Method for measuring a fluid density or a fluid viscosity
View Patent ↗A method and device for estimating a density value ρ m indicative of a true density ρ or for estimating a viscosity value η m indicative of a true viscosity η of a fluid is disclosed. For this, a first resonance frequency f R of a first mechanical oscillator in a reference volume and a second resonance frequency f F of a second mechanical oscillator in contact with the fluid are measured. The estimated value ρ m or η m is then derived using these resonance frequencies f R and f F . During this derivation, at least one fluid-temperature- or fluid-pressure-dependent parameter of the fluid is used. Additionally or alternatively, the first (i.e. reference) mechanical oscillator is arranged in contact with a reference fluid. Thus, fundamental errors in the derivation of the estimated value ρ m or η m are reduced and the estimated value becomes more reliable.
1. A method for deriving an estimated value ρ m which is indicative of a density ρ of a fluid with a fluid temperature T F and a fluid pressure p F , the method comprising the steps of:
a) measuring a first resonance frequency f R of a resonant vibration of a first mechanical oscillator, wherein said first mechanical oscillator is arranged in a reference volume and wherein said first mechanical oscillator is secluded from said fluid;
b) measuring a second resonance frequency f F of a resonant vibration of a second mechanical oscillator, wherein said second mechanical oscillator is arranged in a measurement volume, wherein said measurement volume comprises said fluid, and wherein said fluid is in contact with said second mechanical oscillator;
c) deriving said estimated value ρ m using said first resonance frequency f R and said second resonance frequency f F ;
wherein in said step c) said fluid temperature T F and/or said fluid pressure p F and/or at least one parameter which is dependent on said fluid temperature T F and/or on said fluid pressure p F is/are used for deriving said estimated value ρ m ;
wherein in said step c) a fluid-temperature-dependent viscosity function η(T F ) is used for deriving said estimated value ρ m , wherein the fluid-temperature-dependent viscosity function η(T F ) is known, pre-measured or pre-modeled;
wherein said estimated value ρ m , which is indicative of said density ρ of said fluid, is derived; and
wherein in said step c) a fluid-temperature-dependent offset parameter C(T F ) is used for deriving said estimated value ρ m , wherein said fluid-temperature-dependent offset parameter C(T F ) is indicative of a temperature-dependent frequency offset between said first and said second mechanical oscillators, and/or between a first oscillator circuit connected to and used to operate said first mechanical oscillator and a second oscillator circuit connected to and used to operate said second mechanical oscillator.
2. The method of claim 1 , wherein a plurality of values of η for different fluid temperatures T F are pre-stored in a lookup-table or calculated on-the-fly.
3. The method of claim 1 , wherein in said step c) a fluid-pressure-dependent viscosity function η(p F ) is used for deriving said estimated value ρ m , wherein a plurality of values of η for different fluid pressures p F are prestored in a lookup-table or calculated on-the-fly, by fitting and/or interpolation or extrapolation algorithms.
4. The method of claim 1 ,
wherein in said step c) a fluid-pressure-dependence of the offset parameter C(T F , p F ) is also used for deriving said estimated value ρ m .
5. The method of claim 1 , wherein a reference-fluid-temperature-dependence δη/δT F of a viscosity function η(T R ) of the reference fluid is equal to or differs less than ±30% from a fluid-temperature-dependence δη/δT F of the fluid-temperature-dependent viscosity function η(T F ) of said fluid, at least for fluid temperatures T F and reference fluid temperatures T R in a range between 170 K and 400 K.
6. The method of claim 1 , wherein said estimated value ρ m is derived according to:
f
R
-
f
F
=
A
ρ
m
+
B
~
ρ
m
η
(
p
f
,
T
f
)
+
C
(
p
F
,
T
F
)
with
A
=
c
1
t
2
ρ
q
w
f
d
and
B
~
=
c
2
2
ρ
q
w
f
d
π
and with c 1 , c 2 , t, and w being oscillator-geometry-dependent constants, with ρ q being an effective density of a material of said mechanical oscillators with η(p F ,T F ) being a fluid-pressure- and/or fluid-temperature-dependent viscosity function of said fluid, with f d being a common design resonance frequency of said first and second mechanical oscillators, and with C(p F ,T F ) being a fluid-pressure- and/or fluid-temperature-dependent offset parameter which is indicative of a frequency offset between said first and said second mechanical oscillator and/or between a first oscillator circuit connected to said first mechanical oscillator and a second oscillator circuit connected to said second mechanical oscillator;
wherein said reference fluid temperature T R in Kelvin is equal to or differs less than ±5%, from said fluid temperature T F ; and
wherein a reference fluid pressure p R of a reference fluid is at most 0.1 mbar over a reference fluid temperature range of T R >200 K and T R <400 K.
