HK1061066B

HK1061066B - Apparatus and method for compensating mass flow rate of a material when the density of the material causes an unacceptable error in flow rate

Info

Publication number: HK1061066B
Application number: HK04104078.3A
Authority: HK
Inventors: J. Hays Paul; T. Patten Andrew
Original assignee: Micro Motion, Inc.
Priority date: 2000-11-03
Filing date: 2001-10-26
Publication date: 2006-08-04

Description

Apparatus and method for compensating for material mass flow rate when material density causes unacceptable error in flow rate

Technical Field

The present invention relates to the calculation of the mass flow rate of a material through a Coriolis (Coriolis) flowmeter. In particular, the present invention relates to compensating for flow rate errors in measuring flow rate caused by the density of the material being measured. More particularly, the present invention relates to determining when a material density causes unacceptable errors in mass flow rate and compensating for density-induced errors in flow rate.

Background

It is known to use Coriolis effect mass flowmeters to measure mass flow and other information of materials flowing through a conduit as disclosed in U.S. patent No.4,491,025 issued to j.e.smith et al at 1 st 1 1985 and re.31,450 issued to j.e.smith at 11 st 2 st 1982. These flow meters have one or more flow tubes that are structurally bent. Each flow tube configuration in a Coriolis mass flowmeter has a set of natural vibration modes that can be simple bending, torsional, radial, or coupled types. Each flow tube is driven to resonate in one of these natural modes. The natural vibration mode of vibration, the material fill system, is defined in part by the combined mass of the flow tube and the material in the flow tube. Material enters the flow meter from a connecting pipe on the inlet side of the flow meter. The material then passes through the flow tube and out of the flow meter to a conduit attached to the outlet side.

One driver will apply a force to the flow tube. The force vibrates the flow tube. When no material flows through the flowmeter, all points along the flow tube vibrate in phase. As the material begins to flow through the flow tube, Coriolis acceleration causes each point along the flow tube to have a different phase than other points along the flow tube. The phase on the inlet side of the flow tube lags the driver and the phase on the outlet side leads the driver. The sensors are placed at two different points on the flow tube to generate sinusoidal signals indicative of the motion of the flow tube at these two points. The phase difference between the two signals received from the sensors is calculated in units of time.

The phase difference between the two sensor signals is proportional to the mass flow rate through the flow tube material. The mass flow rate of the material is determined by multiplying the phase difference by a flow calibration factor. The flow calibration factor is determined by material properties and cross-sectional properties of the flow tube.

Material properties can affect the mass flow rate measured by a Coriolis flowmeter, which is a problem. Some material properties that may affect the measured flow rate include density, temperature, pressure, and viscosity. In most cases, Coriolis flow meters are designed to be insensitive to errors caused by these properties. In other cases, the meter electronics compensates for errors in measuring the mass flow rate caused by these properties. For example, meter electronics can typically compensate for errors caused by material temperature and pressure.

Under normal operating conditions sometimes the errors caused by material properties are negligible and the errors in the flow rate are not corrected. However, after a certain threshold is exceeded, the properties of the material may cause unacceptable errors. For example, in most flow meters, the density of the material does not generally affect the flow rate for most densities. However, in low flow rate Coriolis flow meters, the density of the material is found to affect the measured flow rate of the material after a certain threshold. For this discussion, the low flow rate is 5 lbs./minute or less. At this time, it is not known what caused the errors.

It is therefore desirable to determine when the density of the measured material exceeds a threshold and to compensate for density-induced errors in the flow rate.

Disclosure of Invention

The above and other problems are solved and an advance in the art is made by providing a method and apparatus for compensating for density-induced errors in the measurement of mass flow rate by a Coriolis flowmeter. One advantage of the present invention is that errors in the measured flow rate due to density are corrected. A second advantage of the present invention is that when a non-linear equation capable of more accurately fitting the measurement data is used to determine the compensation factor, its compensation is more accurate than other systems. A third advantage of the present invention is that compensation only occurs after the density exceeds a certain threshold, wherein the error caused by the density exceeds an unacceptable level. This reduces the amount of compensation required to provide an accurate flow rate.

