Compensating for frequency change in flowmeters
View Patent ↗A method for calculating a property of a fluid includes inducing motion in a conduit such that the conduit oscillates in a first mode of vibration and a second mode of vibration. The first mode of vibration has a corresponding first frequency of vibration and the second mode of vibration has a corresponding second frequency of vibration. The conduit contains a fluid. The first frequency of vibration is determined, and the second frequency of vibration is determined. A property of the fluid based on the first frequency of vibration and the second frequency of vibration is calculated.
1. A method comprising:
inducing motion in a conduit such that the conduit oscillates in a first mode of vibration and a second mode of vibration, the first mode of vibration having a corresponding first frequency of vibration and the second mode of vibration having a corresponding second frequency of vibration, wherein the conduit contains a fluid;
determining the first frequency of vibration;
determining the second frequency of vibration; and
calculating a density of the fluid based on the first frequency of vibration and the second frequency of vibration using
ρ
0
=
1
2
(
D
4
+
E
4
+
4
D
2
E
2
ω
1
2
ω
2
2
+
(
D
4
-
E
4
)
2
)
,
where ω 1 is the first frequency, ω 2 is the second frequency, and D 2 , D 4 , E 2 , and E 4 are calibration constants related to physical properties of the conduit.
2. The method of claim 1 further comprising:
determining a first temperature and a second temperature; and
determining the calibration constants based on the first and second temperatures such that the calculation of the density is compensated for the affect of a differential between the first temperature and the second temperature.
3. The method of claim 1 , further comprising calculating a mass flow rate of the fluid.
4. The method of claim 3 further comprising:
measuring the oscillation of the conduit at a first location along the conduit and at a second location along the conduit;
determining a phase difference based on the oscillation at the first location and the oscillation at the second location; and
wherein the mass flow rate is calculated using:
Mfact
=
(
ω
2
2
ω
1
2
(
1
-
2
k
tan
2
(
φ
2
)
)
-
1
)
(
ω
20
2
ω
10
2
-
1
)
nom
m
.
correcrted
=
Mfact
·
K
(
ω
20
2
ω
10
2
-
1
)
nom
·
1
ω
2
tan
(
φ
2
)
·
(
1
+
k
m
tan
2
(
φ
2
)
)
,
where ω 1 is the first frequency, ω 2 is the second frequency, ω 10 is the first frequency at a zero-flow rate, ω 20 is the second frequency at the zero-flow rate, k and k m are calibration constants related to physical properties of the conduit, and φ is the phase difference.
5. The method of claim 1 further comprising:
receiving at least one signal from a sensor configured to monitor the oscillation of the conduit; and
wherein determining the first frequency and the second frequency includes determining the first frequency and the second frequency based on the at least one sensor signal.
6. The method of claim 1 further comprising:
determining physical properties associated with the conduit;
determining an expression associated with one of the first frequency or the second frequency based on the physical properties; and
using the expression to determine one of the first frequency or the second frequency.
7. The method of claim 1 , wherein the first frequency is determined based on the second frequency by calculating:
ω
1
2
=
ω
2
2
(
E
2
+
(
E
2
-
D
2
)
t
2
)
2
(
E
2
+
(
D
4
-
E
4
)
t
2
ω
2
2
)
(
D
2
+
(
D
4
-
E
4
)
(
1
+
t
2
)
ω
2
2
)
,
where ω 1 is the first frequency, ω 2 is the second frequency,
t
2
=
k
tan
2
(
φ
2
)
where φ is the phase difference k, D 2 , D 4 , E 2 , and E 4 are calibration constants related to physical properties of the conduit.
