Enhanced supercritical fluid measurement with vibratory sensors

1 . A method for inferring an inferred speed of sound of a flow fluid, the method being conducted by a computer system ( 200 ) having a processor ( 210 ) and a memory ( 220 ), the processor ( 210 ) configured to execute instructions from the memory ( 220 ) and store data in the memory ( 220 ), the memory ( 220 ) having a SoS inference module ( 202 ), the method comprising:

providing a vibratory flow sensor ( 5 ) fluidly coupled to a conduit ( 160 ) through which the flow fluid flows and configured to determine a flow measurement of the flow fluid;

providing a density sensor ( 10 ) fluidly coupled to the conduit, the density sensor being substantially immune from speed of sound effects of the flow fluid, and having at least one of: 1) a smaller diameter than the vibratory flow sensor, 2) a lower vibrating frequency than the vibratory flow sensor, and 3) a predetermined distance threshold with respect to the vibratory flow sensor;

measuring, by the density sensor, the density of the flow fluid;

inferring, by the SoS inference module ( 202 ), the inferred speed of sound of the flow fluid based on an inferential relationship between a measured density and a heat capacity ratio of the flow fluid and the inferred speed of sound of the flow fluid; and

transmitting, by the density sensor, the inferred speed of sound of the fluid to the vibratory flow sensor in order to correct the flow measurement and improve accuracy in the vibratory flow sensor.

2 . A method as claimed in claim 1 , wherein the inferential relationship between the inferred speed of sound of the flow fluid and the density of the flow fluid is an inverse relationship between the inferred speed of sound of the flow fluid and the square root of the measured density of the flow fluid.

3 . A method as claimed in claim 2 , wherein the inferential relationship between the inferred speed of sound of the flow fluid and the density of the flow fluid further accounts for a pressure of the flow fluid, wherein the pressure of the flow fluid is one or more of a measured pressure measured by a pressure sensor ( 20 ) and a pressure inferred from a density sensor ( 10 ) stiffness determination.

4 . A method as claimed in claim 3 , wherein the inferential relationship is based on a relationship between the inferred speed of sound of the flow fluid and a square root term, the square root term having a square root of a product of the heat capacity ratio and the pressure, divided by the square root of the measured density.

5 . A method as claimed in claim 4 , wherein the heat capacity ratio is associated with one or more of the flow fluid and a class of flow fluids of which the flow fluid is a member and wherein the heat capacity ratio is one or more of temperature dependent and pressure dependent, such that the heat capacity ratio is determined based on a corresponding predetermined relationship between the heat capacity ratio and one or more of the measured temperature and the pressure.

6 . A method as claimed in claim 3 , wherein the computer system ( 200 ) is a vibratory flow sensor meter electronics ( 110 ) of the vibratory flow sensor ( 5 ), the method further comprising:

receiving, by the computer system ( 200 ), the measured density from the density sensor ( 10 );

receiving, by the computer system ( 200 ), the pressure of the flow fluid; and

determining, by the computer system ( 200 ), a corrected mass flowrate, based on the inferred speed of sound of the flow fluid.

7 . A method as claimed in claim 1 , wherein the computer system ( 200 ) is a density sensor meter electronics ( 120 ) of the density sensor ( 10 ).

8 . A method as claimed in claim 7 , further comprising, if the inferential relationship between a measured density of the flow fluid and the inferred speed of sound of the flow fluid accounts for a flow fluid pressure, inferring, by the density sensor meter electronics ( 120 ), an inferred flow fluid pressure based on a measured stiffness of elements of the density sensor ( 10 ) determined by the density sensor ( 10 ).

9 . A method as claimed in claim 7 , wherein the vibratory flow sensor ( 5 ) one or more of:

vibrates vibratory sensor ( 5 ) vibratory elements at a frequency that is greater than or equal to 300 hertz; and

has an inner diameter that is greater than or equal to two inches, and wherein the density sensor ( 10 ) one or more of:

vibrates density sensor ( 10 ) vibratory elements at a frequency that is less than 300 hertz; and

has an inner diameter that is less than two inches.

10 . A method as claimed in claim 1 , wherein the flow fluid is in a supercritical state and comprises one or more of ethylene, ethane, carbon dioxide, and argon.

