CN108252708B - Method for identifying working fluid level of oil well - Google Patents

Abstract

The invention discloses a method for identifying the working fluid level of an oil well, which comprises the following steps: firstly, obtaining a working fluid level depth estimated value and collecting an echo signal; filtering the echo sampling signal; thirdly, frequency domain transformation of the band-pass filtering echo signal; fourthly, extracting the sound velocity of the echo signal; fifthly, data return-to-zero processing of the echo sampling signal; sixthly, filtering the return-to-zero echo sampling signal; seventhly, searching a sudden change peak value of the position of the working fluid level and a sampling point of the position of the working fluid level; eighthly, acquiring sampling time of the position of the working fluid level; and ninthly, identifying the actual depth of the working fluid level. According to different oil well depths, the method determines the window length of the band-pass filtering echo signal and the step length of the window, identifies the echo periodic signal based on the oil pipe coupling, extracts the sound velocity of the echo signal, calculates the sound velocity accurately, finds the sudden change peak value of the working fluid level position and the sampling point of the working fluid level position to obtain the sampling time of the working fluid level position, and solves the problem that the working fluid level signal cannot be directly identified when being submerged by noise.

Description

Method for identifying working fluid level of oil well

Technical Field

The invention belongs to the technical field of underground working fluid level identification, and particularly relates to a method for identifying the working fluid level of an oil well.

Background

In the oil production of oil wells in oil fields, the working fluid level depth is an important parameter for monitoring the exploitation condition of oil reservoirs. The working fluid level reflects the liquid supply capacity of the oil well, is used for detecting the oil extraction condition, analyzing the water injection effect and reflecting the oil well production conditions such as sand blockage, wax deposition and the like of the oil well. Two types of moving liquid level identification methods, namely a time domain method and a frequency domain method, exist, wherein the time domain method comprises manual identification, amplitude-zero crossing rate function method identification of moving liquid level, fuzzy clustering method and the like; the frequency domain method comprises spectral subtraction, wherein the spectrum of the sound wave reflection signal is subtracted from the spectrum of the background noise, and the signal spectrum is extracted, so that the working fluid level is identified. Under the normal condition, the well condition is good, and when no environmental noise, the working fluid level reflection signal is stronger, and the characteristic is obvious, can clearly see the reflection signal of corresponding working fluid level position on the measured signal, can obtain working fluid level position signal through manual discernment, and then confirms the working fluid level degree of depth. When the noise statistics are known, spectral subtraction can extract the meniscus information. However, the practical situation is very complex, the well condition is severe, various environmental noises exist, particularly, the noise is far greater than the reflected signal when the working fluid level of the oil well is measured during working, the simple statistical characteristic is not provided, and the working fluid level signal cannot be visually identified by naked eyes, so that the existing working fluid level identification method cannot be suitable for various oil well environments, and the universality is poor.

Disclosure of Invention

The technical problem to be solved by the invention is to provide an oil well working fluid level identification method aiming at the defects in the prior art, the window length and the window step length of a band-pass filtering echo signal are determined according to different oil well depths, the echo periodic signal based on an oil pipe coupling is identified, the sound velocity of the echo signal is extracted, the sound velocity is accurately calculated, the abrupt change peak value of the working fluid level position and the sampling point of the working fluid level position are searched, the sampling time of the working fluid level position is obtained, the problem that the working fluid level signal cannot be directly identified due to noise submergence is solved, and the method is convenient to popularize and use.

In order to solve the technical problems, the invention adopts the technical scheme that: a method for identifying the working fluid level of an oil well is characterized by comprising the following steps:

the method comprises the following steps of firstly, obtaining a working fluid level depth estimated value and acquiring an echo signal: obtaining working fluid level depth estimated value Y by using installation position of oil pump in oil well_hControlling a sound generator to send an infrasonic signal by using a computer, reflecting the infrasonic signal in an annular space formed between an oil pipe and a sleeve pipe through a working fluid level, the oil pipe and an oil pipe coupling to form an echo signal, receiving the echo signal by using an echo receiver, and using a sampling frequency f for a working fluid level measuring instrument_sAcquiring the echo signal to obtain an echo sampling signal s (i), and sending the echo sampling signal s (i) to a computer, wherein i is the number of sampling points;

the device comprises a sound wave generator, an echo receiver, a computer, a dynamic liquid level measuring instrument and a control system, wherein the sound wave generator and the echo receiver are both arranged at a wellhead of an oil well, the input end of the sound wave generator is connected with the output end of the computer, the output end of the echo receiver is connected with the input end of the dynamic liquid level measuring instrument, and the dynamic liquid level measuring instrument is communicated with the computer in a wired or; the oil pipe is arranged in the sleeve and is formed by sequentially connecting a plurality of pipe joints, and two adjacent pipe joints are connected by adopting an oil pipe coupling;

step two, filtering the echo sampling signal, wherein the process is as follows:

step 201, pre-estimating fundamental frequency f of infrasonic waves on single pipe joint_BThe range of (A): according to the formula f_Bmin≤f_B≤f_BmaxEstimating fundamental frequency f of infrasonic wave on single pipe joint_BWherein f is_BminIs the fundamental minimum frequency of infrasonic waves on a single pipe joint, an

f_BmaxFor the fundamental maximum frequency of infrasonic waves on a single pipe section and

l is the length of a single pipe section, v_minIs the minimum sound velocity, v, of the propagation of infrasonic waves in the annular space formed between the tubing and the casing_maxThe maximum sound velocity of the infrasonic wave propagating in an annular space formed between the oil pipe and the casing pipe;

step 202, obtaining the range of the normalized fundamental wave frequency of the infrasonic wave on a single pipe joint through normalization processing: according to the formula

For fundamental minimum frequency f of infrasonic wave on single pipe joint_BminNormalization is carried out to obtain the normalized fundamental wave minimum frequency f of the infrasonic wave on a single pipe joint_NminFor the maximum frequency f of fundamental wave of infrasonic wave on a single pipe joint_BmaxNormalization is carried out to obtain the normalized fundamental wave maximum frequency f of the infrasonic wave on a single pipe joint_NmaxAccording to f_Nmin≤f_N≤f_NmaxObtaining the normalized fundamental frequency f of the infrasonic wave on a single pipe joint_NRange of (a), (b), (c) and (d)_NFor fundamental frequency f of infrasonic waves on a single pipe section_BNormalizing the result;

step 203, selecting a band-pass filter: the computer selects a band-pass filter based on a Kaiser window function, and the lower limit frequency f of the band-pass filter_BL＝ρ₁f_NminUpper limit frequency f of said band-pass filter_BU＝ρ₂f_NmaxWhere ρ is₁Is a lower limit frequency coefficient and is more than 0.5 rho₁＜1，ρ₂Is an upper limit frequency coefficient and 5 < rho₂＜8；

Step 204, filtering: the computer uses the band-pass filter selected in step 203 to perform band-pass filtering on the echo sampling signal s (i) to obtain a band-pass filtered echo signal s_p(i)；

Step three, frequency domain transformation of the band-pass filtering echo signal, the process is as follows:

step 301, determining the starting position of the window: computer slave band-pass filtering echo signal s_p(i) The first sampling point in (a) starts to look up backwards, and a band-pass filtered echo signal s is determined_p(i) Stopping searching after three continuous echo periodic signals, and filtering the band-pass echo signal s_p(i) The starting position of the first echo periodic signal in the three continuous echo periodic signals is used as the starting position of the window;

step 302, determining the window length of the band-pass filtering echo signal and the step length of the window: according to the formula

Calculating the number q of pre-estimated sampling points on a single pipe joint, and when the alpha multiplied by L is more than or equal to Y_hWindow length of time-band-pass filtered echo signal

At this time, the window does not need to set the step length Δ Q of the window, and step 303 is executed; when in use

And the window length Q of the band-pass filtering echo signal is equal to alpha Q, and at the moment, the step length delta Q of the window satisfies the following conditions: when Q is more than delta Q and less than or equal to 3Q, executing step 304; when in use

