Method for evaluating a material on a remote side of a partition using ultrasonic measurements
Methods are disclosed for evaluating a material on a remote side of a partition separating first and second domains wherein flexural waves within the partition are received by spaced-apart ultrasonic receivers and processed to determine the velocity of the waves propagating into the second domain from a first receiver to a second receiver located more remote from the transmitter than the first receiver and whose separation from the first receiver is known. Comparison of a theoretical phase velocity with the measured phase velocity of the recorded waves allows determination as to whether the flexural wave is propagating through solid. This may be based on a measurable deviation between the two curves occurring at a critical frequency, which may be identified by a perturbation in a group velocity plot. Discrimination may also be based on the gradient of a straight line that best-fits the attention dispersion of the frequency spectrum.
1. A method for evaluating a material on a remote side of a partition separating a first domain from a second domain, the method comprising:
disposing at least one ultrasonic transmitter and a plurality of ultrasonic receivers in longitudinally spaced-apart relationship along a first side of the partition in the first domain;
activating the at least one ultrasonic transmitter to propagate a transmitted signal that hits the partition at an oblique incidence and excites, inside the partition, ultrasonic waveforms that comprise propagated quasi leaky-Lamb waves constituting an extensional wave and a flexural wave having respective symmetric and antisymmetric zero-order modes within the partition, wherein the spaced-apart receivers record the ultrasonic waveforms;
processing the recorded ultrasonic waveforms to determine a measured phase velocity of the flexural wave propagating through the second domain on the second side of the partition from a longitudinal position of a first receiver to a longitudinal position of a second receiver that is located more remote from the transmitter than the first receiver and whose separation from the first receiver is known;
computing a theoretical phase velocity of the flexural wave propagating through the second domain; and
establishing that the second domain contains a solid if the measured phase velocity deviates from the theoretical phase velocity by an amount that is not accountable by noise alone;
wherein establishing that the second domain contains a solid comprises:
processing the recorded ultrasonic waveforms to calculate the group velocity of the flexural wave propagating through the second domain;
identifying a perturbation in the group velocity plot when group velocity is plotted in the frequency domain and identifying a first critical frequency at which the perturbation occurs; and
comparing the theoretical phase velocity at the first critical frequency to a predetermined threshold to determine if the second domain contains a liquid or a solid.
2. The method of claim 1 , wherein calculating the group velocity of the flexural wave propagating through the second domain includes (i) obtaining the frequency spectrum of the flexural wave; (ii) estimating from the frequency spectrum a phase angle between respective flexural waves extracted from the ultrasonic waveforms recorded by adjacent receivers; and (iii) calculating the group velocity of the flexural wave propagating through the second domain from the phase angle.
3. The method according to claim 2 , wherein the phase angle is estimated from a portion of the frequency spectrum where an amplitude of the flexural wave exceeds a predetermined minimal signal strength that eliminates the effect of noise.
4. Method The method according to claim 1 , wherein identifying the perturbation in the group velocity of the flexural wave comprises performing the identifying within a frequency range where an amplitude of the flexural wave exceeds a predetermined minimal signal strength that eliminates the effect of noise.
5. The method according to claim 1 , wherein identifying the perturbation in the group velocity comprises (i) computing a group velocity dispersion curve, and (ii) identifying a perturbation exceeding a predefined magnitude of deviation from the group velocity dispersion curve.
6. The method according to claim 1 , wherein establishing that the second domain contains a solid comprises:
identifying a deviation in a measured phase velocity curve when the measured phase velocity is plotted in the frequency domain and identifying a second critical frequency at which the deviation occurs;
determining the computed phase velocity at the second critical frequency; and
comparing the computed phase velocity to a predetermined threshold to determine if the second domain contains a liquid or a solid.
7. The method according to claim 1 , wherein the partition comprises a casing and an annular fill installed in a borehole traversing a formation.
8. Method according to claim 1 , wherein each transmitter and receiver is directed toward the partition at an angle of incidence close to 30°.
9. A computer program product comprising a non-transient computer readable medium storing program code instructions, which when executed on at least one processor that receives as input data representative of the recorded ultrasonic waveforms from a pair of spaced apart receivers, carries out the processing and computing operations of claim 1 .
10. A method for evaluating a material on a remote side of a partition separating a first domain from a second domain, the method comprising:
disposing at least one ultrasonic transmitter and a plurality of ultrasonic receivers in longitudinally spaced-apart relationship along a first side of the partition in the first domain;
activating the at least one ultrasonic transmitter to propagate a transmitted signal that hits the partition at an oblique incidence and excites inside the partition guided ultrasonic waveforms that comprise propagated quasi leaky-Lamb waves constituting an extensional wave and a flexural wave having respective symmetric and antisymmetric zero-order modes within the partition, wherein the spaced-apart receivers record the ultrasonic waveforms;
processing the recorded guided ultrasonic waveforms to determine a measured phase velocity of the flexural wave propagating through the second domain on the second side of the partition from a longitudinal position of a first receiver to a longitudinal position of a second receiver that is located more remote from the transmitter than the first receiver and whose separation from the first receiver is known;
computing a theoretical phase velocity of the flexural wave propagating through the second domain; and
establishing that the second domain contains a solid if the measured phase velocity deviates from the theoretical phase velocity by an amount that is not accountable by noise alone; wherein establishing that the second domain contains a solid comprises:
identifying a deviation in the measured phase velocity curve when the measured phase velocity is plotted in the frequency domain and identifying a critical frequency f lim at which the deviation occurs;
determining the computed phase velocity at the critical frequency; and
comparing the computed phase velocity to a predetermined threshold to determine if the second domain contains a liquid or a solid.
11. A computer program product comprising a non-transient computer readable medium storing program code instructions, which when executed on at least one processor that receives as input data representative of recorded ultrasonic waveforms from a pair of spaced apart receivers, carries out the processing, computing, determining, and comparing operations of claim 10 .