System and method of locating downhole objects in a wellbore
The present disclosure provides novel systems and methods of locating downhole objects in a wellbore, the condition of casing within the wellbore, and characteristics of a subterranean formation. More specifically, data associated with a hydraulic impulse in fluid in the wellbore is used to determine a location of a downhole object. Data associated with the hydraulic impulse is collected and then processed in the frequency domain to identify the location of the downhole object. The downhole object may be a tool positioned within the wellbore or a fracture network that communicates with the wellbore by a perforation through wellbore casing. The system and method of the present disclosure can also be used to identify locations of unintended holes or perforations in casing and other tubulars. One aspect of the present disclosure is a system and method of locating a downhole object by analyzing pressure data from a hydraulic impulse transmitted through a fluid in a wellbore and that reflects off of the downhole object.
1. A method of locating a position of a downhole object in a wellbore or an anomaly in a subterranean formation, comprising:
generating a hydraulic impulse in a fluid in the wellbore, wherein the hydraulic impulse reflects between a surface boundary and a downhole boundary, and wherein the downhole boundary is one of the downhole object or the formation anomaly;
collecting data at a wellhead of the wellbore on pressure in the fluid as the hydraulic impulse reflects between the surface boundary and the downhole boundary, wherein the data is collected by a sensor at a sample rate of greater than 1.5 Hz;
transforming the collected data into frequency domain data;
identifying component frequencies in the frequency domain data, wherein the component frequencies are associated with pressure peaks in the frequency domain data;
determining a second normalized fundamental frequency of the hydraulic impulse by normalizing a component frequency of a second pressure peak identified in the frequency domain data, wherein the second pressure peak has a second frequency value that is higher than a first frequency value of a first pressure peak, and wherein the second normalized fundamental frequency of the hydraulic impulse is determined using Equation 1:
f
1
=
f
n
2
n
-
1
where f 1 is the normalized fundamental frequency, and f n is the n th harmonic;
determining a velocity of a wave in the wellbore; and
determining a distance from the surface boundary to the downhole boundary using the wave velocity, the second normalized fundamental frequency, and either equation 2A (when the wellbore has an open downhole boundary) or equation 2B (when the wellbore has a closed downhole boundary):
L
=
α
4
f
2
Equation
2
A
L
=
α
2
f
2
Equation
2
B
where:
L is the distance;
α is the wave velocity; and
f 2 is the second normalized fundamental frequency.
2. The method of claim 1 , wherein the downhole object is an isolation plug in the wellbore.
3. The method of claim 1 , wherein generating the hydraulic impulse comprises one or more of altering a flow rate of a pump injecting fluid into the wellbore, opening a valve, and closing a valve.
4. The method of claim 1 , further comprising detrending the collected data by fitting a linear equation to the collected data, wherein the detrending is performed before transforming the collected data into frequency domain data.
5. The method of claim 1 , wherein transforming the collected data into frequency domain data comprises applying a Fourier transform to the collected data according to Equation 3:
P (ω)=∫ −∞ ∞ P ( t ) e jωt dt
where:
t is time in seconds;
j is an imaginary number;
ω is an angular frequency of oscillation in radians per second;
p(t) is pressure as a function of time in psi; and
p(ω) is pressure as a function of frequency in psi.
6. The method of claim 1 , further comprising determining if the fluid in the wellbore is at a predetermined pressure of between 1,000 PSI and 2,000 PSI prior to generating the hydraulic impulse, and wherein when the fluid is not at the predetermined pressure the method further comprises adjusting the pressure of the fluid in the wellbore to the predetermined pressure.
7. The method of claim 1 , wherein the sensor has an accuracy of +/−0.025% of a measured value.
8. The method of claim 1 , wherein the sample rate of the sensor is greater than approximately 10 Hz.
9. The method of claim 8 , wherein the sample rate of the sensor is between 25 Hz and approximately 75 Hz.
10. The method of claim 1 , further comprising:
discarding the first pressure peak identified in the frequency domain data.
11. The method of claim 1 , wherein the formation anomaly is one or more of: a fracture depth, a fracture density, a fracture length, a fracture permeability, a fracture flow characteristic, a perforation density, and a penetration depth.