And the window length Q of the band-pass filtering echo signal is equal to alpha Q, and at the moment, the step length delta Q of the window satisfies the following conditions: when Q is more than delta Q and less than or equal to 3Q, executing step 305; wherein alpha is the number of pipe sections selected continuously, and alpha is more than 30 and less than 40 [. alpha. ]]Is a rounding function;

step 303, the computer filters the band-pass echo signal s_p(i) After zero filling processing, fast Fourier transform is carried out to obtain frequency domainEcho signals f (k);

step 304, the computer filters the band-pass echo signal s_p(i) Carrying out beta frequency domain transformation by using the step length of Q as the window length and delta Q as the window to obtain a frequency domain echo signal sequence F_β(k) Wherein beta is more than or equal to 2 and less than or equal to 4;

band-pass filtering echo signal s by computer_p(i) When the frequency domain transformation is carried out for beta times by taking Q as the window length and delta Q as the step length of the window, zero filling processing is adopted and then fast Fourier transformation is carried out to obtain a frequency domain echo signal sequence F_β(k)；

Step 305, the computer filters the band-pass echo signal s_p(i) Carrying out gamma frequency domain transformation by using the step length of Q as the window length and delta Q as the window to obtain a frequency domain echo signal sequence F_γ(k) Wherein gamma is more than 4 and less than 15;

band-pass filtering echo signal s by computer_p(i) Zero padding is adopted when gamma-time frequency domain transformation is carried out by using the step length with Q as the window length and delta Q as the window length, and then fast Fourier transformation is carried out to obtain a frequency domain echo signal sequence F_γ(k)；

Step four, extracting the sound velocity of the echo signal, and the process is as follows:

step 401, the computer extracts m times of frequency multiplication frequency corresponding to the maximum energy value of the frequency domain echo signal, and when the frequency domain echo signal is the frequency domain echo signal F (k), step 402 is executed; when the frequency domain echo signal is a frequency domain echo signal sequence F_β(k) Then, step 403 is executed; when the frequency domain echo signal is a frequency domain echo signal sequence F_γ(k) Then, step 404 is executed, m is a positive integer not greater than 5;

step 402, the computer processes the frequency domain echo signal F (k) from the frequency value f_NminBegin to find the frequency value f_NmaxFinding is at f_NminAnd f_NmaxNormalized frequency value corresponding to the spectral line having the greatest energy between, when f_NminAnd f_NmaxThe spectral line with the maximum energy exists between the two, and the normalized frequency value corresponding to the spectral line with the maximum energy is the normalized fundamental frequency f of the infrasonic wave on a single pipe joint_NThe normalized fundamental frequency f of the infrasonic wave on a single pipe joint_NAccurate value ofIs a frequency f which is a 1-fold multiple of the frequency domain echo signal F (k)_N1Then the frequency values are respectively 2f on the frequency domain echo signals F (k)_N、3f_N、4f_NAnd 5f_NSearching for the 2-time frequency f corresponding to the spectral line with the maximum energy between the left neighborhood and the right neighborhood_N23 times of the frequency f _N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5According to the formula

Calculating the sound velocity v of the echo signal;

when f is_NminAnd f_NmaxThere is no spectral line with maximum energy, the computer search is at 2f_NminAnd 2f_NmaxThe frequency value corresponding to the spectral line with the maximum energy is 2 times of the frequency doubling frequency f of the frequency domain echo signal F (k)_N2Then the frequency values are respectively

And

searching for the frequency multiplication frequency f of 3 times corresponding to the spectral line with the maximum energy between the left neighborhood and the right neighborhood _N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5According to the formula

Calculating the sound velocity v of the echo signal;

step 403, the computer compares the frequency domain echo signal sequence F_β(k) In each frequency domain echo signal, respectively carrying out echo signal sound velocity calculation, and a frequency domain echo signal sequence F_β(k) The echo signal sound velocity calculation methods of each frequency domain echo signal are the same; computer to frequency domain echo signal sequence F_β(k) All the echo signals of any frequency domain have the frequency value f_NminBegin to find the frequency value f_NmaxFinding is at f_NminAnd f_NmaxCorresponding to the spectral line with the highest energyNormalized frequency value, when f_NminAnd f_NmaxThe spectral line with the maximum energy exists between the two, and the normalized frequency value corresponding to the spectral line with the maximum energy is the normalized fundamental frequency f of the infrasonic wave on a single pipe joint_NThe normalized fundamental frequency f of the infrasonic wave on a single pipe section_NThe accurate value of is a frequency domain echo signal sequence F_β(k) Frequency f of 1 times of the echo signal of the selected frequency domain_N1Then in the frequency domain_β(k) The frequency values of the echo signals of the selected frequency domain are respectively 2f_N、3f_N、4f_NAnd 5f_NSearching for the 2-time frequency f corresponding to the spectral line with the maximum energy between the left neighborhood and the right neighborhood_N23 times of the frequency f _N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5According to the formula

Calculating a frequency domain echo signal sequence F_β(k) The sound velocity v of the echo signal corresponding to the echo signal of the selected frequency domain_ε；

When f is_NminAnd f_NmaxThere is no spectral line with maximum energy, the computer search is at 2f_NminAnd 2f_NmaxThe frequency value corresponding to the spectral line with the maximum energy is the frequency domain echo signal sequence F_β(k) Frequency f of 2 times of the echo signal of the selected frequency domain_N2Then in the frequency domain_β(k) Wherein the frequency values of the echo signals of the selected frequency domain are respectively

And

searching for the frequency multiplication frequency f of 3 times corresponding to the spectral line with the maximum energy between the left neighborhood and the right neighborhood _N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5According to the formula

Calculating a frequency domain echo signal sequence F_β(k) The sound velocity v of the echo signal corresponding to the echo signal of the selected frequency domain_εWhere ε is the frequency domain echo signal sequence F_β(k) The number of the intermediate frequency domain echo signal is not less than epsilon and not more than beta;

according to the formula

Calculating the sound velocity v of the echo signal;

step 404, the computer compares the frequency domain echo signal sequence F_γ(k) In each frequency domain echo signal, respectively carrying out echo signal sound velocity calculation, and a frequency domain echo signal sequence F_γ(k) The echo signal sound velocity calculation methods of each frequency domain echo signal are the same; computer to frequency domain echo signal sequence F_γ(k) All the echo signals of any frequency domain have the frequency value f_NminBegin to find the frequency value f_NmaxFinding is at f_NminAnd f_NmaxNormalized frequency value corresponding to the spectral line having the greatest energy between, when f_NminAnd f_NmaxThe spectral line with the maximum energy exists between the two, and the normalized frequency value corresponding to the spectral line with the maximum energy is the normalized fundamental frequency f of the infrasonic wave on a single pipe joint_NThe normalized fundamental frequency f of the infrasonic wave on a single pipe section_NThe accurate value of is a frequency domain echo signal sequence F_γ(k) Frequency f of 1 times of the echo signal of the selected frequency domain_N1Then in the frequency domain_γ(k) The frequency values of the echo signals of the selected frequency domain are respectively 2f_N、3f_N、4f_NAnd 5f_NSearching for the 2-time frequency f corresponding to the spectral line with the maximum energy between the left neighborhood and the right neighborhood_N23 times of the frequency f _N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5According to the formula

Computing frequency domain loopsWave signal sequence F_γ(k) The sound velocity v of the echo signal corresponding to the echo signal of the selected frequency domain_φ；

When f is_NminAnd f_NmaxThere is no spectral line with maximum energy, the computer search is at 2f_NminAnd 2f_NmaxThe frequency value corresponding to the spectral line with the maximum energy is the frequency domain echo signal sequence F_γ(k) Frequency f of 2 times of the echo signal of the selected frequency domain_N2Then in the frequency domain_γ(k) Wherein the frequency values of the echo signals of the selected frequency domain are respectively

And

searching for the frequency multiplication frequency f of 3 times corresponding to the spectral line with the maximum energy between the left neighborhood and the right neighborhood _N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5According to the formula

