HK1021412B - Vibrating tube densimeter - Google Patents

Description

Vibrating tube densimeter

The present invention relates to a vibrating tube densitometer and, more particularly, to a coriolis effect vibrating tube densitometer with density output data having improved accuracy and an expanded operating range.

Early coriolis effect vibrating tube densitometers, such as that disclosed in U.S. patent No. 4,876,879 issued to Ruesch, 10/31 1989, were designed and operated on the assumption that the accuracy of the density measurement was not affected by changes in the mass flow rate, temperature, viscosity, or pressure of the fluid being measured. The density measurement in a vibrating tube densitometer is based on the measurement of the natural frequency of vibration of the vibrating tube. Early densitometer designs assumed that changes in the natural frequency of the driven flow tube were caused only by changes in the density of the material flowing through the flow tube. The density measurements of these early densitometers were determined by these densitometers directly from the measured natural frequency.

US patent US5,295,084 issued to aracahalam et al on 3/15 of 1994 finds that the natural frequency of a vibrating flow tube is not only influenced by the density of the fluid within the tube, and in this patent document there is a clear development in the theory and operation of densitometers. It has been analytically and experimentally recognized that the natural frequency of a vibrating tube filled with a flowing substance decreases as the mass flow rate of the material in the vibrating tube increases. Density reading accuracy is improved by measuring the natural frequency of the vibrating tube and correcting the measured natural frequency to compensate for the decrease in natural frequency caused by the mass flow rate of the substance in the flow tube. The corrected natural frequency is then used for the calculation of the standard density.

Experimentation and further studies of the mathematical model disclosed in the U.S. patent to Aranachalum revealed a drawback in the device described by Aranachalum. The aranaachalam densitometer is calibrated by proposing three calibration constants. The first two constants, calculated in the same manner as done by Ruesch, were used for the basic density measurement. However, in addition to applying the measured tube frequency to the fundamental density measurement calculation, a third correction factor is also proposed to facilitate correction of the mass flow rate effect for the measured tube frequency. The compensated tube frequency is then applied to the basis density measurement calculation. The third correction factor is measured by measuring the natural frequency of the vibrating flow tube when a material of known density is passed through the tube at a known mass flow rate. The change in the tube frequency is thus related to the mass flow rate.

However, it has been known analytically and experimentally that the reduction in natural frequency caused by the mass flow rate of material through the vibrating tube is itself dependent on the density of the flowing material. In other words, the decrease in natural frequency of the vibrating tube is different for different densities of material at a given mass flow rate. The lower the density of the material passing through the vibrating tube, the more the natural frequency of the vibrating tube decreases per unit mass flow rate. In practical applications, it is very rare that densitometers are used to measure the same material from which they are calibrated.

Thus, there is also a problem with the densitometer described by Aranachalum. Although they have an order of magnitude increase in their density measurement over earlier densitometers, their performance is reduced if, in operation, they are used to measure a flowing material other than that upon which the calibrated densitometer is based. There is a need for a densitometer that compensates for the effects of mass flow rate independent of the density of the material being measured.

Another disadvantage of current densitometers is the inability to compensate for the effects of temperature variations on existing density compensation schemes. It is well known that the material properties of vibrating flow tubes vary with temperature and this fact has been considered in coriolis mass flowmeters, since coriolis mass flowmeters were originally developed as commercially available devices. In particular, the prior art coriolis mass flowmeters compensate for changes in Young's Modulus of the flow tube material due to temperature changes during operation of the coriolis mass flowmeter. However, the aracahalum compensation scheme itself is affected by temperature changes, thereby reducing its performance.

Accordingly, there is a need for a densitometer with improved performance characteristics. That is, there is a need for a densitometer that compensates for the effect of the mass flow rate of material through a vibrating tube independent of the density of the material being measured. There is also a need for a densitometer that provides compensation for the effects of mass flow rate on density measurements, which itself is compensated for temperature variations.

The present invention allows high accuracy output data to be obtained from a flow meter independent of the mass flow rate of a substance passing therethrough and independent of the temperature of the vibrating flow tube, and both the solution of the above problem and the advancement in the art have been achieved by means of the present invention. The present invention provides such a vibrating tube densitometer: such densitometers can give density measurements whose effects of mass flow rate and temperature are compensated for, thereby improving density measurement performance to previously unattainable levels.

The basic principle of operation of the vibrating tube densitometer is as follows: the natural frequency of vibration of the vibrating tube or tubes varies with the density of the material being measured within the vibrating tube. The change in natural frequency of the vibrating tube is tracked and related to the density of the measured fluid. Researchers in this field know that: the natural frequency of the vibrating tube is also affected by factors other than the change in density of the fluid flowing through the vibrating tube. The vibrating tube natural frequency decreases as the mass flow rate of the substance through the vibrating tube increases. In addition to this, changes in temperature affect the material properties of the vibrating tube and thus affect the natural frequency and mass flow rate effect or frequency of the vibrating tube.