12. A non-transitory computer readable medium comprising a set of instructions stored thereon that, when executed by a processor of a control system, cause the processor to determine a distance to a downhole object in a wellbore or a characteristic of a subterranean formation, comprising:
an instruction to receive data collected over time on pressure in a fluid within the wellbore, wherein the data is collected at or near a wellhead of the wellbore, and wherein the pressure data is collected as a hydraulic impulse reflects in the wellbore between a downhole boundary and a surface boundary;
an instruction to detrend the received pressure data by fitting a linear equation to the collected data, wherein detrending the received pressure data reduces one or more of high amplitude and low-frequency contribution of leakoff to the subterranean formation;
an instruction to transform the detrended pressure data into frequency domain data;
an instruction to identify a second component frequency in the frequency domain data;
an instruction to normalize the second component frequency to determine a second normalized fundamental frequency using Equation 1:
f
1
=
f
n
2
n
-
1
where f 1 is the normalized fundamental frequency, and f n is the n th harmonic; and
an instruction to determine a distance to the downhole boundary using Equation 2A (when the downhole boundary is open) or Equation 2B (when the downhole boundary is closed) based on a velocity of a wave in the wellbore and at least the second normalized fundamental frequency:
L
=
α
4
f
2
Equation
2
A
L
=
α
2
f
2
Equation
2
B
where:
L is the distance;
α is the wave velocity; and
f 2 is the second normalized fundamental frequency.
13. The non-transitory computer readable medium of claim 12 , further comprising an instruction to apply a Fourier transform to the detrended data to transform the received data into the frequency domain data using Equation 3:
P (ω)=∫ −∞ ∞ P ( t ) e jωt dt
where:
t is time in seconds;
j is an imaginary number;
ω is an angular frequency of oscillation in radians per second;
p(t) is pressure as a function of time in psi; and
p(ω) is pressure as a function of frequency in psi.
14. The non-transitory computer readable medium of claim 12 , further comprising:
an instruction to identify the pressure of the fluid within the wellbore before the hydraulic impulse is generated; and
an instruction to activate a pump located at the wellhead to increase the pressure within the fluid to at least 1,000 PSI if the pressure of the fluid within the wellbore is less than 1,000 PSI, and an instruction to open a valve located at the wellhead to lower the pressure to at most 2,000 PSI if the pressure of the fluid within the wellbore is greater than 2,000 PSI.
15. The non-transitory computer readable medium of claim 12 , wherein the data is collected by a sensor at a sample rate of greater than 1.5 Hz.
16. A system configured to determine a location of a downhole object in a wellbore or a characteristic of a subterranean formation, comprising:
a sensor to collect data over time on pressure of a fluid within the wellbore, the sensor positioned at or near a wellhead of the wellbore and located a predetermined distance from a surface boundary, wherein the pressure data is collected as a hydraulic impulse travels in the wellbore between a downhole boundary and the surface boundary, the sensor being operable to collect data at a sample rate of at least about 1.5 Hz;
a pump and a valve located at the wellhead of the wellbore, the surface boundary being one of the pump and the valve; and
a control system including at least a memory, a processor in communication with the memory, and instructions stored on the memory and executable by the processor, the control system operable to:
receive the pressure data collected by the sensor;
fit a linear equation to the pressure data to provide detrended pressure data;
transform the detrended pressure data into frequency domain data; and
normalize a second component frequency in the frequency domain data to determine a second normalized fundamental frequency using Equation 1:
f
1
=
f
n
2
n
-
1
where f 1 is the normalized fundamental frequency, and f n , is the n th harmonic; and
determine a distance to the downhole boundary using Equation 2A (when the downhole boundary is an open boundary) or Equation 2B (when the downhole boundary is a closed boundary) based on a velocity of a wave in the wellbore and at least the second normalized fundamental frequency:
L
=
α
4
f
2
Equation
2
A
L
=
α
2
f
2
Equation
2
B
where:
L is the distance;
α is the wave velocity; and
f 2 is the second normalized fundamental frequency.
17. The system of claim 16 , wherein the control system is further operable to determine at least one harmonic frequency in the pressure data collected by the sensor.
18. The system of claim 16 , wherein the control system is further operable to apply a Fourier transform to the detrended pressure data to transform the detrended pressure data into the frequency domain data.
19. The system of claim 16 , wherein the control system is further operable to determine the pressure of the fluid within the wellbore before the hydraulic impulse is reflected off the downhole boundary.
20. The system of claim 19 , wherein the control system is further operable to control the pump to adjust the pressure of the fluid within the wellbore.
21. The system of claim 16 , wherein sample rate of the sensor is greater than approximately 10 Hz.