Calculating a frequency domain echo signal sequence F_γ(k) The sound velocity v of the echo signal corresponding to the echo signal of the selected frequency domain_φWhere phi is the frequency domain echo signal sequence F_γ(k) The number of the intermediate frequency domain echo signals is phi less than or equal to gamma;

computer to frequency domain echo signal sequence F_γ(k) Screening gamma echo signal sound velocities corresponding to the medium gamma frequency domain echo signals, screening 4 continuous sound velocity values with the minimum change rate, and solving the average value of the 4 sound velocity values as an echo signal sound velocity v;

step five, data return-to-zero processing of the echo sampling signals: the computer extracts the amplitude eta (i) of each sampling point in the echo sampling signal s (i), and the amplitude eta (i) is obtained according to a formula

Calculating the average amplitude of each sampling point

Wherein M is the total number of sample points in the echo sampling signal s (i);

according to the formula

Calculating the return-to-zero amplitude eta '(i) of each sampling point to obtain a return-to-zero echo sampling signal s' (i);

sixthly, filtering the return-to-zero echo sampling signal: estimating value Y according to working fluid level depth_hFiltering the return-to-zero echo sampling signal s' (i) when Y is_hWhen the depth is more than 600m, the oil well is regarded as a deep well, and step 601 is executed; when Y is_hWhen the distance is less than or equal to 600m, the oil well is regarded as a shallow well, and step 602 is executed;

601, filtering the return-to-zero echo sampling signal s' (i) by a computer by sequentially adopting a first low-pass filter, a band-stop filter and a second low-pass filter to obtain a deep well return-to-zero echo filtering signal S (i), wherein the cut-off frequency of the first low-pass filter is 0.01Hz, the sidelobe attenuation of the first low-pass filter is 80dB, the stopband attenuation of the band-stop filter is 80dB, the cut-off frequency of the second low-pass filter is 0.02Hz, and the sidelobe attenuation of the second low-pass filter is 80 dB;

step 602, the computer filters the return-to-zero echo sampling signal S '(i) by using a second low-pass filter to obtain a shallow well return-to-zero echo filtering signal S' (i);

step seven, searching the abrupt peak value of the position of the working fluid level and the sampling point of the position of the working fluid level: the computer determines a working fluid level depth searching range according to the depth of the oil well, and determines a sudden change peak value of the working fluid level position and a sampling point of the working fluid level position in the working fluid level depth searching range, the deep wells are divided into a first deep well, a second deep well and a third deep well, and the working fluid level depth estimated value Y of the first deep well_hSatisfies the following conditions: y is more than 600m_h< 1100 m; the working fluid level depth estimated value Y of the second deep well_hSatisfies the following conditions: y is more than or equal to 1100m_hLess than or equal to 1800 m; the third depthWell working fluid level depth estimate Y_hSatisfies the following conditions: y is_h＞1800m；

When the oil well is a shallow well, the working fluid level depth search range is 0.7Y_h～1.2Y_hComputer at 0.7Y_h～1.2Y_hCollecting each peak value in the shallow-well return-to-zero echo filtering signal S' (i) in the corresponding sampling point

When it is, will h_jThe abrupt peak value h of the working fluid level position is regarded as the abrupt peak value of the working fluid level position_jThe corresponding sampling point j is regarded as the sampling point of the position of the working fluid level, wherein h_-And h₊Respectively, the sudden change peak value h of the working fluid level_jLeft and right adjacent peak values;

when the oil well is the first deep well, the working fluid level depth searching range is 0.4Y_h～1.3Y_hComputer at 0.4Y_h～1.3Y_hAcquiring each peak value in the deep well return-to-zero echo filter signal S (i) in a corresponding sampling point, wherein the acquisition modes of the sudden change peak value of the working fluid level position of the first deep well and the sampling point of the working fluid level position are the same as the acquisition modes of the sudden change peak value of the working fluid level position of the shallow well and the sampling point of the working fluid level position of the shallow well;

when the oil well is the second deep well, the working fluid level depth searching range is 0.5Y_h～1.3Y_hComputer at 0.5Y_h～1.3Y_hCollecting each peak value in the return-to-zero echo filtering signal S (i) of the deep well in a corresponding sampling point, wherein the acquisition modes of the sudden change peak value of the working fluid level position of the second deep well and the sampling point of the working fluid level position are the same as the acquisition modes of the sudden change peak value of the working fluid level position of the shallow well and the sampling point of the working fluid level position;

when the oil well is a third deep well, the working fluid level depth search range is 0.6Y_h～1.2Y_hComputer at 0.6Y_h～1.2Y_hCollecting each peak value in the deep well return-to-zero echo filter signal S (i), the abrupt change peak value of the working fluid level position of the third deep well and the sampling point acquisition mode of the working fluid level position of the shallow well and the abrupt change peak value of the working fluid level position of the shallow well and the working fluid level in the corresponding sampling pointThe sampling points of the positions are obtained in the same mode;

step eight, acquiring the sampling time of the working fluid level position: respectively searching a sampling point j-1 and a sampling point j +1 on the left side and the right side of the sampling point j of the working fluid level position by the computer, wherein the corresponding amplitude of the sampling point j-1 is h_j-1The corresponding amplitude of the sampling point j +1 is h_j+1Using (j-1, h)_j-1)、(j,h_j) And (j +1, h)_j+1) Three points are used to obtain a quadratic function y ═ ax using sampling point as variable x and amplitude as function value y²+ bx + c, wherein a, b, and c are constants; obtaining a quadratic function y ═ ax²The extreme point coordinate of + bx + c

According to the formula

Calculating the sampling time t of the position of the working fluid level;

step nine, identifying the actual depth of the working fluid level: according to the formula

Calculating the actual depth Y of the working fluid level_s。

The method for identifying the working fluid level of the oil well is characterized by comprising the following steps of: the sound wave generator is an implosion type sound wave generator or an external explosion type sound wave generator, and when the sound wave generator is the implosion type sound wave generator, the abrupt change peak value h of the working fluid level position in the step seven_jTaking a positive peak value; when the sound wave generator is an external explosion type sound wave generator, the abrupt change peak value h of the working fluid level position in the step seven_jTaking the negative peak value.

The method for identifying the working fluid level of the oil well is characterized by comprising the following steps of: sampling frequency f of the dynamic liquid level measuring instrument_sIs 470 Hz.

The method for identifying the working fluid level of the oil well is characterized by comprising the following steps of: minimum sound velocity v of infrasonic wave propagating in annular space formed between oil pipe and casing in step 201_min220m/s, the maximum sound velocity v of the infrasonic wave propagating in the annular space formed between the oil pipe and the casing_maxIs 400 m/s.

The method for identifying the working fluid level of the oil well is characterized by comprising the following steps of: the spectral line with the maximum energy represents that the spectral amplitude corresponding to the frequency is not less than 2 times of the spectral amplitude corresponding to the frequency in the neighborhood around the frequency.

The method for identifying the working fluid level of the oil well is characterized by comprising the following steps of: abscissa of the extreme point coordinates

Satisfies the following conditions:

compared with the prior art, the invention has the following advantages:

1. the invention utilizes the band-pass filter to carry out band-pass filtering on the echo sampling signal, determines the cut-off frequency of the echo sampling signal, and carries out time domain to frequency domain conversion on the band-pass filtering echo signal, because the lengths of the measured data obtained by different well depths are different, the window length of the needed band-pass filtering echo signal is different, the window length of the band-pass filtering echo signal and the step length of the window are determined according to different oil well depths, the echo periodic signal based on an oil pipe coupling is identified, the sound velocity of the echo signal is extracted, the universality is strong, the sound velocity under various well conditions can be accurately calculated, the precondition is provided for realizing accurate automatic dynamic liquid level detection, and the popularization and the use.