7. The method of claim 1 , wherein said first mechanical oscillator is in contact with a reference fluid with a reference fluid pressure p R of at least 10 mbar, over a reference fluid temperature range of T R >200 K and T R <400 K; and
wherein said estimated value ρ m is derived according to
f
R
-
f
F
=
A
F
ρ
m
+
(
B
~
F
ρ
-
B
~
R
ρ
R
)
·
η
(
p
F
,
T
F
)
++
D
(
p
F
,
T
F
)
with
D
(
p
F
,
T
F
)
=
C
(
p
F
,
T
F
)
-
A
R
ρ
R
with A F , A R , {tilde over (B)} F , and {tilde over (B)} R being oscillator-geometry-dependent constants, with subscripts R, F relating to the first and second mechanical oscillator, respectively;
with ρ R being a density of said reference fluid, wherein said density ρ of said fluid is equal to or differs less than ±50% from said density ρ R of said reference fluid;
with η(p F ,T F ) being a fluid-pressure- and/or fluid-temperature-dependent viscosity function of said fluid, which is equal to or differs less than ±50% from a reference-fluid-pressure- and/or reference-fluid-temperature-dependent viscosity function η R (p R ,T R ) of said reference fluid;
and with C(p F ,T F ) being a fluid-pressure- and/or fluid-temperature-dependent offset parameter which is indicative of a frequency offset between said first and said second mechanical oscillators and/or between a first oscillator circuit connected to said first mechanical oscillator and a second oscillator circuit connected to said second mechanical oscillator;
wherein said first and second mechanical oscillators are selected such that said oscillator-geometry-dependent constants {tilde over (B)} F and {tilde over (B)} R are equal or differ less than ±50% from each other; and
wherein said reference fluid temperature T R in Kelvin is equal to or differs less than ±5% from said fluid temperature T F .
8. The method of claim 1 , wherein said fluid temperature T F and/or a reference fluid temperature T R and/or a temperature of said first mechanical oscillator and/or a temperature of said second mechanical oscillator is or are controlled by at least one temperature regulator.
9. The method of claim 1 , wherein said first mechanical oscillator, said second mechanical oscillator, said fluid, and said reference fluid have the same temperature.
10. The method of claim 1 , wherein said first mechanical oscillator is in contact with a reference fluid with a reference fluid temperature T R and a reference fluid pressure p R , and said reference volume comprises said reference fluid.
11. The method of claim 1 , wherein the temperature dependence δC/δT of the offset parameter C is pre-measured or pre-modeled and is used for calibration of the method, or that the mechanical oscillators are selected such that the temperature dependence δC/δT is less than 0.1 Hz/K.
12. The method of claim 1 , further comprising deriving an estimated value η m indicative of a viscosity η of the fluid, using said first resonance frequency f R and said second resonance frequency f F ;
wherein said fluid temperature T F and/or said fluid pressure p F and/or at least one parameter which is dependent on said fluid temperature T F and/or on said fluid pressure p F is/are used for deriving said estimated value η m ; and
wherein said first mechanical oscillator is in contact with a reference fluid with a reference fluid temperature T R and a reference fluid pressure p R , said reference volume comprises said reference fluid, and said reference fluid temperature T R in Kelvin is equal to or differs less than ±5% from said fluid temperature T F .
13. The method of claim 12 , wherein said reference fluid pressure p R is at most 0.1 mbar over a reference fluid temperature range of T R >200 K and T R <400 K, or said reference fluid pressure p R is at least 1 mbar over a reference fluid temperature range of T R >200 K and T R <400 K.
14. The method of claim 12 , further comprising the step of
deriving said fluid temperature T F by said first and/or said second mechanical oscillator; and/or
deriving said fluid temperature T F and/or a reference fluid temperature T R by at least one temperature sensor, a resistance temperature detector, a thermocouple, an integrated circuit temperature sensor, and/or an optical temperature sensor.
15. The method of claim 12 , wherein the estimated value η m which is indicative of the viscosity n of the fluid is derived by solving the equation
η
m
(
T
F
)
=
(
f
F
-
f
R
-
(
A
ρ
+
C
(
T
F
)
)
B
~
ρ
)
2
with f R being said reference fluid temperature-dependent first resonance frequency, with f F being said fluid temperature-dependent second resonance frequency, with ρ being a known, pre-measured, or pre-modeled density function of the fluid, with A and {tilde over (B)} being oscillator-specific constants, and with C(T F ) being a fluid-temperature-dependent frequency offset parameter between the first and second mechanical oscillators and/or oscillator circuits.