According to the invention, the determination of the density compensated mass flow rate is performed in the following manner. First, the material flows through a vibrating conduit of a Coriolis flowmeter. The pipe vibrates and a sensor attached to the pipe generates a signal indicative of the movement of the pipe. Signals from sensors attached to the vibrating conduit are received by meter electronics. The uncompensated flow rate of the material is then calculated by the meter electronics from the received signals. A density compensation factor is then determined using the uncompensated flow rate and non-linear information relating density to error in the flow rate. The density compensated flow rate is then generated by applying the density compensation factor to the uncompensated flow rate.

According to the present invention, the meter electronics can also calculate the material density from the signals received from the sensors. The calculated density is then compared to a threshold value to determine if the density exceeds the threshold value. A density compensated flow rate is generated if the density exceeds a threshold. Otherwise, outputting the uncompensated flow rate.

In an alternative embodiment, if the threshold is not exceeded, a linear density compensation factor may be calculated using the uncompensated flow rate and linear information relating the error in mass flow rate to material density. A compensated flow rate can be calculated by applying the linear density compensation to the uncompensated mass flow rate.

According to the present invention, the density compensation factor may be determined by inserting the uncompensated flow rate into an nth order polynomial equation relating density to flow rate error data, where N is greater than 1. The polynomial of degree N is a curve fit to the density with respect to error rate in the measured mass flow. The polynomial expression may be generated by performing an N-th order curve fit to the density for the flow rate error data, where N is greater than 1.

One aspect of the present invention is a method of determining a density compensated flow rate of material through a vibrating conduit, comprising the steps of: the method includes receiving a signal from a sensor attached to the vibrating conduit, calculating an uncompensated flow rate of the material from the signal, determining a density compensation factor from the uncompensated flow rate and nonlinear information relating density to error in flow rate, and generating the density compensated flow rate by applying the density compensation factor to the uncompensated flow rate.

Another aspect is to calculate a density of the material from the signal, determine whether the density exceeds a threshold, and generate the density compensated flow rate in response to the density exceeding the threshold.

Another aspect is a pseudo density with the threshold value of 1.030.

Another aspect is that the tubing diameter is.130 inches.

Another aspect is responsive to the density not exceeding the threshold value, determining a linear density compensation factor based on the uncompensated flow rate and linear information relating an error in the uncompensated flow rate to the density of the material, and generating the compensated flow rate by applying the linear density compensation factor to the uncompensated flow rate.

Another aspect is that the step of determining a density compensation factor includes the step of inserting the uncompensated flow rate into an nth order polynomial equation relating density to flow rate error data, where N is greater than 1.

Another aspect is performing an N-th order curve fit to the density for flow rate error data to determine the N-th order polynomial equation, where N is greater than 1.

Another aspect is that the step of performing N times a curve fit comprises the step of performing a least squares curve fit once.

Another aspect is that N equals 4.

Another aspect is to calculate an uncompensated density of the material from the signal.

Another aspect is that the step of determining a density compensation factor includes the step of inserting the uncompensated flow rate and the uncompensated density into a two-dimensional polynomial equation of degree N that relates density to flow rate error data, where N is greater than 1.

Another aspect is to perform a two-dimensional N-th order curve fit on the uncompensated density and the uncompensated flow rate for the density compensation factor to determine the N-th order polynomial.

Another aspect is that the step of performing a two-dimensional nth order curve fit comprises the step of performing a first order least squares curve fit to the data for the uncompensated flow velocity and the uncompensated density to determine the two-dimensional nth order polynomial.

Another aspect is meter electronics for a Coriolis flowmeter having a processing unit providing a density compensated flow rate and including instructions for controlling the processing unit to receive signals from a sensor attached to a vibrating conduit, calculate an uncompensated flow rate for the material based on the signals, determine a density compensation factor based on the uncompensated flow rate and non-linear information relating density to error in flow rate, and generate the density compensated flow rate by applying the density compensation factor to the uncompensated flow rate. The meter electronics further includes a medium readable by the processing unit storing the instructions.