2. In the frequency domain transformation process of the band-pass filtering echo signal, the initial position of the window is determined, because the signal noise interference of the band-pass filtering echo signal starting to be reflected is strong, the interference signal is required to be cut off when the characteristic of the band-pass filtering echo signal based on the tubing coupling is analyzed, in addition, after the well depth reaches a certain depth, the band-pass filtering echo signal based on the tubing coupling disappears, therefore, the search is stopped after three continuous echo periodic signals in the band-pass filtering echo signal are determined, the initial position of the first echo periodic signal in the three continuous echo periodic signals of the band-pass filtering echo signal is used as the initial position of the window, and the use effect is good.

3. According to different oil well depths, after window lengths and window step lengths of band-pass filtering echo signals are determined, fast Fourier transform is carried out on the band-pass filtering echo signals on each window length to obtain a frequency domain echo signal sequence, then echo signal sound velocity calculation is carried out on each frequency domain echo signal, the echo signal sound velocity is calculated in an averaging mode, the precision is high, and when echo signal sound velocity calculation is carried out on any frequency domain echo signal, the position f of the position f is used for calculating the echo signal sound velocity_NminAnd f_NmaxThe normalized frequency value corresponding to the spectral line with the maximum energy is used as the 1-time frequency f of the frequency domain echo signal selected in the frequency domain echo signal sequence_N1Then, the 2 times of the frequency f corresponding to the spectral line with the maximum energy is searched successively_N23 times of the frequency f _N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5And acquiring the echo signal sound velocity corresponding to the selected frequency domain echo signal in the frequency domain echo signal sequence by using an averaging method.

4. According to the method, a return-to-zero echo sampling signal is filtered according to the depth of an oil well, and when the oil well is a deep well, the return-to-zero echo sampling signal is filtered by adopting a first low-pass filter, a band elimination filter and a second low-pass filter to obtain a return-to-zero echo filtering signal of the deep well; when the oil well is a shallow well, the return-to-zero echo sampling signal is filtered by the second low-pass filter to obtain a shallow return-to-zero echo filtering signal, the position of the peak value of the working fluid level signal cannot be changed, and the precision of the working fluid level depth is improved.

5. The method comprises the steps of determining a working fluid level depth searching range according to the depth of an oil well, determining a sudden change peak value of the working fluid level position and sampling points of the working fluid level position in the working fluid level depth searching range, then constructing a quadratic function by using the sampling points of the working fluid level position and the sampling points on the left side and the right side of the working fluid level position, obtaining an extreme point coordinate of the quadratic function, further calculating the sampling time of the working fluid level position, improving the precision of data processing, reducing the calculation error of the sampling time of the working fluid level position, and providing a precise time condition for realizing accurate automatic working fluid level detection.

6. The method has the advantages of simple steps, strong adaptability and accurate sound velocity calculation, solves the problem that the working fluid level signal is submerged by noise and cannot be directly identified, and is convenient to popularize and use.

In conclusion, according to different oil well depths, the window length of the band-pass filtering echo signal and the window step length are determined, the echo periodic signal based on the oil pipe coupling is identified, the sound velocity of the echo signal is extracted, the sound velocity is accurately calculated, the abrupt change peak value of the working fluid level position and the sampling point of the working fluid level position are searched, the sampling time of the working fluid level position is obtained, the problem that the working fluid level signal is submerged by noise and cannot be directly identified is solved, and the method is convenient to popularize and use.

The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.

Drawings

FIG. 1 is a schematic block diagram of a circuit connecting a sound wave generator, an echo receiver, a working fluid level measuring instrument and a computer according to the present invention.

FIG. 2 is a schematic view of the installation relationship of the oil pipe, the casing and the pumping unit.

FIG. 3 is a block diagram of a method flow of the present invention.

Description of reference numerals:

1-a sound generator; 2-an echo receiver; 3-a working fluid level gauge;

4-a computer; 5, an oil pipe; 6-tubing coupling;

7, sleeving a sleeve; 8-working fluid level; 9-oil pumping unit.

Detailed Description

As shown in fig. 1 to 3, the method for identifying the working fluid level of an oil well according to the present invention comprises the steps of:

the method comprises the following steps of firstly, obtaining a working fluid level depth estimated value and acquiring an echo signal: obtaining working fluid level depth estimated value Y by using installation position of oil pump in oil well_hControlling the sound generator 1 to emit an infrasonic wave signal by using the computer 4, reflecting the infrasonic wave signal in an annular space formed between the oil pipe 5 and the sleeve 7 through the working fluid level 8, the oil pipe 5 and the oil pipe coupling 6 to form an echo signal, receiving the echo signal by using the echo receiver 2, and measuring the working fluid level3 at a sampling frequency f_sAcquiring the echo signal to obtain an echo sampling signal s (i), and sending the echo sampling signal s (i) to the computer 4, wherein i is the number of sampling points;

the acoustic wave generator 1 and the echo receiver 2 are both installed at the wellhead of an oil well, the input end of the acoustic wave generator 1 is connected with the output end of the computer 4, the output end of the echo receiver 2 is connected with the input end of the dynamic liquid level measuring instrument 3, and the dynamic liquid level measuring instrument 3 is communicated with the computer 4 in a wired or wireless mode; the oil pipe 5 is arranged in the casing pipe 7, the oil pipe 5 is formed by sequentially connecting a plurality of pipe joints, and two adjacent pipe joints are connected by adopting an oil pipe coupling 6;

it should be noted that the estimated value Y of the working fluid level depth is obtained by using the installation position of the oil pump in the oil well_hThe oil well is provided with an oil pumping unit 9 with the rotating speed adjusted according to the depth of the working fluid level 8, and the sound wave generator 1 and the echo receiver 2 are both installed at the wellhead of the oil well so as to facilitate the generation and the acquisition of signals and the maintenance of equipment.

Step two, filtering the echo sampling signal, wherein the process is as follows:

step 201, pre-estimating fundamental frequency f of infrasonic waves on single pipe joint_BThe range of (A): according to the formula f_Bmin≤f_B≤f_BmaxEstimating fundamental frequency f of infrasonic wave on single pipe joint_BWherein f is_BminIs the fundamental minimum frequency of infrasonic waves on a single pipe joint, an

f_BmaxFor the fundamental maximum frequency of infrasonic waves on a single pipe section and

l is the length of a single pipe section, v_minIs the minimum speed of sound, v, of the propagation of infrasonic waves in the annular space formed between the tubing 5 and the casing 7_maxThe maximum sound velocity for the infrasonic wave propagating in the annular space formed between the oil pipe 5 and the casing 7;

in this embodiment, the infrasonic wave is in the oil pipe 5 and the sleeve in step 201Minimum speed of sound v propagating in the annular space formed between the tubes 7_min220m/s, the maximum sound velocity v of the infrasonic wave propagating in the annular space formed between the oil pipe 5 and the casing 7_maxIs 400 m/s.

It should be noted that the infrasonic wave propagates in the annular space formed between the oil pipe 5 and the casing 7, the propagation speed of the infrasonic wave changes due to the difference of air density in the annular space, and the minimum sound velocity v of the infrasonic wave propagating in the annular space formed between the oil pipe 5 and the casing 7 in the step 201 is set according to the actual logging experience value_min220m/s, the maximum sound velocity v of the infrasonic wave propagating in the annular space formed between the oil pipe 5 and the casing 7_maxIs 400 m/s.

Step 202, obtaining the range of the normalized fundamental wave frequency of the infrasonic wave on a single pipe joint through normalization processing: according to the formula

For fundamental minimum frequency f of infrasonic wave on single pipe joint_BminNormalization is carried out to obtain the normalized fundamental wave minimum frequency f of the infrasonic wave on a single pipe joint_NminFor the maximum frequency f of fundamental wave of infrasonic wave on a single pipe joint_BmaxNormalization is carried out to obtain the normalized fundamental wave maximum frequency f of the infrasonic wave on a single pipe joint_NmaxAccording to f_Nmin≤f_N≤f_NmaxObtaining the normalized fundamental frequency f of the infrasonic wave on a single pipe joint_NRange of (a), (b), (c) and (d)_NFor fundamental frequency f of infrasonic waves on a single pipe section_BNormalizing the result;

in this embodiment, the sampling frequency f of the working fluid level measuring instrument 3_sIs 470 Hz.