The theoretical model that considers the effect of the mass flow rate of the material flowing through the vibrating tube was first applied to the commercially available density measuring device in the aranaachalum patent. This model is presented in the form of a formula called Housner's, which is an undamped, transverse free-running vibration illustrating a flow tube containing a flowing substanceThe formula of the dynamic one-dimensional fluid-elasticity is as follows:in which the number of the first and second groups is reduced,

E-Young's modulus of elasticity of flow tube

I-moment of inertia of the flow tube

ρ_fDensity of material

ρ_sDensity of flow tube

A_fCross-sectional area of flow region

A_sCross-sectional area of flow tube

V_oVelocity of flow

u (x, t) ═ transverse displacement of flow tubes

This mixed partial derivative term is referred to as the coriolis term of the Housner's equation. The second partial derivative corresponding to the term of the spatial variable (x) is referred to as the centrifuge term of the Housner's equation. This mode was used to derive the compensation scheme of the aracahalum patent and its use in commercial densitometers provides an order of magnitude improvement over the current densitometer density measurement performance. Due to the complexity of the Housner's formula, its analytical solution is limited to a straight tube densitometer configuration. These straight tube results were then extrapolated to a curvilinear tube densitometer structure. While the improvement in the performance of the density measurement thus obtained is significant for a curvilinear tube densitometer configuration, the present invention further significantly improves the performance of the densitometer by taking into account the features specific to the curvilinear tube densitometer configuration.

The present invention utilizes a new understanding of the principles of operation of vibrating tube densitometers. This new understanding is embodied in a more accurate analysis mode as described below, and is used to provide a compensation independent of the density of the material being measured that is different from the compensation provided by the aranaachalum patent.

In the case of vibrating tubes (whether straight or curved), one effect of the material flowing through the vibrating tube is to create some force on the vibrating tube. These forces are illustrated by Housner's equations, which include centrifugal force and Coriolis force. It is the centrifugal force that primarily causes the natural frequency of the vibrating tube to decrease as the mass flow rate increases. The coriolis force also plays a role in influencing the natural frequency with the mass flow rate, but it is the centrifugal force that plays the main role. However, the types of these centrifugal forces are different for the linear vibrating tube and the curvilinear vibrating tube.

Both linear and curvilinear vibrating tubes encounter a force that may be referred to as a dynamic centrifugal force. Dynamic centrifugal forces are caused by the local curvature of the vibrating tube caused by the vibration of the vibrating tube. Both linear and curved tube densitometers operate by vibration of their respective tubes, and the vibrating tube, whether linear or curved, is subjected to the dynamic centrifugal forces generated in each case. The effect of dynamic centrifugal force on the natural frequency of a vibrating tube is related to the mass flow rate and density of the fluid. It is the dynamic centrifugal force of the Housner's equation that is compensated for by the density compensation scheme of the Aracahalum patent.

In the case of densitometers or coriolis mass flowmeters that employ a curved tube, the bending of the curved tube causes another type of centrifugal force, referred to as the steady state centrifugal force. Steady state centrifugal forces are the result of a change in direction of the flowing material as it flows around a curved portion of the flow tube. Some tension is generated in response to this steady state centrifugal force. When the relevant components of these tensions are substituted into Housner's equation, it can be seen that: the steady state centrifugal force, expressed in terms of tension, virtually eliminates the dynamic centrifugal force. There is no steady state centrifugal force in a linear tube densitometer, since there is no fixed bend in such a tube. Therefore, the dynamic centrifugal force cannot be eliminated with the steady-state centrifugal force in the linear tube densitometer.

The equation below represents the Housner's equation for a bent tube substituted with the relevant tension term.

In which the number of the first and second groups is reduced,

T＝ρ_fA_fV_o ²the tension term (steady state centrifugal force) eliminates the dynamic centrifugal force term, yielding the following expression for the Housner's equation.

As is known above, the centrifugal force, which opposes the coriolis force, is primarily responsive to the effect on the natural frequency of the vibrating tube caused by the mass flow rate of material through the vibrating tube. Since the dynamic centrifugal force and the steady-state centrifugal force cancel each other out in a curved tube densitometer as just described, a densitometer employing a curved tube has far lower sensitivity to mass flow rate than a densitometer employing a straight tube, since only the coriolis force affects the density measurement.

In the aranaachalum patent compensation scheme, centrifugal force is the dominant force, and it is the dynamic centrifugal force and coriolis force effects on the vibrating tube that are compensated for. The compensation provided by aranaachalum must include a dependence on density. This is due to the aranaachalum compensation involving measuring the tube frequency, determining the tube period by calculating the inverse of the tube frequency and multiplying the tube period by a factor including the measured volumetric flow rate. The measured density is used in part in coriolis flowmeters to determine volumetric flow rate, and therefore, aracahalum density compensation includes an inherent dependence on the material being measured.

In the present invention, it is the influence of the coriolis force on the vibrating tube that is compensated for because the centrifugal forces cancel. The compensation factors provided and utilized by the present invention do not include a density term that is indicative of being part of the compensation factor. As a result, the density compensation provided by the present invention is independent of the density of the material to be measured. Thus, for application to a curvilinear tube densitometer, the present invention provides a density measurement that is not affected by the mass flow rate of material through the vibrating tube, and the compensation itself is not affected by the density of the material being measured.

The method and apparatus of the present invention first determines the measured density using the density measurement calculation method described in U.S. patent to Ruesch:in which the number of the first and second groups is reduced,

D_mthe density (g/cm) of the material is measured³)

T_mFor the measured tube period(s)

K₁Is equal to K₂T_a ²-D_a

K₂Is equal to d/(T)_w ²-T_a ²)

D_wFor the density of water (g/cm) at the time of calibration³)

D_aFor correcting the density of air (g/cm)³)

D is D_w-D_a(g/cm³)

t_cFor temperature compensation factors [ (in terms of T)² _mChange in/° c%)/100]

ta is the tube period of the air not flowing at the time of correction, and is corrected to 0 ℃(s)

T_wTo correct the tube period of stagnant water at 0 deg.C(s)

t_mIs the measured temperature (. degree. C.)

