RU2453816C2 - Wet gas measurement - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: multiphase working fluid medium is passed through a vibration Venturi tube. Motion is generated in the vibration Venturi tube. A first observable property of the multiphase working fluid medium is determined based on movement of the vibration Venturi tube, and an observable intermediate value associated with the multiphase working fluid medium is determined based on the first observable property. A corrected intermediate value is determined based on the mapping between the observable intermediate value and the previous corrected intermediate value. The phase-dependent phase property of the multiphase working fluid medium is determined based on the corrected intermediate value.

EFFECT: high accuracy of determining mass flow and density of each phase of a multiphase fluid medium.

25 cl, 98 dwg

Description

Link to related applications

This application claims priority to provisional application US No. 60 / 823,753, filed August 28, 2006, under the name WET GAS MEASUREMENT SYSTEM, which is incorporated in its entirety by reference. US Provisional Application No. 60 / 913,148, filed April 20, 2007 under the name WET GAS CALCULATIONS, is incorporated herein by reference in its entirety.

FIELD OF THE INVENTION

This description applies to flow meters.

State of the art

Flow meters provide information on materials transported by pipeline. For example, mass flow meters provide a direct indication of the mass of material transported through the pipeline. Similarly, density flow meters or densitometers provide an indication of the density of the material flowing through the pipeline. Mass flowmeters can also provide an indication of material density.

Coriolis type mass flowmeters are based on the well-known Coriolis effect, in which material flowing through a rotating pipeline becomes a radially moving mass, which is subjected to the Coriolis force and therefore experiences acceleration. Many Coriolis-type mass flowmeters generate a Coriolis force due to a sinusoidal oscillation of the pipeline relative to the axis of rotation perpendicular to the length of the pipeline. In such mass flowmeters, the Coriolis reaction force acting on the mass of a moving fluid is transferred to the pipeline itself and appears as a deviation or displacement of the pipeline in the direction of the Coriolis force vector in the plane of rotation.

Energy is supplied to the pipeline by an excitation mechanism that exerts a periodic force to vibrate the pipeline. One type of excitation mechanism is an electromechanical exciter that exerts a force proportional to the applied voltage. In an oscillatory flow meter, the applied voltage is periodic and, in general, sinusoidal. The input voltage period is selected so that the movement of the pipeline corresponds to the resonant mode of oscillation of the pipeline. This reduces the energy needed to maintain vibrations. An oscillating flow meter can use a feedback loop in which a sensor signal that carries information on the instantaneous frequency and phase associated with the oscillation of the pipeline is amplified and fed back to the pipeline using an electromechanical exciter.

SUMMARY OF THE INVENTION

In one general aspect, a multiphase working fluid is passed through a venturi. A movement is created in the venturi. The first observed property of the multiphase working fluid is determined based on the movement of the vibrating venturi, and the observed intermediate value associated with the multiphase working fluid is determined based on the first observed property. The adjusted intermediate value is determined based on the mapping between the observed intermediate value and the adjusted intermediate value. The phase-dependent phase property of the multiphase working fluid is determined based on the adjusted intermediate value.

Embodiments may include one or more of the following features. The mapping may be a neural network capable of detecting an error in the intermediate value due to the presence of a multiphase working fluid. The observed intermediate value can be defined as being in the first predetermined range of values prior to determining the corrected intermediate value, and the adjusted intermediate value can be determined as being in the second preset range of values until the phase-dependent phase property of the multiphase working fluid is determined.

The multiphase working fluid may be a wet gas. A multiphase working fluid may include a first phase and a second phase, the first phase may include a non-gaseous fluid, and the second phase may include gas. A multiphase working fluid may include a first phase including a first non-gaseous fluid, and a second phase including a second non-gaseous fluid, and a third phase including a gas.

The step of determining the first observed property of the multiphase working fluid may include determining the second observed property of the multiphase working fluid. The first observable property of a multiphase working fluid may be a mass flow rate, and the second observable property may be a density.

One or more measurements may be taken corresponding to an additional property of the working fluid. An additional property of the multiphase fluid may include one or more of the temperature of the multiphase fluid, the pressure associated with the multiphase fluid, and the water cut of the multiphase fluid, and determining the observed intermediate value associated with the multiphase fluid based on the first observed property may include determining an intermediate value based on the first observed property and the additional property.

Determining the observed intermediate value associated with the multiphase working fluid based on the first observed property may include determining the volume fraction associated with the amount of non-gaseous fluid in the multiphase working fluid and the volumetric flow rate of the multiphase fluid. Determining the observed intermediate value associated with the multiphase working fluid based on the first observed property may include determining a first Froude number corresponding to the non-gas phase of the multiphase fluid and a second Froude number corresponding to the gas phase of the multiphase fluid.

The determination of the phase-dependent phase property of the multiphase working fluid based on the adjusted intermediate value may include determining the mass flow rate of the non-gas phase of the multiphase fluid.

Embodiments of any of the above methods may include a method or process, system, flowmeter, or instructions stored in a transmitter memory of the flowmeter. Details of specific embodiments are provided in the accompanying drawings and the following description. Other features will be apparent from the following description, including the drawings, and the claims.

Embodiments of any of the above methods may include a method or process, system, flowmeter, or instructions stored in a transmitter memory of the flowmeter. Details of specific embodiments are provided in the accompanying drawings and the following description. Other features will be apparent from the following description, including the drawings, and the claims.

Brief Description of the Drawings

Figure 1 is a block diagram of a digital mass flow meter.

2A and 2B are perspective and side views of the mechanical components of a mass flow meter.

3A-3C are diagrams of three modes of motion of the flowmeter shown in FIG.

4 is a block diagram of an analog control and measurement circuit.

5 is a block diagram of a digital mass flow meter.

Fig.6 is a logical block diagram showing the operation of the meter shown in Fig.5.

7A and 7B are graphs showing sensor data.

8A and 8B are graphs of sensor voltage versus time.

Fig.9 is a logical flowchart of the approximation curve.

Figure 10 is a logical flowchart of a procedure for generating phase differences.

11A-11D, 12A-12D and 13A-13D are the exciter and sensor voltages during system startup.

Fig. 14 is a flowchart of a procedure for measuring the frequency, amplitude and phase of these sensors using the synchronous modulation method.

15A and 15B are block diagrams of a mass flow meter.

FIG. 16 is a flowchart of a procedure implemented by the meter shown in FIGS. 15A and 15B.

Fig - control of the logarithm of the amplitude of the transfer function.

Fig. 18 is a diagram of a root hodograph.

19A-19D are performance graphs of an analog-to-digital converter versus temperature.

20A-20C are graphs of phase measurements.

21A and 21B are graphs of phase measurements.

FIG. 22 is a flowchart of a procedure for compensating for a zero offset. FIG.

23A-23C, 24A, and 24B are graphs of phase measurements.

25 is a graph of sensor voltage.

Fig. 26 is a flowchart of a dynamic effects compensation procedure.

Figa-35E are graphs showing the application of the procedure shown in Fig.29.

36A-36L are graphs showing phase measurement.

37A is a graph of sensor voltages.

Figv and 37C are graphs of phase and frequency measurements corresponding to the voltages of the sensors shown in figa.

Fig. 37D and 37E are graphs of correction parameters for phase and frequency measurements shown in Fig. 37B and 37C.

Figa-38H - graphs of raw measurements.

Figa-39H - graphs of the adjusted measurements.

40A-40H are graphs showing aeration correction.

Fig is a block diagram showing the effect of aeration in the pipeline.

Fig. 42 is a flowchart of a tuning adjustment procedure.

Figa-43C are graphs showing the application of the procedure shown in Fig.41.

Fig. 44 is a graph for comparing the performance of digital and analog flow meters.

Fig is a logical block diagram showing the operation of the meter with automatic verification.

Fig. 46 is a block diagram of a two-wire digital mass flow meter.

Figa-47C are graphs showing the response of a digital mass flow meter in conditions of humidity and void.

Fig. 48A is a diagram showing dosing test results from an empty state.

Figv is a diagram of an experimental hydrodynamic installation.

Fig. 49 is a graph showing mass flow rate errors relative to the difference in observed density.

Fig. 50 is a graph showing residual mass flow errors after applying the corrections.

Fig. 51 is a graph showing the operational response of a digital mass flow meter with automatic verification of a two-phase flow.

Fig. 52 is a block diagram of a digital controller implementing a neural network processor that can be used with a digital mass flow meter.

Fig. 53 is a flowchart of a method for implementing a neural network for predicting a mass flow rate error and generating an error correction coefficient for correcting a mass flow measurement signal when a two-phase flow is detected.

Fig. 54 is a three-dimensional graph showing attenuation changes in a two-phase flow.

Fig - computer interface of the experimental hydrodynamic installation.

Fig. 56 is a three-dimensional graph illustrating the true mass flow rate error under two-phase flow conditions.

Fig. 57 is a three-dimensional graph showing the corrected mass flow rate error under two-phase flow conditions.

Fig. 58 is a graph that compares an uncorrected mass flow measurement signal with a mass flow measurement signal adjusted by a neural network.

Fig. 59 is a flowchart of an error compensation procedure in a multiphase flow condition.

60 is a block diagram of a digital controller that implements a neural network processor that can be used with a digital mass flow meter for multiphase fluid flows.

Fig. 61 is a flowchart of a method for realizing a neural network for predicting a mass flow rate error and generating an error correction coefficient for correcting a mass flow measurement signal when waiting and / or detecting multiphase flows.

Fig. 62 is a graphical representation of a test table for wellheads tested based on actual tests at various well pressures and gas velocities.

63 is a graphical representation of the raw density errors at various percentages of the liquid void fraction and for wells at various speeds and pressures.

Fig. 64 is a graphical representation of the unprocessed mass flow rate errors at various percentages of the liquid void fraction and for wells at various speeds and pressures.

Fig. 65 is a graphical representation of an unprocessed liquid void fraction of error for wells at various speeds and pressures.

Fig is a graphical representation of the raw volumetric flow rate error for wells at various speeds and pressures.

Fig. 67 is a graphical representation of corrected fluid void fractions for wells at various speeds and pressures.

Fig - graphical representation of the adjusted volumetric flow rate of the mixture for wells at various speeds and pressures.

Fig - graphical representation of the adjusted mass flow rate of gas for wells at various speeds and pressures.

FIG. 70 is a graphical representation of the adjusted integral gas probability of a test digital flowmeter.

Fig - graphical representation of the adjusted errors of the mass flow rate of the fluid for the wells at various speeds and pressures.

Fig. 72 is a graphical representation of the adjusted integral gas probability of a digital digital flow meter under test.

The implementation of the invention

Methods are provided for taking into account the effects of a multiphase flow, for example, in a digital flow meter. The multiphase stream may be, for example, a two-phase stream or a three-phase stream. In general, a two-phase flow is a fluid that includes two (a) phases or components. For example, a two-phase flow may include a phase that includes a non-gaseous fluid (e.g., liquid) and a phase that includes a gas. A three-phase flow is a fluid that includes three phases. For example, a three-phase flow may be a fluid with a gas phase and two non-gaseous liquids. For example, a three-phase stream may include natural gas, oil, and water. The two-phase flow may include, for example, natural gas and oil.

Although the digital flowmeter continues to operate in the presence of a multiphase fluid, any properties (for example, mass flow rate and multiphase fluid density) determined by the digital flowmeter may be inaccurate, since the determination of these properties using traditional methods is generally based on the assumption that the fluid flowing through the flowmeter is single-phase. Thus, even if the fluid is not a single-phase fluid, the flow meter may continue to operate and generate observable property values, for example, mass flow and multiphase fluid density. As described below in FIGS. 59-72, in one embodiment, parameters, for example, mass flow rate and density of each phase of the multiphase flow can be determined from the observed mass flow rate and the observed density of the multiphase fluid. In particular, as discussed in more detail below, in one embodiment, one or more intermediate values, for example, liquid volume fraction and volume flow rate or gas and non-gas Froude numbers, are determined from the observed mass flow rate and the observed density of the multiphase fluid, and the intermediate ( s) value (s) can be adjusted for multiple phases in a fluid using a neural network or other mapping. The mass flow rate and density of each phase of the multiphase fluid can be determined from the adjusted intermediate value (s). Using the intermediate value (s) instead of the mass flow rate and density of the multiphase fluid can improve the accuracy of determining the mass flow rate and density of each phase of the multiphase fluid.

Before starting to describe the methods with reference to FIG. 59, consider digital flowmeters with reference to FIGS. 1-39. Various methods for taking into account the effects of a multiphase flow, for example, in a digital flowmeter are discussed starting from FIG. 40.

1, a digital mass flow meter 100 includes a digital controller 105, one or more motion sensors 110, one or more pathogens 115, a pipe 120 (also referred to as a venturi) and a temperature sensor 125. The digital controller 105 can be implemented using one or several, for example, a processor, a user-programmable gate array, an ASIC, other programmable logic or a gate matrix, or programmable logic with a processor core. The digital controller generates a mass flow measurement through conduit 120 based on at least the signals received from the motion sensors 110. The digital controller also causes pathogens 115 to create movement in the conduit 120. This motion is sensed by the motion sensors 110.

The mass flow rate through the pipe 120 is associated with the movement excited in the pipeline due to the application of the driving force generated by the pathogens 115. In particular, the mass flow rate is associated with the phase and frequency of movement, as well as the temperature of the pipe. A digital mass flowmeter can also measure the density of material flowing through a pipeline. Density is related to the frequency of movement and the temperature of the pipeline. Many of the methods described are applicable to a densitometer, which provides a density measurement rather than a mass flow measurement.

The temperature in the pipeline, which is measured using the temperature sensor 125, affects some properties of the pipeline, for example, its rigidity and size. A digital controller compensates for these temperature effects. The temperature of the digital controller 105 affects, for example, the operating frequency of the digital controller. In general, the temperature effects of the controller are quite small, so they can be neglected. However, in some cases, the digital controller can measure the temperature of the controller using a semiconductor device and can compensate for the effects of the temperature of the controller.

A. Mechanical construction

In one embodiment, which is shown in FIGS. 2A and 2B, conduit 120 is designed to fit into a trunk pipe (not shown), a small portion of which is removed or reserved to accommodate the conduit. The pipe 120 includes mounting flanges 12 for connection to the main pipe and a central manifold block 16 supporting two parallel planar contours 18 and 20 that are oriented perpendicular to the main pipe. Electromagnetic pathogens 46 and sensors 48 are connected between the ends of both circuits 18 and 20. Each of the two pathogens 46 corresponds to the pathogen 115 shown in FIG. 1, and each of the two sensors 48 corresponds to the sensor 110 shown in FIG. 1.

Pathogens 46 at opposite ends of the loops are fed with a current of equal amplitude but opposite sign (i.e., currents shifted in phase by 180 °), which causes the straight sections 26 of loops 18, 20 to rotate relative to their perpendicular bisector 56, which intersects with pipe at point P (figv). A repeated rotation (for example, according to a sinusoidal law) of the supply current supplied to the pathogens causes each rectilinear section 26 to oscillate, noticing a figure in the form of a bow tie in a horizontal plane around line 56-56, which is the axis of symmetry of the contour. The full lateral range of the contours on the lower rounded coils 38 and 40 is small, of the order of 1/16 inch for a two-foot straight section of pipe 26 having a diameter of one inch. The oscillation frequency is usually from about 80 to 90 Hz.

B. Pipeline movement

The movement of the straight sections of the circuits 18 and 20 is shown in three modes in FIGS. 3A, 3B and 3C. In the drive mode shown in FIG. 3B, the loops are driven with a phase shift of 180 ° relative to their respective points P, as a result of which the two loops rotate synchronously, but in the opposite direction. Therefore, the corresponding ends, for example A and C, periodically approach and move away.

The driving motion shown in FIG. 3B gives rise to the Coriolis motion shown in FIG. 3A, which is carried out in opposite directions between the contours and, as a result of which, the straight sections 26 are slightly moved towards each other (or from each other). The Coriolis effect is directly related to mvW , where m is the mass of material in the cross section of the contour, v is the speed with which the mass moves (volume flow), W is the angular velocity of the contour ( W = W ₀ sinω t ), and mv is the mass flow. The Coriolis effect is maximum when two rectilinear sections are excited sinusoidally and have a sinusoidally varying angular velocity. Under these conditions, the Coriolis effect is 90 ° out of phase with respect to the excitation signal.

FIG. 3C shows motion in an undesirable general mode in which the contours deviate in the same direction. This type of movement can be generated by axial vibration in the main pipe in the example shown in FIGS. 2A and 2B, since the contours are perpendicular to the main pipe.

The oscillation type shown in FIG. 3B is called the antisymmetric mode, and the Coriolis mode shown in FIG. 3A is called the symmetric mode. The natural frequency of oscillations in the antisymmetric mode depends on the torsion elasticity of the taps. Typically, the resonant frequency of the antisymmetric mode for pipelines, the shape of which is shown in FIGS. 2A and 2B, is higher than the resonant frequency of the symmetric mode. To reduce noise sensitivity when measuring mass flow, it is advisable to maximize the Coriolis force at a given mass flow. As noted above, the loops are excited at their resonant frequency, and the Coriolis force is directly related to the frequency at which the loops oscillate (i.e., the angular velocity of the loops). Accordingly, the circuits are excited in an antisymmetric mode, which usually has a higher resonant frequency.

Other embodiments may include other piping designs. For example, a single circuit or a straight pipe segment can be used as a pipeline.

C. Electronic design

The digital controller 105 determines mass flow by processing the signals generated by sensors 48 (i.e., motion sensors 110) located at opposite ends of the loops. The signal generated by each sensor includes a component corresponding to the relative speed at which the circuits are excited by the pathogen located after the sensor, and a component corresponding to the relative speed of the circuits due to the Coriolis forces created in the circuits. The circuits are excited in the antisymmetric mode, therefore the components of the sensor signals corresponding to the excitation speed are equal in magnitude but opposite in sign. The resulting Coriolis force acts in a symmetrical mode, therefore, the components of the sensor signals corresponding to the Coriolis speed are equal in magnitude and sign. Thus, subtracting the signals neutralizes the components of the Coriolis velocity and gives a difference that is proportional to the rate of excitation. Similarly, summing the signals neutralizes the components of the excitation speed and gives a sum that is proportional to the Coriolis speed, which, in turn, is proportional to the Coriolis force. This amount can then be used to determine the mass flow rate.

1. Analog control system

The digital mass flow meter 100 provides significant advantages over traditional, analog mass flow meters. For use in further consideration, FIG. 4 shows an analog control system 400 of a conventional mass flow meter. Each sensor 48 provides a voltage signal, wherein the signal V _A0 is generated by the sensor 48a, and the signal V _B0 is generated by the sensor 48b. V _A0 and V _B0 correspond to the speed of the circuits relative to each other in the positions of the sensors. Prior to processing, the signals V _A0 and V _{B0 are} amplified at respective input amplifiers 405 and 410 to produce signals V _A1 and V _B1 . To correct the imbalance on amplifiers and sensors, the input amplifier 410 has a variable gain, which is controlled by a balance signal coming from a feedback loop that contains a synchronous demodulator 415 and an integrator 420.

At the output of amplifier 405, the signal V _A1 has the form:

and, at the output of amplifier 410, the signal V _B1 has the form:

where V _D and V _C are, respectively, the excitation voltage and the Coriolis voltage, and ω is the circular frequency of the excitation mode.

Voltages V _A1 and V _{B1 are} differentiated by operational amplifier 425 to create a signal

where V _DRV corresponds to the exciting movement and is used to power pathogens. In addition to supplying exciters, the V _{DRV is} supplied to the zero crossing detector 430 in the positive direction, which creates an output square wave F _DRV whose frequency corresponds to the frequency of the V _DRV signal (ω = 2F _DRV ). F _{DRV is} used as an input to digital phase locked loop 435. F _DRV also arrives at processor 440.

Voltages V _A1 and V _B1 are summed by the operational amplifier 445 to create a signal

where V _COR is associated with an excited Coriolis movement.

V _COR arrives at synchronous demodulator 450, which produces an output voltage V _M that is directly proportional to the mass, discarding V _COR components that do not have the same frequency as the gate signal Q and are not in phase with it. A phase locked loop 435 generates Q, which is a quadrature reference signal having the same frequency (ω) as V _DRV and is 90 ° out of phase with respect to V _DRV (i.e., in phase with V _COR ). Accordingly, synchronous demodulator 450 discards frequencies other than ω, therefore, V _M corresponds to the amplitude of V _COR at ω. This amplitude is directly proportional to the mass in the pipeline.

V _{M is} supplied to the voltage-to-frequency converter 455, which produces a square wave signal F _M whose frequency corresponds to the amplitude of the signal V _M. Processor 440 then divides F _M by F _DRV to create a mass flow measurement.

The digital phase-locked loop 435 also creates a reference signal I in phase with V _DRV and used to gate the synchronous demodulator 415 in the feedback loop controlling the amplifier 410. When the amplification factors of the input amplifiers 405 and 410 times the excitation components of the corresponding input signals are equal , the summing operation on the operational amplifier 445 creates a zero excitation component in the V _COR signal (i.e., there is no common mode signal with V _DRV ). When the amplification factors of the input amplifiers 405 and 410 are not equal, an excitation component exists in V _COR . This excitation component is extracted by the synchronous demodulator 415 and integrated by the integrator 420 to generate an error voltage that corrects the gain of the input amplifier 410. When the gain is too high or too low, the synchronous demodulator 415 produces an output voltage, according to which the integrator changes the error voltage, which changes the gain. When the gain reaches the desired value, the output of the synchronous modulator reaches zero, and the error voltage stops changing to maintain the desired value of the gain.

2. Digital control system

FIG. 5 shows a block diagram of an embodiment 500 of a digital mass flow meter 100, which includes conduit 120, drivers 46 and sensors 48 shown in FIGS. 2A and 2B, together with a digital controller 505. The analog signals from sensors 48 are converted to digital signals are converted by analog-to-digital (“A / D”) converters 510 to the controller 505. A / D converters can be implemented as separate converters or as separate channels of a single converter.

Digital-to-analog ("D / A") converters 515 convert the digital control signals from the controller 505 into analog signals to drive the pathogens 46. Using a separate drive signal for each pathogen has several advantages. For example, the system can easily switch between symmetric and antisymmetric excitation modes for diagnostic purposes. In other implementations, the signals generated by the converters 515 can be amplified by amplifiers before being fed to the exciters 46. In still other embodiments, a single D / A converter can be used to create an excitation signal applied to both pathogens, the excitation signal being inverted before being fed to one of the pathogens to excite the pipeline 120 in the antisymmetric mode.

High precision resistors 520 and amplifiers 525 are used to measure the current supplied to each driver 46. A / D converters 530 convert the measured current to digital signals and provide digital signals to controller 505. Controller 505 uses the measured currents to generate field signals.

Temperature sensors 535 and pressure sensors 540 measure, respectively, the temperature and pressure at the inlet 545 and the outlet 550 of the pipeline. A / D converters 555 convert the measured values to digital signals and provide digital signals to the controller 505. The controller 505 uses the measured values in different ways. For example, the difference between the measured pressures can be used to determine the back pressure in the pipeline. Since the stiffness of the pipeline varies depending on the back pressure, the controller can take into account the stiffness of the pipeline based on the determined back pressure.

