Measuring the speed of electromagnetic wave propagation in a fluid within a conduit

1 . A computer-implemented method, comprising:

acquiring, at each of a number of instants of time from each antenna of an array of at least two antennas distributed at predetermined locations along a conduit, spatio-temporally-sampled data for electromagnetic (EM) wave propagation through a fluid in the conduit, the at least two antennas operating at transmitted frequencies that are above a first cutoff frequency of the conduit;

generating, based on the spatio-temporally-sampled data and using a spectral-based algorithm technique, a k-ω plot plotting curves having a kinematic relationship relative to an angular frequency of a spectral component of EM disturbances, a wavenumber, and a speed of the EM wave propagation;

identifying, using the k-ω plot, a spectral ridge on the curves, and determining parameters for calculating a slope of the spectral ridge;

determining, using the spectral ridge on the curves and the parameters the slope of the spectral ridge;

determining the speed of EM wave propagation assuming a relation between the speed of EM wave propagation and the slope of the spectral ridge;

determining, using the speed of EM wave propagation and the slope of the spectral ridge, components of the fluid flowing in the conduit; and

controlling wellbore operations based on the components of the fluid flowing in the conduit.

2 . The computer-implemented method of claim 1 , wherein the array of the at least two antennas comprises antennas distributed around a circumference of the conduit.

3 . The computer-implemented method of claim 1 , wherein the spectral-based algorithm technique uses a spectrum-like function of a speed EM wave propagation formation and parametric methods of solution.

4 . The computer-implemented method of claim 3 , wherein the spectral-based algorithm technique is a spectral-based algorithms using a deterministic maximum likelihood method selected from the group consisting of a Capon method and MUSIC method.

5 . The computer-implemented method of claim 1 , wherein the fluid is a liquid, a gas, or a multiphase fluid.

6 . The computer-implemented method of claim 1 , wherein a ridge is identified in the k-ω plot based on power or color intensity in the k-ω plot.

7 . The computer-implemented method of claim 1 , wherein determining the slope of the spectral ridge comprises an average phase velocity of the speed of EM wave.

8 . A non-transitory, computer-readable medium storing one or more instructions executable by a computer system to perform operations comprising:

acquiring, at each of a number of instants of time from each antenna of an array of at least two antennas distributed at predetermined locations along a conduit, spatio-temporally-sampled data for electromagnetic (EM) wave propagation through a fluid in the conduit, the at least two antennas operating at transmitted frequencies that are above a first cutoff frequency of the conduit;

generating, based on the spatio-temporally-sampled data and using a spectral-based algorithm technique, a k-ω plot plotting curves having a kinematic relationship relative to an angular frequency of a spectral component of EM disturbances, a wavenumber, and a speed of the EM wave propagation;

identifying, using the k-ω plot, a spectral ridge on the curves, and determining parameters for calculating a slope of the spectral ridge;

determining, using the spectral ridge on the curves and the parameters the slope of the spectral ridge;

determining the speed of EM wave propagation assuming a relation between the speed of EM wave propagation and the slope of the spectral ridge;

determining, using the speed of EM wave propagation and the slope of the spectral ridge, components of the fluid flowing in the conduit; and

controlling wellbore operations based on the components of the fluid flowing in the conduit.

9 . The non-transitory, computer-readable medium of claim 8 , wherein the array of the at least two antennas comprises antennas distributed around a circumference of the conduit.

10 . The non-transitory, computer-readable medium of claim 8 , wherein the spectral-based algorithm technique uses a spectrum-like function of a speed EM wave propagation formation and parametric methods of solution.

11 . The non-transitory, computer-readable medium of claim 10 , wherein the spectral-based algorithm technique is a spectral-based algorithms using a deterministic maximum likelihood method selected from the group consisting of a Capon method and MUSIC method.

12 . The non-transitory, computer-readable medium of claim 8 , wherein the fluid is a liquid, a gas, or a multiphase fluid.

13 . The non-transitory, computer-readable medium of claim 8 , wherein a ridge is identified in the k-ω plot based on power or color intensity in the k-ω plot.

14 . The non-transitory, computer-readable medium of claim 8 , wherein determining the slope of the spectral ridge comprises an average phase velocity of the speed of EM wave.

15 . A computer-implemented system, comprising:

one or more processors; and

a non-transitory computer-readable storage medium coupled to the one or more processors and storing programming instructions for execution by the one or more processors, the programming instructions instructing the one or more processors to perform operations comprising:

acquiring, at each of a number of instants of time from each antenna of an array of at least two antennas distributed at predetermined locations along a conduit, spatio-temporally-sampled data for electromagnetic (EM) wave propagation through a fluid in the conduit, the at least two antennas operating at transmitted frequencies that are above a first cutoff frequency of the conduit;

generating, based on the spatio-temporally-sampled data and using a spectral-based algorithm technique, a k-ω plot plotting curves having a kinematic relationship relative to an angular frequency of a spectral component of EM disturbances, a wavenumber, and a speed of the EM wave propagation;

identifying, using the k-ω plot, a spectral ridge on the curves, and determining parameters for calculating a slope of the spectral ridge;

determining, using the spectral ridge on the curves and the parameters the slope of the spectral ridge;

determining the speed of EM wave propagation assuming a relation between the speed of EM wave propagation and the slope of the spectral ridge;

determining, using the speed of EM wave propagation and the slope of the spectral ridge, components of the fluid flowing in the conduit; and

controlling wellbore operations based on the components of the fluid flowing in the conduit.

16 . The computer-implemented system of claim 15 , wherein the array of the at least two antennas comprises antennas distributed around a circumference of the conduit.

17 . The computer-implemented system of claim 15 , wherein the spectral-based algorithm technique uses a spectrum-like function of a speed EM wave propagation formation and parametric methods of solution.

18 . The computer-implemented system of claim 17 , wherein the spectral-based algorithm technique is a spectral-based algorithms using a deterministic maximum likelihood method selected from the group consisting of a Capon method and MUSIC method.

19 . The computer-implemented system of claim 15 , wherein the fluid is a liquid, a gas, or a multiphase fluid.

20 . The computer-implemented system of claim 15 , wherein a ridge is identified in the k-ω plot based on power or color intensity in the k-ω plot.