Another aspect is instructions that control the processing unit to calculate a density of the material from the signal, determine whether the density exceeds a threshold, and generate the density compensated flow rate in response to the density exceeding the threshold.

Another aspect is a density with the threshold value of 1.030.

Another aspect is instructions that control the processing unit to determine a linear density compensation factor based on the uncompensated flow rate and linear information relating an error in the uncompensated flow rate to the material density and to generate the compensated flow rate by applying the linear density compensation to the uncompensated mass flow rate in response to the density not exceeding the threshold.

Another aspect is an instruction to control the processing unit to insert the uncompensated flow rate into an nth order polynomial equation relating density to flow rate error data, where N is greater than 1.

Another aspect is an instruction that controls the processing unit to perform an nth order curve fit on the density of flow rate error data to determine the nth order polynomial equation, where N is greater than 1.

Another aspect is an instruction to control the processing unit to perform a least squares curve fit once on the density of error data.

Another aspect is that N equals 4.

Another aspect is an instruction to control the processing unit to calculate an uncompensated density of the material from the signal.

Another aspect is an instruction to control the processing unit to insert the uncompensated flow rate and the uncompensated density into a two-dimensional polynomial equation of degree N relating density to flow rate error data, where N is greater than 1.

Another aspect is an instruction to control the processing unit to perform a two-dimensional N-th order curve fit on the uncompensated density and the uncompensated flow rate with respect to the density compensation factor to determine the N-th order polynomial.

Another aspect is the instructions that control the processing unit to perform a first least squares curve fit on the data for the uncompensated flow velocity and the uncompensated density to determine the two-dimensional polynomial of degree N.

Brief Description of Drawings

The above and other advantages and aspects of the invention are explained in the following detailed description and drawings:

FIG. 1 illustrates a Coriolis flowmeter incorporating the method and apparatus of the present invention;

FIG. 2 illustrates a graph showing error rate versus flow rate for varying densities;

FIG. 3 illustrates a first embodiment of a method for compensating for density-induced errors in flow velocity in accordance with the present invention;

FIG. 4 illustrates a second embodiment of a method for compensating for density-induced errors in accordance with the present invention; and

fig. 5 illustrates a processor.

Detailed Description

The present invention relates to providing mass flow rate measurements based on a Coriolis flowmeter that compensates for errors in flow rate caused by material density. FIG. 1 illustrates a typical Coriolis flowmeter that provides a compensated mass flow rate in accordance with the present invention. The Coriolis flowmeter 100 includes a flowmeter element 110 and meter electronics 150. Meter electronics 150 is connected to flow meter component 110 by leads 120 to provide, for example, but not limited to, density, mass flow rate, volumetric flow rate, and aggregate mass flow rate information on path 125. A Coriolis flowmeter configuration is described, although it will be apparent to those skilled in the art that the present invention may be used in practice with any device having a load requiring alternating voltage current.

A Coriolis flowmeter configuration is described, although it will be apparent to those skilled in the art that the present invention may be used in practice with any device having a vibrating conduit to measure a property of a material flowing through the conduit. Another example of such a device is a vibrating tube densitometer that does not have the additional measurement capability provided by a Coriolis mass flowmeter.

The flow meter assembly 110 includes a pair of flanges 101 and 101', a manifold 102, and conduits 103A and 103B. Driver 104, sensors 105 and 105' and temperature sensor 107 are connected to conduits 103A and 103B. Spacers 106 and 106 'are used to define the axis W and W' of vibration of each pipe.

When the Coriolis flowmeter 100 is inserted into a piping system (not shown) carrying a process material to be measured, the material enters the flowmeter element 110 through the flange 101, passes through the manifold 102, where it is directed into the conduits 103A and 103B. The material then flows through the conduits 103A and 103B and back to the manifold 102 where it exits the meter assembly 110 through the flange 101'.

The conduits 103A and 103B are selected and appropriately mounted to the manifold 102 so as to have substantially the same mass distribution, inertia about the bending axes W-W and W '-W', and spring module moments, respectively. The tubes 103A-103B extend outwardly from the manifold in a substantially parallel manner.