An optional temperature sensor 560 measures the temperature of the crystal oscillator 565 used by the A / D converters. An A / D converter 570 converts this temperature measurement into a digital signal for use by the controller 505. The ratio between the input and output of the A / D converters varies depending on the operating frequency of the converters, and the operating frequency varies depending on the temperature of the crystal oscillator. Accordingly, the controller uses temperature measurement to adjust the data provided by the A / D converters, or when calibrating the system.

In the embodiment shown in FIG. 5, the digital controller 505 processes the digitized sensor signals generated by the A / D converters 510 according to the procedure 600 shown in FIG. 6 to generate a mass flow measurement and an excitation signal supplied to the exciters 46. Initially, the controller collects data from the sensors (step 605). Using this data, the controller determines the frequency of the sensor signals (step 610), eliminates the zero offset from the sensor signals (step 615), and determines the amplitude (step 620) and phase (step 625) of the sensor signals. The controller uses these calculated values to generate an excitation signal (step 630) and to generate mass flow and other measurements (step 635). After generating excitation and measurement signals, the controller collects a new data set and repeats the procedure. The steps of procedure 600 may be performed sequentially or in parallel, and may be carried out in a varying manner.

Due to the relationships between frequency, zero offset, amplitude and phase, an estimate of one can be used to calculate the other. Thanks to this, the repetition of calculations increases accuracy. For example, the initial frequency definition used to determine the zero offset in the sensor signals can be clarified using sensor signals with the offset corrected. In addition, if necessary, the values generated for the period can be used as initial estimates for the next period.

a. Data collection

For simplicity of consideration, the digitized signals from the two sensors will be denoted as signals SV ₁ and SV ₂ , the signal SV ₁ coming from the sensor 48a, and the signal SV ₂ coming from the sensor 48b. Although new data is constantly being generated, it is assumed that the calculations are based on data corresponding to one full period of both sensors. With significant data buffering, this condition will be met while the average data processing time is less than the time it takes to collect data. Tasks to be performed during the period include deciding that the period has ended, calculating the frequency of the period (or frequencies SV ₁ and SV ₂ ), calculating the amplitudes SV ₁ and SV _2, and calculating the phase difference between SV ₁ and SV ₂ . In some implementations, these calculations are repeated for each period using the endpoint of the previous period as the start of the next period. In other embodiments, the periods overlap 180 ° or to another degree (eg, 90 °), and therefore the period overlaps with the previous or next period.

On figa and 7B shows two vectors of sample data from the signals SV ₁ and SV ₂ , which are indicated, respectively, sv1_in and sv2_in. The first sample point of each vector is known and corresponds to the intersection of zero with a sine wave represented by the vector. For sv1_in, the first sample point is the zero crossing from a negative value to a positive value, while for sv2_in the first sample point is a zero crossing from a positive value to a negative value.

The actual starting point of the period (i.e., the actual zero crossing) will rarely exactly match the sample point. For this reason, starting sample points (start_sample_SV1 and start_sample_SV2) are sample points that occur immediately before the start of the period. To account for the difference between the first sample point and the actual start of the period, the approach also uses the position (start_offset_SV1 or start_offset_SV2) between the initial sample and the next sample with which the period actually begins.

Since there is a phase shift between the signals SV ₁ and SV ₂ , sv1_in and sv2_in can start at different sample points. If the sampling rate and the phase difference are large, there may be a difference of several samples between the beginning of sv1_in and the beginning of sv2_in. This difference provides a rough estimate of the phase shift, and it can be used to verify the calculated phase shift, which is discussed below. For example, when sampling at 55 kHz, one sample corresponds to a phase shift of about 0.5 degrees, and one period corresponds to approximately 800 sample points.

When the controller uses functions, for example, the sum (A + B) and the difference (AB), where B is weighted so as to have the same amplitude as A, additional variables (e.g. start_sample_sum and start_offset_sum) track the beginning of the period for each function. The sum and difference functions have a phase shift halfway between SV ₁ and SV ₂ .

In one embodiment, the data structure used to store data from the sensors is a cyclic list for each sensor, the capacity of which is at least twice the maximum number of samples in a period. Due to this data structure, processing can be performed on data for the current period, while interrupts or other methods are used to add data for the next period to the lists.

Processing is carried out on data corresponding to the full period in order to avoid errors when using approaches based on sine waves. Accordingly, the first task in collecting data during a period is to determine the beginning and end of the period. When using non-overlapping periods, the beginning of the period can be identified as the end of the previous period. When using overlapping periods, and when the periods overlap 180 °, the beginning of the period can be identified as the midpoint of the previous period or as the end point of the period preceding the previous period.

The end of the period can be initially estimated based on the parameters of the previous period and based on the fact that the parameters will not change by more than a predetermined value from period to period. For example, five percent can be used as the maximum allowable change from the value of the last period, which is reasonable because, at sampling frequencies of 55 kHz, a repeated increase or decrease of five percent in amplitude or frequency over successive periods will lead to changes of about 5,000 percent in one second .

When assigning percent as the maximum allowable increase in amplitude and frequency and assuming a maximum phase change of 5 ° for successive periods, a conservative estimate for the upper limit at the end of the period for signal SV ₁ can be defined as:

,

,

where start_sample_SV1 is the first sample sv1_in, sample_rate is the sampling rate, and est_freq is the frequency from the previous period. Similarly, you can define the upper limit at the end of the period for the signal SV2 (end_sample_SV2).

After identifying the end of a period, you can make simple checks to determine if the period is being processed correctly. The period may not be correctly processed when, for example, the pipeline is blocked, or the vibrational signals of the sensors are strongly distorted. Processing only suitable periods provides a significant reduction in calculations.

One way to determine the suitability of a period is to check for specific points in the period to confirm expected behavior. As noted above, the amplitudes and frequencies of the last period provide useful initial estimates of the corresponding values for the current period. Using these values, points corresponding to 30 °, 150 °, 210 ° and 330 ° of the period can be checked. If the amplitude and frequency coincide exactly with the amplitude and frequency for the previous period, these points will have values corresponding to est_amp / 2, est_amp / 2, -est_amp / 2 and -est_amp / 2, respectively, where est_amp is the estimated signal amplitude (t .e., amplitude from the previous period). Due to the fact that a five percent change in amplitude and frequency is permissible, inequalities can be generated for each quarter of the period. For the point 30 °, the inequality has the form:

Inequalities for other points have the same form where the degree of the offset term (x / 360) and the sign of the term est_amp_SV1 have the corresponding values. These inequalities can be used to verify that the piping vibrates properly.

Measurements are processed on the vectors sv1_in (start: end) and sv2_in (start: end), where:

start = min (start_sample_SV1, start_sample_SV2), and

end = max (end_sample_SV1, end_sample_SV2).

The difference between the start and end points for the signal indicates the frequency of the signal.

b. Frequency determination

The sampling frequency of a strictly sinusoidal wave can be calculated by detecting a transition between periods (i.e., by detecting positive or negative zero intersections) and counting the number of samples in each period. Using this method, sampling, for example, a 82.2 Hz sine wave at 55 kHz will provide a frequency estimate with a maximum error of 0.15 percent. Higher accuracy can be achieved by evaluating the fractional part of the sample at which the zero crossing actually occurs, using, for example, start_offset_SV1 and start_offset_SV2. Random noise and zero offset can reduce the accuracy of this approach.

8A and 8B, a refined method for determining the frequency uses quadratic interpolation of the square of the sine wave. According to this method, a square of a sine wave is calculated, an approximation is made by a quadratic function, the minimum of which coincides with the minimum point of the squared sine wave, and the zones of the quadratic function are used to determine the frequency. If

where sv _t is the sensor voltage at time t , A is the oscillation amplitude, x _t is the angle in radians at t (i.e., x _t = 2π ft ), δ is the zero offset, ε _t is a random variable with distribution N (0,1) and σ is the noise variance, then the squared function is defined as follows:

When x _t is close to 2π, sin x _t and sin ² x _t can be approximated by the functions x _0t = x _t -2π and x _0t ² , respectively. Accordingly, for values of x _t close to 2π, a _t can be approximated as follows:

This is a strictly quadratic function (with a nonzero minimum, assuming δ = 0) plus noise, and the amplitude of the noise depends on σ and δ. You can also use linear interpolation.

The sources of errors associated with this method of curve fitting are random noise, zero offset, and deviation from a true quadratic function. The curve approximation is very sensitive to the level of random noise. A zero offset in the voltage of the sensor increases the amplitude of the noise as a function of the square of the sine and illustrates the importance of eliminating the zero offset (discussed below). When moving away from the minimum, the square of even a strictly sinusoidal wave is not strictly quadratic. The most significant additional member is a fourth-order member. In contrast, the most significant additional term for linear interpolation is the third-order term.

The degrees of freedom associated with this curve fitting method are related to how many and which data points are used. The minimum number is three, but more can be used (at higher computational costs) using the least squares approximation. Such an approximation is less susceptible to random noise. On figa shows that the quadratic approximation is good within about 20 ° from the minimum point. Using data points farther from the minimum will reduce the effect of random noise, but will increase errors due to non-quadratic terms (i.e., fourth order and higher) as a function of the sine squared.

FIG. 9 shows a procedure 900 for implementing a curve fitting method. In a first step, the controller initializes the variables (step 905). These variables include end_point, the best estimate of the zero crossing point; ep_int, the integer value closest to end_point; s [0..i], the set of all sample points; z [k], the square of the sample point closest to end_point; z [0..n-1], the set of squares of sample points used to calculate end_point; n, the number of sample points used to calculate end_point (n = 2k + 1); step_length, the number of samples in s between consecutive values in z; and iteration_count, a counter of iterations performed by the controller.

The controller then generates a first end_point score (block 910). The controller generates this estimate by calculating the estimated zero crossing point based on the estimated frequency from the previous period and searching around the estimated crossing point (forward and backward) to find the nearest true intersection point (i.e., the appearance of successive samples with different signs). The controller then sets end_point to a sample point, which is smaller than the samples surrounding the true intersection point.

Then, the controller sets n, the number of points for approximating the curve (step 915). The controller sets n to 5 for a sampling frequency of 11 kHz and equal to 21 for a sampling frequency of 44 kHz. The controller then sets iteration_count to 0 (step 920) and increases iteration_count (step 925) to start the iteration part of the procedure.

In the first step in the iteration part of the procedure, the controller selects step_length (step 930) based on the value of iteration_count. The controller sets step_length to 6, 3, or 1, depending on whether iteration_count is 1, 2, or 3, respectively.

The controller then defines ep_int as the integer part of the sum of end_point and 0.5 (step 935) and populates the z array (step 940). For example, when n is 5, z [0] = s [ep_int-2 * step_length] ² , z [1] = s [ep_int-step_length] ² , z [2] = s [ep_int] ² , z [3] = s [ep_int + step_length] ² and z [4] = s [ep_int + 2 * step_length] ² .

The controller then uses a filter, such as the Savitsky-Golay filter, to calculate the smoothed values of z [k-1], z [k] and z [k + 1] (step 945). The Savitsky-Golay smoothing filters are reviewed by Press et al. In Numerical Recipes in C , pp. 650-655 (2nd ed., Cambridge University Press, 1995), which is incorporated by reference. The controller then performs quadratic interpolation between z [k-1], z [k] and z [k + 1] (step 950) and calculates the minimum value of the quadratic function (z *) and the corresponding position (x *) (step 955).

If x * is between the points corresponding to k-1 and k + 1 (step 960), then the controller sets end_point to x (step 965). Then, if iteration_count is less than 3 (step 970), then the controller increases iteration_count (step 925) and repeats the iterative part of the procedure.

If x * is not between the points corresponding to k-1 and k + 1 (step 960), or if iteration_count is 3 (step 970), then the controller leaves the iteration part of the procedure. The controller then calculates the frequency based on the difference between the end point and the start point for the period that is known (step 975).

In essence, procedure 900 instructs the controller to make three attempts to target end_point, with a decrease in step_length on each subsequent attempt. If the resulting minimum for any attempt falls outside the points used to approximate the curve (i.e., if there is extrapolation instead of interpolation), this indicates the unsuitability of the previous or new estimate and that reducing the step size is inappropriate.

Procedure 900 can be applied to at least three different sine waves generated by the sensors. They include signals SV ₁ and SV ₂ and their weighted sum. In addition, based on the fact that the zero offset has been eliminated, the frequency estimates created for these signals are independent. This is true for signals SV ₁ and SV ₂ , since the errors on each of them are independent. However, this is also true for the weighted sum, provided that the mass flow rate and the corresponding phase difference between the signals SV ₁ and SV ₂ are large enough to calculate the frequency in order to rely on different samples in each individual case. When this is true, random errors in frequency estimates will also be independent.

Three independent frequency estimates can be combined to provide an improved estimate. This combined estimate is simply the average of three frequency estimates.

c. Zero Offset Compensation

An important source of errors in the Coriolis transmitter is the zero offset in the voltage of each of the sensors. A zero offset is introduced into the sensor voltage signal due to drift in the pre-amplification circuit and the analog-to-digital converter. The effect of zero bias can be worsened due to small differences in the gain of the preamplifier for positive and negative voltages due to the use of differential circuits. Each source of errors varies between transmitters and will vary with the temperature of the transmitter and, more generally, with time due to component wear.

An illustrative method for compensating for a zero offset used by the controller is described in detail below. In general, the controller uses a frequency estimate and an integration method to determine the zero offset in each of the sensor signals. The controller then removes the zero offset from these signals. After eliminating the zero offset from the signals SV ₁ and SV ₂ , the controller can recalculate the frequency of these signals to provide an improved frequency estimate.

d. Amplitude Definition

The amplitude of the oscillations can be used in many cases. They include regulating pipeline vibrations through feedback, balancing the contributions of sensor voltages in the synthesis of vibrational pathogen signals, calculating the sums and differences for measuring the phase, and calculating the rate of change of amplitude in order to correct the measurements.

In one implementation, the controller uses the estimated amplitudes of the signals SV ₁ and SV ₂ to calculate the sum and difference of the signals SV ₁ and SV ₂ and the product of the sum and difference. Before determining the sum and the difference, the controller compensates for one of the signals to take into account the differences between the gains of the two sensors. For example, the controller may compensate for the data for the signal SV ₂ based on the ratio of the amplitude of the signal SV ₁ to the amplitude of the signal SV ₂ so that both signals have the same amplitude.

The controller may generate an additional frequency estimate based on the calculated amount. This estimate can be averaged with previous frequency estimates to create an updated estimate of the signal frequency, or it can replace previous estimates.

The controller can calculate the amplitude according to the Fourier method to eliminate the effects of higher harmonics. The sensor voltage x (t) during the period T (established using zero crossing methods) can be represented as an offset and a number of harmonic terms as follows:

In this representation, a nonzero offset a ₀ generates nonzero cosine terms a _n . Although the amplitude of interest to us is the amplitude of the main component (i.e., the amplitude at the frequency ω), tracking the amplitudes of the higher harmonic components (i.e., at the frequencies k ω, where k is greater than 1) may be important for diagnostics. The values of a _n and b _n can be calculated as follows:

and

The amplitude A _{n of} each harmonic is defined as follows:

Integrals are calculated using the Simpson quadratic correction method (described below). The main computational costs of the method are reduced to the calculation of strictly sinusoidal and cosine functions.

e. Phase determination

The controller can use several approaches to calculate the phase difference between the signals SV ₁ and SV ₂ . For example, the controller can determine the phase shift of each harmonic relative to the time t = 0 in the form:

The phase shift is interpreted in relation to a single oscillatory signal as the difference between the beginning of the period (i.e., the zero crossing point) and the zero phase point for the component SV (t) of frequency ω. Since the phase shift is the average over the entire vibrational signal, it can be used as a phase shift from the midpoint of the period. Ideally, in the absence of a zero bias and at a constant amplitude, the phase shift should be zero for each period. The controller can determine the phase difference by comparing the phase shift of each sensor voltage over the same time period.

Amplitude and phase can be generated using the Fourier method, which eliminates the effects of higher harmonics. This method has the advantage that it does not assume that both ends of the pipelines oscillate at the same frequency. At the first stage of the method, a frequency estimate is created using zero crossings to measure the time between the beginning and the end of the period. If a linear change in frequency is assumed, this estimate is equal to the frequency averaged over time over the period. Using the estimated, presumably time-invariant, frequency ω for the period, the controller calculates:

и

and

where SV (t) is the oscillation signal of the sensor voltage (i.e., SV ₁ (t) or SV ₂ (t)). The controller then determines the amplitude and phase estimates:

и

and

The controller then calculates the phase difference based on the fact that the average phase and frequency of each sensor signal represents the entire oscillatory signal. Since these frequencies are different for SV ₁ and SV ₂ , the corresponding phases are scaled to the middle frequency. In addition, the phases shift to the same starting point (i.e., the midpoint of the period on SV ₁ ). After scaling, they are subtracted to provide a phase difference:

и

and

where h is the length of the sample, and the midpoints are given through the samples:

In the general case, the phase and amplitude are not calculated over the same time interval for two sensors. When the flow rate is zero, the two midpoints of the period coincide. However, they diverge at high costs, so the calculations are based on sets of samples that do not coincide in time. This leads to an increase in phase noise in a changing mass flow rate. At full flow, a phase shift of 4 ° (out of 360 °) means that only 99% of the samples in the SV ₁ and SV ₂ datasets match. Even larger phase shifts can be observed under aeration conditions, which can lead to even greater degrees of overlap.

Figure 10 presents a modified approach 1000, which solves this issue. First, the controller finds the frequencies (f ₁ , f ₂ ) and midpoints (m ₁ , m ₂ ) of the data sets (d ₁ , d ₂ ) SV ₁ and SV ₂ (step 1005). Assuming a linear frequency shift from the last period, the controller calculates the frequency SV ₂ at the midpoint SV ₁ (f _2m1 ) and the frequency SV ₁ at the midpoint SV ₂ (f _1m2 ) (step 1010).

The controller then calculates the start and end points of the new data sets (d _1m2 and d _2m1 ) with _midpoints m ₂ and m _1, respectively, with the estimated frequencies f _1m2 and f _2m1 (step 1015). These endpoints do not have to coincide with the zero crossing points. However, this is not required for calculations based on Fourier analysis.

Then, the controller performs Fourier calculations of the phase and amplitude on the sets d ₁ and d _2m1 , and the above-described calculations of the phase difference (step 1020). Since the midpoints d ₁ and d _{2m1 are} identical, scale_shift_SV _{2 is} always zero and can be ignored. The controller repeats these calculations for the data sets d ₂ and d _1m2 (block 1025). The controller then generates average values of the calculated amplitude and phase difference for use in generating measurements (block 1030). If there is sufficient separation between the midpoints m ₁ and m ₂ , the controller can also use two sets of results to provide local estimates of the relationship between phase change and amplitude.

The controller can also use the difference-amplitude method, which involves calculating the difference between SV ₁ and SV ₂ , squaring the calculated difference and integrating the result. According to another approach, the controller synthesizes a sine wave, multiplies the sine wave by the difference of the signals SV ₁ and SV _2, and integrates the result. The controller can also integrate the product of signals SV ₁ and SV ₂ , which is a sine wave having a frequency of 2f (where f is the average frequency of the signals SV ₁ and SV ₂ ), or it can square the product and integrate the result. The controller can also synthesize a cosine wave compared to the sine wave of the product and multiply the synthesized cosine wave by the sine wave of the product to create a 4f sine wave, which the controller then integrates. The controller can also use several of these approaches to create individual phase measurements and then can calculate the average of the individual measurements as the final phase measurement.

The difference-amplitude method begins with:

where φ is the phase difference between the sensors. Basic trigonometric identities can be used to specify the sum (Sum) and the difference (Diff) between signals as follows:

и

and

These functions have amplitudes 2A ₁ cos (φ / 2) and 2A ₁ sin (φ / 2), respectively. The controller computes the data sets for Sum and Diff from the data for SV ₁ and SV ₂ and then uses one or more of the above methods to calculate the amplitude of the signals represented by these data sets. The controller then uses the calculated amplitudes to calculate the phase difference φ.

Alternatively, the phase difference can be calculated using the Prod function defined as:

which is a function with amplitude A ² sinφ and frequency 2f. Prod can be generated sample by sample, and φ can be calculated from the amplitude of the resulting sine wave.

The calculation of the phase, in particular, depends on the accuracy of the previous calculations (i.e., the calculation of the frequencies and amplitudes of SV ₁ and SV ₂ ). The controller may use several methods to provide separate (if not completely independent) phase estimates that can be combined to provide an improved estimate.

f. Excitation signal generation

The controller generates an excitation signal by applying a gain to the difference of the signals SV ₁ and SV ₂ . The controller can apply either a positive gain (providing positive feedback) or a negative gain (providing negative feedback).

In general, the Q of the pipeline is quite high, so that the pipeline will resonate only at certain discrete frequencies. For example, the lowest resonant frequency for some pipelines is from 65 Hz to 95 Hz, depending on the density of the working fluid, and regardless of the frequency of excitation. Therefore, it is desirable to energize the pipe at a resonant frequency to minimize energy loss from period to period. The reverse voltage supply of the sensor to the exciters allows the excitation frequency to move to the resonant frequency.

As an alternative to using feedback to generate an excitation signal, strictly sinusoidal waves having phases and frequencies determined as described above can be synthesized and applied to pathogens. This approach provides the benefits of eliminating unwanted high frequency components, such as resonant frequency harmonics. This approach also allows you to compensate for the time delays introduced by analog-to-digital converters, processing, and digital-to-analog converters to ensure that the phase of the excitation signal corresponds to the midpoint of the phases of the sensor signals. This compensation can be achieved by determining the time delay of the system components and introducing a phase shift corresponding to the time delay.

Another approach to exciting a pipeline is to use square pulses. This is another synthesis method, and fixed (positive and negative) DC sources are turned on and off at predetermined time intervals to provide the necessary energy. The switching is synchronized with the voltage phase of the sensor. The advantage is that this approach does not require digital-to-analog converters.

In the general case, the amplitude of the pipeline oscillations must quickly reach the desired value at start-up in order to quickly provide the measurement function, but it must do this without a significant outlier that could damage the meter. The necessary quick start can be achieved by setting a very high gain so that the presence of random noise and a high Q pipeline is sufficient to initiate the movement of the pipeline. In one implementation, high gain and positive feedback are used to initiate pipeline movement. Upon achieving stable operation, the system switches to a synthesis mode for generating excitation signals.

11A-13D, synthesis methods can also be used to initiate pipeline motion when a high gain is not enough. For example, if the DC voltage offset of the voltage of the sensors significantly exceeds random noise, the application of a high gain will not generate oscillatory motion. This state is shown in FIGS. 11A-11D, according to which a high gain is applied for approximately 0.3 seconds. 11A and 11B, due to the use of a high gain, one of the drive signals takes a large positive value (FIG. 11A) and the other takes a large negative value (FIG. 11B). The magnitude of the excitation signals varies with noise in the sensor signals (FIGS. 11C and 11D). However, amplified noise is not enough to change the sign of the excitation signals to generate oscillations.

On figa-12D shows that the imposition of a square wave over several periods can reliably provide a quick start oscillations. Fluctuations in a pipeline having a diameter of two inches can be established in approximately two seconds. The establishment of pipeline oscillations is indicated by a decrease in the amplitude of the excitation signals shown in FIGS. 12A and 12B. 13A-13D show that vibrations of a one inch pipe can be established in about half a second.