Then, the compensation factor K is used as shown in the following equation₃Correcting the measured density (D)_m)：

D_c＝D_m-K₃(M_m)²

In which the number of the first and second groups is reduced,

D_mis measured as density (g/cm)³)

D_cIs compensated density (g/cm)³)

M_mFor the measured mass flow rate (g/s)

K₃Is equal to D_k3/(M_k3 ²)

D_k3(g/cm³) At a mass flow rate M_k3(g/s) error in density measured during the correction. K is determined in a calibration procedure by measuring density reading errors at a known mass flow rate₃. A corrected density is thus derived from the measured density.

Another advantage of the present invention is that the compensation described above can also be improved so that the mass flow rate effect compensation of the density can itself be compensated for temperature effects. It has been determined experimentally and analytically: the density measurement error due to mass flow rate also varies with temperature. The present invention provides compensation for this temperature effect.

Additional correction constant K₄Is defined as follows:in which the number of the first and second groups is reduced,

D_k4is at a temperature t_k4And mass flow rate M_k4Error in measured Density (D)_m)。

K₃Is a previously determined correction constant

t_k3Is to determine K₃Temperature (. degree.C.)

t_k4Is to determine K₄Temperature (. degree.C.)

M_k4Is to determine K₄Mass flow rate in g/s K₄For determining K at operating temperature deviation₃Regulating K in the case of temperature₃The value of (c). Determining K during calibration₃K is then determined as described above by changing the temperature of the flowing substance and measuring the density of the flowing substance again₄. The change in temperature causes an error in the compensated densitometry value, and K is calculated as described above₄。

Using the correction constant K during the operation of the invention₄K is adjusted as follows₃The value of (c):

D_c＝D_M-K₃[1+K₄(t_m-t_k3)](M_m)²in which the number of the first and second groups is reduced,

D_mis the measured density (g/cc)

D_cIs corrected density (g/cc)

M_mIs the measured mass flow rate (g/s)

t_mIs the measured temperature (. degree. C.)

t_k3Is to calculate K₃Temperature (. degree.C.)

K₃And K₄As defined above K₄Thus making the temperature pair K₃The effect of the compensation factor is linearized.

According to the invention, the sensor device, which is connected or integrated with one or several vibrating flow tubes, is connected to a signal processing circuit which generates data indicative of the measured density of the substance flowing through the vibrating tube. The signal processing circuit takes into account the following factors: the measured density cannot be kept constant due to changes in the mass flow rate of the substance to be measured and/or the temperature of the vibrating tube. In this case, the signal processing circuit corrects the measured density and generates an output signal that determines a corrected density independent of the mass flow rate of the substance whose density is being measured. The mass flow rate compensation factor itself is also compensated for the effects of temperature changes in the vibrating tube. The method of the present invention is most ideally applied to a curved tube densitometer, but may also be applied to a straight tube densitometer.

Fig. 1 shows one of the most typical possible embodiments of the invention.

Fig. 2 shows further details of the metering electronics 20 of fig. 1.

FIG. 3 is a graph illustrating the measured density error versus mass flow rate for a vibrating tube densitometer.

Fig. 4 is a flow chart describing the operation of the metering electronics 20 and its processing circuitry 210 in measuring density at the metering electronics and correcting for the measured density for the effect of mass flow rate on the density measurement.

Fig. 5 is a graph illustrating the effect of mass flow rate at various temperatures for measuring density.

Fig. 6 is a flow chart depicting the operation of the metering electronics 20 and its processing circuitry 210 in measuring density in the metering electronics and correcting the measured density for the effect of mass flow rate on the density measurement, taking into account the effect of temperature on this effect.

Fig. 7 is a graph illustrating the improvement in density measurement performance using the present invention.

A possibly preferred exemplary embodiment is shown in figures 1 to 7. It is to be specifically understood that the present invention is not limited to this exemplary embodiment. Other embodiments and improvements are also intended to be included in the inventive idea described in the claims. The invention may also be practiced with other instruments than those described above. Successful practice of the present invention is not dependent on any instrument geometry, although practice in a curvilinear tube densitometer may be selected.

Description of the general System (FIG. 1)

Fig. 1 shows a coriolis densitometer 5 that includes a coriolis meter assembly 10 and meter electronics 20. The metering assembly 10 is responsive to the mass flow rate and density of the process material. The metering electronics 20 are connected to the metering assembly 10 via leads 100 to provide density, mass flow rate and temperature information, as well as other information not pertinent to the present invention, via lines 26. A coriolis flowmeter structure is described herein, although it will be apparent to those skilled in the art that the present invention may be implemented in the form of a vibrating tube densitometer without the additional measurement capability provided by a coriolis mass flowmeter.

The coriolis densitometer is convenient and desirable because its inherent capability, as described below, enables it to provide the mass flow rate information necessary for the operation of the present invention. If a vibrating tube densitometer of the non-coriolis type is used, the mass flow rate information needs to be input from a separate such information source.

The metering assembly 10 includes a pair of manifolds 150 and 150 ', a pair of flanges 103 and 103' having flange necks 110 and 110 ', a pair of parallel flow tubes 130 and 130', a drive mechanism 180, a temperature sensor 190, and a pair of speed sensors 170_LAnd 170_R. The flow tubes 130 and 130 'have two substantially straight inlet legs 131 and 131' and a pair of outlet legs 134 and 134 'that converge toward each other on the flow tube support blocks 120 and 120'. The flow tubes 130 and 130' are curved at two symmetrical locations along their length and are substantially parallel along their entire length. The brace bars 140 and 140 'are used to determine the axes W and W' upon which each vibrating tube vibrates.