Conduits 103A-103B are driven by driver 104 in opposite directions about respective bending axes W and W' and in a mode referred to as the first out of phase bending of the meter. The driver 104 may comprise any of a number of well-known arrangements, such as a magnet mounted to the conduit 103A and a counter-coil mounted to the conduit 103B through which an alternating current is passed to vibrate the two conduits. Meter electronics 150 applies the appropriate drive signals to driver 104 via path 112.

Sensors 105 and 105' are attached to at least one of the conduits 103A and 103B at opposite ends of the conduit to measure vibration of the conduit. The sensors 105 and 105' generate first and second sensor signals as the conduits 103A-103B vibrate. The first and second sensor signals are applied to paths 111 and 111'. The driver rate signal is applied to path 112.

A temperature sensor 107 is attached to at least one of the conduits 103A and/or 103B. The temperature sensor 107 measures the pipe temperature in order to modify the equation for the system temperature. Path 111 "carries the temperature signal from the temperature sensor 107 to meter electronics 150.

Meter electronics 150 receives the first and second sensor signals displayed on paths 111 and 111', respectively. Meter electronics 150 processes the first and second rate signals to calculate the mass flow rate, density, or other property of the material flowing through the flow meter component 10. This calculation information is applied by meter electronics 150 to an application device (not shown) on path 125. It is known to those skilled in the art that Coriolis flowmeter 100 is very similar in construction to a vibrating tube densitometer. Vibrating tube densitometers also use a vibrating conduit through which the liquid flows or, in a sampling type densitometer, in which the liquid is held. Vibrating tube densitometers also use a drive system that excites the tube to vibrate. Vibrating tube densitometers typically use only a single feedback signal because density measurements require only frequency measurements and no phase measurements. The description of the invention herein applies equally to vibrating tube densitometers.

In the Coriolis flowmeter 100, the meter electronics 150 is physically separated into two elements, a master system 170 and a signal conditioner 160. In conventional meter electronics, these elements are located in one component.

The signal conditioner 160 includes a driving circuit 163 and a sensor signal conditioning circuit 161. Those skilled in the art will recognize that in practice the driver circuit 163 and the sensor conditioning circuit 161 may be separate analog circuits or may be separate functions provided by a digital signal processor or other digital components. Driver circuit 163 generates a drive signal and applies an alternating drive current to driver 104 via path 112 of path 120. The circuitry of the present invention may be included in driver circuit 163 to provide alternating current to driver 104.

In practice, path 112 is a first and second conductor. Driver circuit 163 is communicatively coupled to sensor signal conditioning circuit 161 via path 162. Path 162 allows the drive circuit to monitor the incoming sensor signal to adjust the drive signal. Power to operate the driving circuit 163 and the sensor signal conditioning circuit 161 is supplied from the main system 170 through the first wire 173 and the second wire 174. The first wire 173 and the second wire 174 may be part of a conventional 2-wire, 4-wire cable or part of a multi-pair cable.

Sensor signal conditioning circuit 161 receives input signals from first sensor 105, second sensor 105 'and temperature sensor 107 via paths 111, 111', and 111 ″. The sensor signal conditioning circuit 161 determines the frequency of the sensor signal and may also determine the material properties flowing through the conduits 103A-103B. After determining the frequency and material properties of the signal input from the sensor 105 and 105', a parameter signal carrying such information is generated and sent to the secondary processing unit 171 in the primary system 170 via path 176. In a preferred embodiment, path 176 includes 2 wires. However, those skilled in the art will recognize that the path 176 may be carried over the first wire 173 and the second wire 174 or any other number of wires.

The main system 170 includes a power supply 172 and a secondary processing unit 171. The power supply 172 receives current from a power source and converts the received current to the appropriate power required by the system. The secondary processing unit 171 receives the parameter signals from the sensor signal conditioning circuit 161 and then performs a method of providing the user-desired material properties of the flow through the conduits 103A-103B. Such attributes may include, but are not limited to, density, mass flow rate, and volumetric flow rate.

The following invention is implemented by a processing unit. The digital signal processor or secondary processing unit 171 in the signal conditioner 160 may implement the present invention. FIG. 5 illustrates a conventional processing unit operable to implement the present invention.