11 . A system for inferring an inferred speed of sound of a flow fluid, the system comprising:

a vibratory flow sensor ( 5 ) fluidly coupled to a conduit ( 160 ) through which the flow fluid flows and configured to determine a flow measurement of the flow fluid;

a density sensor ( 10 ) fluidly coupled to the conduit, the density sensor being substantially immune from speed of sound effects of the flow fluid, and having at least one of: 1) a smaller diameter than the vibratory flow sensor, 2) a lower vibrating frequency than the vibratory flow sensor, and 3) a predetermined distance threshold with respect to the vibratory flow sensor; and

a computer system ( 200 ) having a processor ( 210 ) and a memory ( 220 ), the processor ( 210 ) configured to execute instructions from the memory ( 220 ) and store data in the memory ( 220 ), the memory ( 220 ) having a SoS inference module ( 202 ), the computer system ( 200 ) configured to:

measure, by the density sensor, the density of the flow fluid;

infer, by the SoS inference module ( 202 ), the inferred speed of sound of the flow fluid based on an inferential relationship between a measured density and heat capacity ratio of the flow fluid and the inferred speed of sound of the flow fluid; and

transmit, by the density sensor, the inferred speed of sound of the fluid to the vibratory flow sensor in order to correct the flow measurement and improve accuracy in the vibratory flow sensor.

12 . A system as claimed in claim 11 , wherein the inferential relationship between the inferred speed of sound of the flow fluid and the density of the flow fluid is an inverse relationship between the inferred speed of sound of the flow fluid and the square root of the measured density of the flow fluid.

13 . A system as claimed in claim 12 , wherein the inferential relationship between the inferred speed of sound of the flow fluid and the density of the flow fluid further accounts for a pressure of the flow fluid, wherein the pressure of the flow fluid is one or more of a measured pressure measured by a pressure sensor ( 20 ) and a pressure inferred from a density sensor ( 10 ) stiffness determination.

14 . A system as claimed in claim 13 , wherein the inferential relationship is based on a relationship between the inferred speed of sound of the flow fluid and a square root term, the square root term having a square root of a product of the heat capacity ratio and the pressure, divided by the square root of the measured density.

15 . A system as claimed in claim 14 , wherein the heat capacity ratio is associated with one or more of the flow fluid and a class of flow fluids of which the flow fluid is a member and wherein the heat capacity ratio is one or more of temperature dependent and pressure dependent, such that the heat capacity ratio is determined based on a corresponding predetermined relationship between the heat capacity ratio and one or more of the measured temperature and the pressure.

16 . A system as claimed in claim 13 , wherein the computer system ( 200 ) is a vibratory flow sensor meter electronics ( 110 ) of the vibratory flow sensor ( 5 ), the computer system ( 200 ) further configured to:

receive the measured density from the density sensor ( 10 );

receive the pressure of the flow fluid; and

determine a corrected mass flowrate based on the inferred speed of sound of the flow fluid.

17 . A system as claimed in claim 11 , wherein the computer system ( 200 ) is a density sensor meter electronics ( 120 ) of the density sensor ( 10 ).

18 . A system as claimed in claim 17 , wherein if the inferential relationship between a measured density of the flow fluid and the inferred speed of sound of the flow fluid accounts for a flow fluid pressure, the density sensor meter electronics ( 120 ) is configured to infer an inferred flow fluid pressure based on a measured stiffness of elements of the density sensor ( 10 ) determined by the density sensor ( 10 ).

19 . A system as claimed in claim 16 , wherein the vibratory flow sensor ( 5 ) one or more of:

vibrates vibratory sensor ( 5 ) vibratory elements at a frequency that is greater than or equal to 300 hertz; and

has an inner diameter that is greater than or equal to two inches, and wherein the density sensor ( 10 ) one or more of:

vibrates density sensor ( 10 ) vibratory elements at a frequency that is less than 300 hertz; and

has an inner diameter that is less than two inches.

20 . A system as claimed in claim 11 , wherein the flow fluid is in a supercritical state and comprises one or more of ethylene, ethane, carbon dioxide, and argon.