The side branches 131 and 131 ' and 134 ' of the flow tubes 130 and 130 ' are fixedly mounted to flow tube support blocks 120 and 120 ' which are, in turn, fixedly mounted to manifolds 150 and 150 '. This provides a continuous closed material conduit through coriolis metering assembly 10.

When flanges 103 and 103 ' having bores 102 and 102 ' are connected via inlet end 104 and outlet end 104 ' to a flow tube system (not shown) carrying process material to be measured, material is directed through inlet end 104 of bore 101 of flange 103 through manifold 150 to flow tube support block 120 having a surface 121. Material is diverted within the manifold 150 and bypasses the flow tubes 130 and 130'. Upon exiting the flow tubes 130 and 130 ', the process material is recombined in the manifold 150 into a single flow stream and then routed to the outlet end 104' which is connected to a flow pipe system (not shown) with a flange 103 'having a plurality of bolt holes 102'.

Flow tubes 130 and 130 ' are selected and suitably mounted to flow tube support blocks 120 and 120 ' so as to have substantially the same mass distribution, moment of inertia, and young's modulus about bending axes W-W and W ' -W ', respectively. These bending axes pass through support bars 140 and 140'. Since the young's modulus of the flow tube varies with temperature and this variation affects the flow and density calculations, a high temperature resistance detector (RTD)190, typically a platinum RTD device, is mounted to the flow tube 130' to facilitate continuous temperature determination of the flow tube. The temperature of the flow tube and the voltage developed across the RTD for a given current to pass therethrough is controlled by the temperature of the material passing through the flow tube. The temperature dependent voltage developed across the RTD is used by the meter electronics 20 in a known manner to compensate for changes in the elastic modulus of the flow tubes 130 and 130' due to any changes in the temperature of the flow tubes. Tube temperature is also used in accordance with the present invention to compensate for the effects of changes in temperature of the vibrating tube on mass flow rate density compensation. The RTD is connected to instrument circuitry 20 by lead 195.

Both flow tubes 130 and 130 'are driven by the driver 180 in opposite directions about their respective bending axes W and W' and at a location referred to as the first out-of-phase natural frequency of the meter. Both flow tubes 130 and 130' vibrate like the tuning fork tines. Such a drive mechanism 180 may comprise any of a number of well-known devices, such as a magnet mounted to the flow tube 130' and a counter-acting coil mounted to the flow tube 130 and through which an alternating current is passed for vibrating the flow tube. An appropriate drive signal is applied to the drive mechanism 180 by the metering electronics 20 via lead 185.

The meter electronics receives the RTD temperature signal on lead 195 and the left and right velocity signals appearing on leads 165L and 165R, respectively. The meter electronics 20 generates a drive signal that is present on lead 185 to drive the drive mechanism 180 and the vibrating tubes 130 and 130'. The metering electronics 20 process the left and right velocity signals and the RTD signal to facilitate calculation of the mass flow rate and density of the material passing through the metering assembly 10. This information, along with other information, is applied by the metering electronics 20 to the application device 29 via line 26. In determining the density, the electronic circuitry 20 modifies the measured density of the material passing through the flow tubes 130 and 130' in accordance with the methods taught by the present invention.

Description of the metering electronics (FIG. 2)

Fig. 2 shows a schematic diagram of the metering electronics 20, which includes a mass flow measurement circuit 201, a flow tube drive circuit 202, a density measurement processing circuit 210, and an RTD input circuit 203.

The flow tube drive circuit 202 provides a repetitive alternating or pulsed signal to the drive mechanism 180 through the lead 185. Drive circuit 202 synchronizes the drive signal to the left velocity signal on line 165L and maintains the opposite sinusoidal motion of both flow tubes 130 and 130' at their fundamental natural frequencies. This frequency is affected by a number of factors including the characteristics of the flow tube, the density, and the mass flow rate of the material flowing therethrough. Since the circuit 202 is known in the art and its specific apparatus does not form part of the present invention, it will not be discussed further herein. The reader is interested in referring to U.S. patent 5009109 (issued to p. kalotay et al, 4/23 1991); 4934196 (p. romano on 6/19/1990) and 4876879 (j. ruesch on 10/31/1989), which further describe some different embodiments of flow tube driver circuits.

Any one of a number of known methods may be utilized in the metering electronics 20 and in particular in the mass flow measurement circuit 201 for the sensor 170_LAnd 170_RThe generated signals are processed to calculate the mass flow rate of the material flowing through the flowmeter. One of these processing paths is depicted in fig. 2. The mass flow measurement circuit 201 includes two independent input channels: a left channel 220 and a right channel 230. Each channel includes an integrator and two level crossing detectors 222 and 223. In two channels, from left and right sensors 170_LAnd 170_RThe emitted left and right velocity signals are provided to respective integrators 221 and 231. Each of these two integrators effectively forms a low pass filter. Integrators 221 and 231 are provided to level crossing detectors (actually comparators) 222 and 223 whenever the corresponding integrated speed signal exceeds a predetermined voltage level defined by a small predetermined positive and negative voltage levelFlat, e.g., ± 2.5V, the two detectors generate level change signals. The outputs of level crossing detectors 222 and 223 are supplied as control signals to counter 204 to measure the timing intervals (in clock pulse numbers) that occur between corresponding changes in these outputs. This interval is represented by left sensor 170_LGenerated signal and right sensor 170_RThe phase difference between the generated signals. The phase difference is proportional to the mass flow rate of the material flowing through the tubes 130 and 130'. This value representing the phase difference (in units of counter counts) is provided as input data to the processing circuit 210 via line 205.