The processing system 500 includes a Central Processing Unit (CPU) 501. CPU501 is a processor, microprocessor, or combination of processors and/or microprocessors that may execute instructions stored in a memory. A memory bus 502 connects the CPU501 to the memory required for executing instructions. Permanent memory, such as Read Only Memory (ROM)510, is connected to memory bus 502 by path 511. The ROM501 stores configuration instructions and other instructions needed to properly operate the processing system 500. Volatile memory, such as random access memory 520, is coupled to memory bus 502 by path 521. RAM520 stores instructions and data needed to execute applications executed by CPU 501.

An input/output (I/O) bus 503 connects the CPU501 to other devices required to execute instructions. The analog-to-digital (A/D) converter 530 allows the CPU501 to receive signals from analog circuitry, such as the sensor 105 and 105' of FIG. 1. A/D converter 530 is connected to I/O bus 503 by path 532 and receives analog signals from other circuitry (not shown). Peripheral device 540 is another device that can perform the functions required by processing system 500 in order to provide data to CPU 501. Peripheral device 540 is connected to I/O bus 503 by path 541. The memory 550 is a device such as a disk drive or diskette that provides additional data storage capability to the processing system 500. Memory 550 is connected to I/O bus 503 by path 551.

It is a problem that mass flow measurements provided by Coriolis flowmeters, such as Coriolis flowmeter 100, can be affected by the measured material properties. One such property is the density of the material. Small Coriolis flowmeters are particularly sensitive to errors caused by the density of the measured material. For purposes of discussion, a small Coriolis flowmeter is a flowmeter having a.130 inch diameter flow tube. An example of such a flow meter, the CMF 010 Coriolis flow meter, is manufactured by Micro Motion corporation, located in Boulder, Colorado.

Fig. 2 illustrates a graphical representation of the error in flow rate with a variable density material. Line 201 represents the error in the uncompensated flow rate when the flow rate of the material having a density of.9957 is varied. Line 202 represents the error in the uncompensated flow rate when the flow rate of the material having a density of.9489 is varied. Line 203 represents the error in the uncompensated flow rate when the flow rate of the material having a density of. 85284 was varied. Line 204 represents the error in the uncompensated flow rate of the material having a density of. 78922. Line 205 represents the error in the uncompensated flow rate of the material having a density of. 90452.

As can be seen from fig. 2, materials with densities close to 1.0 cause a smaller percentage error. Densities that do not approach 1.0 tend to have a percentage error of greater than.1%.

From the graph of fig. 2, one skilled in the art can see that a density that is not close to 1.0 results in a small flow meter providing an inaccurate flow rate. The present invention corrects the flow rate by multiplying the measured flow rate by a density compensation factor.

The density compensation factor may be calculated in any of the following ways: the least squares polynomial fit of the density to the uncompensated density, or the two-dimensional least squares curve fit of the uncompensated density and mass flow rate, is compared based on a lookup of the uncompensated flow rate for the compensation factor. Those skilled in the art will recognize that other data fitting methods may be used to determine the density compensation factor.

The relationship between density and flow rate can be used to compensate for flow rate errors caused by density. Fig. 3 and 4 illustrate alternative methods for providing flow rate with density compensation in accordance with the present invention. The methods illustrated in fig. 3 and 4 are performed by meter electronics 150 or by a secondary processing unit that receives data from meter electronics 150. The method 300 illustrated in fig. 3 is in accordance with a first alternative embodiment of the present invention. In method 300, each flow rate measurement is compensated for density in the following manner.

The method 300 begins at step 301 with a signal indicative of mass flow rate received from a sensor attached to a vibrating conduit. Those skilled in the art will recognize that these signals may be analog signals received directly from the sensors or digital signals representing the phase difference between the sensor signals. This is a design choice and varies depending on the type of circuitry used to perform the method.

An uncompensated flow rate is calculated in step 302. The flow rate is calculated in a conventional manner well known in the art and the description of the flow rate calculation is omitted for simplicity and clarity.

The density compensation factor is then determined in step 303. The density compensation factor may be determined in a number of different ways. A first solution is to maintain a memory storing the flow rate and an associated compensation factor or compensated flow rate. A simple lookup may then be performed to determine the compensation factor or compensation flow rate.