A square wave can also be used during operation to solve the problems of pipeline vibrations. For example, in some cases, it is known that the pipelines of a flowmeter begin to oscillate at harmonics of the resonant frequency of the pipeline, for example, frequencies of the order of 1.5 kHz. When detecting vibrations of such a high frequency, a square wave having a more desirable frequency can be used to return the vibrations of the pipeline to the resonant frequency.

g. Measurement generation

The controller digitally generates mass flow measurement by analogy with the approach used by the analog controller. The controller can also generate other measurements, such as density.

In one implementation, the controller calculates the mass flow based on the phase difference in degrees between the two sensor signals (phase_diff), pipeline vibration frequency (freq), and process temperature (temp):

T _z = temp - T _c ,

noneu_mf = tan (π * phase_diff / 180), and

massflow = 16 (MF ₁ * T _z ² + MF ₂ * T _z + MF ₃ ) * noneu_mf / freq,

where T _c is the calibration temperature, MF ₁ -MF ₃ are the calibration constants calculated in the calibration procedure, and noneu_mf is the mass flow rate in dimensionless units.

The controller calculates the density based on the oscillation frequency of the pipeline and the process temperature:

T _z = temp - T _c ,

c ₂ = freq ² , and

density = (D ₁ * T _z ² + D ₂ * T _z + D ₃ ) / c ₂ + D ₄ * T _z ² ,

where D ₁ -D ₄ are the calibration constants generated in the calibration procedure.

D. Integration Methods

There are many integration methods, and different methods require different levels of computational load and provide different levels of accuracy. In the described implementation, versions of the Simpson method are used. The main method can be expressed as:

where t _k is the sampling time k, y _k is the corresponding value of the function, and h is the step length. This rule can be reapplied to any data vector with an odd number of data points (i.e., three or more points), which is equivalent to fitting and integrating a cubic spline to data points. If the number of data points is even, then the so-called 3/8 rule can be applied at one end of the interval:

As indicated above, each period begins and ends at the same offset (for example, start_offset_SV1) from the sample point. The accuracy of integration methods is greatly enhanced by taking these biases into account. For example, when integrating a half-wave of a sine wave, the regions corresponding to partial samples should be included in the calculations to avoid a significant underestimation of the estimate as a result.

In the described calculations, two types of functions are integrated: either the sine function or the function of the square of the sine. Both are easily approximated near zero, where the end points are. At the end points, the sine wave is approximately linear, and the function of the square of the sine is approximately quadratic.

In view of these two types of functions, three different integration methods were evaluated. These are the Simpson method without boundary correction, the Simpson method with linear boundary correction, and the Simpson method with quadratic correction.

Integration methods were tested by generating and discretizing the strict functions of the sine and square of the sine, without simulating any analog-to-digital truncation error. The integrals were calculated and the results were compared with the true signal amplitudes. The only source of error in these calculations was due to integration methods. The results are presented in Tables A and B.

Table A - Integration of the Sinusoidal Function % error (based on 1000 acts of modeling) Wed errors (%) s.o. errors (%) Max. error (%) only simpson method -3.73e-3 1.33e-3 6,17e-3 Simpson method + linear correction 3.16e-8 4.89e-8 1,56e-7 Simpson method + quadratic correction 2,00e-4 2,19e-2 5.18e-1

Table B - Integration of the Sine Square Function % error (based on 1000 acts of modeling) Wed errors (%) s.o. errors (%) Max. error (%) only simpson method -2.21e-6 1,10e-6 4.39e-3 Simpson method + linear correction 2.21 e-6 6.93e-7 2,52e-6 Simpson method + quadratic correction 2.15e-11 6.83e-11 1.88e-10

For sinusoidal functions, the linearly corrected Simpson method did not have an offset with the smallest standard deviation, while the uncorrected Simpson method had an offset to a negative error, and the quadratic-corrected Simpson method had a relatively high standard deviation. For the functions of the squared sine, errors are generally reduced, and the quadratic correction provides the best result. Based on these estimates, linear correction is used to integrate the sinusoidal functions and quadratic correction is used to integrate the functions of the square sine.

E. Synchronous Modulation Method

On Fig shows an alternative procedure 1400 for processing sensor signals. Procedure 1400 is based on synchronous modulation, such as that described by Denys et al., In "Measurement of Voltage Phase for the French Future Defense Plan Against Losses of Synchronism", IEEE Transactions on Power Delivery, 7 (1), 62-69 , 1992 and Begovic et al. In "Frequency Tracking in Power Networks in the Presence of Harmonics", IEEE Transactions on Power Delivery, 8 (2), 480-486, 1993, both of which are incorporated by reference.

First, the controller generates an initial estimate of the nominal operating frequency of the system (step 1405). Then the controller tries to measure the deviation of the signal frequency x [k] (for example, SV ₁ ) from this nominal frequency:

where A is the amplitude of the sinusoidal part of the signal, ω ₀ is the nominal frequency (for example, 88 Hz), Δω is the deviation from the nominal frequency, h is the sampling interval, Φ is the phase shift, and ε (k) corresponds to the added noise and harmonics.

To generate this measurement, the controller synthesizes two signals that oscillate at the nominal frequency (block 1410). The signals are phase shifted by 0 and π / 2 and have a unit amplitude. The controller multiplies each of these signals by the original signal to create signals y ₁ and y ₂ (step 1415):

и

and

where the first terms y ₁ and y ₂ are high-frequency (e.g., 176 Hz) components, and the second terms are low-frequency (e.g., 0 Hz) components. The controller then eliminates the high-frequency components using a low-pass filter (block 1420):

и

and

where ε ₁ [ k ] and ε ₂ [ k ] represent the filtered noise from the original signals. The controller combines these signals to create u [ k ] (block 1425):

which carries essential information about frequency deviation. As shown, u ₁ [ k ] represents the real component u [ k ], and u ₂ [ k ] represents the imaginary component.

The controller uses the real and imaginary components u [ k ] to calculate the frequency deviation, Δ f (step 1430):

The controller then adds the frequency deviation to the nominal frequency (step 1435) to obtain the actual frequency:

The controller also uses the real and imaginary components u [ k ] to determine the amplitude of the original signal. In particular, the controller determines the amplitude as (block 1440):

The controller then determines the phase difference between the two sensor signals (step 1445). Based on the fact that any noise (ε ₁ [ k ] and ε ₂ [ k ]) remaining after applying the low-pass filter described below will be negligible, silent versions y ₁ '[ k ] and y ₂ ' [ k ] ( y ₁ ^* [ k ] and y ₂ ^* [ k ]) can be expressed as:

и

and

Multiplication of these signals gives:

Filtering this signal with a low-pass filter having a cutoff frequency near 0 Hz removes the unwanted component and leaves:

where can I calculate the phase difference:

This procedure relies on the accuracy with which the operating frequency was originally estimated, since the procedure only measures deviations from this frequency. If the provided rating is good, a very narrow-band filter can be used, which makes the procedure very accurate. For typical flow meters, operating frequencies are around 95 Hz (empty) and 82 Hz (full). The first definition of half the range (88 Hz) is used, which allows a low-pass filter cut-off of 13 Hz. Care must be taken to select the cutoff frequency, since a very low cutoff frequency can reduce the amplitude of the sine wave.

The accuracy of the measurement also depends on the applied filtering characteristics. The attenuation of the filter in the dead zone determines the degree of harmonic rejection, while the reduced cutoff frequency increases the noise rejection.

F. PI meter

On figa and 15B shows the meter 1500 having a controller 1505, which uses a different method to generate signals supplied to the pathogen. Analog-to-digital converters 1510 digitize the signals from the sensors 48 and provide the digitized signals to the controller 1505. The controller 1505 uses the digitized signals to calculate the gain for each driver, and the gain is suitable for generating the necessary vibrations in the pipeline. Gain factors can be either positive or negative. The controller 1505 then provides amplification factors to the multiplying digital-to-analog converters 1515. In other implementations, two or more multiplying digital-to-analog converters arranged in a row can be used to implement one, more sensitive, multiplying digital-to-analog converter.

Controller 1505 also generates drive signals using digitized sensor signals. Controller 1505 provides these excitation signals to digital-to-analog converters 1520, which convert the signals to analog signals, which are then fed to multiplying digital-to-analog converters 1515.

Multiplying D / A converters 1515 multiply the analog signals by gains from the controller 1505 to generate signals for driving the pipe. Amplifiers 1525 then amplify these signals and feed them to the exciters 46. Similar results can be obtained using the controller 1505, which performs multiplication on a multiplying digital-to-analog converter, and the multiplying digital-to-analog converter can be replaced with a standard digital-to-analog converter.

On figv in more detail shows the approach to management. In the controller 1505, the digitized sensor signals are fed to an amplitude detector 1550, which determines the measurement, a ( t ), of the amplitude of movement of the pipeline using, for example, the method described above. The adder 1555 then uses the amplitude a ( t ) and the desired amplitude a ₀ to calculate the error e ( t ) as follows:

The error e ( t ) is used by the proportional-integral ("PI") control block 1560 to generate a gain K ₀ ( t ). This gain is multiplied by the difference of the sensor signals to generate an excitation signal. The PI control unit allows a high-speed response to changing conditions. Amplitude detector 1550, adder 1555, and PI control unit 1560 may be implemented as software executed by controller 1505, or as a separate circuit.

1. Management procedure

The meter 1500 operates according to the procedure 1600 shown in Fig.16. Initially, the controller receives digitized data from the sensors (step 1605). Then, the procedure 1600 includes three parallel branches: a measurement branch 1610, an excitation signal generation branch 1615, and a gain generation branch 1620.

In the measurement branch 1610, digitized sensor data is used to generate amplitude, frequency, and phase measurements as described above (block 1625). These measurements are then used to calculate the mass flow (block 1630) and other process variables. In general, the controller 1505 implements a measurement branch 1610.

In the excitation signal generation branch 1615, the digitized signals from the two sensors are differentiated to generate a signal (step 1635), which is multiplied by a gain to create an excitation signal. As described above, this differentiation operation is performed by the controller 1505. In general, the differentiation operation creates a weighted difference that takes into account differences in amplitude between the sensor signals.

In the gain generating branch 1620, the gain is calculated using a proportional-integral control unit. As noted above, the amplitude, a ( t ), of the movement of the pipeline (step 1640) is determined and subtracted from the desired amplitude a ₀ (step 1645) to calculate the error e ( t ). Amplitude generation, a ( t ), although shown as a separate step, may correspond to amplitude generation in measurement generation step 1625. Finally, the control unit PI uses the error e ( t ) to calculate the gain (block 1650).

The calculated gain is multiplied by the difference signal to generate an excitation signal supplied to the exciters (step 1655). As described above, this multiplication operation is performed by a D / A multiplying converter, or may be performed by a controller.

2. PI control unit

The task of the PI control unit is to maintain strictly sinusoidal oscillations with an amplitude a ₀ in the pipeline. The pipeline can be modeled as a simple load-spring system, the behavior of which can be expressed as:

where x is a function of time and expresses the displacement of the load from the equilibrium point, ω _n is the natural frequency and ζ is the attenuation coefficient, which is assumed to be small (for example, 0.001). The solution to this equation of motion in the form of a function of the output y ( t ) and input i ( t ) is similar to the solution for an electric circuit in which the transfer function between the supplied current, i ( s ) and the perceived output voltage, y ( s ), has the form:

To achieve the desired oscillations in the pipeline, a positive feedback loop having a gain of K ₀ ( t ) is automatically controlled by a “slow” external loop to obtain:

It is assumed that the system has the “two time scales” property, which means that changes in K ₀ ( t ) occur so slowly that solutions to the equation for x presented above can be obtained assuming constant attenuation.

The binomial PI control unit, which provides a zero stationary state error, can be expressed as:

where the error, e ( t ) (i.e., a ₀ - a (t)), is the input to the PI control unit, and K _p and K _i are constants. In one implementation, with a ₀ = 10, the controller constants K _p = 0.02 and K _i = 0.0005 provide a response in which oscillations are quickly established. However, this PI control unit is non-linear, which can lead to structural and operational difficulties.

A linear model of the behavior of the amplitude of the oscillations can be derived on the basis that x ( t ) is equal to A ε ^j ω ^t , which gives:

и

and

Substituting these expressions into the expression for the oscillations of the contour and dividing it into real and imaginary terms, we obtain:

и

and

A ( t ) can also be expressed as:

The solution to this equation has the form:

Transforming the variables by setting a ( t ) equal to log A ( t ), the equation for A ( t ) can be rewritten in the form:

where K ₀ now explicitly depends on time. Applying the Laplace transform, we obtain:

what can be interpreted in relation to the transfer functions shown in Fig.17. This figure is especially important for the design of controllers, since it is linear for all K ₀ and a , with the only assumption that there are two timeline properties. Closed loop performance is robust according to this assumption, which makes it easy to provide fast, practical achievable responses.

According to Figure 17, member ζω _n expresses the "load disturbance" which must be eliminated by the controller (i.e. kK _0/2 must be equal ζω _n, to a (t) is constant). For a zero stationary state error, this implies that the external loop controller must have an integrator (or a very large gain). Therefore, we can assume that the correct PI controller, C (s), should have the form K _p (1 + 1 / sT _i ), where T _i is a constant. A proportional term is necessary for stability. However, the term ζω _n does not affect the stability or design of the controller, which, instead, is based on the transfer function of the open loop:

On Fig shows the root locus for the changing K _p . For small K _p , these are roots with slow subcritical attenuation. With increasing K _p , the roots become valid at point P, at which the controller gain is K _p = 8 / ( kT _i ). We note, in particular, that the theory does not impose any restrictions on the choice of T _i . Therefore, the response, in principle, can be made critically damped and arbitrarily fast by properly choosing K _p and T _i .

Although the poles at P are purely valid, this does not mean that no ejection occurs in the stepped response of a closed loop. This is easiest to see by considering the transfer function between the desired value a ₀ and error e :

where p ₂ is a second-order polynomial. With a step input, a ₀ ( s ) = α / s , the response can be expressed as α p '( t ), where p ( t ) is the inverse transformation 1 / p ₂ ( s ) and is equal to a ₁ exp (-λ ₁ t ) + a ₂ exp (-λ ₂ t ). The signal p ( t ) increases and then decreases to zero, therefore e ( t ), which is proportional to p ', must change sign, implying a surge in a ( t ). Setting a ₀ can be pre-filtered to obtain a psevdonastroyki ₀ ^*:

where T _i is a known controller parameter. Thanks to this pre-filter, the actual controller poles must provide ejection-free step responses. This feature is useful because there may be physical restrictions on the discharge (e.g. mechanical interference or component overload).

The root hodograph shown in Fig. 18 suggests that the dynamics is due only to the transfer function of the gain / logarithm of the amplitude of the inner loop (Fig. 16) and PI of the controller C (s) of the outer loop (i.e., that the logarithm of the amplitude is a = log A measured instantly). However, A is the amplitude of the oscillations, which can increase or decrease and, therefore, cannot, in the general case, be measured without taking into account the underlying sinusoid. There are several methods for measuring A , in addition to those discussed above. Some of them are more suitable for use in quasi-stationary conditions. For example, you can apply a phase-locked loop in which a sinusoidal signal s ( t ) = sin (ω _n t + Ф ₀ ) is synchronized in phase with the measured oscillatory signal y ( t ) = A ( t ) sin (ω _n t + Ф ₁ ). Thus, the amplitude measure a = log A is set by dividing these signals (with the appropriate fuses and filters). This method is probably satisfactory near the stationary state, but not under conditions of establishment before synchronization.

Another approach uses a peak tracking unit, which includes a zero crossing detector in conjunction with a peak tracking algorithm implemented in the controller. However, zero crossing methods may be subject to noise. In addition, the results of the peak tracking block are available only once every half-time, which determines the sampling interval for controller updates.

, где F{} - это подходящий фильтр низких частот с единичным коэффициентом усиления постоянного тока. AM детектор является простейшим подходом. Кроме того, он не требует наличия колебаний на любой конкретной частоте и, следовательно, полезен в условиях пуска. Он страдает тем недостатком, что существует утечка гармоник во внутренний контур, что будет влиять на спектр результирующих колебаний. Кроме того, фильтр добавляет дополнительную динамику во внешний контур, что требует нахождения компромисса между скоростью отклика и спектральной чистотой. В частности, эффект фильтра состоит в ограничении выбора наилучшего T _i.Finally, an AM detector can be used. If there is a sinusoidal wave y ( t ) = A sinω _n t , the estimate of A can be obtained from

where F {} is a suitable low-pass filter with a unity gain of direct current. AM detector is the simplest approach. In addition, it does not require oscillations at any particular frequency and, therefore, is useful in starting conditions. It suffers from the disadvantage that there is a leak of harmonics into the internal circuit, which will affect the spectrum of the resulting oscillations. In addition, the filter adds additional dynamics to the external circuit, which requires a compromise between the response speed and spectral purity. In particular, the filter effect is to limit the selection of the best T _i .

The Fourier series for abs ( y ) has a known form:

Therefore, the output signal must be scaled by n / 2 to ensure the correct DC output signal A , and the (even) harmonic terms a _k cos2 k ω _n t must be filtered out. Since all the filter has to do is skip the DC component and weaken all other frequencies, a brick wall filter with a cut-off below 2ω _{n is} enough. However, the dynamics of the filter will affect the behavior of the closed loop. Usually choose a Butterworth filter. For example, a third-order low-pass filter with a critical frequency design ω _b is expressed as:

At a design frequency, the response is 3 dB lower; at 2ω _b it is -18 dB (0.12), and at 4ω _b it is -36 dB (0.015). Higher-order Butterworth filters have a steeper characteristic, but most of their poles are complex and can adversely affect the root locus of the control loop.

G. Zero offset compensation

As noted above, a zero offset can be introduced into the sensor voltage signal due to drift in the pre-amplification circuit and an analog-to-digital converter. Slight differences in the preamp gain for positive and negative voltages due to the use of differential circuits can worsen the effect of zero bias. Errors vary between transmitters and with transmitter temperature and component wear.

Analog-to-digital converters of audio quality (i.e., relatively low cost) can be used for economic reasons. These devices do not have DC bias stability and amplitude among the high priorities. On figa-19D shows how to change the offset and positive and negative gains depending on the operating temperature of the chip for one such Converter (Converter AD1879). The repeatability of the trends shown is unreliable, and even with temperature compensation based on the trends, there remains a residual zero offset and a mismatch of positive / negative gain factors.

If the phase is calculated using the time difference between the zero crossing points for the two sensor voltages, a DC bias can lead to phase errors. This effect is shown in FIGS. 20A-20C. Each graph shows the calculated phase shift, which is measured by a digital transmitter when the true phase shift is zero (i.e. at zero flow).

On figa shows the phase calculated on the basis of the total periods starting with positive zero crossings. The average value is 0.00627 degrees.

20B shows a phase calculated starting from negative zero crossings. The average value is 0.0109 degrees.

On figs shows the phase calculated for each half-cycle. In FIG. 20C, the data from FIGS. 20A and 20B are alternated. The middle phase (-0.00234) is closer to zero than in FIGS. 20A and 20B, but the standard deviation of the signal is about six times larger.

More advanced phase measurement methods, such as those based on Fourier methods, are resistant to DC bias. However, it is desirable to eliminate the zero offset, even when these methods are used, since the data is processed in packets of the full period, separated by zero crossing points. This makes it possible to simplify the analysis of effects, for example, amplitude modulation, at the observed phase and frequency. In addition, a mismatch in the gain between positive and negative voltages will introduce errors into any measurement method.

The zero crossing method for phase determination can be used to demonstrate the effect of zero offset and gain mismatch errors, and their subsequent removal. On figa and 21B shows a long-term drift, synchronized in phase with zero flow. Each point represents the average value of operational data for one minute. On figa shows the middle phase, and figv shows the standard deviation of the phase. In a few hours, the drift becomes noticeable. Thus, even if the meter is zeroed every day, which in many applications is considered an excessive maintenance requirement, significant phase drift will still remain.

1. Payment Method

The method of compensating for voltage bias and mismatch of gain factors uses the computational capabilities of a digital transmitter and does not require a zero flow condition. The method uses a set of calculations in each period, which, when averaged over a reasonable period (for example, 10,000 periods) and excluding areas of strong change (for example, changes in settings, the onset of aeration), converges to the desired compensations for zero offset and mismatch of gain factors.

Assuming the presence of up to three higher harmonics, the desired vibrational voltage signal of the sensor SV (t) can be expressed as:

,

,

where A ₁ denotes the amplitude of the main frequency component and A ₂ -A ₄ denote the amplitudes of the three harmonic components. However, in practice, the actual oscillation signal is disturbed by a zero offset of Z ₀ (which has a value close to zero) and a mismatch between the negative and positive amplification factors G _n and G _p . Without loss of generality, we can assume that G _p is equal to one, and that G _n is defined as follows:

where ε _G represents the mismatch of the gain.

The method assumes that the amplitudes A _i and frequency ω are constant. This is valid because the estimates of Z ₀ and ε _G are based on average values taken over a large number of periods (for example, 10,000 intermittent periods occurring over approximately 1 minute of operation). When implementing the method, the controller checks for significant changes in frequency and amplitude to ensure the analysis is correct. The presence of higher harmonics causes the use of Fourier methods to extract phase and amplitude information for specific harmonics. This involves the integration of SV (t) and multiplication by the modulating function of the sine or cosine.

Zero offset affects the limits of integration, as well as the type of function. Since there is a zero offset, the starting point for calculating the amplitude and phase does not coincide with the zero phase point of the periodic oscillation signal SV (t). For a zero offset of Z ₀ , the corresponding phase shift is approximately equal to

с соответствующей задержкой по времени

For a small phase,

with a corresponding time delay

The integrals are scaled so that the boundary value (i.e., when Z ₀ and ω _G approach zero) is equal to the amplitude of the corresponding harmonic. The first two integrals of interest are as follows:

и

and

These integrals represent what in practice is calculated in the course of a normal Fourier analysis of sensor voltage data. The subscript 1 indicates the first harmonic, N and P indicate, respectively, a negative or positive half-cycle, and s and c indicate, respectively, whether a sine or cosine is used as a modulating function.

Strictly speaking, the midpoint of zero intersection and, consequently, the corresponding integration limits should be set equal to π / ω - t _z0 , and not π / ω + t _z0 . However, the use of an exact midpoint instead of an exact zero crossing point simplifies the analysis and improves numerical behavior (in principle, due to errors in the position of the zero crossing point). The only mistake made when using the exact midpoint is that a small part of each of the above integrals is multiplied by an incorrect gain (1 instead of 1 + ε _G and vice versa). However, these errors are of the order of Z ₀ ² ε _G and are considered negligibly small.

Using computer algebra and assuming small Z ₀ and ε _G , first-order estimates for integrals can be derived in the form:

и

and

You can define useful functions associated with them, including the sum, difference, and ratio of the integrals and their estimates. The sum of the integrals can be expressed as:

and the sum of the ratings is:

Similarly, the difference of the integrals can be expressed as:

and the difference in estimates is equal to:

Finally, the ratio of the integrals is equal to:

and the ratio of ratings is:

The corresponding integrals of cosine are given in the form:

и

and

with ratings:

и

and

and amounts:

и

and

The second harmonic integrals are expressed as:

и

and

иwith ratings:

and

and amounts:

и

and

Integrals can be calculated numerically for each period. As discussed below, equations that evaluate the values of the integrals based on various amplitudes and values of the zero offset and gain can be converted to obtain estimates of the zero offset and gain based on the calculated integrals.