Step 203, selecting a band-pass filter: the computer selects a band-pass filter based on a Kaiser window function, and the lower limit frequency f of the band-pass filter_BL＝ρ₁f_NminUpper limit frequency f of said band-pass filter_BU＝ρ₂f_NmaxWhere ρ is₁Is a lower limit frequency coefficient and is more than 0.5 rho₁＜1，ρ₂Is an upper limit frequency coefficient and 5 < rho₂＜8；

The echo sampled signal is band-pass filtered by a band-pass filter to determine a cut-off frequency and a lower limit frequency coefficient ρ of the echo sampled signal₁Satisfies the following conditions: rho is more than 0.5₁< 1 is to define a lower cut-off frequency, an upper frequency coefficient ρ₂Satisfies the following conditions: rho is more than 5₂< 8 is to define the upper cut-off frequency.

Step 204, filtering: the computer uses the band-pass filter selected in step 203 to perform band-pass filtering on the echo sampling signal s (i) to obtain a band-pass filtered echo signal s_p(i)；

Note that, the band-pass filter filters out periodic high-frequency noise in the echo sampling signal s (i).

Step three, frequency domain transformation of the band-pass filtering echo signal, the process is as follows:

step 301, determining the starting position of the window: the computer 4 filters the echo signal s from the band pass_p(i) The first sampling point in (a) starts to look up backwards, and a band-pass filtered echo signal s is determined_p(i) Stopping searching after three continuous echo periodic signals, and filtering the band-pass echo signal s_p(i) The starting position of the first echo periodic signal in the three continuous echo periodic signals is used as the starting position of the window;

it should be noted that, in the process of frequency domain transformation of the band-pass filtered echo signal, by determining the initial position of the window, since the interference of signal noise reflected by the band-pass filtered echo signal is strong, the interference signal must be cut off when analyzing the characteristics of the band-pass filtered echo signal based on the tubing coupling, and in addition, after the well depth reaches a certain depth, the band-pass filtered echo signal based on the tubing coupling disappears, so that the search is stopped after three continuous echo periodic signals in the band-pass filtered echo signal are determined, and the initial position of the first echo periodic signal in the three continuous echo periodic signals in the band-pass filtered echo signal is used as the initial position of the window.

Step 302, determining the window length of the band-pass filtering echo signal and the step length of the window: according to the formula

Calculating the number q of pre-estimated sampling points on a single pipe joint, and when the alpha multiplied by L is more than or equal to Y_hWindow length of time-band-pass filtered echo signal

At this time, the window does not need to set the step length Δ Q of the window, and step 303 is executed; when in use

And the window length Q of the band-pass filtering echo signal is equal to alpha Q, and at the moment, the step length delta Q of the window satisfies the following conditions: when Q is more than delta Q and less than or equal to 3Q, executing step 304; when in use

And the window length Q of the band-pass filtering echo signal is equal to alpha Q, and at the moment, the step length delta Q of the window satisfies the following conditions: when Q is more than delta Q and less than or equal to 3Q, executing step 305; wherein alpha is the number of pipe sections selected continuously, and alpha is more than 30 and less than 40 [. alpha. ]]Is a rounding function;

it should be noted that, according to different oil well depths, the window length of the band-pass filtering echo signal and the window step length are determined, when the value of alpha x L is more than or equal to Y_hWhen the well is a shallow well, the estimated value Y is estimated according to the depth from the well head of the well to the working fluid level_hPerforming fast Fourier transform for the window length to obtain a frequency domain echo signal F (k);

when in use

The window length Q of the band-pass filtered echo signal is α Q, and the computer 4 sets the band-pass filtered echo signal s according to the depth of the oil well_p(i) Performing fast Fourier transform for 2 to 4 times to obtain a frequency domain echo signal sequence F_β(k)；

When in use

The window length Q of the band-pass filtered echo signal is α Q, and the computer 4 sets the band-pass filtered echo signal s according to the depth of the oil well_p(i) 5 to 14 times of rapidFourier transform to obtain frequency domain echo signal sequence F_γ(k) Along with the increase of the well depth, the reflected signal is weaker, and the band-pass filtering echo signal s is not needed_p(i) And performing more fast Fourier transforms.

Step 303, computer 4 filters the band-pass echo signal s_p(i) After zero filling processing, fast Fourier transform is carried out to obtain a frequency domain echo signal F (k);

step 304, computer 4 filters the band-pass echo signal s_p(i) Carrying out beta frequency domain transformation by using the step length of Q as the window length and delta Q as the window to obtain a frequency domain echo signal sequence F_β(k) Wherein beta is more than or equal to 2 and less than or equal to 4;

computer 4 band-pass filtered echo signal s_p(i) When the frequency domain transformation is carried out for beta times by taking Q as the window length and delta Q as the step length of the window, zero filling processing is adopted and then fast Fourier transformation is carried out to obtain a frequency domain echo signal sequence F_β(k)；

Step 305, the computer 4 filters the band-pass echo signal s_p(i) Carrying out gamma frequency domain transformation by using the step length of Q as the window length and delta Q as the window to obtain a frequency domain echo signal sequence F_γ(k) Wherein gamma is more than 4 and less than 15;

computer 4 band-pass filtered echo signal s_p(i) Zero padding is adopted when gamma-time frequency domain transformation is carried out by using the step length with Q as the window length and delta Q as the window length, and then fast Fourier transformation is carried out to obtain a frequency domain echo signal sequence F_γ(k)；

Step four, extracting the sound velocity of the echo signal, and the process is as follows:

step 401, the computer 4 extracts m times of frequency multiplication frequency corresponding to the maximum energy value of the frequency domain echo signal, and executes step 402 when the frequency domain echo signal is a frequency domain echo signal f (k); when the frequency domain echo signal is a frequency domain echo signal sequence F_β(k) Then, step 403 is executed; when the frequency domain echo signal is a frequency domain echo signal sequence F_γ(k) Then, step 404 is executed, m is a positive integer not greater than 5;

step 402, the computer 4 processes the frequency domain echo signal F (k) with the frequency value f_NminBegin to find the frequency value f_NmaxLooking up atf_NminAnd f_NmaxNormalized frequency value corresponding to the spectral line having the greatest energy between, when f_NminAnd f_NmaxThe spectral line with the maximum energy exists between the two, and the normalized frequency value corresponding to the spectral line with the maximum energy is the normalized fundamental frequency f of the infrasonic wave on a single pipe joint_NThe normalized fundamental frequency f of the infrasonic wave on a single pipe joint_NIs 1 times the frequency f of the frequency domain echo signal F (k)_N1Then the frequency values are respectively 2f on the frequency domain echo signals F (k)_N、3f_N、4f_NAnd 5f_NSearching for the 2-time frequency f corresponding to the spectral line with the maximum energy between the left neighborhood and the right neighborhood_N23 times of the frequency f _N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5According to the formula

Calculating the sound velocity v of the echo signal;

when f is_NminAnd f_NmaxThere is no spectral line with the maximum energy in between, the computer 4 looks for a spectral line at 2f_NminAnd 2f_NmaxThe frequency value corresponding to the spectral line with the maximum energy is 2 times of the frequency doubling frequency f of the frequency domain echo signal F (k)_N2Then the frequency values are respectively

And

searching for the frequency multiplication frequency f of 3 times corresponding to the spectral line with the maximum energy between the left neighborhood and the right neighborhood _N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5According to the formula

Calculating the sound velocity v of the echo signal;

it should be noted that, step 402 represents the calculation of the sound velocity of the echo signal of the shallow well, and only the frequency domain needs to be found on the frequency domain echo signal f (k)1-fold frequency f of echo signals F (k)_N12 times of the frequency f_N23 times of the frequency f _N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5And (4) calculating the sound velocity v of the echo signal by adopting an averaging method.