8. The method of claim 1 , wherein the first mode is a Coriolis mode, and the second mode is a driven mode.
9. A flowmeter comprising:
a vibratable conduit, the conduit containing a fluid;
a driver configured to impart motion to the conduit such that the conduit oscillates in a first mode of vibration and a second mode of vibration, the first mode of vibration having a corresponding first frequency of vibration and the second mode of vibration having a corresponding second frequency of vibration;
a sensor configured to sense the motion of the conduit and generate a sensor signal; and
a controller to receive the sensor signal and configured to:
determine the first frequency of vibration,
determine the second frequency of vibration, and
calculate a density of the fluid based on the first frequency of vibration and the second frequency of vibration wherein the density of the fluid is calculated using
ρ
0
=
1
2
(
D
4
+
E
4
+
4
D
2
E
2
ω
1
2
ω
2
2
+
(
D
4
-
E
4
)
2
)
,
where ω 1 is the first frequency, ω 2 is the second frequency, and D 2 , D 4 , E 2 , and E 4 are calibration constants related to physical properties of the conduit.
10. The flowmeter of claim 9 further comprising:
a first temperature sensor configured to determine a first temperature;
a second temperature sensor configured to determine a second temperature; and
wherein the controller is further configured to:
determine the calibration constants based on the first and second temperatures such that the calculation of the density is not affected by a temperature differential between the first and second temperatures.
11. The flowmeter of claim 9 , further comprising calculating a mass flow rate of the fluid.
12. The flowmeter of claim 11 , wherein the controller is further configured to:
determine the oscillation of the conduit at a first location along the conduit and at a second location along the conduit; and
determine a phase difference based on the oscillation at the first location and the oscillation at the second location, wherein the mass flow rate is calculated using:
Mfact
=
(
ω
2
2
ω
1
2
(
1
-
2
k
tan
2
(
φ
2
)
)
-
1
)
(
ω
20
2
ω
10
2
-
1
)
nom
m
.
corrected
=
Mfact
·
K
(
ω
20
2
ω
10
2
-
1
)
nom
·
1
ω
2
tan
(
φ
2
)
·
(
1
+
k
m
tan
2
(
φ
2
)
)
,
where ω 1 is the first frequency, ω 2 is the second frequency, ω 10 is the first frequency at a zero-flow rate, ω 20 is the second frequency at the zero-flow rate, k and k m are calibration constants related to physical properties of the conduit, and φ is the phase difference.
13. The flowmeter of claim 9 , wherein the controller is further configured to determine the first frequency and the second frequency based on the sensor signal.
14. The flowmeter of claim 9 , wherein the controller is further configured to:
determine physical properties associated with the conduit;
determine an expression associated with one of the first frequency or the second frequency based on the physical properties; and
use the expression to determine one of the first frequency or the second frequency.
15. A flowmeter transmitter comprising:
at least one processing device; and
a storage device, the storage device storing instructions for causing the at least one processing device to:
induce motion in a conduit such that the conduit oscillates in a first mode of vibration and a second mode of vibration, the first mode of vibration having a corresponding first frequency of vibration and the second mode of vibration having a corresponding second frequency of vibration, wherein the conduit contains a fluid;
determine the first frequency of vibration;
determine the second frequency of vibration; and
calculate a density of the fluid based on the first frequency of vibration and the second frequency of vibration, wherein the density of the fluid is calculated using:
ρ
0
=
1
2
(
D
4
+
E
4
+
4
D
2
E
2
ω
1
2
ω
2
2
+
(
D
4
-
E
4
)
2
)
,
where ω 1 is the first frequency, ω 2 is the second frequency, and D 2 , D 4 , E 2 , and E 4 are calibration constants related to physical properties of the conduit.
16. The transmitter of claim 15 further storing instructions for causing the at least one processing device to:
determine a first temperature and a second temperature; and
determine the calibration constants based on the first and second temperatures such that the calculation of the density is not affected by a temperature differential between the first and second temperatures.
17. The transmitter of claim 15 , further comprising calculating a mass flow rate of the fluid.
18. The transmitter of claim 17 further storing instructions for causing the at least one processing device to:
determine the oscillation of the conduit at a first location along the conduit and at a second location along the conduit; and
determine a phase difference based on the oscillation at the first location and the oscillation at the second location, wherein the mass flow rate is calculated based on:
Mfact
=
(
ω
2
2
ω
1
2
(
1
-
2
k
tan
2
(
φ
2
)
)
-
1
)
(
ω
20
2
ω
10
2
-
1
)
nom
m
.
corrected
=
Mfact
·
K
(
ω
20
2
ω
10
2
-
1
)
nom
·
1
ω
2
tan
(
φ
2
)
·
(
1
+
k
m
tan
2
(
φ
2
)
)
,
where ω 1 is the first frequency, ω 2 is the second frequency, ω 10 is the first frequency at a zero-flow rate, ω 20 is the second frequency at the zero-flow rate, k and k m are calibration constants related to physical properties of the conduit, and φ is the phase difference.