2. Example

The accuracy of the estimation equations can be illustrated by an example. For each main integral, three values are provided: the "true" value of the integral (calculated in Mathcad using Romberg integration), the value using the estimation equation, and the value calculated by the digital transmitter operating in simulation mode using the Simpson method with boundary correction.

Thus, for example, the value of I _1Ps calculated according to

,

,

is 0.101353, while the estimated value (I _1Ps _ _est ), calculated as

,

,

equal to 0.101358. The value calculated using the digital transmitter in simulation mode is 0.101340. These calculations use the parameter values given in Table C.

Table C Parameter Value Comment ω 160π This corresponds to a frequency of = 80 Hz, a typical value. A ₁ 0.1 This value is usually 0.3, but may be less in the case of aeration. A ₂ 0.01 This value is usually 0.005, but may be greater in the case of aeration. A ₃ and A ₄ 0,0 In digital modeling of the Coriolis effect, only two harmonics are required, therefore these higher harmonics can be ignored. However, they are small (<0.002). Z ₀ 0.001 It follows from practice that this is of great importance for zero bias. ε _G 0.001 From practice it follows that this is of great importance for the mismatch of gain.

The exact, estimated and model results obtained using these parameter values are shown in Table D.

Table D Integral 'Exact value Rating Digital Coriolis Effect Modeling I _1Ps 0,101353 0,101358 0,101340 I _1Ns 0.098735 0.098740 0,098751 I _1pc 0,007487 0.007488 0,007500 I _1Nc -0.009496 -0.009498 -0.009531 I _2Ps 0.009149 0.009151 0.009118 I _2Ns 0,010857 0,010859 0,010885

Thus, at least for the particular values selected, estimates obtained from first-order equations are extremely accurate. When Z ₀ and ε _G approach zero, errors in estimation and modeling approach zero.

3. Implementation

First-order estimates for the integrals give rise to a series of nonlinear equations for the amplitudes of harmonics, zero bias, and gain mismatch. Since the equations are nonlinear, an exact solution cannot be obtained. However, the approximation, accompanied by corrective iterations, provides sufficient convergence with a limited computational load.

For A ₁ -A ₄ , a relationship depending on the pipeline can be provided. Therefore, no attempt is made to calculate all the amplitudes A ₁ -A ₄ . Instead, only A ₁ and A ₂ are estimated using the above integral equations. Based on the behavior of the relative amplitudes, A ₃ can be approximately expressed as A _2/2, and A ₄ can be approximately expressed as A _2/10.

The zero offset compensation method can be implemented according to procedure 2200 shown in FIG. During each period, the controller calculates the integrals I _1Ps , I _1Ns , I _1Pc I _1Nc , I _2Ns and the associated functions sum _1s , ratio _1s , sum _1c and sum _2s (step 2205). This requires minimal additional computational burden beyond traditional Fourier calculations used to determine frequency, amplitude and phase.

Every 10,000 periods, the controller checks the amplitude slope of the voltage sensor A ₁ using the traditional method of estimating the rate of change (step 2210). If the amplitude is constant (step 2215), then the controller proceeds to the calculation of the zero offset and the mismatch of the gain. This test can be extended to frequency stability testing.

To perform the calculations, the controller generates average values of the functions (for example, sum _1s ) over the last 10,000 periods. Then, the controller determines a first estimate of the zero offset and the gain mismatch (block 2225):

Z ₀ = -Sum _1c / 2, and

ε _G = 1 / Ratio _1s - 1

Using these values, the controller calculates the inverse gain (k) and amplitude coefficient (amp_factor) (step 2230):

k = 1.0 / (1.0 + 0.5 * ε _G ), and

amp_factor = 1 + 50/75 * Sum _2s / Sum _1s

The controller uses the inverse gain and amplitude coefficient to generate a first amplitude estimate (step 2235):

A ₁ = k * [Sum _1s / 2 + 2 / π * Z ₀ * ε _G * amp_factor], and

A ₂ = k * [Sum _2s / 2 - 4 / (3 * π) * Z ₀ * ε _G ]

The controller then improves the estimate through the following calculations, if necessary, repeated (step 2240):

The controller uses standard methods for checking the convergence of the values of Z ₀ ε _G. In practice, the corrections turn out to be small after the first iteration, and it follows from practice that three iterations are sufficient.

Finally, the controller adjusts the raw data to exclude Z ₀ and ε _G (step 2245). Then the controller repeats the procedure. After eliminating the zero offset and the mismatch of the gain from the raw data, the functions (i.e., sum _1s ) used to generate the subsequent values of Z ₀ and ε _G are based on the adjusted data. Accordingly, these subsequent values of Z ₀ and ε _G reflect the residual zero offset and the gain mismatch, and are combined with previously generated values to create the actual zero offset and gain mismatch. According to one approach to adjusting raw data, the controller generates adjustments (eg, S1_off and S2_off) that are used to convert the analog signals from the sensors to digital data.

On figa-23C, 24A and 24B shows the results obtained using the procedure 2200. Short-term behavior is illustrated in figa-23C. Shown here are consecutive phase estimates obtained five minutes after the start, provided to give the procedure time to begin to influence the output signal. The phase is shown based on positive zero crossings, negative zero crossings, and both of them.

The difference between the positive and negative average values is reduced by a factor of 20, with a corresponding decrease in the average zero offset in the interleaved data set. The corresponding standard deviation is reduced by a factor of approximately 6.

Longer-term behavior is shown in FIGS. 24A and 24B. Initially, a large zero offset is quickly corrected, and then the phase shift remains near zero for many hours. The average phase displacement, with the exception of the first few values, is 6.14e ^-6 , which clearly indicates that the procedure successfully compensates for changes in voltage bias and gain imbalance.

Typical values of Z ₀ and ε _G for a digital Coriolis meter are Z ₀ = -7.923e ^-4 and ε _G = -1.754e ^-5 for signal SV ₁ , and Z ₀ = -8.038e ^-4 and ε _G = +6, 93e ^-4 for the SV ₂ signal.

H. Dynamic analysis

In general, traditional measurement calculations for Coriolis meters assume that the frequency and amplitude of oscillations on each side of the pipeline are constant, and that the frequency on each side of the pipeline is the same and equal to the so-called resonant frequency. Phases, in general, are not measured separately on each side of the pipeline, and the phase difference between the two sides is assumed to be constant throughout the measurement process. Accurate measurements of frequency, phase, and amplitude in each half-cycle using a digital meter demonstrate that these assumptions are valid only when parameter values are averaged over a time period of the order of seconds. When observed at 100 Hz or higher frequencies, these parameters show a noticeable change. For example, during normal operation, the frequency and amplitude values of SV ₁ may show a strong negative correlation with the corresponding SV ₂ values. Accordingly, traditional measurement algorithms are subject to noise due to these dynamic changes. Noise increases with increasing measurement calculation speed. Other noise terms can be caused by physical factors, such as the dynamics of the venturi, dynamic nonlinearities (e.g., changes in the stiffness of the venturi with amplitude), or the dynamic effects of voltage sensors that provide speed data instead of absolute position data.

The described methods use the high accuracy of a digital meter to track and compensate for the dynamic behavior of the pipeline to reduce noise in order to provide more accurate measurements of process variables, such as mass flow and density. This is achieved by monitoring and compensating for effects such as rates of change of frequency, phase and amplitude, the dynamics of the venturi and dynamic physical imperfections. The calculation of the phase difference, in which the same frequency is not assumed on each side, has already been described above. Other compensation methods are described below.

Monitoring and compensation of dynamic effects can be carried out at the level of individual sensors to provide adjusted estimates of phase, frequency, amplitude or other parameters. Additional compensation can also be carried out at the pipeline level, where data from both sensors are combined, for example, when calculating the phase difference and the average frequency. These two levels can be used together to provide full compensation.

Thus, measurements of the instantaneous mass flow rate and density of the flowmeter can be improved by modeling and accounting for the dynamic effects of the flowmeter. In general, 80% or more of the phase noise in a Coriolis flowmeter can be attributed to the dynamics of the venturi (sometimes referred to as “ringing”) rather than the measured process conditions. The use of a dynamic model can reduce phase noise with a factor of 4 to 10, leading to a significant increase in the performance of flow measurement. A single model is effective for all costs and amplitudes. In general, computational requirements are negligible.

Dynamic analysis can be performed on each of the sensor signals separately from each other. This avoids or at least delays the simulation of dynamic interaction between the two sides of the pipeline, which is probably much more complicated than the dynamics on each sensor. In addition, the analysis of individual sensor signals is likely to succeed in conditions such as batch start-up and aeration, when two sides of the pipeline are exposed to different forces from the working fluid.

In the general case, the dynamic analysis considers the influence of the change in time of the amplitude, frequency, and phase on the calculated values of these parameters. Although the frequency and amplitude are easy to set for individual sensor voltages, the phase is traditionally set in relation to the difference between the sensor voltages. However, when using the Fourier analysis, the phase for an individual sensor can be set in relation to the difference between the midpoint of the period and the midpoint of 180 ° phase point.

Three types of dynamic effects are measurement error and the so-called “feedback” and “speed” effects. The measurement error is due to the fact that the algorithms for calculating the amplitude and phase assume that the frequency, amplitude and phase are constant during the time interval of interest. The performance of measurement algorithms can be improved by amending the changes in these parameters.

The feedback effect is due to the supply of energy to the pipeline, in which, taking into account energy leakage from the pipeline, a constant amplitude of oscillations is maintained. The need for additional energy supply to the pipeline is revealed only when the amplitude of the oscillations begins to deviate from the desired setting. As a result, the damping term in the equation of motion for an oscillating pipeline is nonzero and constantly oscillates around zero. Although the natural frequency of the pipeline does not change, it is masked by shifts at zero crossings (i.e., phase changes) associated with these small changes in amplitude.

The speed effect is due to the fact that the sensor voltages reflect the speed of the pipeline, but are analyzed as if they represent the position of the pipeline. The consequence of this is that the rate of change of the amplitude affects the observed frequency and phase, even if the true values of these parameters are constant.

1. Compensation for amplitude modulation at the sensor level

One approach to the correction of dynamic effects involves monitoring the amplitudes of sensor signals and making adjustments based on changes in amplitudes. In order to analyze dynamic effects, it is assumed that estimates of phase, frequency, and amplitude can be determined for each sensor voltage over each period. As shown in FIG. 25, the calculations are based on complete but overlapping periods. Each period begins at the intersection of zero, in the middle of the previous period. Positive periods begin with positive voltages immediately after the initial zero crossing, while negative periods begin with negative voltages. Thus, period n is positive, and periods n-1 and n + 1 are negative. It is assumed that the correction of the zero offset was made so that the zero offset was negligible. It is also assumed that higher harmonics may be present.

A linear change in amplitude, frequency and phase is assumed. Based on this assumption, the average value of each parameter during the period is equal to the instantaneous value of the parameter at the midpoint of the period. Since the periods overlap 180 degrees, the average value for the period is equal to the initial value for the next period.

For example, the period n represents a time interval from 0 to 2π / ω. The average values of the amplitude, frequency, and phase are equal to the instantaneous values at the midpoint, π / ω, which is also the starting point for the period n + 1, which is the time interval from π / ω to 3π / ω. Of course, these time limits are approximate, since ω also varies with time.

a. Dynamic Effect Compensation Procedure

The controller takes into account dynamic effects according to procedure 2600, presented in Fig.26. The controller first creates a frequency estimate (block 2605) using zero crossings to measure the time between the beginning and the end of the period, as described above. Based on the fact that the frequency varies linearly, this estimate is equal to the frequency averaged over time during the period.

The controller then uses the estimated frequency to generate a first estimate of the amplitude and phase using the Fourier method described above (step 2610). As noted above, this method eliminates the effects of higher harmonics.

The phase is interpreted in relation to a single oscillatory signal as the difference between the beginning of the period (i.e., the zero crossing point) and the zero phase point for the component SV (t) of frequency ω, expressed as a phase shift. Since the phase shift is the average over the entire vibrational signal, it can be used as a phase shift from the midpoint of the period. Ideally, in the absence of a zero bias and at a constant amplitude, the phase shift should be zero for each period. However, in practice, it exhibits a high level of variation and provides a good basis for correcting mass flow taking into account dynamic changes in amplitude.

The controller then calculates the phase difference (step 2615). Although various definitions of the phase difference are possible, the analysis assumes that the average phase and frequency of each sensor signal represents the entire oscillatory signal. Since these frequencies are different for SV1 and SV2, the corresponding phases are scaled to the middle frequency. In addition, the phases shift to the same starting point (i.e., the midpoint of the period on SV1). After scaling, they are subtracted to provide a phase difference.

Then, the controller determines the rate of change of amplitude for the period n (step 2620):

This calculation assumes that the amplitude from period n + 1 is available when calculating the rate of change of period n. This is possible if corrections are made one period after receiving the raw amplitude calculations. The advantage of having an accurate estimate of the rate of change and, therefore, good measurement correction outweighs the delay in providing corrected measurements, which, in one implementation, is of the order of 5 milliseconds. The most recently generated information is always used to control the pipeline (i.e. to generate an excitation signal).

If desired, an updated estimate of the rate of change can be calculated after applying the amplitude correction (as described below). As a result, the iteration converges to the best values of the amplitude and rate of change.

b. Frequency compensation of feedback effects and speed

As noted above, the dynamic aspects of the feedback loop introduce time-dependent phase shifts due to small amplitude deviations from the setting. As a result, the measured frequency, which is based on zero crossings, differs from the natural frequency of the pipeline. If speed sensors are used, an additional phase shift occurs. This additional shift is also associated with changes in the amplitude of the position of the pipeline. Dynamic analysis allows you to track and compensate for these effects. Accordingly, the controller uses the calculated amplitude change rate to adjust the frequency estimate (block 2625).

The position of the oscillating pipeline in the feedback loop, which is used to maintain a constant amplitude of the oscillations of the pipeline, can be expressed as:

where θ (t) is the phase delay due to the feedback effect. The mechanical Q of an oscillating pipeline is usually of the order of 1000, which provides for small deviations in amplitude and phase. Under these conditions, θ (t) is defined as follows:

Since each sensor measures speed:

where γ (t) is the phase delay due to the speed effect:

Since the mechanical Q of a pipeline is usually of the order of 1000, and therefore the changes in amplitude and phase are small, it is reasonable to assume:

This means that the expression for SV (t) can be simplified to:

and, for some reason, the expression for phase delay due to velocity displacement can be simplified to:

Summing the phase delays due to feedback and speed effects gives the total phase delay:

and the following expression for SV (t):

This makes it possible to distinguish the actual oscillation frequency from the natural oscillation frequency. Although the former is observable, the latter is useful for density calculations. Over any reasonable period of time and assuming proper amplitude control, the average values of these two frequencies will coincide (since the average rate of change of amplitude should be zero). However, for an improved measurement of instantaneous density, it is advisable to correct the actual frequency of the oscillations for dynamic effects to obtain the natural frequency. This is especially useful when working with aerated fluids, whose instantaneous density can change rapidly over time.

The observed frequency, monitored during period n, is limited by zero crossings occurring at the midpoints of periods n-1 and n + 1. The phase delay due to a change in speed will affect the observed beginning and end of the period:

Based on this analysis, the correction can be applied using the integrated error term:

и

and

where the value of error_summ at startup (i.e. the value in the zero period) is:

Although these equations include a constant term that has a value of 1 / 8π ² , evidence suggests that a constant term of 1 / 8π is more suitable. This difference can be explained by unmodeled dynamics, which can be determined by additional analysis.

The above calculations assume that the true oscillation amplitude, A, is available. However, in practice, only the voltage of the SV sensor can be observed. This sensor voltage can be expressed as:

.

.

The amplitude, amp_SV (t), in this expression is:

The rate of change of this amplitude is:

therefore, the following estimate can be used:

.

.

c. Apply frequency compensation for feedback and speed effects

On figa-32B shows how the application of procedure 2600 improves the assessment of the natural frequency and, therefore, the density of the process, for real data from a meter having a pipe with a diameter of one inch. Each of the figures shows 10,000 samples collected in just 1 minute.

27A and 27B show amplitude and frequency data from SV ₁ obtained by applying random changes to the amplitude setting. Since the pipeline is filled with water and there is no flow, the natural frequency is constant. However, the observed frequency changes significantly with a change in amplitude. The average frequency value is 81.41 Hz, with a standard deviation of 0.057 Hz.

On figa and 28B, respectively, shows the deviation of the frequency from the average value and the correction term generated according to procedure 2600. Gross deviations are very well consistent. However, there is an additional change in frequency that is not associated with changes in amplitude. Another important feature shown in FIG. 28B is that the mean is close to zero as a result of the correct initialization of the above error term.

In FIGS. 29A and 29B, the raw frequency data (FIG. 29A) are compared with the results of applying the correction function (FIG. 29B). The shift in the middle frequency is negligible, and the standard deviation decreased with a factor of 4.4. From figv follows that in the adjusted frequency data there is a residual structure. It is assumed that additional analysis, based on the phase change during the period and its effect on the observed frequency, will further reduce noise.

On figa and 30B shows the corresponding effect on the average frequency obtained by averaging the instantaneous frequency voltage of the sensor. Since the average frequency is used to calculate the density of the working fluid, noise reduction (here, with a factor of 5.2) will affect the density calculation.

On figa and 31B shows the raw and adjusted mid-frequencies for the pipeline with a diameter of 2 inches, the amplitude setting of which is a random variable. The 2 "venturi shows a smaller frequency change than 1" for both raw and adjusted data. The noise reduction coefficient is 4.0.

32A and 32B show more typical results with real flow data for a one inch Venturi. The random tuning algorithm is replaced by the normal constant tuning. As a result, the amplitude change is smaller than in the previous examples, which leads to a lower noise reduction coefficient of 1.5.

d. Phase Compensation for Amplitude Modulation

26, the controller then compensates for the phase measurement taking into account amplitude modulation, assuming the phase calculation provided above (step 2630). In the Fourier method described above, it is assumed that the amplitude of the oscillations is constant throughout the data period over which the calculations are made. This section describes a correction that assumes a linear change in amplitude over a period of data.

Ignoring the higher harmonics and assuming that any zero offset has been eliminated, the expression for the sensor voltage is specified as follows:

,

,

where λ _A is a constant corresponding to a relative change in amplitude with time. As discussed above, the integrals I ₁ and I ₂ can be expressed as:

и

and

Estimating these integrals, we obtain:

и

and

Substituting these expressions in the calculation of the amplitude and expanding in a series of λ _A , we obtain:

Assuming λ _A small and neglecting all terms after the first-order term, this expression can be reduced to:

This is equal to the amplitude SV (t) at the midpoint of the period (t = π / ω). Accordingly, the calculation of the amplitude provides the desired result without correction.

To calculate the phase, it is assumed that the true phase difference and frequency are constant, and that no voltage bias exists, which means that the phase value must be zero. However, as a result of amplitude modulation, the correction to be applied to the raw phase data to compensate for amplitude modulation has the form:

Based on the fact that the expression in parentheses is small, the arctangent function can be ignored.

A more detailed analysis takes into account the effects of higher harmonics. Based on the fact that the sensor voltage can be expressed as:

,

,

according to which the amplitudes of all harmonics increase at the same relative speed during the period, the resulting integrals can be expressed as:

and

for positive periods, and

for negative periods.

For the amplitude, substituting these expressions in the calculations, we find that the calculation of the amplitude is affected only by members of the second order and higher, therefore, for the approximation of the first order for the amplitude, correction is not required. For phase, the correction term has the form:

for positive periods, and

for negative periods. These corrective terms suggest that amplitudes of higher harmonics are known. Although they can be calculated using the usual Fourier method, some or all of them can also be approximated using the estimated harmonics. For example, for one implementation of a pipeline with a diameter of one inch, typical amplitude ratios are A ₁ = 1.0, A ₂ = 0.01, A ₃ = 0.005, and A ₄ = 0.001.

e. Apply amplitude modulation compensation to phase

Modeling was performed using a digital transmitter, which includes modeling of higher harmonics and amplitude modulation. In one example, f = 80 Hz, A ₁ (t = 0) = 0.3, A ₂ = 0, A ₃ = 0, A ₄ = 0, X _A = 1e-5 * 48 kHz (sampling frequency) = 0, are used 47622, which corresponds to a high rate of change in amplitude, but without higher harmonics. The theory predicts a phase shift of -0.02706 degrees, when modeling over 1000 periods, the average displacement is -0.02714 degrees, with a standard deviation of only 2.17e-6. The difference between the model and theory (approx. 0.3% of the modeling error) is due to the fact that the theory assumes a linear change in the amplitude for each period, while an exponential change in the amplitude is generated during the simulation.

The second example includes the second harmonic and has parameters f = 80 Hz, A ₁ (t = 0) = 0.3, A ₂ (t = 0) = 0.003, A ₃ = 0, A ₄ = 0, λ _A = -1e-6 * 48 kHz (sampling frequency) = -0.047622. In this example, the theory predicts a phase shift of + 2.706e-3, ± 2.66% for positive or negative periods. Modeling gives 2.714e-3 ± 2.66%, i.e., again, a good match.

On figa-34B shows examples of how this correction improves the actual data of the flow meter. Fig. 33A shows the raw phase data from SV ₁ collected from a 1 "diameter pipeline in which a low flow rate is reasonably assumed to be constant. Fig. 33B shows a correction coefficient calculated using the above formula, and Fig. 33C shows the resulting corrected phase The most noticeable feature is that the correction increased the dispersion of the phase signal, although it produced a general decrease in the standard deviation of the phase difference (ie, SV ₂ - SV ₁ ) with a factor of 1.26, as shown in FIGS. 34A and 34B Promotion zvoditelnosti is because this correction improves the correlation between the two phases, leading to a decrease in the phase difference. The method works equally well in other flow conditions and other conduit sizes.

f. Speed effect compensation for phase measurement

The calculation of the phase measurement is also affected by the speed effect. A very effective and simple correction factor, in radians, has the form

where Δ SV ( t _k ) is the relative rate of change of amplitude, which can be expressed as:

where t _k is the end time of the period for which Δ SV ( t _k ) is determined, t _{k + 1} is the end time of the next period, and t _k-1 is the end time of the previous period. Δ SV is an estimate of the rate of change of SV , scaled by its absolute value, which is also called the proportional rate of change of SV .

On figa-35E shows this method. On figa shows the raw phase data from one sensor (SV ₁ ), after applying the above correction for amplitude modulation. FIG. 35B shows a correction coefficient in degrees calculated using the above equation, and FIG. 35C shows the resulting corrected phase. Note that the standard deviation of the corrected phase actually increased relative to the raw data. However, when the corresponding calculations are performed on another sensor (SV ₂ ), an increase in the negative correlation (from -0.8 to -0.9) between the phases of the two signals is observed. As a result, the calculation of the phase difference based on the raw phase measurements (Fig. 35D) has significantly greater noise than the corrected phase measurements (Fig. 355E).