One prior art method of determining the compensation factor is linear or first order curve fitting of the data. The uncompensated flow rate is inserted into the equation and the appropriate density compensation factor is determined.

However, a first order curve fit does not provide an accurate representation of the data. Therefore, it is preferable to generate an nth order polynomial equation that performs a better fit to the collected data to represent the compensation factor. The uncompensated flow rate is then inserted into the equation to solve for the density compensation factor. In a preferred embodiment, a 4 th order polynomial has been determined to best fit the data, so a 4 th order equation is used. However, those skilled in the art will recognize that other sub-equations may be used depending on the accuracy of the results.

In a preferred embodiment, the following 4-degree equation has been determined to best fit the data.

DCF＝α₀+α₁m+α₂m²+α₃m³+α₄m⁴

Wherein:

α₀＝+.9983；

α₁＝+.0052；

α₂＝+.0094；

α₃＝+.0051；

α₄0008, as ═ 0008; and

m is the uncompensated flow rate

A second method of determining the compensation factor is by two-dimensional curve fitting to a polynomial of degree N. A two-dimensional curve fit is a curve fit to two data variables. In this case, curve fitting is used for the mass flow rate denoted by m and the density denoted by d. In a preferred embodiment, a least squares fit is made to the density and mass flow rate for the compensation factor. By experiments with fitting data to different polynomials, a 4 th order polynomial fit to the density and mass flow rate for the compensation factor has been determined, as shown in the following equation:

compensation factor alpha₀+(α₁×m)+(α₂×m²)+(α₃×m³)+(α₄×m⁴)+(α₅×m×d)+(α₆×d)+(α₇×d²)+(α₈×d³)+(α₉×d⁴)

Wherein:

α₁、α₂、α₃、α₄、α₅、α₆、α₇、α₈、α₉a coefficient;

m is mass flow rate; and

d is density

After the density compensation factor is determined in step 303, the density compensation factor is applied to the uncompensated mass flow rate to produce a density compensated mass flow rate in step 304, and the method 300 ends.

The method 400 illustrated in fig. 4 illustrates a second alternative embodiment for providing a flow rate that compensates for density-induced errors. In such an embodiment, the density compensation factor need not be applied to the measured flow rate if the material density is within a range that does not add unacceptable error to the measured flow rate.

The method 400 begins at step 401 by receiving a signal indicative of mass flow rate from a sensor attached to a vibrating conduit. This signal is then used to calculate an uncompensated flow rate in step 402. The flow rate is calculated in a conventional manner well known to those skilled in the art.

In step 403, the density of the material is calculated from the signal according to a conventional or well-known equation, such as:

wherein

p is the material density;

p₁density of a first known material, such as water;

p₂density of a second known material, such as air;

K₁a constant of a first known material, such as water;

K₂common to a second known material, e.g. airAn amount; and

τ is the vibration rate of the flow tube.

After the density is calculated, the calculated density is compared to a threshold density in step 404. The density may exceed, be greater than or less than a threshold density. The comparison method used is left to the person skilled in the art.

If the calculated density exceeds the threshold density, a density compensation factor is determined in step 405. The density compensation factor is determined in the manner described above in step 303 of fig. 3. The density compensation factor is then applied to the uncompensated mass flow rate and a compensated mass flow rate is generated in step 406.

If the calculated density does not exceed the threshold density, then an uncompensated flow rate may be returned at step 420. Alternatively, since it is known that linear density compensation is sufficient, the density compensation can be determined in step 411 using linear compensation. A compensated flow rate is then generated in step 412 by applying the linear density compensation factor to the uncompensated flow rate.

In step 420, the compensated flow rate calculated in step 406 or step 412 is returned and the method 400 ends.

The above is a description of a method of compensating for errors in mass flow rate caused by material density. It is expected that one of ordinary skill will be able to and will design alternative ways of implementing the system that do not depart from the literal or equivalent principles set forth in the claims below.