The mass and volumetric flow rates of the material through the tubes 130 and 130' may be accomplished using any of a number of known methods. These additional methods of calculating mass flow rate are well known to those of ordinary skill in the art, and the reader is therefore interested in referring to the following patents which further illustrate the calculation of mass flow rate: U.S. patent Re31450 to Smith on 11/1982, U.S. patent 5231884 to Zolock on 3/8/1993 and U.S. patent 4914956 to Young et al on 10/4/1990.

The natural frequency of vibration of the flow tubes 130 and 130' is measured by monitoring the signal from one of the two sensors. From right sensor 170_RThe resulting signal is supplied via line 206 to processing circuitry 210. The processing circuit 210 can operate on the right sensor 170_RThe frequency output counts to determine the frequency of vibration of vibrating tubes 130 and 130'.

Temperature element RTD190 is connected by line 195 to RTD input circuit 203 which provides a constant current to temperature element RTD190, linearizes the voltage across the RTD and converts this voltage to a pulse stream having a proportional frequency that varies proportionally to any change in RTD voltage using a voltage-to-frequency converter (not shown). The resulting pulse stream produced by circuit 203 is provided as an input signal to processing circuit 210 via line 209.

The density measurement processing circuit 210 in fig. 2 includes a microprocessor 211 and some memory devices including a ROM memory 212 and a RAM memory 213. The ROM212 stores permanent information used by the microprocessor 211 in performing its functions, and the RAM213 stores temporary information used by the microprocessor 211. The microprocessor with its ROM and RAM memories and the bus system 214 controls all functions of the processing circuit 210 so that it can accept input signals as described herein and process them as needed to provide the various data items produced by the coriolis effect densitometer of the invention to the application device 29 via line 26. The processing circuit 210 periodically updates the information available on the application device 29. The information provided to the application device 29 via line 26 includes mass flow rate, volumetric flow rate and density information. The application device 29 may either comprise a meter that visually displays the density information generated or may comprise a process control system controlled by the density signal on line 26.

The processing circuitry 210, including the microprocessor 211 and the memory devices 212 and 213, operate in accordance with the present invention to provide high precision density information. As described in detail below in connection with fig. 4 and 5, this high accuracy density information is derived according to the following steps, which include: according to the speed sensor 170_LAnd 170_RThe signal provided measures the natural frequency of the vibrating tube, calculates the measured density according to known equations, and modifies the measured density to compensate for the effects of such factors as the measured density varies with the mass flow rate of the material flowing through the tubes 130 and 130 ', and with the temperature of the tubes 130 and 130'. The accuracy of such density output data is much greater than when the measured density is not corrected or when the natural frequency is corrected without correcting the density.

Effect of Mass flow Rate on Density measurement (FIG. 3)

As mentioned above, the natural frequency of a vibrating tube decreases as the mass flow rate of material flowing through the tube increases. Since the basic density measurement depends on the relationship between the frequency and the density of the vibrating tube, this effect directly affects the measured density.

Figure 3 shows the effect of mass flow rate on the accuracy of density measurement. The vertical axis of FIG. 3 corresponds to density error at.001 g/cm³And (4) showing. The horizontal axis represents mass flow rate in pounds per minute (pounds per minute). Lines 301 and 302 represent the effect of a straight tube densitometer configuration on mass flow rate. Line 301 represents the error in density measurement over a range of mass flow rates for a flowing material having a Specific Gravity Unit (SGU) of 1.194. Line 302 represents the error in density measurement over a range of mass flow rates for a flowing material having a Specific Gravity Unit (SGU) of 0.994. In both cases, the physical vibration structure is the same. Except that the flow material within the tube is vibrated. Figure 3 depicts that the density measurement is dependent on the mass flow rate of the material flowing through the flow tube. Lines 301 and 302 show that the dependence of mass flow rate for materials of different densities is different for a straight tube densitometer. Lines 303 and 304 represent the effect of mass flow rate on density for a curvilinear tube densitometer having a fluid capacity similar to that of the straight tube densitometer used to generate the data for lines 301 and 302. As mentioned above, the resonant frequency of a curved tube densitometer is less sensitive to the effect of mass flow rate than the resonant frequency of a straight tube densitometer, which is shown in FIG. 3. Line 303 represents data for the same fluid as line 301 (1.194SGU) and line 304 represents data for the same fluid as line 302 (0.994 SGU). It is apparent in fig. 3 that the difference between the data of line 303 and the data of line 304 is difficult to distinguish, which illustrates the fact that in a curvilinear tube densitometer, the density reading error due to mass flow rate does not change for fluids of different densities.

The effect of the temperature of the vibrating tube on the density measurement is not shown in fig. 3. FIG. 6, discussed below, illustrates the combined effect of mass flow rate and temperature.

Description of Density correction (FIG. 4)

Fig. 4 illustrates in flow chart form how microprocessor 211 and memories 212 and 213 operate to calculate density values that compensate for the effect of mass flow rate on measured density. Yet another embodiment of the present invention that further compensates for the effects of temperature on density compensation is discussed below with reference to fig. 5 and 6.

During process step 401, the density measurement process begins with the microprocessor 211 accepting input and setting information from the ROM212 and RAM213 via the system bus 214, and the input signals to the processing circuitry 210 are as described. The signals received by the microprocessor 211 during this process are a signal indicative of the flow tube vibration Frequency (FREQ), a temperature signal (RTD) and a measured mass flow rate signal (M)_m). Also provided to the microprocessor 211 during process step 401 are several constants that the microprocessor 211 uses in determining the density. These constants K₁、K₂、K₃And t_cStored in ROM212 and RAM213 when calibrating the mass flow sensor 10 and the metering electronics 20.