A comparison of Figs. 35D and 35E demonstrates the advantage of this noise reduction technique. From FIG. 3-5 it is immediately evident that the process variable is reduced, and that the measurement has a noticeable periodicity, and the periods are typical, possibly for a poorly adjusted pump. Nothing of the kind can be distinguished in the uncorrected phase difference data presented in FIG. 35D.

g. Application of noise reduction at the sensor level

The combination of the above phase noise reduction methods can significantly improve the measurement of the instantaneous phase difference in different flow conditions, illustrated in figa-36L. Each graph shows three measurements of the phase difference, calculated simultaneously in real time by a digital Coriolis transmitter operating on a one-inch pipeline. The middle bar 3600 shows phase data calculated using a simple time difference method. Outer band 3605 shows phase data calculated using the Fourier method described above.

Perhaps unexpectedly, the Fourier method, which uses much more data, more sophisticated analysis, and significantly higher computational load, produces a noisier calculation. This can be explained by the sensitivity of the Fourier method to the above dynamic effects. Internal data band 3610 shows the same Fourier data after applying noise reduction methods at the sensor level. You can see that in each case there is a significant decrease in noise, as evidenced by the values of the standard deviation presented on each graph.

On figa shows measurements in the absence of flow, with a full pipeline and in the absence of pump noise. Fig. 36B shows measurements in the absence of flow, with full piping and with the pumps turned on. On figs shows measurements with an empty, wet pipeline. Fig. 36D shows measurements at a low flow rate. 36E shows measurements at high flow rates. Fig. 36F shows measurements at a high flow rate and an oscillation amplitude of 0.03 V. Fig. 36G shows measurements at a low flow rate with low aeration. Fig. 36H shows low flow measurements with high aeration. On figi shows measurements at high flow rate with low aeration. 36J shows measurements at high flow rate with high aeration. Fig. 36K shows measurements during the transition from an empty state to a high flow rate. Fig. 36L shows measurements during the transition from a high flow rate to an empty state.

2. Dynamic simulation at the venturi

A dynamic model can be implemented in two main stages. At the first stage, a model is created using system identification methods. The venturi is “stimulated” to manifest its dynamics, while the true mass flow and density are kept constant. The response of a venturi is measured and used to generate a dynamic model. In the second stage, the model is applied to normal flow data. The effects of the dynamics of a venturi are predicted for phase and frequency. Then the predicted values are subtracted from the observed data with the formation of the residual phase and frequency, which should be determined only by the process. Each stage is described in more detail below.

a. System identification

System identification begins when the venturi is full of water in the absence of flow. The oscillation amplitude, which is usually kept constant, is changed by assigning an arbitrary setting between 0.05 V and 0.3 V, where 0.3 V is the usual value. The resulting sensor voltages are shown in FIG. 37A, and FIG. 37B and 37C respectively show the corresponding calculated phase and frequency values. These values are calculated once per period. It is shown that the phase and frequency are highly “structured”. Since the phase and frequency corresponding to the mass flow rate are constant, this structure is most likely related to the dynamics of the venturi. The observed variables that will predict this structure when it is not known whether the true phase and frequency are constant can be expressed in the form presented below.

First of all, as noted above, Δ SV ( t _k ) can be expressed as:

This expression can be used to determine ΔSV ₁ and ΔSV ₂ .

The phase of the venturi is associated with Δ ^- , which is expressed as ΔSV ₁ - ΔSV ₂ , and the frequency is associated with Δ ⁺ , which is expressed as ΔSV ₁ + ΔSV ₂ . These parameters are shown in Fig.37D and 37E. Comparing FIG. 37B with FIG. 37D and FIG. 37C with FIG. 37E, an unusual relationship between Δ ^- and phase and between Δ ⁺ and frequency can be seen.

Some correction for the dynamics of the venturi can be obtained by subtracting a multiple of the corresponding prediction function from the phase and / or frequency. Improved results can be obtained using the model in the form of:

where y ( k ) is the output signal (i.e., phase or frequency) and u is the prediction function (i.e., Δ ^- or Δ ⁺ ). The system identification method provides values for orders n and m , and coefficients a _i and b _j forming polynomials that depend on time. The y ( k ) value can be calculated every period and subtracted from the observed phase or frequency to obtain the residual value of the process.

It should be understood that, even in the absence of dynamic corrections, the digital flowmeter gives very good accuracy over a long period of time. For example, when combining a portion of 200 kg, the device easily achieves a repeatability of less than 0.03%. The goal of dynamic modeling is to increase dynamic accuracy. Thus, unprocessed and compensated values should have close average values, but reduced “variance” or “standard deviation”.

On figa and 39A shows the raw and adjusted frequency values. The average values are similar, but the standard deviation is reduced by a factor of 3.25. Although sharp frequency deviations have been eliminated, a noticeable “structure” remains in the residual noise. This structure does not appear to be related to the Δ ⁺ function. The model used is a simple first-order model, where m = n = 1.

On figv and 39B shows the corresponding phase correction. The average value is minimally affected, while the standard deviation is reduced by a factor of 7.9. The model orders are n = 2 and m = 10. It seems that some structure has been preserved in the residual noise. It is assumed that this structure is due to insufficient excitation of the phase dynamics by tuning changes.

A more efficient phase identification was achieved by further modeling the dynamics of the venturi by continuously shaking the venturi during data collection (changes are still being made). FIGS. 38C and 39C show correction effects under these conditions. It was shown that the standard deviation decreased by a factor of 31. This more efficient model is used in further considerations.

b. Apply to stream data

The real test of the identified model is the improvements that it provides for new data. At first, it is useful to make a few observations. First of all, the middle phase, averaged over, for example, ten seconds or more, gives sufficient accuracy. In the examples shown, the phase values are marked on the graph at a frequency of 82 Hz or close to it. The registered standard deviation will be approximately 1/3 of the displayed values when averaged to 10 Hz and 1/9 when averaged to 1 Hz. For reference, on a one-inch Venturi, a phase difference of one degree corresponds to a flow rate of about 1 kg / s.

The alleged advantage of the method is to provide a significantly better dynamic response to the true process of change, and not to increase the average accuracy. Therefore, in the following examples, where the flow rate is not equal to zero, small stepwise flow changes are made every ten seconds or so, in the expectation that the corrected phase will more clearly show step changes.

On fig.38D and 39D shows the correction applied to a full venturi at zero flow rate, as after starting. The curtain effect characteristic of the start-up is clearly observed in the raw data (Fig.38D), but is eliminated by correction (Fig.39D), which leads to a decrease in the standard deviation with a coefficient of 23 over the entire data set. Note that the corrected measurement strongly resembles white noise, and this indicates that the dynamics of the venturi are largely understood.

FIGS. 38E and 39E show the resulting correction for a “drained” venturi. Noise decreased by a factor of 6.5 or so. Note, however, that there appears to be some residual structure in the noise.

The effects of the method are also illustrated at low (Fig. 38F and 39F), average (Fig. 38G and 39G) and high (Fig. 38H and 39H) flows, each with stepwise changes in flow every ten seconds. In each case, the pattern is the same: the adjusted average costs (Fig. 39F-39H) are identical to the unprocessed average costs (Fig. 38F-38H), but the dynamic noise is significantly reduced. On fig.39H, this leads to the manifestation of step changes, which were previously buried in noise (fig.38H).

3. Development of dynamic monitoring and compensation methods

The previous sections described various methods (physical modeling, system identification, hysteresis) used to monitor and compensate for various aspects of dynamic behavior (frequency and phase noise due to amplitude modulation, velocity effect, dynamics of the venturi at the sensor level and at the level of the venturi ) Through natural development, similar methods well known to practical specialists in control and / or equipment, including specialists in artificial intelligence, neural networks, fuzzy logic and genetic algorithms, as well as classical methods of modeling and identification, can be applied to these and other aspects of the dynamic performance of the meter. In particular, they may include monitoring and compensation of changes in frequency, amplitude and / or phase at the level of the sensors, as well as the average frequency and phase difference at the level of the venturi, since these changes occur in each measurement interval, as well as during between measurement intervals (when measurement intervals do not overlap).

This method is new in providing noise reduction and improved dynamic response for processing measurement changes. Therefore, the method is expected to be very valuable in relation to flow measurement.

I. Aeration (two-phase flow)

The digital flowmeter provides increased productivity with aeration (also known as two-phase flow) in the pipeline. Aeration leads to energy losses in the pipeline, which can have a significant negative effect on the measurements made by the mass flow meter, and can lead to blocking of the pipeline. Experiments have shown that a digital flowmeter has significantly improved performance when there is aeration relative to traditional, analogue flowmeters. This increase in productivity can be explained by the ability of the meter to provide a very wide range of gain, to use negative feedback, to accurately calculate measurements at very low amplitude levels and to compensate for dynamic effects, such as the rate of change of amplitude and dynamics of the venturi. The increase in performance can also be explained by the fact that the meter uses an algorithm for precise digital amplitude control.

A digital flowmeter detects the onset of aeration when the required pathogen gain increases simultaneously with a drop in the observed fluid density. The digital flow meter can then respond directly to detected aeration. In general, the meter tracks the presence of aeration by comparing the observed density of the material flowing through the pipeline (i.e., the density measurement obtained by normal measurement methods) with the known density of the material without aeration. The controller determines the aeration level based on any difference between the observed and actual densities. The controller then adjusts the mass flow measurement accordingly.

The controller determines the density of the material without aeration by monitoring the density over time periods during which there is no aeration (i.e., periods during which density has a stable value). Alternatively, the control system to which the controller is connected may provide density without aeration as an initialization parameter.

In one implementation, the controller uses three corrections to account for aeration effects: correction for the bubble effect, correction for the attenuation effect, and correction for the imbalance of the sensors. 40A-40H show the effects of the correction procedure.

On figa shows the error in the measurement of the phase with a decrease in the measured density (i.e., with increasing aeration) for different mass flow rates, in the absence of correction of aeration. It is shown that the phase error is negative, and its value increases with increasing aeration. FIG. 40B shows that the resulting mass flow rate error is also negative. It is also important to note that the digital flowmeter operates at high aeration levels. On the contrary, as indicated by the vertical line 4000, traditional analog meters have a tendency to block in the presence of low levels of aeration.

Blocking occurs when the flowmeter is unable to provide a substantially large gain of the pathogen to provide a large excitation current at low oscillation amplitudes. If the attenuation level requires a higher gain of the pathogen than the Venturi can provide to maintain oscillations with a certain amplitude, then insufficient excitation energy is supplied to the pipeline. This leads to a decrease in the amplitude of the oscillations, which, in turn, leads to the supply of even lower excitation energy due to the limitation on the maximum gain. As a result, a catastrophic collapse occurs, and the oscillation of the venturi is impossible until the attenuation drops to a level at which the flowmeter can give the corresponding requirement for the gain of the pathogen.

The correction for the bubble effect is based on the assumption that the mass flow rate decreases as the level of aeration, also called the void fraction, increases. Without trying to predict the actual relationship between the void fraction and the bubble effect, this correction suggests, with good theoretical justification, that the effect on the observed mass flow rate will be the same as the effect on the observed density. Since the true density of the fluid is known, the correction for the bubble effect corrects the mass flow rate in the same proportion. This correction is a linear adjustment that is the same for all expenses. 40C and 40D show, respectively, the residual phase and mass flow rate errors after correction for the bubble effect. It is shown that the residual errors are now positive and significantly smaller in magnitude than the initial errors.

The attenuation coefficient correction takes into account the attenuation of the pipe movement due to aeration. In general, the correction for the attenuation coefficient is based on the following relationship between the observed phase, φ _obs , and the actual phase, φ _true :

where λ is the attenuation coefficient and k is a constant. 40E shows attenuation correction for different mass flow rates and different aeration levels. 40F shows the residual phase error after attenuation correction. It is shown that the phase error is significantly reduced relative to the phase error remaining after correction for the bubble effect.

Sensor balance correction is based on differences in density between different ends of the pipeline. According to Fig. 41, the pressure difference between the inlet and the outlet of the pipeline leads to an increase in the size of the bubble from the inlet to the outlet. Since the material flows sequentially through two piping contours, the bubbles on the inlet side of the pipeline (i.e. the side adjacent to the first sensor / exciter pair) will be smaller than the bubbles on the outlet side of the pipeline (i.e. the side adjacent to the second sensor / exciter pair ) This difference in bubble size leads to a difference in mass and density between the two ends of the pipeline. This difference is reflected in the sensor signals (SV ₁ and SV ₂ ). Accordingly, the correction of the balance of the sensors is based on the ratio of the two sensor signals.

Fig. 40G shows the correction of the balance of the sensors for different mass flow rates and different levels of aeration. 40H shows a residual phase error after applying sensor balance correction. At low flow rates and low aeration levels, the phase error improves with respect to the phase error remaining after attenuation correction.

You can also use other correction factors. For example, you can track the phase angle of each sensor signal. In general, the average phase angle for a signal should be zero. However, the average phase angle tends to increase with increasing aeration. Accordingly, a correction factor can be generated based on the average phase angle value. Another correction factor may be based on the temperature of the pipeline. In general, due to the use of correction factors, mass flow rate errors are maintained at one percent or less. In addition, it is assumed that these correction factors are applicable over a wide range of flow rates and aeration levels.

J. Adjustment

The digital flowmeter provides improved tuning adjustment for the amplitude of fluctuations in the pipeline. In an analog meter, feedback control is used to maintain the amplitude of the pipeline fluctuations at a fixed level corresponding to the desired peak voltage of the sensor (for example, 0.3 V). A stable oscillation amplitude leads to a decrease in the frequency dispersion and phase measurements.

In general, a large oscillation amplitude is desired, since such a large amplitude provides a large Coriolis signal for measurement purposes. The large amplitude of the oscillations also leads to the conservation of a higher energy level in the pipeline, which provides increased resistance to external vibrations.

Circumstances may arise in which it is impossible to maintain a large amplitude of oscillations due to restrictions on the current supplied to the pathogens. For example, in one implementation of an analog transmitter, the current is limited to 100 mA for safety reasons. This is usually 5-10 times less than the current required to maintain the desired oscillation amplitude. However, if the working fluid provides significant additional attenuation (for example, by means of a two-phase flow), then the optimal amplitude may no longer be stable.

Similarly, a low-power flow meter, for example a two-wire meter, described below, may have significantly lower power to drive the pipeline. In addition, the power level may change when the pipeline is excited by the discharge of a capacitor.

42, the 4200 control procedure implemented by the digital flow meter controller can be used to select the highest stable setting at a given maximum allowable current level. In general, the procedure is carried out each time the desired output excitation current is selected, which usually occurs once per period or once per half period, if intermittent periods are used.

The controller starts by setting the default value (for example, 0.3 V), and initializing the filtered representations of the sensor voltage (filtered_SV) and field current (filtered_DC) (step 4205). Each time the procedure is performed, the controller updates the filtered values based on the current values of the sensor voltage (SV) and the excitation current (DC) (step 4210). For example, the controller may generate a new value for filtered_SV as the sum of ninety-nine percent of filtered_SV and one percent of SV.

The controller then determines whether the procedure is paused to allow time for the entry into force of previous tuning adjustments (step 4215). The suspension of the procedure is indicated by the suspension period counter, which has a value greater than zero. If the procedure is suspended, the controller takes no other actions during the period and decreases the counter of the suspension periods (step 4220).

If the procedure is not suspended, the controller determines whether the filtered field current exceeds a threshold level (block 4225). In one implementation, the threshold level is ninety-five percent of the maximum allowable current. If the current exceeds a threshold, the controller decreases the setting (step 4230). To give the meter time to stabilize after changing the setting, the controller then pauses the procedure by setting the pause period counter to the corresponding value (for example, 100) (step 4235).

If the procedure is not paused, the controller determines whether the filtered field current is less than the threshold level (step 4240), and whether the setting is less than the maximum allowed setting (step 4245). In one implementation, the threshold level is seventy percent of the maximum allowable current. If both conditions are met, the controller determines a possible new setting (step 4250). In one implementation, the controller defines the new setting as eighty percent of the maximum allowable current multiplied by the ratio of filtered_SV to filtered_DC. In order to avoid small changes (i.e., jitter) of the setting, the controller then determines whether the possible new setting exceeds the current setting by a sufficient amount (step 4255). In one implementation, a possible new setting should exceed the current setting by 0.02 V and ten percent.

If the possible new setting is large enough, the controller determines whether it exceeds the maximum allowed setting (step 4260). If so, the controller sets the setting to the maximum allowed setting (step 4265). Otherwise, the controller sets the setting equal to the possible new setting (step 4270). The controller then implements the suspension of the procedure by setting the counter of the suspension periods to the corresponding value (block 4235).

On figa-43C shows the implementation of the adjustment procedure settings. According to Fig. 43C, the system starts with a setting of 0.3 V. At about the eighth second of operation, aeration leads to a drop in the observed density of the material in the pipeline (Fig. 43A). The increased attenuation accompanying aeration leads to an increase in the excitation current (Fig. 43B) and an increase in noise in the voltage of the sensor (Fig. 43C). No changes occur at this time, as the meter is able to support the desired setting.

At about the fifteenth second of operation, aeration increases and the observed density is further reduced (Fig. 43A). At this aeration level, the exciter current (Fig. 43B) reaches a maximum value that is not enough to maintain a setting of 0.3 V. Accordingly, the sensor voltage drops to 0.26 V (Fig. 43C), a voltage level that allows you to maintain the maximum current pathogen. In this regard, the controller adjusts the setting (approximately 28 seconds of operation) to a level (0.23 V), which does not require the generation of the maximum exciter current.

At approximately 38 seconds of operation, the aeration level decreases and the observed density increases (Fig. 43A). This leads to a decrease in the field current (Fig. 43B). At 40 seconds of operation, the controller responds to this condition by increasing the setting (FIG. 43C). The aeration level decreases, and the observed density increases again by approximately 48 seconds of operation, and the controller responds by increasing the setting to 0.3 V.

K. Performance Results

The digital flowmeter has shown a marked increase in performance relative to traditional analog flowmeters. In one experiment, the ability of two types of meters to accurately measure a portion of a material was tested. In each case, a portion was passed through an appropriate flow meter into the tank, where the portion was weighed. For portions weighing 1,200 and 2,400 pounds, the analog meter provided an average displacement of 500 pounds, with a repeatability of 200 pounds. In contrast, the digital meter provided an average bias of 40 pounds, with repeatability of two pounds, which is obviously a significant improvement.

In each case, the piping and surrounding pipes were empty at the start of the serving. This is important in many batch applications where it is not practical to start a batch with full piping. Servings ended with a full venturi. Some positive bias is expected, as the flow meter measures the material that needs to be filled in the pipe before filling the weighing tank. Delays in start-up, or displacements due to flow aeration or low oscillation amplitudes, are likely to introduce negative biases. For real batch applications, the most important issue is measurement repeatability.

The results show that with an analog flowmeter there are large negative biases and a repeatability of only 200 pounds. This is explained by the presence of a period of time before start-up after the onset of the flow (during which the flow rate is not measured) and measurement errors until the full amplitude of the oscillations is reached. In contrast, the digital flowmeter achieves a positive bias due to the filling of an empty pipe, and repeatability of two pounds.

In another experiment, the overall measurement accuracy for two types of meters was compared. On Fig shows the accuracy and corresponding uncertainty of measurements made by two types of meters at different percentages of the maximum recommended flow meters. At high flow rates (i.e., flow rates of 25% or more of the maximum flow rate), the analog meter creates measurements that correspond to actual values within 0.15% or less, compared with 0.005% or less for a digital meter. At lower costs, the analog meter offset is on the order of 1.5%, compared with 0.25% for the digital meter.

L. Meter with automatic verification

A digital flowmeter can be used in a control system that includes sensors with automatic verification. For this, a digital flowmeter can be implemented as a meter with automatic verification. Meters and other sensors with automatic verification are described in US patent No. 5570300 under the name "SELF-VALIDATING SENSORS", which is incorporated by reference.

In general, a meter with automatic verification provides, based on all the information available to the meter, the best estimate of the value of the parameter being monitored (for example, mass flow). Since the best estimate is based in part on non-measuring data, the best estimate is not always consistent with the value indicated by the current, possibly failed, measurement. The meter with automatic verification also provides information on the unreliability and reliability of the best estimate, as well as information on the operational status of the sensor. Unreliability information is derived from a known unreliability analysis and is provided even in the absence of failures.

In general, a meter with automatic verification provides four main parameters: the verified measurement value (VMV), the verified uncertainty (VU), the indication (status MV) of the state in which the measurement was made, and the status of the device. VMV is the best meter rating for the measured parameter value. VU and MV status are associated with VMV. The meter creates separate VMV, VU and MV status for each measurement. Device status indicates the operational status of the meter.

The meter may also provide other information. For example, upon request from the control system, the meter can provide detailed diagnostic information about the status of the meter. In addition, when the measurement exceeds or is close to exceeding a predetermined limit, the meter can issue an alarm to the control system. Different alarm levels can be used to indicate the degree to which the measurement deviated from a predetermined value.

VMV and VU are numerical values. For example, VMV may be a temperature measurement evaluated at 200 ° C, and VU, the uncertainty of VMV may be 9 °. In this case, there is a high probability (usually 95%) that the actual measured temperature falls within the envelope of the VMV and is determined by the VU (i.e., from 191 to 209 ° C).

The controller generates a VMV based on the underlying data from the sensors. The controller first outputs the raw measurement value (RMV), which is based on the signals from the sensors. In general, when the controller does not detect anomalies, the controller has a nominal confidence of RMV and sets the VMV to RMV. When the controller detects an anomaly in the sensor, the controller does not set the VMV to RMV. Instead, the controller sets the VMV to a value that the controller considers to be a better estimate than the RMV of the actual parameter.

The controller generates a VU based on a raw unreliability signal (RU), which is the result of a dynamic RMV invalid analysis. The controller performs this uncertainty analysis during each sampling period. Unreliability analysis originally described in Describing Uncertainties in Single Sample Experiments, SJ Kline & FA McClintock, Mech. Eng. 75, 3-8 (1953), is widely used and has reached the status of an international calibration standard. In essence, an analysis of uncertainty provides an indication of the "quality" of a measurement. Each measurement is associated with an error, which, of course, is unknown. However, the reasonable limit of this error can often be expressed by a single number of unreliability (ANSI / ASME PTC 19.1-1985 Part 1, Unreliability of measurements: instruments and equipment).

As described by Kline & McClintock, for any observable measurement of M , the uncertainty of M , w _M can be determined as follows:

,

,

where M is true ( M _true ) at a certain level of confidence (usually 95%). This uncertainty is easily expressed in relative form as the proportion of the measurement (i.e., w _M / M ).

In general, VU has a non-zero value even under ideal conditions (i.e., sensor failure-free operation under controlled, laboratory conditions). The reason is that the measurement made by the sensor is never absolutely reliable, and there is always the possibility of error. As with VMV, when the controller does not detect anomalies, the controller sets the VU to RU. When the controller detects a failure that only partially affects the reliability of the RMV, the controller usually carries out a new uncertainty analysis that takes into account the effects of the failure and sets the VU equal to the results of this analysis. The controller sets the VU equal to the value based on previous performance when the controller determines that the RMV is not based on the actual measured value.

To ensure that the management system uses VMV and VU correctly, the MV status provides information on how they are calculated. The controller creates VMV and VU in all conditions - even when the sensors are idle. The management system needs to know whether VMVs and VUs are based on live or historical data. For example, if the control system uses VMV and VU in feedback control and the sensors are inactive, the control system should know that the VMV and VU are determined based on past performance.

