between the measured density of the flowing fluid and the estimated sound speed of the flowing fluid, the density sensor electronics (120) may be The density sensor (10) determines a measured stiffness of an element of the density sensor (10) based on the measured stiffness of the element of the density sensor (10). The apparatus of claim 16 configured to estimate an estimated pressure of the moving fluid.

18. The device is a vibrating flow sensor (5), the computer system (200) is a vibrating flow sensor electronic measuring instrument (110) of the vibrating flow sensor (5), and the computer system (200) configured to receive the measured density from a density sensor (10); configured to receive the pressure of the flowing fluid; The apparatus of any one of claims 13 to 15, further configured to determine a corrected mass flow rate based on the estimated speed of sound of the flowing fluid.

19. The vibration sensor (5) Vibrating the vibration element of a vibration sensor (5) at a frequency of 300 Hz or more; and The inside diameter is 2 inches or more. Any one or more of the following: The density sensor (10) vibrating a vibration element of a density sensor (10) at a frequency of less than 300 Hertz; and The inside diameter is less than 2 inches, The device according to claims 16 to 18, wherein the device is any one or more of the following:

20. 20. The apparatus of claims 11-19, wherein the flowing fluid is in a supercritical state and comprises any one or more of ethylene, ethane, carbon dioxide, and argon.

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