Time-reversed nonlinear acoustic downhole pore pressure measurements
Apparatus ( 10 ) and methods for measurement of pore pressure in rock formations through a metal borehole casing ( 32 ) after a well is cased and cemented, are described. Such measurements may be accomplished by using the Dynamic Acoustic Elasticity (DAE) method for characterizing nonlinear parameters by perturbing a selected rock formation region with a High Amplitude, Low Frequency (HALF) acoustic strain wave, and probing this region using a Low Amplitude, High Frequency (LAHF) acoustic wave ( 18 ), ( 22 ). Time reversal techniques ( 36 ) may be employed for focusing acoustic energy into the formation in the vicinity of the pipe or open hole. The change in wave speed of the probe pulses as the HALF induced strain wave oscillation propagates through the formation, as a function of the induced strain, may be used to determine the nonlinear elastic parameters α, β, δ, and A of the pore pressure, from which the pore pressure may be determined in the region of the HALF wave.
1. A method for determining pore pressure in a formation through a borehole having a metal casing, comprising:
generating strain in a subsurface volume surrounding the borehole by focusing a low frequency, periodic acoustic signal on the subsurface volume, the low frequency, periodic acoustic signal having a first amplitude at a first time and a second amplitude at a second time, wherein the first amplitude of the low frequency, periodic acoustic signal generates first strain in the subsurface volume and the second amplitude of the low frequency, periodic acoustic signal generates second strain in the subsurface volume;
transmitting pulsed, high frequency acoustic signals through the subsurface volume simultaneously with the generation of strain in the subsurface volume with the low frequency, periodic acoustic signal;
measuring signals generated in the formation in the subsurface volume relating to particle velocity or particle acceleration in the formation;
determining the strain in the subsurface volume from the signals generated in the formation in the subsurface volume relating to the particle velocity or the particle acceleration in the formation, wherein the strain determined in the volume includes the first strain corresponding to the first amplitude of the low frequency, periodic acoustic signal and the second strain corresponding to the second amplitude of the low frequency, periodic acoustic signal;
measuring time-of-flight of the pulsed, high frequency acoustic signals through the subsurface volume as a function of strain within the subsurface volume during the generation of strain in the subsurface volume with the low frequency, periodic acoustic signal, the time-of-flight of the pulsed, high frequency acoustic signals including a first time-of-flight corresponding to the first strain and a second time-of-flight corresponding to the second strain;
determining change of the time-of-flight of the pulsed, high frequency acoustic signals as the function of the strain within the subsurface volume, the change of the time-of-flight of the pulsed, high frequency acoustic signals as the function of the strain within the subsurface volume including change from the first time-of-flight corresponding to the first strain to the second time-of-flight corresponding to the second strain;
determining nonlinear elastic parameters α, β, and δ based on the change of the time-of-flight of the pulsed, high frequency acoustic signals as the function of the strain within the subsurface volume, wherein determination of the nonlinear elastic parameters α, β, and δ includes determination of the nonlinear elastic parameter α based on an inverse of the particle acceleration and a ratio of change in perturbed velocity to linear velocity; and
determining pore pressure in the subsurface volume based on the nonlinear elastic parameters α, β, and δ.
2. The method of claim 1 , wherein the low frequency, periodic acoustic signal is focused using time reversal.
3. The method of claim 1 , wherein the pulsed, high frequency acoustic signals are generated in the borehole.
4. The method of claim 1 , wherein the low frequency, periodic acoustic signal is focused in the borehole.
5. The method of claim 1 , wherein the particle velocity or the particle acceleration is measured from vibrational signals on the metal casing.
6. The method of claim 1 , wherein the low frequency periodic acoustic signal is between 1 Hz and 1000 Hz.
7. The method of claim 1 , wherein the pulsed, high frequency acoustic signals have a frequency between 200 kHz and 1.5 MHz.
8. An apparatus configured to determine pore pressure in a formation through a borehole having a metal casing, comprising:
a transceiver trained to focus time-reversed acoustic signals in a focal volume centered on said borehole and generate strain in the focal volume, wherein a first strain is generated in the focal volume at a first time and a second strain is generated in the focal volume at a second time;
a probe source comprising a transmitting transducer configured to transmit high frequency acoustic pulses into the focal volume while the transceiver focuses the time-reversed acoustic signals in the focal volume;
a receiver comprising a receiving transducer configured to receive, from the focal volume, the high frequency acoustic pulses transmitted by the probe source;
a signal processor configured to determine time-of-flight of the received high frequency acoustic pulses; and
a sensor disposed in contact with the metal casing configured to generate signals conveying particle velocity or particle acceleration
wherein:
the strain in the focal volume is determined based on the signals conveying the particle velocity or the particle acceleration, wherein the strain determined in the focal volume includes the first strain at the first time and the second strain at the second time;
the time-of-flight of the received high frequency acoustic pulses include a first time-of-flight corresponding to the first strain and a second time-of-flight corresponding to the second strain;
change of the time-of-flight of the received high frequency acoustic pulses as the function of the strain in the focal volume is determined, the change of the time-of-flight of the received high frequency acoustic pulses as the function of the strain in the focal volume including change from the first time-of-flight corresponding to the first strain to the second time-of-flight corresponding to the second strain;
nonlinear elastic parameters α, β, and δ are determined based on the change of the time-of-flight of the received high frequency acoustic pulses as the function of the strain in the focal volume, wherein determination of the nonlinear elastic parameters α, β, and δ includes determination of the nonlinear elastic parameter α based on an inverse of the particle acceleration and a ratio of change in perturbed velocity to linear velocity; and
pore pressure in the focal volume is determined based on the nonlinear elastic parameters α, β, and δ.
9. The apparatus of claim 8 , wherein said transmitting transducer is placed in contact with the metal casing of the borehole.
10. The apparatus of claim 8 , wherein said receiving transducer is placed in contact with the metal casing of the borehole.
11. The apparatus of claim 8 , wherein the time-reversed acoustic signals are between 1 Hz and 1000 Hz.
12. The apparatus of claim 8 , wherein the high frequency acoustic pulses have a frequency between 200 kHz and 1.5 MHz.