MV status is based on the expected stability of any abnormal condition and on the controller's confidence in RMV. The four main states for the MV state are generated according to Table 1.

Table 1 Expected sustainability Confidence in RMV MV status not applicable nominal Clear not applicable reduced BLURRED short zero DAZZLED long zero BLIND

The MV CLEAR status occurs when the RMV is in the normal range for these process conditions. The MV DAZZLED status indicates that RMV is completely abnormal, but it is assumed that the anomaly has a short duration. Typically, the controller sets the MV status to DAZZLED when a sudden change in the signal from one of the sensors occurs, and the controller is not able to clearly determine whether this change is due to an undetected failure of the sensor or a sharp change in the measured variable. The MV BLURRED status indicates that RMV is abnormal, but reasonably related to the measured parameter. For example, the controller may set the MV status to BLURRED when the RMV is a noisy signal. The BLIND MV status indicates that RMV is completely unreliable, and that failure is supposedly robust.

Two additional states for MV status are UNVALIDATED and SECURE. The MV status is UNVALIDATED when the controller does not perform a VMV check. MV status is SECURE when VMV is generated from redundant measurements in which the controller has a nominal confidence.

The device status is a general, discrete value, expressing the health of the meter. It is used, first of all, by the procedures for detecting and eliminating failures in the control system. Typically, device state 32 is one of six states, each of which indicates a particular operational state of the meter. These states are: GOOD, TESTING, SUSPECT, IMPAIRED, BAD, or CRITICAL. GOOD device status means that the meter is in normal condition. The status of the TESTING device means that the meter is performing a self-test and that this self-test can be responsible for any temporary decrease in the quality of the measurement. The status of the SUSPECT device means that the meter returned an abnormal response, but the controller does not have a detailed failure diagnosis. IMPAIRED device status means that the meter has experienced a diagnosed failure, which has had a slight impact on performance. The status of the BAD device means that the meter is seriously damaged and needs repair. Finally, the state of the CRITICAL device means that the meter is damaged to such an extent that the meter can cause (or has already caused) a risk, for example, leakage, fire or explosion.

On Fig shows a procedure 4500, according to which the meter controller with automatic verification processes the digitized sensor signals to generate excitation signals and a verified measurement of mass flow together with the uncertainty and measurement status. Initially, the controller collects data from the sensors (step 4505). Using this data, the controller determines the frequency of the sensor signals (step 4510). If the frequency falls within the expected range (step 4515), the controller eliminates the zero offset from the sensor signals (step 4520) and determines the amplitude (step 4525) and phase (step 4530) of the sensor signals. The controller uses these calculated values to generate an excitation signal (step 4535) and to generate an unprocessed mass flow measurement and other measurements (step 4540).

If the frequency does not fall within the expected range (step 4515), then the controller implements a blocking procedure (step 4545) to determine if the pipeline has stalled and to respond accordingly. In the blocking procedure, the controller maximizes the gain of the pathogen and performs an advanced search for zero crossings to determine if the pipeline is oscillating at all.

If the pipeline does not oscillate correctly (i.e., if it does not oscillate or oscillates at an unacceptably high frequency (for example, at the highest harmonic of the resonant frequency)) (step 4550), the controller attempts to restore normal vibrational motion (step 4555) of the pipeline, for example, giving a square wave to the pathogens. Trying to restore the oscillatory motion, the controller sets the MV status to DAZZLED (step 4560) and generates empty raw measurement values (step 4565). If the pipeline oscillates correctly (step 4550), the controller eliminates the zero offset (step 4520) and proceeds to the above steps.

After generating the raw measurement values (steps 4540 or 4565), the controller performs diagnostics (step 4570) to determine if the meter is working correctly (step 4575). (Note that the controller is not required to perform this diagnostics during each period.)

The controller then performs an unreliability analysis (block 4580) to generate an unprocessed unreliability value. Using raw measurements, diagnostic results, and other information, the controller generates VMV, VU, MV status, and device status (step 4585). The controller then collects a new data set and repeats the procedure. The steps of procedure 4500 can be performed sequentially or in parallel and can be performed in a changing order.

In another example, when aeration is detected, mass flow rate corrections are applied as described above, the MV status is set to BLURRED, and the uncertainty increases to reflect the likely error of the correction method. For example, for a Venturi tube operating at 50% flow rate under normal operating conditions, the uncertainty should be about 0.1 - 0.2% of the flow rate. If aeration occurs and is corrected using the methods described above, the uncertainty should increase, possibly up to 2% of the reading. Uncertainty values should decrease with a better understanding of the effects of aeration and an increased ability to compensate for aeration. In portioned cases, when the flow uncertainty is variable (e.g., high at the beginning / end when dosing from / to the empty state, or during temporary aeration or cavitation incidents), the uncertainty of the full portion will reflect the weighted importance of periods of high uncertainty relative to the remaining portion with a nominal low inaccuracy. This is a very useful quality metric in fiscal and other measurement applications.

M. Two-wire flowmeter

According to Fig. 46, the above methods can be used to implement a "two-wire" Coriolis flowmeter 4600, which provides two-way communication over a pair of wires 4605. The power supply circuit 4610 receives power for the operation of the digital controller 4615 and for supplying the exciter (s) 4620, creating vibration of the pipeline 4625 For example, a power circuit may include a constant output circuit 4630 that provides operating power to a controller and an excitation capacitor 4635 that is charged using excess power. The power circuit may receive power over wires 4605 or over a second pair of wires. A digital controller receives signals from one or more 4640 sensors.

When the drive capacitor is sufficiently charged, the controller 4615 discharges the capacitor 4635 to drive the pipe 4625. For example, the controller can drive the pipe every 10 periods. Controller 4615 receives and analyzes signals from sensors 4640 to create a mass flow measurement, which the controller then passes through wires 4605.

N. Empty Dosing

The digital mass flow meter 100 provides increased productivity when operating in a challenging environment called dosing from an empty state. There are many methods, in particular in the food and petrochemical industries, where the high accuracy and direct mass flow measurement provided by Coriolis technology has the advantage of measuring portions of the material. However, in many cases, ensuring that the flowmeter remains filled with fluid from the beginning to the end of the portion is impractical and highly inefficient. For example, when filling and emptying a tanker, it is difficult to avoid air entrainment. When processing food, hygiene rules may require cleaning pipes between batches.

In traditional Coriolis meters, dosing from an empty state can lead to large errors. For example, water hammer and high gain may be due to flow in an empty venturi, which leads to large measurement errors and blockage.

The digital mass flow meter 100 is resistant to dosing conditions from an empty state. In particular, the amplitude controller has a fast response; high gain range prevents blocking of venturi; measurement data can be calculated up to 0.1% of the normal amplitude of oscillations; and there is a correction for the rate of change of amplitude.

These characteristics are shown in FIGS. 47A-47C, where the response of a digital mass flow meter 100 is shown to excite a wet and empty 25 mm venturi during the first seconds of full flow. According to FIG. 47A, the excitation gain necessary to excite a wet and empty tube before flow (in about 4.0 seconds) has a value of about 0.1, which is higher than a value of about 0.034 required for a full venturi. The onset of flow is characterized by a significant increase in gain and a corresponding decrease in the amplitude of oscillations. According to FIG. 47B, about 1.0 second after initiation, selecting a reduced setting helps to stabilize the amplitude when the full flow mode is established. After approximately 2.75 seconds, the last remaining entrained air is removed, the traditional setting is restored, and the excitation gain assumes a nominal value of 0.034. The behavior of the untreated and adjusted phase difference is shown in FIG. 47C.

According figa-47C, these phases are continuously set during the transition. In such circumstances, the analog control system is blocked and is not able to provide measurement data until the required field amplification coefficient returns to a value close to the nominal value and a long start-up procedure is completed. It is also shown that the correction for the rate of change of amplitude clearly demonstrates an advantage, especially after 1.0 second. Oscillations in amplitude lead to significant deviations in phase calculations in the frequency and time dimensions, but they decrease significantly in the corrected phase measurement. Even in the most difficult part of the transition, from 0.4 to 1.0 seconds, the correction provides some noise reduction.

Of course, erroneous data still exists in this interval. For example, a stream generating a phase difference in excess of about 5 ° is physically impossible. However, from the point of view of a sensor with automatic verification, for example, discussed above, this phase measurement still constitutes raw data that can be corrected. In some implementations, a higher-level verification process can identify data from the interval 0.4-1.0 seconds as not representing the true value of the process (based on gain, amplitude, and other internal parameters) and can generate DAZZLED mass flow to suppress extreme values measurements.

According figa, the response of the digital mass flow meter 100 to the onset of flow leads to increased accuracy and repeatability. 48B shows an illustrative hydrodynamic installation 4800. Upon receipt of the results shown in FIG. 48A, as well as upon receipt of the results shown in FIG. 44, fluid was pumped through a magnetic flowmeter 4810 and Coriolis flowmeter 4820 into a weighing tank 4830, wherein Coriolis flowmeter is a digital flowmeter or a traditional analog flowmeter. Valves 4840 and 4860 were used to ensure that the 4810 magnetic flowmeter is always full, while the 4820 Coriolis flowmeter tube is empty at the start of each batch. At the start of the batch, the adders in the magnetic flowmeter 4810 and in the Coriolis flowmeter 4820 were reset and the flow started. At the end of the batch, the 4850 shutoff valve was closed and the amounts were frozen (therefore, the 4820 Coriolis flowmeter was full at the end of the batch). Three amounts were recorded, one from the 4810 magnetic flowmeter, one from the 4820 Coriolis flowmeter, and one from the weights associated with the 4830 weighing tank. These sums are not assumed to be consistent since there is a finite time delay to the 4820 Coriolis flowmeter, and then finally a weighing tank 4830 observes the flow of fluid. Thus, it can be expected that the magnetic flowmeter 4810 will record the highest total flow rate, the Coriolis flowmeter 4820 will register the second after the highest total flow rate, and the weighing tank 4830 will record the lowest total flow rate.

On figa shows the results obtained from a series of test runs using the hydrodynamic installation 4800, shown in figv, and with each test run through the hydrodynamic installation passes about 550 kg of material. The tracking value shown is the offset observed between the balance and the 4810 magnetic flowmeter or 4820 Coriolis flowmeter. As explained above, it is assumed that both instruments are receiving positive offsets. The 4810 magnetic flowmeter (always full) produces a consistent positive bias, with a repeatability (defined here as the maximum difference in recorded values for identical experiments) of 4.0 kg. The analog control system associated with the 4810 magnetic flowmeter generates large negative offsets, with an average value of -164.2 kg and a repeatability of 87.7 kg. This low performance is due to the inability of the analog control system to work with the onset of flow and the varying time required to restart the venturi. In contrast, the 4820 Digital Coriolis mass flowmeter shows an average positive offset of 25.6 kg and a repeatability of 0.6 kg.

It would be difficult to estimate the true mass flow through the venturi, provided that it is initially empty. As expected, the recorded total mass is between the mass determined by the magnetic flowmeter 4810, and the mass determined using the scales. In industrial applications, the issue of repeatability is often more important as portion recipes are often adjusted according to bias. Of course, the repeatability of the filling process is at the lower limit of the repeatability of the total mass determined by the Coriolis flowmeter. Similar repeatability can be achieved in an arbitrary industrial batch production process. In addition, as shown, the digital mass flow meter 100 provides a significant increase in performance over its analogue equivalent (magnetic flowmeter 4810) under the same conditions. Again, it can be concluded that the digital mass flow meter 100 under these conditions is not a significant source of measurement error.

O. Two-phase flow

As discussed above with reference to FIG. 40A, a two-phase flow caused by aeration is another flow condition that creates difficulties for analog control systems and analog mass flowmeters. A two-phase flow can be sporadic or continuous and occurs when the material in the flowmeter includes a gas component and a liquid component moving through a venturi. The basic mechanisms are very similar to the case of dosing from an empty state in that the dynamics of a two-phase gas-liquid flow causes high attenuation. To maintain oscillation, a high excitation gain is required. However, the maximum excitation gain of the analog control system is usually achieved at low levels of the gas fraction in the two-phase material, as a result of which the venturi is blocked.

The digital mass flow meter 100 is capable of supporting fluctuations in the presence of a two-phase flow. As a result, in none of the laboratory experiments carried out so far, it was possible to block a tube of any size at any gas phase level under the control of a digital controller 105. On the contrary, a typical analog control system is blocked when the gas phase fraction is about 2%.

Maintaining oscillation is only the first step in obtaining a satisfactory measurement performance from the flowmeter. As was briefly discussed above, a simple model called the “bubble” model was constructed as one method for predicting mass flow rate errors.

In a “bubble” or “effective mass” model, a sphere or bubble of a low-density gas is surrounded by a higher-density fluid. If both are subject to acceleration (for example, in a vibrating tube), then the bubble moves in a fluid, leading to a decrease in the observed inertia of the system as a whole. Defining the void fraction α as the volume fraction of gas, we find that the effective mass decreases with coefficient R , where

For a Coriolis flowmeter, the model predicts that the observed mass flow rate will be less than the true mass flow rate with coefficient R , as, in the more general case, the observed density. 49 shows the observed mass flow rate errors for a series of runs at different flow rates, all using a 25 mm horizontal alignment venturi, and for a mixture of water and air at ambient temperature. The x-axis represents the observed decrease in density, not the void fraction. In laboratory conditions, the void fraction can be calculated, for example, by measuring the pressure and flow rate of the gas before it is mixed with the fluid, together with the pressure of the two-phase mixture. However, under factory conditions, only the observed decrease in density is available, and the true void fraction is not available. Note that with an analog flowmeter, air-water mixtures with a density drop of more than 5% cause the Venturi to be silenced, which does not allow data collection.

The dashed line 4910 shows the relationship between the mass flow rate error and the density drop predicted by the bubble model. The experimental data follow a similar set of curves, although the model almost always predicts a more negative mass flow rate error. As discussed above with reference to FIG. 40A, empirical mass flow rate corrections can be derived based on the observed density, as well as some other internally observable variables, such as excitation gain and sensor voltage ratios. It is reasonable to assume that the density of the pure fluid is known or deducible. For example, in many applications, the density of the fluid is relatively constant (especially if the temperature coefficient is embedded in the controller software).

On Fig shows the corrected measurements of mass flow. Correction is based on the least squares approximation of several internal variables, as well as the bubble model itself. The correction process is limited only by applicability and is less suitable for lower costs (the largest errors are observed for 1.5-1.6 kg / s). With a horizontal orientation, the gas and liquid phases begin to separate at reduced flow rates, and significantly higher mass flow rate errors are observed. In these circumstances, the assumptions of the bubble model are no longer true. However, the correction is valid for higher costs. During operational experimental tests, a similar correction algorithm was limited to mass flow rate errors within about 2.5% of the mass flow rate reading.

On Fig shows how a digital mass flow meter 100 with automatic verification responds to the onset of a two-phase flow when measuring mass flow. The lower vibrational signal 5110 shows an uncorrected measurement of the mass flow rate in the two-phase flow state, and the upper vibrational signal 5120 shows the corrected measurement of the mass flow rate and the margin of uncertainty in the same state of the two-phase flow. With a single-phase flow (up to t = 7 s), the mass flow measurement is in the CLEAR state and has a low uncertainty of about 0.2% of the mass flow reading. When a two-phase flow occurs, a number of processes are activated. First, a two-phase flow is detected based on the behavior of the internal observable parameters. Secondly, the measurement correction method is applied, and the output state of the measurement together with the corrected measurement is set to BLURRED. Thirdly, the unreliability of the mass flow rate increases with the level of the void fraction to a maximum of about 2.3% of the mass flow rate indication. For comparison, an uncorrected mass flow measurement 5110 is shown immediately below the adjusted mass flow measurement 5120. Thus, the user can continue to work with reduced quality of the adjusted mass flow, switching to an alternative measurement, if available, or stopping the process.

P. Application of neural networks

Another method for improving the accuracy of measuring mass flow in a two-phase flow environment involves using a neural network to predict mass flow error and to generate an error correction coefficient to correct any error in mass flow measurement due to the effects of two-phase flow. The correction coefficient is generated using the internal observable parameters supplied to the digital signal processor and neural network, and demonstrates the preservation of errors within 2%. Internal observable parameters may include temperature, pressure, gain, density drop, and observed flow rate.

52 shows a digital controller 5200 that can be used in place of the digital controller 105 or 505 of the digital mass flow meters 100, 500 shown in FIGS. 1 and 5. In this implementation of the digital controller 5200, process sensors 5204 connected to the venturi generate process signals including one or more sensor signals, a temperature signal and one or more pressure signals (as described above). The analog process signals are converted to digital data of the A / D signals by converters 5206 and stored in the memory buffers 5208 of the sensor and exciter signal data for use by the 5200 digital controller. The exciters 5245 connected to the venturi generate an excitation current signal and can transmit this signal to A / D converters 5206. Then, the excitation current signal is converted into digital data and stored in the data buffers 5208 of the sensor and exciter signals. Alternatively, the digital field amplification signal and the digital field current signal may be generated by the amplitude adjustment module 5235 and transmitted to the memory buffers 5208 of the sensor and driver signals for storage and use by the 5200 digital controller.

The digital data of the signals of the sensors and pathogens of the process are additionally analyzed and processed by the module 5210 for processing parameters of the sensors and pathogens, which generates physical parameters including the frequency, phase, current, attenuation and amplitude of the oscillations. The raw mass flow measurement module 5212 generates a raw mass flow measurement signal using the methods discussed above with respect to the flow meter 500.

The state machine 5215 flow conditions takes as input signals the physical parameters from the module 5210 processing parameters of the sensors and pathogens, the raw signal of the measurement of mass flow and density measurement 5214, which is calculated as described above. Then, the state machine 5215 flow states detects the state of the flow of material passing through the digital mass flow meter 100. In particular, the state machine 5215 flow states determines whether the material is in a single-phase flow state or in a two-phase flow state. The state machine state of the flow 5215 also enters the raw signal of the measurement of mass flow in block 5230 output measurement of mass flow.

When a single-phase flow condition is detected, the output unit 5230 checks the raw mass flow measurement signal and can perform an unreliability analysis to generate an unreliability parameter associated with the verified mass flow measurement. In particular, when the state machine 5215 detects the presence of a single-phase flow state, the correction coefficient does not apply to the raw mass flow measurement, and the output unit 5230 checks the mass flow measurement. If the 5200 controller does not detect errors during the measurement, the output unit 5230 can assign a traditional uncertainty parameter associated with the fail-safe measurement to the measurement and can set the status flag associated with the measurement to CLEAR. If the 5200 controller detects errors during the measurement, the output unit 5230 can change the uncertainty parameter to give it a higher uncertainty value, and can set the status flag to a different value, such as BLURRED.

When the flow state machine 5215 detects the presence of a two-phase flow state, the two-phase flow error correction module 5220 receives the raw mass flow measurement signal. Two-phase flow error correction module 5220 includes a neural network processor for predicting mass flow rate errors and for calculating error correction coefficient. A neural network processor can be implemented in a software procedure or, alternatively, can be implemented as a separate programmable hardware processor. The operation of the neural network processor is described in more detail below.

A neural network coefficient and training module 5225 stores a predetermined set of neural network coefficients that are used by the neural network processor. Module 5225 coefficients and training the neural network can also carry out the function of online learning using training data, which allows you to calculate an updated set of coefficients for use by the neural network. Although a predetermined set of neural network coefficients is generated during extensive laboratory tests and experiments based on known two-phase mass flow rates, the on-line learning function provided by module 5225 can be used at the initial stage of commissioning the flowmeter or each time the flowmeter is initialized.

The error correction coefficient generated by the error correction unit 5220 is supplied to the mass flow measurement output unit 5230. Using the raw mass flow measurement and the error correction coefficient (if received from the error correction module 5220, it indicates a two-phase flow), the mass flow measurement output unit 5230 applies the error correction coefficient to the raw mass flow measurement to generate a corrected mass flow measurement. Then, the mass flow measurement output unit 5230 verifies the corrected mass flow measurement and can perform an unreliability analysis to generate an unreliability parameter associated with the verified mass flow measurement. Thus, the mass flow measurement output unit 5230 generates a verified mass flow measurement signal, which may include the inaccuracy and condition associated with each verified mass flow measurement and the state of the device.

The sensor parameter processing module 5210 also introduces a damping parameter and an oscillation amplitude parameter (described above) into the amplitude adjustment module 5235. The amplitude adjustment module 5235 further processes the attenuation parameter and the oscillation amplitude parameter and generates digital excitation signals. Digital excitation signals are converted to analog excitation signals by D / A converters 5240 to operate with exciters 5245 connected to the venturi of the digital flowmeter. In an alternative implementation, the amplitude control module 5235 may process the attenuation parameter and the oscillation amplitude parameter and generate analog excitation signals for directly operating the exciters 5245.

On Fig shows the procedure 5250, carried out by the digital controller 5200. After the start of processing (step 5251), the measurement signals generated by the process sensors 5204 and pathogens 5245 are quantified during the analog-to-digital conversion (as described above), and memory buffers 5208 filled with digital data from sensors and pathogens (step 5252). For each new processing cycle, the sensor and pathogen parameter processing module 5210 retrieves the sensor and pathogen data from buffers 5208 and calculates the sensor and pathogen variables from the sensor data (block 5254). In particular, the sensor and pathogen parameter processing module 5210 calculates sensor voltages, sensor frequencies, field current, and field gain.

The sensor and pathogen parameter processing module 5210 performs a diagnose_flow_condition processing procedure (block 5256) to calculate statistical values including an average value, standard deviation, and slope for each of the sensor and pathogen variables. Based on statistics computed for each of the variable sensors and pathogens, the state machine 5215 of the flow states detects transitions between any three suitable flow states: FLOW_CONDITION_SHOCK, FLOW_CONDITION_HOMOGENEOUS and FLOW_CONDITION_MIXED.

If the status FLOW_CONDITION_SHOCK is detected (step 5258), the mass flow measurement analysis process is not performed due to the irregularity of the sensor input signals. Upon exiting this state, the processing procedure begins a new cycle (step 5251). Then, the processing procedure searches for a new sinusoidal signal to track in the sensor signals data and resumes processing. In order of this tracking process, the processing procedure must find the beginning and end of the sine wave using the above zero crossing method. If the status FLOW_CONDITION_SHOCK is not detected, the processing procedure calculates the raw measurement of the mass flow rate of the material flowing through the flow meter 100 (step 5260).

If a two-phase flow is not detected (i.e., the status FLOW_CONDITION_HOMOGENOUS is detected) (step 5270), the material flowing through the flow meter 100 is considered to be a single-phase material. In this case, the verified mass flow rate is generated from the raw mass flow measurement (block 5272) by the mass flow measurement output unit 5230. At this point, the verified mass flow rate together with its unreliability parameter and status flag can be transferred to another process controller. Then begins a new processing cycle (step 5251).

If a two-phase flow is detected (i.e., the FLOW_CONDITION_MIXED state is detected) (step 5270), the material flowing through the flow meter 100 is considered a two-phase material. In this case, the two-phase flow error correction module 5220 predicts the mass flow rate error and generates an error correction coefficient using the neural network processor (block 5274). The corrected mass flow rate is generated by the mass flow measurement output unit 5230 using the error correction coefficient (block 5276). Then, the verified mass flow rate can be generated from the adjusted mass flow rate. At this point, the verified mass flow rate together with its unreliability parameter and status flag can be transferred to another process controller. Then begins a new processing cycle (step 5251).