19. The transmitter of claim 15 further storing instructions for causing the at least one processing device to determine the first frequency and the second frequency based on a sensor signal from a sensor configured to sense the motion of the conduit.
20. The transmitter of claim 15 further storing instructions for causing the at least one processing device to:
determine physical properties associated with the conduit;
determine an expression associated with one of the first frequency or the second frequency based on the physical properties; and
use the expression to determine one of the first frequency or the second frequency.
21. The transmitter of claim 15 , wherein the first mode is a Coriolis mode, and the second mode is a driven mode.
22. A flowmeter transmitter comprising:
at least one processing device; and
a storage device, the storage device storing instructions for causing the at least one processing device to:
induce motion in a conduit such that the conduit oscillates in a first mode of vibration and a second mode of vibration, the first mode of vibration having a corresponding first frequency of vibration and the second mode of vibration having a corresponding second frequency of vibration, wherein the conduit contains a fluid;
determine the first frequency of vibration;
determine the second frequency of vibration;
calculate a mass flow rate of the fluid based on the first frequency of vibration and the second frequency of vibration;
determine the oscillation of the conduit at a first location along the conduit and at a second location along the conduit; and
determine a phase difference based on the oscillation at the first location and the oscillation at the second location, wherein the mass flow rate is calculated based on:
Mfact
=
(
ω
2
2
ω
1
2
(
1
-
2
k
tan
2
(
φ
2
)
)
-
1
)
(
ω
20
2
ω
10
2
-
1
)
nom
m
.
corrected
=
Mfact
·
K
(
ω
20
2
ω
10
2
-
1
)
nom
·
1
ω
2
tan
(
φ
2
)
·
(
1
+
k
m
tan
2
(
φ
2
)
)
,
where ω 1 is the first frequency, ω 2 is the second frequency, ω 10 is the first frequency at a zero-flow rate, ω 20 is the second frequency at the zero-flow rate, k and k m are calibration constants related to physical properties of the conduit, and φ is the phase difference.
23. The transmitter of claim 22 , wherein the first mode is a Coriolis mode, and the second mode is a driven mode.
24. The transmitter of claim 22 further storing instructions for causing the at least one processing device to determine the first frequency and the second frequency based on a sensor signal from a sensor configured to sense the motion of the conduit.
25. A flowmeter transmitter comprising:
at least one processing device; and
a storage device, the storage device storing instructions for causing the at least one processing device to:
induce motion in a conduit such that the conduit oscillates in a first mode of vibration and a second mode of vibration, the first mode of vibration having a corresponding first frequency of vibration and the second mode of vibration having a corresponding second frequency of vibration, wherein the conduit contains a fluid;
determine the first frequency of vibration;
determine the second frequency of vibration; and
calculate a property of the fluid based on the first frequency of vibration and the second frequency of vibration, wherein the first frequency is determined based on the second frequency by calculating:
ω
1
2
=
ω
2
2
(
E
2
+
(
E
2
-
D
2
)
t
2
)
2
(
E
2
+
(
D
4
-
E
4
)
t
2
ω
2
2
)
(
D
2
+
(
D
4
-
E
4
)
(
1
+
t
2
)
ω
2
2
)
,
where ω 1 is the first frequency, ω 2 is the second frequency,
t
2
=
k
tan
2
(
φ
2
)
where φ is the phase difference k, D 2 , D 4 , E 2 , and E 4 are calibration constants related to physical properties of the conduit.
26. The transmitter of claim 25 , wherein the first mode is a Coriols mode, and the second mode is a driven mode.
27. The transmitter of claim 25 , wherein the property of the fluid is the density of the fluid.
28. The transmitter of claim 25 , wherein the property of the fluid is the mass flow rate of the fluid.