Correction constant K₁And K₂Is calculated by measuring the period of vibration of one or some of the vibrating tubes for two different materials of known density. Correction constant K₃Is determined by calculating the measured density error from the known mass flow rate. This may be used to determine the correction constant K₁And K₂Or a different material may be used. As mentioned above, K is calculated at the correct densitometer₁、K₂And K₃And stores them in the memory devices 212 and 213.

Correction constant t_cIs related to the young's modulus of the material of which the vibrating tube is made. It is known that the young's modulus, which represents the stiffness of a pipe, varies with temperature. The change in stiffness of the vibrating tube results in a change in the natural frequency of the vibrating tube. The correction constant t is as described below_cFor compensating for variations in the stiffness of the vibrating tube.

During step 402, the microprocessor 211 uses the FREQ signal to determine vibrationThe vibration frequency of the tube. The microprocessor 211 also determines the period of the measuring tube (T) by calculating the reciprocal of the vibration frequency_m)。

During step 403, the microprocessor 211 calculates the measured density (D) according to the following formula_m)：In which D is_mIs the measured density (g/cm) of the material³)T_mIs to measure the tube period (second) K₁Is equal to K₂T_a ²-D_aK₂Is equal to d/(T)_w ²-T_a ²)D_wIs the density of water (g/cm) at the time of correction³)D_aIs the density of air (g/cm) at the time of correction³) D is D_w-D_a(g/cm³)t_cIs the temperature compensation factor (% change, in T)² _m/℃)/100)T_aThe tube period of the air not flowing at the time of correction was corrected to 0 ℃ C (second) T_wThe tube period of water that did not flow at the time of correction was corrected to 0 ℃ C (second) t_mIs the measured temperature (. degree.C.)

Measurement of Density and constant K₁、K₂And t_cThe same calculations as used in prior art densitometers, such as those described by Ruesch.

During step 404, the measured density (D) is measured_m) Compensating for the effect of the mass flow rate in order to determine a compensated density (D)_c)。

Compensated density (D)_c) Calculated as follows:

D_c＝D_m-K₃(M_m)²in which the number of the first and second groups is reduced,

D_mis the measured density (g/cm)³)

D_cIs compensated density (g/cm)³)

M_mIs the measured mass flow rate (g/min)

K₃Is equal to D_k3/M_k3 ²

D_k3At a mass flow rate M_k3Error in density (g/cm) measured when corrected³)。

During step 405, compensated density information (D)_c) Is provided to the application device 29 where the information is displayed, recorded or used in the process control system.

Combined effect of Mass flow Rate and temperature on Density measurement (FIG. 5)

In another embodiment of the invention, the compensation factor K is affected by the effect of the tube temperature on the mass flow rate induced density error₃Compensating itself. The mass flow rate has a slightly different effect on the density measurement at different vibrating tube temperatures due to the change in young's modulus. This effect is shown in fig. 5, where line 501 represents the density error caused by the mass flow rate in a given densitometer at a temperature of 30 ℃, and line 502 represents the density error caused by the mass flow rate in the same densitometer at a temperature of 100 ℃. To compensate for this effect, a correction constant K is set₄。

Calculating K₄The following were used:in which the number of the first and second groups is reduced,

D_k4at a temperature t_k4And mass flow rate M_k4Density reading error (g/cc)

K₃Predetermined correction constant

t_k3Determination of K₃Temperature (. degree.C.) used

t_k4Determination of K₄Temperature (. degree.C.) used

M_k4Determination of K₄Mass flow rate (g/sec) used

K is determined during the calibration in the following manner₄. In calculating K₃Thereafter, the material is again passed through the densitometer at a known mass flow rate, but this time at a different time than calculating K₃At the temperature of (c). Density error determination K at such different operating temperatures is used as described below₄. The correction constant K is used as described below₄So as to compensate the correction constant K for the effect of temperature on the compensation of the mass flow rate₃。

Density correction for Mass flow Rate including temperature Compensation (FIG. 6)

The invention can be used to perform a correction of the measured density for the effect of temperature on the mass flow rate induced density error in exactly the same way as described in figure 4. Therefore, only steps different from the process described in connection with fig. 4 will be described in detail, thereby simplifying the description of fig. 6.

In step 601, the microprocessor 211 accepts all the signals and information described in relation to step 401 of FIG. 4, and in addition thereto, the correction constant K₄And t_k3。

In step 602, the microprocessor 211 determines the frequency and period of the vibrating tube as in step 402 of FIG. 4.

In step 603, the microprocessor 211 calculates the measured density (D) as in step 403 of FIG. 4_m)。

In step 604, the microprocessor 211 calculates the compensated density (D) according to_c)：

D_c＝D_m-K₃[1+K₄(t_m-t_K3)](M_m)²In which D is_mIs the measured density (g/cc) D_cIs a corrected density (g/cc) M_mIs the measured mass flow rate (g/sec) t_mIs the measured temperature (. degree. C.) t_k3Is to calculate K₃At a temperature (. degree. C.) K₃And K₄As defined above

During step 605, the compensated density information is provided to the application means 29 and displayed or used in the same way as described with respect to fig. 4.

From K₄Provided to pair K₃Is linear. The actual functional relationship of density error due to mass flow rate versus temperature is not a simple linear relationship. It will be apparent to one of ordinary skill in the art that at K₄May include different compensation factors in order to characterize the density measurement error versus temperature caused by the mass flow rate in different ways.