52, a neural network processor forming part of a two-phase flow error correction module 5220 is a direct-coupled neural network that provides a non-parametric infrastructure for representing a non-linear functional mapping between input and output spaces. A neural network is used to predict mass flow errors in two-phase flow states in a digital mass flow meter. When the error is predicted by the neural network, the error correction coefficient is applied to the two-phase mass flow measurement for error correction. Thus, the system allows you to quickly predict errors through the neural network using only the internal observable parameters derived from the sensor signal, sensor variables, and sensor statistics.

Of the various neural network models available, networks based on a multilevel perceptron (MLP) and radial basis functions (RBF) were used to implement a digital flowmeter. MLP with one hidden level (each block has a sigmoidal activation function) can equally well approximate any continuous display. Therefore, this type of neural network is suitable for modeling a nonlinear relationship between the error of the mass flow rate of a flow meter in a two-phase flow and some internal parameters of the flow meter.

The network weights needed to implement the desired display are determined during training or optimization. During supervised training, the neural network is repeatedly represented by the training sequence (a set of input examples x _i and the corresponding desired outputs d _i ), and the weights are updated so as to minimize the error function. For the interpolation problem associated with this method, a suitable error function is the error of the sum of squares, which, for MLP with one output, can be represented as:

,

,

where d _i is the target corresponding to the input x _i ; y _i is the actual response of the neural network to x _i and P is the number of examples in the training sequence.

The alternative neural network architecture that was used is the RBF network. RBF methods are based on methods for performing precise interpolations of multiple data points in multidimensional space. The RBF network, in general, has a simple architecture of two levels of weighting coefficients, in which the first level contains the parameters of the basis functions, and the second level forms linear combinations of activation of the basis functions for generating outputs. This is achieved by presenting the network output as a linear superposition of basic functions, one for each data point in the training sequence. In this form, training is faster than for the MLP network.

The internal sensor parameters of interest include observed density, attenuation, observed flow rate, and temperature. Each of these options is discussed below.

1. Observed density

The most common two-phase flow metric is the void (or gas) fraction, defined as the volume fraction of gas. The equation

models the mass flow rate error for a given void fraction. For a Coriolis mass flowmeter, the recorded density of the working fluid provides an indirect measure of the void fraction, based on the fact that the "true" density of the fluid is known. This recorded process density is subject to errors similar to errors in mass flow measurement in the presence of a two-phase flow. These errors have high repeatability, and the density drop is a fairly monotonous, but non-linear indicator of the void fraction, which can be quickly monitored in the flow meter. Note that outside the laboratory conditions, the true void fraction cannot be independently evaluated; on the contrary, it must be modeled as described above.

Information about the "true" density of a single-phase liquid (possibly including a temperature coefficient) can be obtained promptly or it can be set by the user. Both approaches were implemented and showed good results.

For the purposes of these descriptions, the density drop will be used as a parameter of the x axis in graphs showing the behavior of a two-phase flow. Note that in the 3D graphs shown in Figs. 54 and 56-57, which reflect the results of 134 operational experiments, the full range of density decay points is not possible at high flow rates due to restrictions on air pressure in the hydrodynamic installation. In addition, the effects of temperature, although not shown in the graphs, were determined experimentally.

2. Attenuation

Most Coriolis flowmeters use positive feedback to maintain the vibrations of the venturi. The sensor signals provide the frequency and phase of the oscillation of the venturi, which are multiplied by the excitation gain K ₀ to provide currents to the exciters 5245:

Typically, the excitation gain is modified to ensure a constant oscillation amplitude, and it is approximately proportional to the attenuation coefficient of the venturi.

One of the most characteristic features of a two-phase flow is the rapid increase in attenuation. For example, a normally working 25 mm venturi has V _A = 0.3 V, I _D = 10 mA and, therefore, K ₀ = 0.033. With a two-phase flow, the values can reach extreme values V _A = 0.03 V, I _D = 100 mA and K ₀ = 3.3, with a hundredfold increase. On Fig shows how the attenuation changes in a two-phase flow.

3. Observed flow rate and temperature

According to FIG. 49, the mass flow rate error varies with the true flow rate. A change in temperature is also observed. However, the true mass flow rate is not available in the transmitter itself (or the digital controller) when the flowmeter is used in a two-phase flow. However, the observed (erroneous) flow rate, as well as temperature, can be used as input parameters of the neural network processor.

Q. Network training and operational correction of mass flow errors

The implementation of neural network analysis for predicting mass flow measurement errors includes training the neural network processor to recognize the mass flow error pattern in the training experimental data, testing the performance of the neural network processor on a new set of experimental data, and the operational implementation of the neural network processor to predict and correct measurement errors .

The quality of prediction of a neural network processor depends on the richness of training data. To collect neural network data, a series of experiments were conducted on a two-phase air-water mixture using the experimental hydrodynamic unit 5500, shown in Fig. 55. The flow circuit includes a main meter 5510, a SEVA® 100 Coriolis meter with automatic verification, and a 5520 coupler for transferring material from the venturi to the 5530. The Coriolis meter 100 has a summing function that can be triggered by external signals. The control of the hydrodynamic installation is such that the 5520 stream coupler (feed stream to the balance) and Coriolis summation are started by the main meter 5510 at the beginning of the experiment, and, again, after the main meter 5510 registers 100 kg of flow. The total reading of the balance is used as a reference point for calculating the mass flow rate error by comparing with the totalized flow from the digital flowmeter 100 when the main meter 5510 acts as an additional check. The unreliability of the experimental setup is estimated at approximately 0.1% of typical portion sizes of 100 kg. For single-phase experiments, the digital flow meter 100 delivers a total mass flow rate within 0.2% of the total weight reading. For experiments with a two-phase flow, air is injected into the flow after the main meter 5510 and to the Coriolis flow meter 100. At low flow rates, density drops of up to 30% are achieved. At higher costs, at least 15% density drops are achieved.

At the end of each batch, Coriolis flow meter 100 provides an average batch for each of the following parameters: temperature, attenuation, density, flow rate, and total (uncorrected) flow. These parameters are thus available for use as input to a neural network processor.

The output or target of a neural network is a mass flow rate error as a percentage:

56 shows how the mass flow rate error varies with flow rate and density decline. Although the general trend is consistent with the bubble model, there are additional features of interest. For example, at high flow rates and low density drops, the mass flow error becomes slightly positive (about 1%), while the bubble model predicts only a negative error. From Fig. 56 it follows that in this region of the experimental space and for this design of the Venturi, some other physical process takes place to overcome the effects of the missing mass of the two-phase flow.

The best results were obtained using only four input parameters of the neural network: temperature, attenuation, density decline and observed flow rate. Perhaps less satisfactory is the result that the best approximation was achieved using the neural network itself, and not the correction of the bubble model or simplified approximation of the curve.

As part of the implementation, the MLP neural network was used for operational implementation. Comparisons between RBF and MLP networks with the same datasets and inputs showed, on the whole, similar performance on the test set. Thus, it is reasonable to assume that an input set providing the best RBF design will also provide a good (if not better) MLP design. MLP neural networks were trained using a scaled conjugate gradient algorithm. The capabilities of the Neural Network Toolbox of the MATLAB® software package were used to train a neural network. After exploring additional design options, the highest performance is provided by the MLP 4-9-1 network, which has inputs, such as temperature, attenuation, density drop and flow rate, together with a mass flow rate error as an output.

According to the test set, the best neural network provided predictions of mass flow within 2% of the true value. Procedures for detecting and correcting a two-phase flow were encoded and incorporated into a digital Coriolis transmitter. On Fig shows the residual error of mass flow during operational correction for 134 new experiments. All errors are limited to 2%, and most of them are much smaller. The random spread is mainly due to the residual error in the algorithm for correcting the neural network (as indicated above, the uncertainty of the hydrodynamic setup is 0.1%). Any obvious trend in the data involves the amount of additional correction. These errors, of course, refer to the average corrected mass flow rate (i.e., per serving).

On Fig shows how the operational detection and correction of a two-phase flow is reflected in the interface with the automatic verification generated to measure the mass flow. In the graph, the bottom, continuous line 5810 represents the raw mass flow rate. Top line 5820 represents a measurement surrounded by a band of uncertainty and represents a corrected or verified mass flow rate. The dotted line 5830 represents the mass flow rate from the main meter, which is located to the point of air injection (Fig. 55).

For a single-phase flow (up to t = 5 s), the mass flow measurement has a CLEAR measurement value state and a small uncertainty of about 0.2% of the reading. When a two-phase flow is detected, neural network correction is applied every interleaved period (i.e., with a frequency of 180 Hz), based on the values of internal parameters averaged (using a moving window) over the last second. If there is a two-phase flow, the state of the measurement value is set to BLURRED, and the uncertainty increases to reflect a decrease in the accuracy of the corrected measurement. An uncorrected measurement (lower thick line) shows a large bias error of about 30%.

The reading of the main meter is consistent in a first approximation with the corrected measurement of mass flow. The observed delay in its response to the onset of a two-phase flow is due to communication delays in the control system of the installation, and its response, resembling a square wave, is due to the frequency of updating the control system only once per second. Raw and corrected measurements from a digital transmitter show a higher degree of change than with a single-phase flow. The reading of the main meter provides a useful measure of the aqueous phase entering the two-phase zone, and there is a clear similarity between the reading of the main meter and the 'average' corrected reading. However, the cork mode and air compressibility in the complex three-dimensional geometry of the Venturi can not only lead to changes in flow, but the instantaneous mass flow into the system differs from the mass flow from the system.

Using a sensor processing approach with automatic verification, the measurement is not just marked by the sensor as good or bad. Instead, if a failure occurs, correction is applied whenever possible, and the quality of the resulting measurement is indicated by the BLURRED state and the increased uncertainty. Thus, the user evaluates the requirements and application-specific options to decide whether to continue working with reduced quality of the adjusted mass flow rate, whether to switch to an alternative measurement, if available, or to stop the process. If a two-phase flow is present only during a portion of a skipped portion (for example, at the beginning or end), there will be proportional weighting depending on the uncertainty of the total mass of the portion.

Multiphase flows

59 illustrates an exemplary process 5900 used to determine the phase-dependent property of a phase included in a multiphase working fluid. For example, method 5900 can be used to determine the mass flow rate and density of each phase of a multiphase working fluid.

As described below, the observed intermediate value is determined based, for example, on the mass flow rate and multiphase working fluid density (also referred to as total mass flow rate and total density, respectively), as determined, for example, by a Coriolis meter. Although the Coriolis meter continues to operate in the presence of a multiphase working fluid, the presence of a multiphase fluid affects the movement of the venturi (or pipe) that is part of the Coriolis meter. Thus, the output signals detected by the meter may be inaccurate, because the meter operates on the assumption that the working fluid includes one phase. These output signals may be called observable properties or raw properties of a multiphase fluid. Thus, in one implementation, the observed intermediate value is determined based on the observed or untreated properties of the multiphase fluid. Other implementations may determine an intermediate value based on the adjusted form of the observed property (s). To correct inaccuracies, the observed intermediate value is introduced, for example, into the neural network to create a corrected intermediate value that takes into account the effects of using a multiphase working fluid. The adjusted intermediate value is used to determine the mass flow rate and density of each phase of the multiphase working fluid. The use of an intermediate value instead of the observed mass flow rate and density of the multiphase working fluid can improve the accuracy of determining the mass flow and density of each phase of the multiphase working fluid.

A multiphase working fluid is passed through a venturi (5905). A movement is generated in the venturi (5910). The venturi vibration tube may, for example, be a conduit 120, discussed above with respect to FIG. 1. A multiphase working fluid may also be called a multiphase flow. A multiphase fluid may be a biphasic fluid, a three-phase fluid, or a fluid that includes more than three phases. In general, each phase of a multiphase fluid can be considered as a component or component of a multiphase fluid. For example, a two-phase fluid may include a non-gas phase and a gas phase. The non-gas phase may be a liquid, for example, oil, and the gas phase may be a gas, for example, air. A three-phase fluid may include two non-gas phases and one gas phase or one non-gas phase and two gas phases. For example, a three-phase fluid may include a gas and two liquids, for example, water and oil. In another example, a three-phase fluid may include gas, liquid, and a solid (e.g., sand). Additionally, the multiphase fluid may be a wet gas. Although the wet gas may be any of the multiphase fluids described above, the wet gas generally consists of more than 95% of the gas phase by volume. Method 5900 can be applied to any multiphase fluid.

The first property of a multiphase fluid can be determined based on the movement of a vibrating venturi (5915). The first property of a multiphase fluid may be the observed mass flow rate and / or the observed density of the fluid flowing through the venturi. Thus, in the illustrative method 5900, the first property may be mass flow rate or multiphase fluid density. Properties determined from a multiphase fluid may be called observable, or untreated, properties in contrast to the true (or at least adjusted) properties of the multiphase fluid. The observed mass flow rate and density of the multiphase fluid are generally not consistent with the mass flow rate and density of each of the individual phases of the multiphase fluid due to the effect of the multiphase fluid on the movement of the venturi. For example, if a multiphase fluid has a relatively low gas volume fraction (for example, a multiphase fluid includes more liquid than gas), the observed density and the observed mass flow rate of the multiphase fluid obtained from the venturi tend to be lower than the actual density and mass flow rate of the non-gas phase. Although the first property is, in the general case, an observable property, in some implementations, the first property can be an adjusted or actual property. The adjusted or actual property can be obtained, for example, from a model or display.

As discussed in accordance with FIG. 1, the mass flow rate is related to the movement excited in the venturi. In particular, the mass flow rate is associated with the phase and frequency behavior of the movement of the venturi and the temperature of the venturi. Additionally, the density of the fluid is related to the speed and temperature of the venturi. Thus, since the fluid flowing through the venturi includes more than one phase, the venturi provides mass flow and density of the multiphase fluid, rather than the mass flow and density of each phase of the multiphase fluid. As described in more detail below, method 5900 can be used to determine the properties of each phase of a multiphase fluid.

In general, to determine the properties of individual phases in a multiphase fluid, additional information (e.g., known densities of materials in the individual phases) or additional measurements (e.g., multiphase fluid pressure or water cut of a multiphase fluid) may be required at times. However, the properties of a multiphase fluid measured by a meter are usually determined by the modification or correction of traditional single-phase measurement methods due to the effect of the multiphase flow on the venturi compared to a single-phase flow.

Thus, in some implementations, in addition to the property determined based on the movement of the pipeline, for example, the first property discussed above, the additional or “external” properties of the multiphase fluid, for example, temperature, pressure, and water cut, can be measured and used in method 5900, for example , as additional display inputs or to help determine the flow rates of individual components of a multiphase fluid. Additional properties can be measured with a device other than a flowmeter. For example, the water cut of a multiphase fluid that is part of a multiphase fluid, i.e. water can be determined using a water cut meter. An additional property may also include pressure associated with the venturi. The pressure associated with the venturi may be, for example, the pressure of the multiphase working fluid at the inlet of the venturi and / or the pressure drop across the venturi.

The observed intermediate value associated with the multiphase working fluid is determined based on the first property (5920). In some implementations, the second property of the multiphase fluid can also be determined based on the movement of the pipeline. For example, in such an implementation, the observed mass flow rate of the multiphase fluid and the observed density of the multiphase fluid can be determined based on the movement of the pipe, and both of these observed properties can be used to determine one or more observed intermediate values (e.g., liquid volume fraction and volume flow rate or gas Froude number and non-gas Froude number, as described below). In some implementations, observed intermediate values may be intermediate values based on one or more adjusted or actual properties.

In general, the observed intermediate value (or values) is a value associated with a multiphase fluid that reflects inaccuracies due to the inclusion of more than one phase in the multiphase fluid. The observed intermediate value may, for example, be the volume fraction of a multiphase working fluid. The volume fraction may be a volume fraction of a liquid that defines a portion of a multiphase fluid that is not a gas. The volume fraction may also be the volume fraction of gas, which defines the portion of the multiphase fluid that is gas. In general, the volume fraction is a dimensionless quantity that can be expressed as a percentage. The volume fraction of gas can also be called the void fraction. If the multiphase fluid includes liquids and gases, the sum of the volume fractions of the liquid and gas is 100%. In other implementations, the observed intermediate value may be the volumetric flow rate of a multiphase fluid.

In another implementation, observed intermediate values may include the non-gas Froude number and the gas Froude number. Froude numbers are dimensionless quantities that can represent the resistance of an object moving through a fluid and that can be used to describe multiphase fluids. In this implementation, the observed intermediate value may be a non-gas Froude number and / or a gas Froude number. The observed gas Froude number can be calculated using the following equation, where m ^a _g is the observed gas mass flow rate, ρ _g is the estimate of the density of the gas phase based on the laws of an ideal gas, ρ _l is the estimate of the density of the liquid in the non-gas phase of the multiphase fluid, A is the area the cross section of the venturi, D is the diameter of the venturi and g is the acceleration of gravity:

,

,

наблюдаемая скорость газа

.Where

observed gas velocity

.

Similarly, the non-gas Froude number (which may be the liquid Froude number) can be calculated using the following equation, where m ^a _l is the observed mass flow rate of the liquid:

As discussed in more detail below, the observed intermediate value is entered into a display that sets the relationship between the observed intermediate value and the adjusted intermediate value. The mapping may be, for example, a neural network, polynomial, function, or any other type of mapping. Prior to entering the observed intermediate value into the display, the observed intermediate value can be filtered or converted to reduce measurement and process noise. For example, linear filters can be applied to an observed intermediate value to reduce measurement noise. The time constant of the linear filter can be set to a value that reflects the response time of the measuring instruments (for example, 1 second) so that the filter remains resistant to actual changes in the fluid flowing through the venturi (for example, sediments of a non-gaseous fluid), and at the same time time was able to reduce measurement noise.

Constructing a display to correct or improve multiphase measurement involves collecting data in an experimental environment where true or reference measurements are provided with additional calibrated equipment. In the general case, it is impractical to conduct experiments covering all conceivable multiphase conditions, due to the limitations of the test equipment and / or the cost and time associated with the production of possibly thousands of experiments. Additionally, it is hardly possible to maintain multiphase flow conditions exactly constant over any extended period of time, due to the internally unstable flow conditions that occur under multiphase conditions. Accordingly, it is usually required to calculate the average values of any relevant parameters, including the observed and true or reference parameter values, for each experiment, the duration of which can usually be from 30 s to 120 s. Thus, the mapping can be constructed from experimental data, where each data point is derived from the average value of the data for the period, for example, from 30 s to 120 s.

Difficulties may arise when applying the resultant display in the meter during multiphase flow in real time, due to which the specific values of the parameters observed in the meter are not included in the display obtained from previously collected experimental data. This can happen in two main ways. In the first embodiment, although the conditions in which the meter is located, averaged over a time scale of about 15 to 120 seconds, correspond to the conditions covered by the display, the instantaneous values of the parameters may fall out of the area due to measurement noise and / or instantaneous changes in actual conditions due to instabilities, inherent in multiphase flow. As described above, this effect can be weakened to some extent by averaging over time or filtering the parameters used as inputs to the display function, although there is a compromise between the effects of noise reduction of such filtering and the reactivity of the meter to actual changes in conditions in a multiphase flow. Alternatively, the averaged values of the parameters may fall out of the display, since, for example, it was not economically feasible to cover all possible multiphase conditions at the experimental stage.

It may not be beneficial to apply the mapping function (neural network, polynomial, or other function) to data that falls out of the area for which mapping is intended. Applying a mapping to such data can lead to the generation of low-quality measurements. Accordingly, it is possible to apply wrapping procedures to ensure that the behavior of the display procedure is suitable for parameter values outside the displayed area, regardless of the reasons why the parameters are outside the displayed area. The data that is included in the region may be called suitable data.

Thus, the observed intermediate value can be “wrapped” before the observed intermediate value is entered into the display. For implementations that include single-input mappings, the area of suitable data can be defined by one or more limits, range, or threshold. In other implementations, mappings with more than one input may exist. In these implementations, the area of suitable data can be defined by a series of lines, curved surfaces. Accordingly, with an increase in the number of display inputs, defining an area of suitable data is complicated. Thus, it may be desirable to use mappings with fewer inputs. The above-described gas and liquid Froude numbers are examples of observed intermediate values that can be displayed without additional inputs. Thus, the use of gas and non-gas Froude numbers can help reduce the number of entries in the display, which can also help simplify the process of coating the shell. Additionally, the use of a smaller number of display inputs can lead to a simplified display, which can help reduce the computing resources used by the display and increase the speed of determining the adjusted intermediate values based on the display.

An observed intermediate value having a value that is outside the specified area can be defined as unsuitable for input into the display. In general, rules for correcting the observed intermediate value are defined, which are defined as being outside a given area. For example, the observed intermediate value that is outside the specified area may be ignored by the display (for example, the observed intermediate value not corrected by the display), the observed intermediate value may not be entered into the display at all, a fixed correction can be applied to the observed intermediate value, not correction determined by the display, or you can apply a correction corresponding to the correction, which will be applied to the value closest to the observed omezhutochnomu value. You can implement other rules for the correction of the observed intermediate value, which is outside the specified area. In general, a wrapper refers to a particular display and is defined for each display.

The adjusted intermediate value is determined based on the mapping between the observed intermediate value and the adjusted intermediate value (5925). A mapping may be a neural network, a statistical model, a polynomial, a function, or any other type of mapping. A neural network or other mapping can be trained with data obtained from a multiphase fluid for which the values of the constituent phases are known. Similar to the coating of the shell described above according to (5920), the corrected observed value can be coated, or otherwise verified, before use in further processing. The phase-dependent property of the multiphase working fluid can be determined based on the adjusted intermediate value (5930). Using one or more of the observed intermediate values discussed above rather than directly from a venturi (for example, mass flow rate of a multiphase fluid) can improve the accuracy of method 5900. The phase-dependent property may be, for example, mass flow rate and / or density non-gas and gas phases of a multiphase fluid.

The illustrative method described in accordance with FIG. 59 may be implemented in software or hardware. On Fig and 61 describes an example implementation. 60 and 61, optional components are indicated by a dotted line. In particular, FIGS. 60 and 61 show the application of a digital flow meter to a fluid having multiple phases that are often encountered (for example, in the above batch production method), or to a fluid stream having an inhomogeneous mixture of components (one or more gas constituents and / or one or more liquid constituents).

60 shows a digital controller 6200 that can be used in place of the digital controller 105 or 505 of the digital mass flow meters 100, 500 shown in FIGS. 1 and 5. In this implementation of the digital controller 6200, method 6204 sensors connected to a venturi generate method signals including one or more sensor signals, a temperature signal and one or more pressure signals (as described above). The analog signals of the method are converted into digital data of the A / D signals by converters 6206 and stored in the memory data buffers 6208 of the sensor and exciter signals for use by the digital controller 6200. The exciters 6245 connected to the Venturi tube generate an excitation current signal and can transmit this signal to A / D converters 6206. Then, the excitation current signal is converted into digital data and stored in the data buffers of the sensor and exciter signals 6208. Alternatively, a digital drive gain signal and a digital drive current signal may be generated by an amplitude control module 6235 and transmitted to the memory buffers 6208 of the sensor and driver signals for storage and use by the digital controller 6200.

