Systems and methods for interpreting multi-phase fluid flow data

1. A method for interpreting measurements of a multi-phase fluid flow in a conduit, the method comprising:

obtaining a set of holdup measurements from a holdup sensor;

obtaining a set of velocity measurements from a flow velocity sensor;

using one or more processors, fitting a first curve to a first set of the holdup measurements and a first set of velocity measurements; and

using one or more processors, fitting a second curve to a second set of holdup measurements and a second set of velocity measurements, wherein the second curve comprises a shape mutual to the first curve with an independent gain and an independent offset; and

determining a flow rate for one phase of the multi-phase fluid flow based on the first and second curves.

2. The method of claim 1 ,

wherein the first set is the set of holdup measurements and the second set is the set of velocity measurements; and

wherein the first curve is a holdup profile and the second curve is a velocity profile.

3. The method of claim 1 , wherein the first curve comprises one of a function with a linear fit to the measurements; a function with spline interpolations; and a function with spline interpolations and a constant projection.

4. The method of claim 1 , wherein the first curve comprises a hyperbolic tangent curve with at least two adjustable curve-fitting coefficients.

5. The method of claim 1 , further comprising:

modifying one of the first and second curves that is fitted to the velocity measurements according to Prandtl's law at a wall of the conduit, wherein the modified curve comprises a velocity profile.

6. The method of claim 1 , further comprising:

modifying one of the first and second curves that is fitted to the set of velocity measurements based on an averaging effect of the velocity measurements, wherein the modified curve is a modified velocity profile; and

generating a fluid flow rate with a holdup profile and the modified velocity profile.

7. The method of claim 1 , further comprising:

generating a first curve-fitting error for the first curve;

generating a second curve-fitting error for the second curve;

generating a total curve-fitting error as a sum of the first and second curve-fitting errors; and

rejecting the set of holdup measurements and the set of velocity measurements when the total curve-fitting error is above a threshold.

8. The method of claim 7 , further comprising:

validating the set of holdup measurements and the set of velocity measurements when the total curve-fitting error is equal to or below the threshold; and

adjusting at least one curve-fitting parameter of the first curve and the second curve to minimize the total curve-fitting error.

9. The method of claim 1 , wherein the conduit comprises a pipe in an oilfield wellbore.

10. A method for interpreting measurements of a multi-phase fluid flow in a conduit, comprising:

obtaining at least one fluid holdup measurement from a holdup sensor;

obtaining a set of velocity measurements from a flow velocity sensor;

using one or more processors, fitting a first curve to the set of velocity measurements as the velocity profile;

using the first curve constrained by the at least one fluid holdup measurement to form a second curve as the fluid holdup profile; and

determining a flow rate for one phase of the multi-phase fluid flow based on the first and second curves.

11. The method of claim 10 ,

wherein the at least one fluid holdup measurement is one of a pipe average holdup measurement and a local probe holdup measurement.

12. The method of claim 11 ,

wherein the pipe average holdup measurement is obtained from a pulsed-neutron gamma ray-energy discriminating logging tool.

13. A method for interpreting measurements of a multi-phase fluid flow in a conduit, comprising:

obtaining at least one velocity measurement from a holdup sensor;

obtaining a set of fluid holdup measurements from a flow velocity sensor;

using one or more processors, fitting a first curve to the set of fluid holdup measurements as the fluid holdup profile;

using the first curve constrained by the at least one velocity measurement to form a second curve as the velocity profile; and

determining a flow rate for one phase of the multi-phase fluid flow based on the first and second curves.

14. The method of claim 13 , wherein the at least one velocity measurement is one of a pipe average velocity measurement and a local velocity measurement.

15. A system for interpreting measurements of a multi-phase fluid flow in a conduit, the apparatus comprising:

a holdup sensor to obtain a set of fluid holdup measurements;

a flow velocity sensor to obtain a set of velocity measurements;

a processor in electronic communication with the holdup sensor and the flow velocity sensor, the processor fitting a first curve to a first set of fluid holdup measurements a first set of velocity measurements and fitting a second curve to a second set of the fluid holdup measurements or a second set of the velocity measurements, wherein the second curve is fitted using the first curve constrained by at least one of the second set of fluid holdup measurements or the second set of velocity measurements, and wherein the first curve and the second curve comprise a fluid holdup profile and a velocity profile.

16. The system of claim 15 , wherein the second curve has a same shape of the first curve with an independent gain and an independent offset and wherein the first curve and the second curve comprise a fluid holdup profile and a velocity profile.

17. The system of claim 15 , wherein the first curve is a hyperbolic tangent curve with two adjustable curve-fitting coefficients.

18. The system of claim 15 , wherein the holdup sensor and the flow velocity sensor are disposed about a downhole tool configured to move inside the conduit.

19. The system of claim 15 , wherein the processor comprises a computer readable data storage in electronic communication with the processor that stores the set of fluid holdup measurements and the set of velocity measurements.

20. The system of claim 19 , wherein the computer readable data storage further comprises computer executable instructions that, when executed by the processor, causes the processor to compute a fluid flow rate in the conduit.

21. The system of claim 19 , wherein the computer readable data storage further comprises computer executable instructions that, when executed by the processor, causes the processor to constrain a fluid holdup profile by one measurement of the set of velocity measurements.

22. The system of claim 19 , wherein the computer readable data storage further comprises computer executable instructions that, when executed by the processor, cause the processor to constrain a velocity profile by one measurement of the set of fluid holdup measurements.

23. The system of claim 19 , wherein the computer readable data storage further comprises computer executable instructions that, when executed by the processor, cause the processor to:

compute a total curve-fitting error as a function of a first curve-fitting error for the first curve and a second curve-fitting error for the second curve; and

reject the set of velocity measurements and the set of fluid holdup measurements when the total curve-fitting error exceeds a threshold.