Compensating for frequency change in flowmeters
View Patent ↗Motion is induced in a conduit that contains a fluid. The motion is induced 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. At least one of the first frequency of vibration or the second frequency of vibration is determined. A phase difference between the motion of the conduit at a first point of the conduit and the motion of the conduit at a second point of the conduit is determined. A quantity based on the phase difference and the determined frequency is determined. The quality includes a ratio between the first frequency during a zero-flow condition and the second frequency during the zero-flow condition. A property of the fluid is determined based on the quantity.
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 at least one of the first frequency of vibration or the second frequency of vibration;
determining a phase difference between the motion of the conduit at a first point of the conduit and the motion of the conduit at a second point of the conduit;
determining a quantity based on the phase difference and the determined frequency, wherein the quantity includes a ratio between the first frequency during a zero-flow condition and the second frequency during the zero-flow condition; and
determining a property of the fluid based on the quantity.
2. The method of claim 1 , wherein the quantity is determined by:
ω
20
2
ω
10
2
-
1
=
(
D
4
-
E
4
)
ω
2
2
+
D
2
-
E
2
(
D
4
-
E
4
)
ω
2
2
k
tan
2
(
φ
2
)
+
E
2
,
where ω 2 is the second frequency, ω 10 is the first frequency during the zero-flow condition, ω 20 is the second frequency during the zero-flow condition, k, D 2 , D 4 , E 2 , and E 4 are calibration constants related to physical properties of the conduit, and φ is the phase difference.
3. The method of claim 1 , wherein the property includes a density of the fluid contained in the conduit.
4. The method of claim 3 further comprising:
determining density calibration constants based on physical properties of the conduit;
determining a reference temperature;
determining a first temperature that influences the first mode of vibration;
determining a second temperature that influences the second mode of vibration; and
compensating the density calibration constants based on the first temperature, the second temperature, and the reference temperature;
wherein determining the property includes determining the density based the compensated density calibration constants and the quantity.
5. The method of claim 3 , wherein the density is determined based on:
ρ
^
e
=
D
2
ω
2
2
(
1
-
(
ω
20
2
ω
10
2
-
1
)
k
tan
2
(
φ
2
)
)
+
D
4
,
where ω 2 is the second frequency, ω 10 is the first frequency during a zero-flow condition, ω 20 is the second frequency during the zero-flow condition, k, D 2 and D 4 are calibration constants related to physical properties of the conduit, and φ is the phase difference.
6. The method of claim 1 , wherein the property includes a mass flow rate of the fluid contained in the conduit.
7. The method of claim 6 , wherein the mass flow rate is determined based on:
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 K is a factor related to the stiffness of the conduit, ω 2 is the second frequency, ω 10 is the first frequency during a zero-flow condition, ω 20 is the second frequency during the zero-flow condition, k m is a constant specific to the conduit, φ is the phase difference, and Mfact is
Mfact
=
(
ω
2
2
ω
1
2
(
1
-
2
k
tan
2
(
φ
2
)
)
-
1
)
(
ω
20
2
ω
10
2
-
1
)
nom
.
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 flowtube, the flowtube containing a fluid;
a driver connected to the flowtube and configured to impart motion to the flowtube 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 connected to the flowtube and configured to sense the motion of the flowtube and generate a sensor signal; and
a controller to receive the sensor signal and configured to:
determine at least one of the first frequency of vibration or the second frequency of vibration;
determine a phase difference between the motion of the conduit at a first point of the conduit and the motion of the conduit at a second point of the conduit;
determine a quantity based on the phase difference and the determined frequency, wherein the quantity includes a ratio between the first frequency during a zero-flow condition and the second frequency during the zero-flow condition; and
determine a property of the fluid based on the quantity.
10. The flowmeter of claim 9 , wherein the quantity is determined by:
ω
20
2
ω
10
2
-
1
=
(
D
4
-
E
4
)
ω
2
2
+
D
2
-
E
2
(
D
4
-
E
4
)
ω
2
2
k
tan
2
(
φ
2
)
+
E
2
,
where ω 2 is the second frequency, ω 10 is the first frequency during the zero-flow condition, ω 20 is the second frequency during the zero-flow condition, k, D 2 , D 4 , E 2 , and E 4 are calibration constants related to physical properties of the conduit, and φ is the phase difference.