Step 403, the computer 4 processes the frequency domain echo signal sequence F_β(k) In each frequency domain echo signal, respectively carrying out echo signal sound velocity calculation, and a frequency domain echo signal sequence F_β(k) The echo signal sound velocity calculation methods of each frequency domain echo signal are the same; computer 4 pairs of frequency domain echo signal sequence F_β(k) All the echo signals of any frequency domain have the frequency value f_NminBegin to find the frequency value f_NmaxFinding is at f_NminAnd f_NmaxNormalized frequency value corresponding to the spectral line having the greatest energy between, when f_NminAnd f_NmaxThe spectral line with the maximum energy exists between the two, and the normalized frequency value corresponding to the spectral line with the maximum energy is the normalized fundamental frequency f of the infrasonic wave on a single pipe joint_NThe normalized fundamental frequency f of the infrasonic wave on a single pipe section_NThe accurate value of is a frequency domain echo signal sequence F_β(k) Frequency f of 1 times of the echo signal of the selected frequency domain_N1Then in the frequency domain_β(k) The frequency values of the echo signals of the selected frequency domain are respectively 2f_N、3f_N、4f_NAnd 5f_NSearching for the 2-time frequency f corresponding to the spectral line with the maximum energy between the left neighborhood and the right neighborhood_N23 times of the frequency f_N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5According to the formula

Calculating a frequency domain echo signal sequence F_β(k) The sound velocity v of the echo signal corresponding to the echo signal of the selected frequency domain_ε；

When f is_NminAnd f_NmaxThere is no spectral line with the maximum energy in between, the computer 4 looks for a spectral line at 2f_NminAnd 2f_NmaxThe frequency value corresponding to the spectral line with the maximum energy between the spectral lines, the spectral line with the maximum energyThe frequency value corresponding to the line is a frequency domain echo signal sequence F_β(k) Frequency f of 2 times of the echo signal of the selected frequency domain_N2Then in the frequency domain_β(k) Wherein the frequency values of the echo signals of the selected frequency domain are respectively

And

searching for the frequency multiplication frequency f of 3 times corresponding to the spectral line with the maximum energy between the left neighborhood and the right neighborhood _N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5According to the formula

Calculating a frequency domain echo signal sequence F_β(k) The sound velocity v of the echo signal corresponding to the echo signal of the selected frequency domain_εWhere ε is the frequency domain echo signal sequence F_β(k) The number of the intermediate frequency domain echo signal is not less than epsilon and not more than beta;

according to the formula

Calculating the sound velocity v of the echo signal;

it should be noted that the frequency domain echo signal sequence F_β(k) The method comprises 2 to 4 frequency domain echo signals, and during actual calculation, a frequency domain echo signal sequence F is subjected to_β(k) Respectively finding 1 time of frequency multiplication frequency f of the echo signals of the 2 to 4 frequency domains_N12 times of the frequency f_N23 times of the frequency f _N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5Position, calculating the frequency domain echo signal sequence F by averaging_β(k) The sound velocity v of the echo signal corresponding to the echo signal of the selected frequency domain_εThen, the average method is utilized to carry out the averaging on the sound velocity v of the echo signals corresponding to the echo signals of 2 to 4 frequency domains_εAveraging and calculating the sound velocity of echo signalv。

Step 404, the computer 4 processes the frequency domain echo signal sequence F_γ(k) In each frequency domain echo signal, respectively carrying out echo signal sound velocity calculation, and a frequency domain echo signal sequence F_γ(k) The echo signal sound velocity calculation methods of each frequency domain echo signal are the same; computer 4 pairs of frequency domain echo signal sequence F_γ(k) All the echo signals of any frequency domain have the frequency value f_NminBegin to find the frequency value f_NmaxFinding is at f_NminAnd f_NmaxNormalized frequency value corresponding to the spectral line having the greatest energy between, when f_NminAnd f_NmaxThe spectral line with the maximum energy exists between the two, and the normalized frequency value corresponding to the spectral line with the maximum energy is the normalized fundamental frequency f of the infrasonic wave on a single pipe joint_NThe normalized fundamental frequency f of the infrasonic wave on a single pipe section_NThe accurate value of is a frequency domain echo signal sequence F_γ(k) Frequency f of 1 times of the echo signal of the selected frequency domain_N1Then in the frequency domain_γ(k) The frequency values of the echo signals of the selected frequency domain are respectively 2f_N、3f_N、4f_NAnd 5f_NSearching for the 2-time frequency f corresponding to the spectral line with the maximum energy between the left neighborhood and the right neighborhood_N23 times of the frequency f_N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5According to the formula

Calculating a frequency domain echo signal sequence F_γ(k) The sound velocity v of the echo signal corresponding to the echo signal of the selected frequency domain_φ；

When f is_NminAnd f_NmaxThere is no spectral line with the maximum energy in between, the computer 4 looks for a spectral line at 2f_NminAnd 2f_NmaxThe frequency value corresponding to the spectral line with the maximum energy is the frequency domain echo signal sequence F_γ(k) Frequency f of 2 times of the echo signal of the selected frequency domain_N2Then in the frequency domain_γ(k) Wherein the frequency values of the echo signals of the selected frequency domain are respectively

And

searching for the frequency multiplication frequency f of 3 times corresponding to the spectral line with the maximum energy between the left neighborhood and the right neighborhood _N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5According to the formula

Calculating a frequency domain echo signal sequence F_γ(k) The sound velocity v of the echo signal corresponding to the echo signal of the selected frequency domain_φWhere phi is the frequency domain echo signal sequence F_γ(k) The number of the intermediate frequency domain echo signals is phi less than or equal to gamma;

computer 4 pairs of frequency domain echo signal sequence F_γ(k) Screening gamma echo signal sound velocities corresponding to the medium gamma frequency domain echo signals, screening 4 continuous sound velocity values with the minimum change rate, and solving the average value of the 4 sound velocity values as an echo signal sound velocity v;

it should be noted that the frequency domain echo signal sequence F_γ(k) Contains more than 4 frequency domain echo signals, and the frequency domain echo signal sequence F is subjected to actual calculation_γ(k) Respectively finding 1-time frequency f of the echo signals with more than 4 frequency domains_N12 times of the frequency f_N23 times of the frequency f _N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5Position, calculating the frequency domain echo signal sequence F by averaging_γ(k) The sound velocity v of the echo signal corresponding to the echo signal of the selected frequency domain_φThen, 4 consecutive sound velocity values with the smallest change rate are screened out, and the average value of the 4 sound velocity values is obtained as the echo signal sound velocity v.

Step five, data return-to-zero processing of the echo sampling signals: the computer 4 extracts the amplitude eta (i) of each sample point in the echo sampling signal s (i) according to a formula

Calculating the average amplitude of each sampling point

Wherein M is the total number of sample points in the echo sampling signal s (i);

according to the formula

Calculating the return-to-zero amplitude eta '(i) of each sampling point to obtain a return-to-zero echo sampling signal s' (i);

sixthly, filtering the return-to-zero echo sampling signal: estimating value Y according to working fluid level depth_hFiltering the return-to-zero echo sampling signal s' (i) when Y is_hWhen the depth is more than 600m, the oil well is regarded as a deep well, and step 601 is executed; when Y is_hWhen the distance is less than or equal to 600m, the oil well is regarded as a shallow well, and step 602 is executed;

step 601, the computer 4 sequentially adopts a first low-pass filter, a band-stop filter and a second low-pass filter to filter the return-to-zero echo sampling signal s' (i) to obtain a deep well return-to-zero echo filtering signal s (i), wherein the cut-off frequency of the first low-pass filter is 0.01Hz, the sidelobe attenuation of the first low-pass filter is 80dB, the stopband attenuation of the band-stop filter is 80dB, the cut-off frequency of the second low-pass filter is 0.02Hz, and the sidelobe attenuation of the second low-pass filter is 80 dB;

it should be noted that the band-stop filter is based on the Kaiser window function, the stop band cut-off frequency of the band-stop filter is the motor frequency in the pumping unit 9, and since periodic vibration noise such as motor sound in the pumping unit 9 exists in the environment, many periodic high-frequency signals appear in the return-to-zero echo signal s' (i), and the periodic signals can be filtered by adopting the band-stop filter, so that the working fluid level signal is more easily identified.