Density measurement improvements of the invention (FIG. 7)

Figure 7 shows the improvement in density measurement performance obtained with the present invention. The data for making curves 701-704 is generated from the analysis model discussed above. Curve 701 represents uncorrected density measurement error. Curve 702 represents the density measurement error using the present invention when the density measurement is performed at the same temperature at which the density correction is completed. Curve 703 represents the density measurement error compensated for mass flow rate compensation using only mass flow rate compensation and not the temperature effects experienced. The temperature difference between the corrected temperature and the measured temperature represented by curve 703 is 50 ℃. Curve 704 represents the density measurement error using the mass flow rate compensation portion and the temperature compensation portion of the present invention when the measured temperature is different from the temperature at which density correction is accomplished. The temperature difference represented by the data for plot 704 is the same as the temperature difference represented by the data for plot 703.

The advantages of the present invention are apparent in the field of density measurement. It is obvious that the claimed invention illustrates these preferred embodiments, but also includes other modifications and variants within the scope and spirit of the inventive concept.

In addition, the materials whose temperature can be measured using the method and apparatus of the present invention can include liquids, gases, mixtures thereof, and any flowable material, such as different types of slurries. The mass flow rate of the flowable material may be generated by a device including a densitometer, or may be generated by a separate device and provided to a densitometer of the invention. Also, the temperature information utilized by the method of the present invention may be obtained from a temperature sensor that is part of the densitometer, as described herein, or may be provided by some other temperature sensing device.

Claims (19)

1. A method of operating an apparatus (5) for determining the density of a material flowing through a flowmeter (10) having a vibrating tube device (130, 130 ') in which a measured density of the flowing material varies as a flow rate of the flowing material through the vibrating tube device (130, 130') varies, the method comprising the steps of:

measuring the vibration period T of said vibrating tube means while said material is flowing therein_m(FREQ，402)，

Corresponding to said vibration period T_mSaid measuring producing a measured density value D of said flowable material_m，

Receiving a mass flow rate value M representing said mass flow rate of said flow material through said vibrating tube (130, 130')/_m，

The method is characterized in that:

producing a flow rate influencing factor k defining sensitivity of said determining of density in response to a change in said mass flow rate of said flowing material₃；

Applying said flow rate by a factor k₃Multiplied by said measured mass flow rate M_mIn order to determine the mass flow rate induced density error value k₃(M_m)²；

Subtracting said measured density value by a density error value k substantially equal to said mass flow rate induced₃(M_m)²In order to determine a corrected density value D_c(ii) a And

the corrected density value D is added_cTo the output device (29).

2. The method according to claim 1, characterized in that said generating (401) said flow rate effect factor k₃Comprises the following steps:

measuring a difference between a first corrected density of the flow material measured at a first corrected mass flow rate and a second corrected density of the flow material measured at a second corrected mass flow rate;

determining said mass flow rate effect factor relative to said measured density difference;

and storing said mass flow rate effect factor in a memory.

3. The method according to claim 2, characterized in that said mass flow rate influencing factor (K)₃) Is determined by solving the following mathematical formula:

K₃＝(D₁-D₂)/(M₁-M₂)²in which the number of the first and second groups is reduced,

K₃is the mass flow rate correction constant as described,

D₁according to a first mass flow rate (M)₁) A measured first measured density of said flowable material,

D₂according to a second mass flow rate (M)₂) A second measured density of the flowable material measured.

4. Method according to claim 1, characterized in that said corrected density value (D)_c) Is determined by solving the following mathematical formula:

D_c＝D_m-K₃(M_m)²in which D is_cIs corrected density, D_mMeasured Density, K₃Is said flow rate correction constant, M_mIs said measured flow rate.

5. The method of claim 1, wherein the step of generating a measured density value comprises:

calculating the measured density value relative to the measured vibration period, wherein the measured density value is linear with respect to a square of the measured vibration period.

6. Method according to claim 5, characterized in that said measured density (D)_m) Is determined by solving the following mathematical formula:

in which the number of the first and second groups is reduced,

D_mis the measured density (g/cm) of the material³)

T_mIs the measured tube period (seconds)

K₁Is equal to K₂T_a ²-D_a

K₂Is equal to d/(T)_w ²-T_a ²)

D_wIs the density of water (g/cm) at the time of correction³)

D_aIs the density of air (g/cm) at the time of correction³)

D is D_w-D_a(g/cm³)

t_cIs the temperature compensation factor ((% change in terms of T)₂ ^m/℃)/100)

T_aThe tube period of the air not flowing at the time of correction was corrected to 0 deg.C (second)

T_wThe tube period of the water not flowing at the time of correction was corrected to 0 deg.C (second)

t_mIs the measured temperature (. degree. C.)

7. The method of claim 1 wherein said step of calculating trimmed density values further comprises the steps of:

reading from memory a flow rate effect factor of said flow meter, wherein said flow rate effect factor defines a sensitivity of a measured density to a mass flow rate of said flow material;

receiving a temperature value, wherein said temperature value is representative of the temperature of said flowable material;

adjusting the flow rate action factor according to the temperature value; and

applying said temperature-adjusted flow rate influencing factor to said measured density to facilitate determination of a corrected density.

8. The method of claim 7, wherein said step of adjusting said flow rate influencing factor further comprises the steps of:

reading a temperature compensation factor from a second memory, wherein said temperature compensation factor defines a sensitivity of said flow rate influencing factor to temperature changes in said flow material; and

applying said temperature compensation factor to said flow rate effect factor to adjust said flow rate effect factor in response to the effects of temperature changes in said flowing material.

