Time-reversed nonlinear acoustics for downhole pressure measurements

An apparatus for detecting regions of high pressure in a formation ahead of a down-hole well drilling bit, comprising:

• a first signal generator that generates a pulsed sinusoidal acoustic signal, the pulsed sinusoidal acoustic signal having a frequency;
• a first transceiver disposed downhole above said drilling bit;
• a second transceiver disposed downhole, the second transceiver being configured to receive the pulsed sinusoidal acoustic signal, and to produce a first electrical signal therefrom;
• one or more processors configured to receive the electrical signal and to time reverse the electrical signal;
• a second signal generator configured to receive the time-reversed electrical signal, to generate a second acoustic signal therefrom, and to direct the second acoustic signal onto the second transceiver, whereby the second acoustic signal is transmitted;
• whereby the second acoustic signal forms a focal volume centered on the first transceiver, the second acoustic signal including harmonic signals of the frequency of the pulsed sinusoidal acoustic signal which was received by the first transceiver, the first transceiver being configured to produce a second electrical signal reflecting amplitude of the harmonic signals;
• and
• electronic storage configured to store the amplitude of the harmonic signals.

A method for measuring pore pressure in a formation, the method being performed by a system that includes a first transceiver disposed in a borehole, a second transceiver disposed in the borehole, one or more processors, and electronic storage, the method comprising:

• generating, with the first transceiver, a pulsed sinusoidal acoustic signal, the pulsed sinusoidal acoustic signal having a frequency;
• receiving, with the second transceiver, the pulsed sinusoidal acoustic signal;
• generating, with the one or more processors, a time-reversed signal by time reversing the received signal;
• transmitting, with the second transceiver, a time-reversed acoustic signal in accordance with the time-reversed signal, whereby the time-reversed acoustic signal forms a focal volume centered on the first transceiver;
• receiving, with the first transceiver, acoustic signals within the focal volume, such acoustic signals including second and third harmonic signals of the frequency of the pulsed sinusoidal acoustic signal, the second and third harmonic signals being generated in the focal volume on the first transceiver, the second and third harmonic signals having amplitudes;
• and
• storing, to the electronic storage, the amplitudes of the second and third harmonic signals.

An apparatus for measuring pore pressure in a formation, comprising:

• a first signal generator configured to generate a pulsed sinusoidal signal, the pulsed sinusoidal signal having a frequency;
• a first transceiver disposed in a borehole in the formation configured to receive the pulsed sinusoidal signal, and to transmit a pulsed sinusoidal acoustic signal in accordance with the received pulsed sinusoidal signal;
• a second transceiver disposed in the borehole configured to receive the pulsed sinusoidal acoustic signal and to generate a first electrical signal therefrom;
• one or more processors configured to receive the first electrical signal and to time reverse the first electrical signal to generate a time-reversed electrical signal;
• a second signal generator configured to receive the time-reversed electrical signal, and to direct the time-reversed electrical signal to the second transceiver, the second transceiver being further configured to transmit a second acoustic signal in accordance with the time-reversed electrical signal;
• whereby the second acoustic signal forms a focal volume centered on the first transceiver, the second acoustic signal including second and third harmonics of the frequency of the pulsed sinusoidal acoustic signal, the first transceiver being further configured to produce a second electrical signal based on reception of the second acoustic signal, the second electrical signal having an amplitude;
• and
• electronic storage configured to store the amplitude of the second electrical signal and/or information derived from the amplitude of the second electrical signal.

A method for measuring pore pressure in a formation through a borehole having a metal casing, the method being performed by a system that includes a first transceiver disposed in the borehole, a second transceiver disposed in the borehole above the first transceiver, a third transceiver disposed in vibrational communication with the metal casing, and one or more processors, the method comprising:

• generating, with the first transceiver, a pulsed sinusoidal acoustic signal having a frequency;
• receiving, with the second transceiver, the pulsed sinusoidal acoustic signal;
• generating, with the one or more processors, a time-reversed signal by time reversing the pulsed sinusoidal acoustic signal received by the second transceiver;
• transmitting, at a selected intensity with the second transceiver, a time-reversed acoustic signal in accordance with the time-reversed signal, whereby the time-reversed acoustic signal forms a focal volume centered on the first transceiver;
• receiving, with the first transceiver, energy at a second harmonics of the frequency of the pulsed sinusoidal acoustic signal, the energy at the second harmonic having an amplitude;
• determining β with the one or more processors based on the amplitude of the energy received by the first transceiver at the second harmonic;
• receiving, with the third transceiver, a second acoustic signal responsive to vibrational excitation in the focal volume;
• varying, with the second transceiver, the intensity of the transmitted time-reversed acoustic signal;
• and
• determining α with the one or more processors by measuring a time delay of the second acoustic signal relative to the transmitted time-reversed acoustic signal as a function of the intensity of the transmitted time-reversed acoustic signal.

An apparatus for measuring pore pressure in a formation through a borehole having a metal casing, comprising:

• a first signal generator configured to provide a pulsed sinusoidal signal having a frequency;
• a first transceiver disposed in the borehole in the formation configured to receive the pulsed sinusoidal signal from the first signal generator, and to transmit a pulsed sinusoidal acoustic signal in accordance with the pulsed sinusoidal signal from the first signal generator;
• and
• a second transceiver disposed in the borehole configured to receive the pulsed sinusoidal acoustic signal and to generate a first electrical signal therefrom;
• one or more processors configured to receive the first electrical signal and to generate a time-reversed electrical signal by time reversing the first electrical signal;
• a second signal generator configured to receive the time-reversed electrical signal, to generate a second electrical signal therefrom with an intensity that is controlled to vary as a function of time, and to direct the second electrical signal to the second transceiver, such that the second transceiver transmits a second acoustic signal having an intensity that varies as a function of time in accordance with the intensity of the second electrical signal;
• whereby the second acoustic signals forms a focal volume centered on the first transceiver, the first transceiver receiving a second harmonic signal at the second harmonic of the frequency of the pulsed sinusoidal signal;
• wherein the one or more processors are further configured to determine β based on amplitude of the received second harmonic signal;
• and
• a third transceiver disposed in the borehole in vibrational communication with the metal casing, the third transceiver being configured to receive a third acoustic signal responsive to vibrational excitation in the focal volume;
• wherein the one or more processors are still further configured to determine α based on time delay of the third acoustic signal relative to the second acoustic signal as a function of the intensity of the second acoustic signal.