Claims

1. A method (400) of determining a flow rate of a material flowing through a vibrating conduit (103A, 103B), the method comprising the steps of:

receiving a signal (401) from a sensor (105, 105') attached to the vibrating conduit;

calculating an uncompensated flow rate of the material from the signal (402);

calculating a density of the material from the signal;

the method is characterized by the steps of:

determining whether the density exceeds a threshold;

in response to the density exceeding the threshold value,

determining a density compensation factor (405, 411) based on the uncompensated flow rate and information collected by a non-linear data filtering method relating density to error in flow rate, and

calculating a density compensated flow rate by applying the density compensation factor to the uncompensated flow rate (406, 412); and

in response to the density not exceeding the threshold,

outputting a flow rate that is not density compensated by the density compensation factor.

2. The method (400) of claim 1, wherein said threshold value is 1.030.

3. The method (400) of claim 1, wherein said step of determining a density compensation factor comprises the steps of:

the uncompensated flow rate is inserted into an nth order polynomial equation relating density to flow rate error data, where N is greater than 1.

4. The method (400) of claim 3, further comprising the step of:

performing an Nth order curve fit to the density for flow rate error data to determine the Nth order polynomial equation, wherein N is greater than 1.

5. The method (400) of claim 4, wherein said step of performing a curve fit N times comprises the steps of:

a least squares curve fit is performed.

6. The method (400) of claim 3, wherein N equals 4.

7. The method (400) of claim 1, wherein said step of determining a density compensation factor comprises the steps of:

inserting the uncompensated flow rate and the density into a two-dimensional polynomial equation of degree N relating density to flow rate error data, where N is greater than 1.

8. The method (400) of claim 7, further comprising the step of:

performing a two-dimensional N-th order curve fit to the density and the uncompensated flow velocity to determine the N-th order polynomial.

9. The method (400) of claim 8, wherein said performing a two-dimensional N-th order curve fit to determine said two-dimensional N-th order polynomial includes performing a least squares curve fit to the data for said uncompensated flow velocity and said density.

10. Meter electronics (150) for a coriolis flow meter (110), having a processing unit (500) for calculating a mass flow rate, and comprising:

a readable medium (550) for reading data, the readable medium (550) for storing instructions for use by a processing unit (500) for performing the steps of:

receiving a signal from a sensor (105, 105') attached to the vibrating conduit (103A, 103B),

calculating an uncompensated flow rate of the material from the signal,

calculating a density of the material from the signal;

characterized in that said readable medium (550) is designed to store additional instructions for directing a processing unit to perform the steps of:

determining whether the density exceeds a threshold;

in response to the density exceeding a threshold;

determining a density compensation factor based on the uncompensated flow rate and information relating density to flow rate error collected by a non-linear data filtering method, and

calculating a density compensated flow rate by applying the density compensation factor to the uncompensated flow rate; and if said density does not exceed a threshold value, then

11. The meter electronics (150) of claim 10 wherein said threshold value is 1.030.

12. The meter electronics (150) of claim 10 wherein said instructions to determine a density compensation factor comprise:

-instructions controlling the processing unit (500) to perform the steps of:

13. The meter electronics (150) of claim 12 wherein said instructions further comprise:

instructions to control the processing unit (500) to:

performing N curve fits to the density for flow rate error data, wherein N is greater than 1.

14. The meter electronics (150) of claim 13 wherein said instructions to perform a N-time curve fit comprise:

instructions to control the processing unit (500) to:

a least squares curve fit is performed.

15. The meter electronics (150) of claim 12 wherein N equals 4.

16. The meter electronics (150) of claim 10 wherein said instructions to determine a density compensation factor comprise:

instructions to control the processing unit (500) to:

inserting the uncompensated flow rate and the density into a two-dimensional, nth order polynomial equation relating density to flow rate error data, where N is greater than 1.

17. The meter electronics (150) of claim 16 wherein said instructions further comprise:

instructions to control the processing unit (500) to:

18. The meter electronics (150) of claim 17 wherein said instructions to perform a two-dimensional N-th order curve fit to determine said two-dimensional N-th order polynomial comprise instructions to perform a least squares curve fit to the data for said uncompensated flow velocity and said density.