In practical use, when an oil well is waxed or scaled, a noise signal with lower frequency and larger amplitude than the working fluid level signal exists in the echo sampling signal s (i), low-frequency noise is larger than the working fluid level signal after the low-pass filtering is carried out by adopting the first low-pass filter, the low-frequency noise is mistakenly taken as the working fluid level signal, and the signal filtered by the band elimination filter is filtered by arranging the second low-pass filter, so that the working fluid level signal cannot be filtered as the low-frequency noise.

Step 602, the computer 4 filters the return-to-zero echo sampling signal S '(i) by using a second low-pass filter to obtain a shallow well return-to-zero echo filtering signal S' (i);

in actual use, when Y is_hWhen the working fluid level is less than or equal to 600m, the oil well is regarded as a shallow well, the working fluid level signal is strong, the frequency is high, the position of the peak value of the working fluid level signal cannot be changed by setting the second low-pass filter for filtering, and the precision of the working fluid level depth is improved.

Step seven, searching the abrupt peak value of the position of the working fluid level and the sampling point of the position of the working fluid level: the computer 4 determines a working fluid level depth searching range according to the depth of the oil well, and determines a sudden change peak value of the working fluid level position and a sampling point of the working fluid level position in the working fluid level depth searching range, wherein the deep wells are divided into a first deep well, a second deep well and a third deep well, and the working fluid level depth estimated value Y of the first deep well_hSatisfies the following conditions: y is more than 600m_h< 1100 m; the working fluid level depth estimated value Y of the second deep well_hSatisfies the following conditions: y is more than or equal to 1100m_hLess than or equal to 1800 m; the working fluid level depth estimated value Y of the third deep well_hSatisfies the following conditions: y is_h＞1800m；

When the oil well is a shallow well, the working fluid level depth search range is 0.7Y_h～1.2Y_hComputer 4 at 0.7Y_h～1.2Y_hCollecting each peak value in the shallow-well return-to-zero echo filtering signal S' (i) in the corresponding sampling point

When it is, will h_jThe abrupt peak value h of the working fluid level position is regarded as the abrupt peak value of the working fluid level position_jThe corresponding sampling point j is regarded as the sampling point of the position of the working fluid level, wherein h-and h₊Respectively, the sudden change peak value h of the working fluid level_jLeft and right adjacent peak values;

when the well is the first deep wellThe working fluid level depth search range is 0.4Y_h～1.3Y_hComputer 4 at 0.4Y_h～1.3Y_hAcquiring each peak value in the deep well return-to-zero echo filter signal S (i) in a corresponding sampling point, wherein the acquisition modes of the sudden change peak value of the working fluid level position of the first deep well and the sampling point of the working fluid level position are the same as the acquisition modes of the sudden change peak value of the working fluid level position of the shallow well and the sampling point of the working fluid level position of the shallow well;

when the oil well is the second deep well, the working fluid level depth searching range is 0.5Y_h～1.3Y_hComputer 4 at 0.5Y_h～1.3Y_hCollecting each peak value in the return-to-zero echo filtering signal S (i) of the deep well in a corresponding sampling point, wherein the acquisition modes of the sudden change peak value of the working fluid level position of the second deep well and the sampling point of the working fluid level position are the same as the acquisition modes of the sudden change peak value of the working fluid level position of the shallow well and the sampling point of the working fluid level position;

when the oil well is a third deep well, the working fluid level depth search range is 0.6Y_h～1.2Y_hComputer 4 at 0.6Y_h～1.2Y_hCollecting each peak value in the deep well return-to-zero echo filter signal S (i) in a corresponding sampling point, wherein the acquisition modes of the sudden change peak value of the working fluid level position of the third deep well and the sampling point of the working fluid level position are the same as the acquisition modes of the sudden change peak value of the working fluid level position of the shallow well and the sampling point of the working fluid level position of the shallow well;

step eight, acquiring the sampling time of the working fluid level position: the computer 4 respectively searches a sampling point j-1 and a sampling point j +1 at the left side and the right side of the sampling point j of the working fluid level position, and the corresponding amplitude of the sampling point j-1 is h_j-1The corresponding amplitude of the sampling point j +1 is h_j+1Using (j-1, h)_j-1)、(j,h_j) And (j +1, h)_j+1) Three points are used to obtain a quadratic function y ═ ax using sampling point as variable x and amplitude as function value y²+ bx + c, wherein a, b, and c are constants; obtaining a quadratic function y ═ ax²The extreme point coordinate of + bx + c

According to the formula

Calculating the sampling time t of the position of the working fluid level;

in this embodiment, the abscissa of the extreme point coordinate

Satisfies the following conditions:

the method includes the steps of determining a working fluid level depth search range according to the depth of an oil well, determining a sudden change peak value of a working fluid level position and sampling points of the working fluid level position in the working fluid level depth search range, then constructing a quadratic function by using the sampling points of the working fluid level position and the sampling points on the left side and the right side of the sampling points, obtaining extreme point coordinates of the quadratic function, further calculating sampling time of the working fluid level position, improving data processing precision, reducing calculation errors of the sampling time of the working fluid level position, and providing accurate time conditions for accurate and automatic working fluid level detection.

Step nine, identifying the actual depth of the working fluid level: according to the formula

Calculating the actual depth Y of the working fluid level_s。

In this embodiment, the sound generator 1 is an implosion type sound generator or an external explosion type sound generator, and when the sound generator 1 is an implosion type sound generator, the abrupt change peak h of the working fluid level position in the seventh step_jTaking a positive peak value; when the sound wave generator 1 is an external explosion type sound wave generator, the abrupt change peak value h of the working fluid level position in the step seven_jTaking the negative peak value.

In this embodiment, the spectral line with the largest energy represents that the spectral amplitude corresponding to the frequency is not less than 2 times the spectral amplitude corresponding to the frequency in the neighborhood around the frequency.

When the method is used, the window length of the band-pass filtering echo signal and the window step length are determined according to different oil well depths, the echo periodic signal based on the oil pipe coupling is identified, the sound velocity of the echo signal is extracted, the sudden change peak value of the working fluid level position and the sampling point of the working fluid level position are searched, the sampling time of the working fluid level position is obtained, the adaptability is strong, and the problem that the working fluid level signal cannot be directly identified due to the fact that the working fluid level signal is submerged by noise is solved.

The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and all simple modifications, changes and equivalent structural changes made to the above embodiment according to the technical spirit of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims (6)

1. A method for identifying the working fluid level of an oil well is characterized by comprising the following steps:

the method comprises the following steps of firstly, obtaining a working fluid level depth estimated value and acquiring an echo signal: obtaining working fluid level depth estimated value Y by using installation position of oil pump in oil well_hThe computer (4) is used for controlling the sound wave generator (1) to send out an infrasonic wave signal, the infrasonic wave signal is reflected by a working fluid level (8), the oil pipe (5) and an oil pipe coupling (6) in an annular space formed between the oil pipe (5) and the casing pipe (7) to form an echo signal, the echo signal is received by the echo receiver (2), and the working fluid level measuring instrument (3) is used for sampling frequency f_sAcquiring the echo signal to obtain an echo sampling signal s (i), and sending the echo sampling signal s (i) to a computer (4), wherein i is the number of sampling points;

the acoustic wave generator (1) and the echo receiver (2) are both installed at the wellhead of an oil well, the input end of the acoustic wave generator (1) is connected with the output end of the computer (4), the output end of the echo receiver (2) is connected with the input end of the dynamic liquid level measuring instrument (3), and the dynamic liquid level measuring instrument (3) is communicated with the computer (4) in a wired or wireless mode; the oil pipe (5) is arranged in the casing pipe (7), the oil pipe (5) is formed by sequentially connecting a plurality of pipe joints, and two adjacent pipe joints are connected by adopting an oil pipe coupling (6);

step two, filtering the echo sampling signal, wherein the process is as follows:

step 201, pre-estimating fundamental frequency f of infrasonic waves on single pipe joint_BThe range of (A): according to the formula f_Bmin≤f_B≤f_BmaxIs estimatedFundamental frequency f of infrasonic waves on single pipe joint_BWherein f is_BminIs the fundamental minimum frequency of infrasonic waves on a single pipe joint, an

f_BmaxFor the fundamental maximum frequency of infrasonic waves on a single pipe section and

l is the length of a single pipe section, v_minIs the minimum sound velocity, v, of the propagation of infrasonic waves in the annular space formed between the oil pipe (5) and the casing (7)_maxThe maximum sound velocity of infrasonic waves propagating in an annular space formed between the oil pipe (5) and the casing pipe (7);

step 202, obtaining the range of the normalized fundamental wave frequency of the infrasonic wave on a single pipe joint through normalization processing: according to the formula