The digital data of the signals of the sensors and pathogens of the method are further analyzed and processed by the module 6210 for processing the parameters of the sensors and pathogens, which generates physical parameters including the frequency, phase, current, attenuation and amplitude of the oscillations. The raw mass flow measurement calculation module 6212 generates a raw mass flow measurement signal using the methods discussed above with respect to the flow meter 500.

Instead of including a specialized finite state flow state machine, for example 5215, considered in connection with a 5200 flowmeter, a multiphase flow error correction module with one or more neural networks accepts, as an input, physical parameters from a sensor and pathogen parameter processing module 6210 , a raw mass flow measurement signal and a density measurement 6214, which is calculated as described above. For example, if the working fluid is a known two-phase (for example, gas and liquid components), three-phase (for example, gas and two liquid components) or other multiphase flow (for example, one or more gas and one or more liquid components), state determination flow may not be required. In this example, the working fluid may be a moist gas, which is known to include a gas volume fraction (gvf) and a liquid volume fraction (lvf). Wet gas may include, for example, natural gas, liquid oil, and water. Accordingly, the mass flow measurement discussed below can automatically determine the mass flow measurement of each phase of a multiphase working fluid. A dedicated neural network for each state of the multiphase flow can be used in the multiphase flow error correction module 6220. Alternatively or additionally, you can use a single neural network that recognizes a two-phase and / or three-phase (or consisting of more phases) flow and applies correction factors based on the actual state of the multiphase flow.

In multiphase flow conditions, the multiphase flow error correction module 6220 receives an unprocessed (or observed) mass flow measurement signal and an unprocessed density signal. The observed mass flow and density measurement signals reflect the mass flow and density of the multiphase working fluid, and not the mass flow and density of each phase included in the multiphase working fluid. The multiphase flow error correction module 6220 includes a neural network processor for predicting a mass flow rate error due to the presence of a multiphase working fluid. A neural network processor can be implemented in a software procedure or, alternatively, can be implemented as a separate programmable hardware processor. The operation of the neural network processor is described in more detail below.

The input signals of the neural network processor can be observed intermediate values determined from the raw signals of the measurement of mass flow and density measurement. In this implementation, the multiphase flow error correction module 6220 determines the observed intermediate values, for example, the observed intermediate values discussed above in accordance with FIG. 59, from the unprocessed (or observed) mass flow rates and multiphase working fluid density. Observed intermediate values are entered into the neural network processor and adjusted. The corrected observed intermediate values are output to a mass flow measurement output unit 6230. In other implementations, observable (or untreated) mass flow rate and density measurements can be entered into the neural network.

The neural network coefficient and training module 6225 stores a predetermined set or sets of neural network coefficients that are used by the neural network processor for each multiphase flow state. Module 6225 coefficients and training the neural network can also carry out the function of online learning using training data, which allows you to calculate an updated set of coefficients for use by the neural network. Although a predetermined set of neural network coefficients is generated during extensive laboratory tests and experiments based on known two-phase, three-phase, or multiphase mass flow rates, the on-line learning function provided by module 6225 can be used at the initial stage of commissioning the flowmeter or each time the flowmeter is initialized.

The adjusted intermediate values from the neural network are fed to the mass flow measurement output unit 6230. Using the adjusted intermediate values, the mass flow measurement output unit 6230 determines the mass flow rate of each phase of the multiphase working fluid. In some implementations, the mass flow measurement output unit 6230 verifies the mass flow measurements for the phases and may perform an invalid analysis to generate an invalid parameter associated with the verification.

The sensor parameter processing module 6210 also introduces a damping parameter and an oscillation amplitude parameter (described above) into the amplitude adjustment module 6235. The amplitude adjustment module 6235 further processes the attenuation parameter and the oscillation amplitude parameter and generates digital excitation signals. Digital excitation signals are converted into analog D / A excitation signals by converters 6240 for operating exciters 6245 connected to the venturi of the digital flowmeter. In some implementations, the amplitude control module 6235 can process the attenuation parameter and the oscillation amplitude parameter and generate analog excitation signals to operate the exciters 6245 directly.

On Fig shows the procedure 6250, carried out by the digital controller 6200. After the start of processing (6251), the measurement signals generated by the process sensors 6204 and pathogens 6245 are quantified during the analog-to-digital conversion (as described above), and the memory buffers 6208 are filled digital data of sensors and pathogens (6252). For each new processing period, the sensor and pathogen parameter processing module 6210 retrieves the sensor and pathogen data from buffers 6208 and calculates the sensor and pathogen variables from the sensor data (6254). In particular, the sensor and pathogen parameter processing module 6210 calculates sensor voltages, sensor frequencies, field current, and field gain.

The sensor and pathogen parameter processing module 6210 performs an optional diagnose_flow_condition (6256) processing routine to calculate statistical values including the mean, standard deviation, and slope for each of the variable sensors and pathogens. The optional diagnose_flow_condition (6256) processing procedure can be used, for example, to identify the state of a two-phase stream and / or to determine whether the liquid component of a two-phase stream includes separate liquid components, for example, oil and water. Based on the statistics computed for each of the variable sensors and pathogens, you can use the optional state flow state machine (6258) to detect transitions between any three suitable flow conditions: FLOW_CONDITION_SHOCK, FLOW_CONDITION_HOMOGENEOUS and FLOW_CONDITION_MIXED. However, if it is known that the working fluid already includes a heterogeneous mixture, the method may automatically proceed from step 6254 to calculating the raw measurement of mass flow rate 6260.

If the status FLOW_CONDITION_SHOCK (6258) is detected, the method for analyzing the measurement of mass flow is not performed due to the irregularity of the sensor input signals. Upon exiting this state, the processing procedure begins a new cycle (6251). Then, the processing procedure searches for a new sinusoidal signal to track in the sensor signals data and resumes processing. In order of this tracking method, the processing procedure must find the beginning and end of the sine wave using the above zero crossing method. If the status FLOW_CONDITION_SHOCK is not found, the processing procedure calculates the raw measurement of the mass flow rate of the material flowing through the flow meter 100 (6260).

If it is known in advance that a multiphase flow exists in a monitored method, the material flowing through the flow meter 100 is considered, for example, to be a two-phase or three-phase material. For example, the material flowing through the flow meter 100 may be a multiphase working fluid, for example, wet gas. In this case, the multiphase flow error correction module 6220 determines the observed intermediate value and, using the neural network processor (s), corrects the observed intermediate value using (6274). The phase-dependent properties of each phase of the multiphase fluid are determined by the mass flow measurement output unit 6230 using the adjusted intermediate value (6276). Then begins a new processing cycle (6251).

60, a neural network processor forming part of a two-phase flow error correction module 6220 may be a direct-coupled neural network that provides a non-parametric infrastructure for representing a non-linear functional mapping between input and output spaces. Of the various neural network models available, networks based on a multilevel perceptron (MLP) and radial basis functions (RBF) were used to implement a digital flowmeter. MLP with one hidden level (each block has a sigmoidal activation function) can equally well approximate any continuous display.

In one example, the 6200 digital flowmeter can process a stream that is known to be a three-phase fluid. For example, a three-phase stream can be mainly natural gas, with a liquid component, which includes a mixture of oil and water. In other examples, the same or similar method can be applied to a biphasic fluid or a fluid containing more than three components in a mixed fluid.

In particular, the action of the venturi is maintained in a three-phase flow. The main measurements of frequency and phase, amplitudes and amplification factors of the excitation of the sensors are obtained from the sensor signals and the required current. Basic measurements are used, using any available external inputs and information depending on the method or application, to generate estimates of the fluid as a whole and multicomponent mass and volume flows.

For example, estimates of the fluid as a whole and multicomponent mass and volumetric flow rates can be generated as follows. Estimates of frequency, phase and / or amplitude can be improved using known correlations between values, for example, the rate of change of the amplitude correction. Raw estimates of the mass flow rate and density of the mixture can be obtained from the best estimates of the frequency, phase, temperature of the venturi and calibration constants. A simple linear correction is applied to density measurement for the observed fluid pressure. In some implementations, the observed fluid pressure can be obtained from an external inlet. Since the pressure expands and strengthens the venturi, which can lead to an error in the raw density, a simple variable displacement can work well if the gas densities expected in a repeatable method or mixed fluid, while a more complete correction may include additional terms for variable fluid density, if changes in the concentrations of the liquid and / or gas component are provided for in the method. The transmitter may include configuration parameters that specify the expected density of the liquid (with temperature compensation) and the reference density of the gas.

In a three-phase fluid mixture, fixed water cut (WC) can be assumed or can be measured. Water cut is defined as the proportion of water in the mixture. The temperature of the fluid is measured to calculate an estimate of the true density of the fluid (D ₁ ) from the water cut and density of pure oil (D _oil ) and the density of water (D _water ). Estimating the true density of the fluid takes into account the known change in D _oil and D _water depending on the temperature of the fluid and the pressure of the fluid.

A model is provided (based, for example, on an ideal gas model) for changing the gas density (D _g ) depending on the observed fluid pressure and fluid temperature, which can be obtained from external inputs, and the untreated volume fraction of the liquid (raw_LVF) from the untreated density blends (raw_Dm) calculated using

The raw volumetric flow rates of the mixture from the raw mixture are calculated using

A neural network trained using experimental data is used to generate adjusted estimates of the raw volume fraction of the liquid and the raw volume flow, as shown below. In the equations below, the variable "nnfunction" represents a neural network.

The raw volume fraction of liquid (raw_LVF) is 100 - volume fraction of gas (GVF). Additionally, the untreated volume fraction of the liquid is closely related to the decline in density. Raw volume flow can be scaled as speed, for example, as part of the same approach, neural networks can be combined, but different inputs can be used.

The flow rates of liquid and gas are calculated using the following relationships:

The water cut meter can be used to provide a measurement used as an additional input to the neural network (s), and to assist in accurately dividing the fluid flow into its constituent parts. To aid in accurate separation of fluid flow, the following relationships can be used:

Alternatively or additionally, it is possible to determine the observed gaseous and non-gaseous Froude numbers corrected using a neural network, and then use them to determine the mass flow rates of the components of a multiphase fluid. For example, the Froude gas number can be determined on the basis of the following equation, where m ^a _g is the observed gas mass flow rate, ρ _g is the density estimation of the gas phase of a multiphase fluid based on the laws of an ideal gas, ρ _l is an estimate of the density of a liquid in a non-gas phase of a multiphase fluid , A is the cross-sectional area of the venturi, D is the diameter of the venturi, and g is the gravitational acceleration. The observed mass flow rate of gas is a function of the known or estimated density of the components in the multiphase flow, the observed density of the multiphase fluid (the observed total density) and the observed mass flow rate of the multiphase fluid (the observed total mass flow).

,

,

наблюдаемая скорость газа

Where

observed gas velocity

Similarly, the observed non-gas Froude number (which may be the liquid Froude number) can be calculated using the following equation, where m ^a _l is the observed mass flow rate of the fluid, K is the constant given above according to the Froude gas number, and V ^a _l is the observed fluid velocity determined similarly to the observed gas velocity, as shown above:

The observed gas and non-gas Froude numbers are then adjusted using a neural network:

Corrected Froude gas number = nnflinction (observed Froude gas number, observed non-gas Froude number)

Corrected non-gas Froude number = nnflinction (observed gas Froude number, observed non-gas Froude number)

By determining the corrected gas and non-gas Froude numbers, one can determine the mass flow rate for the gas and non-gas components of a multiphase fluid. In particular, after obtaining the corrected values of the gas and non-gas Froude numbers, the values of all parameters for non-gas and gas components of a multiphase fluid, except mass flow, are known. Thus, the corrected mass flow rate of non-gas and gas components of a multiphase fluid can be determined based on the above equations, which are used to determine the observed Froude numbers.

Additionally, as in the implementation using the liquid volume fraction and volumetric flow rate as input signals of the neural network, the water cut meter can be used to help separate the multiphase fluid into its constituent parts. For example, a water cut meter can provide a water cut (WC) of a multiphase fluid that indicates the proportion of water in a multiphase fluid, and a WC can be used to help separate the multiphase fluid into its constituents using the following equations:

As discussed in accordance with FIG. 59, in some cases, a neural network can generate more accurate corrections of the observed gas and non-gas Froude numbers than other observed intermediate values. Thus, the use of the observed gas and non-gas Froude numbers as inputs into the neural network can provide a more accurate determination of the properties of the components of the stream forming a multiphase fluid.

The above description provides an overview of various digital Coriolis mass flow meters, describing the background, implementation, examples of their operation and comparison with previous analog controllers and transmitters. Several improvements were obtained compared to the analog controller in terms of performance, including: high-precision control of the action of the venturi, even when working at very low amplitudes; maintaining the action of the venturi even in conditions of strong attenuation; high accuracy and high measurement speed; compensation of dynamic changes in amplitude; two-phase flow compensation and dosing to / from an empty state. This combination of advantages suggests that the digital mass flow meter represents a significant step forward, and not just the gradual evolution of analog technology. The ability to work with two-phase flow and external vibration means that the digital mass flow meter 100 provides increased performance in traditional Coriolis applications, while expanding the range of applications to which streaming technology can be applied. The digital platform is also a useful and flexible tool for conducting research through Coriolis measurement, because it provides high accuracy, processing power and data transfer rates.

An additional application of the 6200 digital flowmeter to a three-phase fluid, for example a wet gas containing a gas (methane) and a liquid component (oil and water), is described and shown with reference to FIGS. 62-72. On Fig shows a graphical representation of the test table for wellheads, tested on the basis of actual tests at various pressure in the well and gas velocities. On Fig shows a graphical representation of the raw density errors at different percentages of the liquid void fraction and for wells at different speeds and pressures. On Fig shows a graphical representation of the raw mass flow rate errors at various percentages of the liquid void fraction and for wells at various speeds and pressures. On Fig shows a graphical representation of the untreated liquid void fraction of error for wells at various speeds and pressures. On Fig shows a graphical representation of the raw volumetric flow rate error for wells at different speeds and pressures. On Fig shows a graphical representation of the corrected fluid void fraction for wells at different speeds and pressures. On Fig shows a graphical representation of the adjusted volumetric flow rate of the mixture for wells at various speeds and pressures. On Fig shows a graphical representation of the adjusted mass flow rate of gas for wells at various speeds and pressures. On Fig shows a graphical representation of the adjusted integral probability of gas of the tested digital flowmeter. On Fig shows a graphical representation of the corrected errors of the mass flow rate of the fluid for wells at various speeds and pressures. On Fig shows a graphical representation of the adjusted integral probability of gas of the tested digital flowmeter.

According to Figs. 62-72, wet gas test tests containing water and air encompass test well parameters for a variety of meters. Covered points of the volumetric flow rate of the liquid fraction (LVF = 100% - GVF) include: 0.0; 0.2; 0.4; 0.6; 0.8; 1.0; 1.5; 2.0; 3.0; 4.0; 5.0%. With respect to the detected mass flow rate and density errors, the mass flow rate and density errors of the gas-liquid mixture, presumably without a volumetric liquid content, a static mixer to control a stable flow profile under operating conditions and positive density errors due to the volumetric liquid content in the meter. Positive density errors due to the volumetric liquid content in the meter are maximum at low flow rates and at low gas densities. Negative mass flow rate errors are similar to the responses of a two-phase Coriolis meter.

Applicable modeling strategies use the observed mass flow rate and the observed density to apply correction factors or curve fitting for the collected data to create real-world measurements, such as density measurements in real density. However, a wide range of gas densities, for example 175–900 psi (12–62 bar), also contributes to complementary approaches. For example, alternative parameters have been identified, including model parameters, which include two main error parameters. In particular, the volumetric flow rate of the mixture (presumably without slipping between the phases) is based on the mass / density ratio and the volume fraction of liquid (LVF), i.e. 100% - GVF. Corrections for each of them are provided using their raw values and additional pressure data (only). Based on the adjusted LVF and volumetric flow rates, the mass flow rates of the gas and liquid components can be calculated as follows:

The resulting errors are shown in FIGS. 69-72. The model covers a wide range of conditions, including various pressures and flows. A more limited set of conditions can provide improved results, for example, higher pressure, resulting in less unprocessed errors, a “natural” operating range for the meter, very high pressure drops with high LVF and speed and / or the need to analyze the meter’s calibration for wet gas.

The model can be expanded or modified so that the main "corrections" of pressure, which may include fitting the raw data by approximating the curve to directly inferred actual measurements, for example, without a true correction factor, are applied to the density before being applied to the neural network. Current inputs depend on the fluid, for example, the volumetric flow rate depends on the actual density of the fluid. The dimension of the inputs can be reduced, for example, by converting the volume flow to speed, then express the speed as a percentage of the maximum speed at which the pipeline can operate, followed by normalizing the data to determine the components. Operating pressures may include a flow pressure of 60 bar, with a differential of 2-3 bar, and will support higher operating pressures in the range of 150 psi (10.34 bar) to 1000 psi (68.94 bar). The calibration tests of the detailed model shown in FIGS. 62-72 use natural gas in the range of approximately 375 psi (25.86 bar) from the wellhead. The calibration of the venturi can also be determined based on the differential pressure.

R. Source Code Text

The following source code, which is hereby incorporated into this application, is used to implement a mass flow rate processing procedure in accordance with one flowmeter implementation. Obviously, it is possible to implement a mass flow rate processing procedure using another computer code without deviating from the scope of the described methods. Thus, neither the above description, nor the following source code text is intended to limit the described methods.

Source code

/ * calculation of mass flow in dimensionless units * /

/ * conversion to engineering units * /

/ * applying two-phase flow correction if necessary * /

/ * call the neural network to calculate the correction of mass flow * /

t = VMV_temp_stats.mean; // average temperature VMV

x = RMV_dens_stats.mean; // average density RMV

m = RMV_mass_stats.mean; // average mass flow rate RMV;

g = gain_stats.mean; // average gain;

S. Copyright Notice

Part of the disclosure of this patent document contains material subject to copyright protection. The copyright holder does not object to the facsimile reproduction of a patent document or patent disclosure when it is in the form of a file or patent records in the US Patent Office, but otherwise retains all copyrights.

Other implementations are within the scope of the following claims.

Claims (25)

1. A method for determining the properties of a multiphase working fluid, comprising stages in which
passing a multiphase working fluid through a venturi
create movement in a venturi vibration tube,
determining the first observable property of the multiphase working fluid based on the movement of the vibrating venturi,
determining the observed intermediate value associated with the multiphase working fluid based on the first observed property,
determining the corrected intermediate value based on a mapping between the observed intermediate value and the previous corrected intermediate value, and
determining the phase-dependent phase property of the multiphase working fluid based on the adjusted intermediate value. 2. The method of claim 1, wherein the mapping is a neural network. 3. The method according to claim 2, additionally containing phases in which it is determined that the observed intermediate value is in the first predetermined range of values until the corrected intermediate value is determined, and
determining that the adjusted intermediate value is in the second predetermined range of values until the phase-dependent property of the phase of the multiphase working fluid is determined. 4. The method according to claim 1, in which the multiphase working fluid is a wet gas. 5. The method according to claim 4, in which
a multiphase working fluid includes a first phase and a second phase,
the first phase includes a non-gaseous fluid, and the second phase includes a gas. 6. The method according to claim 4, in which the multiphase working fluid includes
a first phase including a first non-gaseous fluid, and
a second phase including a second non-gaseous fluid, and
the third phase, which includes gas. 7. The method according to claim 1, in which at the stage of determining the first observed property of the multiphase working fluid, the second observed property of the multiphase working fluid is determined. 8. The method according to claim 7, in which the first observed property of the multiphase working fluid is a mass flow rate, and the second observed property is a density. 9. The method according to claim 1, further comprising the step of taking one or more measurements corresponding to an additional property of the working fluid. 10. The method according to claim 9, in which
an additional property of the multiphase fluid includes one or more of the temperature of the multiphase fluid, the pressure associated with the multiphase fluid, and the water cut of the multiphase fluid, and
in the step of determining the observed intermediate value associated with the multiphase working fluid, based on the first observed property, the intermediate value is determined based on the first observed property and the additional property. 11. The method according to claim 1, wherein in the step of determining the observed intermediate value associated with the multiphase working fluid, based on the first observed property, the volume fraction associated with the amount of non-gaseous fluid in the multiphase working fluid and the volume flow of the multiphase fluid are determined Wednesday. 12. The method according to claim 1, wherein in the step of determining the observed intermediate value associated with the multiphase working fluid, based on the first observed property, the first Froude number corresponding to the non-gas phase of the multiphase fluid and the second Froude number corresponding to the multiphase gas phase are determined fluid medium. 13. The method according to claim 1, wherein in the step of determining the phase-dependent phase property of the multiphase working fluid, the mass flow rate of the non-gas phase of the multiphase fluid is determined based on the adjusted intermediate value. 14. A flow meter containing
a vibration venturi, wherein the venturi contains a multiphase fluid,
a pathogen connected to the venturi and capable of imparting movement to the venturi so that the venturi vibrates,
a sensor connected to the venturi and capable of sensing the movement of the venturi and generate a sensor signal, and
a controller receiving a sensor signal and configured to:
determining a first observable property of a multiphase working fluid based on the movement of a vibrating venturi,
determining the observed intermediate value associated with the multiphase working fluid based on the first observed property,
determining the adjusted intermediate value based on the mapping between the observed intermediate value and the previous adjusted intermediate value, and
determining the phase-dependent phase property of the multiphase working fluid based on the adjusted intermediate value. 15. The flowmeter of claim 14, wherein the display is a neural network capable of detecting an error in an intermediate value due to the presence of a multiphase working fluid. 16. The flow meter according to 14, in which the controller is additionally configured
determining that the observed intermediate value is in the first predetermined range of values until the corrected intermediate value is determined, and
determining that the adjusted intermediate value is in the second predetermined range of values until the phase-dependent property of the phase of the multiphase working fluid is determined. 17. The flow meter according to 14, in which the multiphase working fluid is a wet gas. 18. The flowmeter of claim 14, wherein determining the first observable property of the multiphase working fluid includes determining a second observable property of the multiphase working fluid. 19. The flow meter according to claim 18, wherein the first observable property of the multiphase working fluid is mass flow and the second observable property is density. 20. The flow meter according to claim 18, wherein the controller is further configured to receive one or more measurements corresponding to a second observable property of the working fluid. 21. The flow meter of claim 14, wherein determining the observed intermediate value associated with the multiphase working fluid based on the first observed property includes determining a first Froude number corresponding to the non-gas phase of the multiphase fluid and a second Froude number corresponding to the gas phase multiphase fluid. 22. The transmitter of the flow meter, containing
at least one processing device, and
a storage device, wherein the storage device stores instructions instructing at least one processing device
determine the first observable property of the multiphase working fluid based on the movement of the vibrating venturi,
determine the observed intermediate value associated with the multiphase working fluid based on the first observed property,
determine the adjusted intermediate value based on the mapping between the observed intermediate value and the previous adjusted intermediate value, and
determine the phase-dependent phase property of the multiphase working fluid based on the adjusted intermediate value. 23. The transmitter of claim 22, wherein the multiphase working fluid is wet gas. 24. The transmitter of claim 22, wherein the storage device further stores instructions instructing the at least one processing device to take one or more measurements corresponding to a second observable property of the working fluid. 25. The transmitter of claim 22, wherein determining the observed intermediate value associated with the multiphase working fluid based on the first observed property includes determining a first Froude number corresponding to the non-gas phase of the multiphase fluid and a second Froude number corresponding to the gas phase multiphase fluid.

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