11. The flowmeter of claim 9 , wherein the property includes a density of the fluid contained in the conduit.
12. The flowmeter of claim 11 , wherein the controllers further configured to:
determine density calibration constants based on physical properties of the conduit;
determine a reference temperature;
determine a first temperature that influences the first mode of vibration;
determine a second temperature that influences the second mode of vibration;
compensate the density calibration constants based on the first temperature, the second temperature, and the reference temperature;
wherein determining the property includes determining the density based the compensated density calibration constants.
13. The flowmeter of claim 11 , wherein the density is determined based on:
ρ
^
e
=
D
2
ω
2
2
(
1
-
(
ω
20
2
ω
10
2
-
1
)
k
tan
2
(
φ
2
)
)
+
D
4
,
first frequency during a zero-flow condition, ω 20 is the second frequency during the zero-flow condition, k, D 2 and D 4 are calibration constants related to physical properties of the conduit, and φ is the phase difference.
14. The flowmeter of claim 9 , wherein the property includes a mass flow rate of the fluid contained in the conduit.
15. The flowmeter of claim 14 , wherein the mass flow rate is determined based on:
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 k is a factor related to the stiffness of the conduit, ω 2 is the second frequency, ω 10 is the first frequency during a zero-flow condition, ω 20 is the second frequency during the zero-flow condition, k m is a constant specific to the conduit, φ is the phase difference, and Mfact is
Mfact
=
(
ω
2
2
ω
1
2
(
1
-
2
k
tan
2
(
φ
2
)
)
-
1
)
(
ω
20
2
ω
10
2
-
1
)
nom
.
16. The flowmeter of claim 9 , wherein:
the first mode is a Coriolis mode, and
The second mode is a driven mode.
17. 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;
determine at least one of the first frequency of vibration or the second frequency of vibration;
determine a phase difference between the motion of the conduit at a first point of the conduit and the motion of the conduit at a second point of the conduit;
determine a quantity based on the phase difference and the determined frequency, wherein the quantity includes a ratio between the first frequency during a zero-flow condition and the second frequency during the zero-flow condition; and
determine a property of the fluid based on the quantity.
18. The transmitter of claim 17 , wherein the quantity is determined based on:
ω
20
2
ω
10
2
-
1
=
(
D
4
-
E
4
)
ω
2
2
+
D
2
-
E
2
(
D
4
-
E
4
)
ω
2
2
k
tan
2
(
φ
2
)
+
E
2
,
where ω 2 is the second frequency, ω 10 is the first frequency during the zero-flow condition, ω 20 is the second frequency during the zero-flow condition, k, D 2 , D 4 , E 2 , and E 4 are calibration constants related to physical properties of the conduit, and φ is the phase difference.
19. The transmitter of claim 17 , wherein the property includes a density of the fluid contained in the conduit.
20. The transmitter of claim 19 , wherein the storage device further stores instructions for causing the at least one processing device to:
determine density calibration constants based on physical properties of the conduit;
determine a reference temperature;
determine a first temperature that influences the first mode of vibration;
determine a second temperature that influences the second mode of vibration;
compensate the density calibration constants based on the first temperature, the second temperature, and the reference temperature;
wherein determining the property includes determining the density based the compensated density calibration constants.
21. The transmitter of claim 19 , wherein the density is determined based on:
ρ
^
e
=
D
2
ω
2
2
(
1
-
(
ω
20
2
ω
10
2
-
1
)
k
tan
2
(
φ
2
)
)
+
D
4
,
where ω 2 is the second frequency, ω 10 is the first frequency during a zero-flow condition, ω 20 is the second frequency during the zero-flow condition, k, D 2 and D 4 are calibration constants related to physical properties of the conduit, and φ is the phase difference.
22. The transmitter of claim 19 , wherein the property includes a mass flow rate of the fluid contained in the conduit.
23. The transmitter of claim 22 , wherein the mass flow rate is determined based on:
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 K is a factor related to the stiffness of the conduit, ω 2 is the second frequency, ω 10 is the first frequency during a zero-flow condition, ω 20 is the second frequency during the zero-flow condition, k m is a constant specific to the conduit, φ is the phase difference, and Mfact is
Mfact
=
(
ω
2
2
ω
1
2
(
1
-
2
k
tan
2
(
φ
2
)
)
-
1
)
(
ω
20
2
ω
10
2
-
1
)
nom
.
24. The transmitter of claim 20 , wherein:
the first mode is a Coriolis mode, and
the second mode is a driven mode.