9. The method of claim 8, wherein the temperature compensation factor is determined by solving the following mathematical formula:in which the number of the first and second groups is reduced,

D_k4at a temperature t_k4And mass flow rate M_k4Measured Density of (D)_m) Error (g/cc)

K₃Is a predetermined correction constant

t_k3Is to determine K₃Temperature (. degree.C.) used

t_k4Is to determine K₄Temperature (. degree.C.) used

M_k4Is to determine K₄Mass flow rate (g/sec) used

10. The method of claim 9 wherein the step of applying said temperature adjusted flow rate influencing factor to said measured density and said measured mass flow rate comprises solving the following mathematical formula:in which the number of the first and second groups is reduced,

D_mis the measured density (g/cc)

D_cIs corrected density (g/cc)

M_mIs the measured mass flow rate (g/sec)

t_mIs the measured temperature (. degree. C.)

t_k3Is to correct K₃Temperature (. degree.C.)

K₃And K₄As defined above

11. An apparatus (20) for determining the density of a material flowing through a flow meter (10) having a vibrating tube device (131, 131'), in which a measured density of the flowing material changes as a flow rate of the material through the vibrating tube device changes, the apparatus comprising:

for measuring (170) the material as it flows therethrough_R206, 210) of said vibrating tube device (131, 131')/said vibrating tube device having a vibration period T_mThe apparatus of (1);

for according to said vibration period T_mSaid measuring of (210) results in a measured density value D of said flowable material_mThe apparatus of (1);

for receiving (170)_L，170_R201, 210) represents the mass flow rate M of the material flowing through said vibrating tube (131, 131')/s_mMass flow rate value M_m，

It is characterized by also comprising:

for generating (210) said flow material defining said measured densityFlow rate effect factor k of sensitivity of change of mass flow rate₃The apparatus of (1);

for applying said flow rate by a factor k₃Multiplying (210) said measured mass flow rate to obtain a mass flow rate induced density error value k₃(M_m)²The apparatus of (1);

for subtracting (210) from said measured density value a value substantially equal to the mass flow rate M_mInduced density error value k₃(M_m)²In order to determine a corrected density value D_cThe apparatus of (1); and

means for transmitting (210, 26) said corrected density value to output means (29).

12. The apparatus of claim 11 wherein said flow rate influencing factor is determined by solving the following mathematical formula:

K₃＝(D₁-D₂)/(M₁-M₂)²in which the number of the first and second groups is reduced,

K₃is the mass flow rate correction constant as described,

D₁according to a first mass flow rate (M)₁) A measured first measured density of said flowable material,

D₂according to a second mass flow rate (M)₂) A second measured density of the flowable material measured.

13. The apparatus of claim 11 wherein said trimmed density value is determined by solving the following mathematical equation:

D_c＝D_m-K₃(M_m)²in which D is_cIs corrected density, D_mIs the measured density, K₃Is said flow rate correction constant, M_mIs said measured flow rate.

14. The apparatus of claim 11, wherein said means for generating a measured density value further comprises:

means (40) for calculating the measured density value from the measured vibration period, wherein the measured density value is linear with the square of the measured vibration period.

15. Apparatus according to claim 11, characterized in that said measured density value (D)_m) Is determined by solving the following mathematical formula:in which D is_mIs the measured density (g/cm) of the material³)T_mIs to measure the tube period (second) K₁Is equal to K₂T_a ²-D_aK₂Is equal to d/(T)_w ²-T_a ²)D_wIs the density of water (g/cm) at the time of correction³)D_aIs the density of air (g/cm) at the time of correction³) D is D_w-D_a(g/cm³)t_cIs the temperature compensation factor ((% change in terms of T)² _m/℃)/100)T_aThe tube period of the air not flowing at the time of correction was corrected to 0 ℃ C (second) T_wThe tube period of water that did not flow at the time of correction was corrected to 0 ℃ C (second) t_mIs the measured temperature (. degree. C.).

16. The apparatus of claim 11 wherein said means for calculating trimmed density values comprises:

means for reading (210, 211, 214) from memory (212) a flow rate impact factor of said flowmeter, wherein said flow rate impact factor defines a sensitivity of a measured density to a mass flow rate of said flowing material;

-means for receiving (190, 203) a temperature value, wherein said temperature value is representative of the temperature of said flowable material;

means for adjusting (210) said flow rate influencing factor in accordance with said temperature value; and

means for applying (210) the temperature-adjusted flow rate effect factor to the measured density to facilitate determination of a corrected density.

17. The apparatus of claim 16 wherein said means for adjusting said flow rate influencing factor comprises:

-means for reading (211, 214) a temperature compensation factor from a second memory (212), wherein said temperature compensation factor defines a sensitivity of said flow rate influencing factor to temperature variations of said flowing material; and

means for applying (604) said temperature compensation factor to said flow rate effect factor to adjust said flow rate effect factor in response to the effect of temperature changes in said flowing material.

18. The apparatus of claim 17 wherein said temperature compensation factor is determined by solving the following mathematical formula:in which the number of the first and second groups is reduced,

D_k4is at a temperature t_k4And mass flow rate M_k4Measured Density of (D)_m) Error of (g/cc)

K₃Is a predetermined correction constant

t_k3Is to determine K₃Temperature (. degree.C.) used

t_k4Is to determine K₄Temperature (. degree.C.) used

M_k4Is to determine K₄Mass flow rate (g/sec) used

19. The apparatus of claim 18 wherein the means for applying the temperature adjusted flow rate influencing factor to the measured density and the measured mass flow rate comprises solving the following mathematical formula:

in which the number of the first and second groups is reduced,

D_mis the measured density (g/cc)

D_cIs corrected density (g/cc)

M_mIs the measured mass flow rate (g/sec)

t_mIs the measured temperature (. degree. C.)

t_k3Is to correct K₃Temperature (. degree.C.)

K₃And K₄As previously defined.