For fundamental minimum frequency f of infrasonic wave on single pipe joint_BminNormalization is carried out to obtain the normalized fundamental wave minimum frequency f of the infrasonic wave on a single pipe joint_NminFor the maximum frequency f of fundamental wave of infrasonic wave on a single pipe joint_BmaxNormalization is carried out to obtain the normalized fundamental wave maximum frequency f of the infrasonic wave on a single pipe joint_NmaxAccording to f_Nmin≤f_N≤f_NmaxObtaining the normalized fundamental frequency f of the infrasonic wave on a single pipe joint_NRange of (a), (b), (c) and (d)_NFor fundamental frequency f of infrasonic waves on a single pipe section_BNormalizing the result;

step 203, selecting a band-pass filter: the computer selects a band-pass filter based on a Kaiser window function, and the lower limit frequency f of the band-pass filter_BL＝ρ₁f_NminUpper limit frequency f of said band-pass filter_BU＝ρ₂f_NmaxWhere ρ is₁Is a lower limit frequency coefficient and is more than 0.5 rho₁＜1，ρ₂Is an upper limit frequency coefficient and 5 < rho₂＜8；

Step 204, filtering: the computer uses the band-pass filter selected in step 203 to perform band-pass filtering on the echo sampling signal s (i) to obtain a band-pass filtered echo signal s_p(i)；

Step three, frequency domain transformation of the band-pass filtering echo signal, the process is as follows:

step 301, determining the starting position of the window: the computer (4) filters the echo signal s from the band pass_p(i) The first sampling point in (a) starts to look up backwards, and a band-pass filtered echo signal s is determined_p(i) Stopping searching after three continuous echo periodic signals, and filtering the band-pass echo signal s_p(i) The starting position of the first echo periodic signal in the three continuous echo periodic signals is used as the starting position of the window;

step 302, determining the window length of the band-pass filtering echo signal and the step length of the window: according to the formula

Calculating the number q of pre-estimated sampling points on a single pipe joint, and when the alpha multiplied by L is more than or equal to Y_hWindow length of time-band-pass filtered echo signal

At this time, the window does not need to set the step length Δ Q of the window, and step 303 is executed; when in use

And the window length Q of the band-pass filtering echo signal is equal to alpha Q, and at the moment, the step length delta Q of the window satisfies the following conditions: when Q is more than delta Q and less than or equal to 3Q, executing step 304; when in use

And the window length Q of the band-pass filtering echo signal is equal to alpha Q, and at the moment, the step length delta Q of the window satisfies the following conditions: when Q is more than delta Q and less than or equal to 3Q, executing step 305; wherein alpha is the number of pipe sections selected continuously, and alpha is more than 30 and less than 40 [. alpha. ]]Is a rounding function;

step 303, the computer (4) filters the band-pass echo signal s_p(i) MakingAfter zero filling processing, fast Fourier transform is carried out to obtain a frequency domain echo signal F (k);

step 304, the computer (4) filters the band-pass echo signal s_p(i) Carrying out beta frequency domain transformation by using the step length of Q as the window length and delta Q as the window to obtain a frequency domain echo signal sequence F_β(k) Wherein beta is more than or equal to 2 and less than or equal to 4;

the computer (4) filters the echo signal s to band pass_p(i) When the frequency domain transformation is carried out for beta times by taking Q as the window length and delta Q as the step length of the window, zero filling processing is adopted and then fast Fourier transformation is carried out to obtain a frequency domain echo signal sequence F_β(k)；

Step 305, the computer (4) filters the band-pass echo signal s_p(i) Carrying out gamma frequency domain transformation by using the step length of Q as the window length and delta Q as the window to obtain a frequency domain echo signal sequence F_γ(k) Wherein gamma is more than 4 and less than 15;

the computer (4) filters the echo signal s to band pass_p(i) Zero padding is adopted when gamma-time frequency domain transformation is carried out by using the step length with Q as the window length and delta Q as the window length, and then fast Fourier transformation is carried out to obtain a frequency domain echo signal sequence F_γ(k)；

Step four, extracting the sound velocity of the echo signal, and the process is as follows:

step 401, the computer (4) extracts m times of frequency multiplication frequency corresponding to the maximum energy value of the frequency domain echo signal, and when the frequency domain echo signal is the frequency domain echo signal F (k), step 402 is executed; when the frequency domain echo signal is a frequency domain echo signal sequence F_β(k) Then, step 403 is executed; when the frequency domain echo signal is a frequency domain echo signal sequence F_γ(k) Then, step 404 is executed, m is a positive integer not greater than 5;

step 402, the computer (4) processes the frequency domain echo signal F (k) from the frequency value f_NminBegin to find the frequency value f_NmaxFinding is at f_NminAnd f_NmaxNormalized frequency value corresponding to the spectral line having the greatest energy between, when f_NminAnd f_NmaxThe spectral line with the maximum energy exists between the two, and the normalized frequency value corresponding to the spectral line with the maximum energy is the normalized fundamental frequency f of the infrasonic wave on a single pipe joint_NAccurate value of (A), infrasonic wave inNormalized fundamental frequency f on a single pipe section_NIs 1 times the frequency f of the frequency domain echo signal F (k)_N1Then the frequency values are respectively 2f on the frequency domain echo signals F (k)_N、3f_N、4f_NAnd 5f_NSearching for the 2-time frequency f corresponding to the spectral line with the maximum energy between the left neighborhood and the right neighborhood_N23 times of the frequency f_N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5According to the formula

Calculating the sound velocity v of the echo signal;

when f is_NminAnd f_NmaxThere is no spectral line with the maximum energy in between, the computer (4) looks for a spectral line at 2f_NminAnd 2f_NmaxThe frequency value corresponding to the spectral line with the maximum energy is 2 times of the frequency doubling frequency f of the frequency domain echo signal F (k)_N2Then the frequency values are respectively

And

searching for the frequency multiplication frequency f of 3 times corresponding to the spectral line with the maximum energy between the left neighborhood and the right neighborhood_N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5According to the formula

Calculating the sound velocity v of the echo signal;

step 403, the computer (4) processes the frequency domain echo signal sequence F_β(k) In each frequency domain echo signal, respectively carrying out echo signal sound velocity calculation, and a frequency domain echo signal sequence F_β(k) The echo signal sound velocity calculation methods of each frequency domain echo signal are the same; computer (4) for frequency domain echo signal sequence F_β(k) All the echo signals of any frequency domain have the frequency value f_NminBegin to look upFind the frequency value f_NmaxFinding is at f_NminAnd f_NmaxNormalized frequency value corresponding to the spectral line having the greatest energy between, when f_NminAnd f_NmaxThe spectral line with the maximum energy exists between the two, and the normalized frequency value corresponding to the spectral line with the maximum energy is the normalized fundamental frequency f of the infrasonic wave on a single pipe joint_NThe normalized fundamental frequency f of the infrasonic wave on a single pipe section_NThe accurate value of is a frequency domain echo signal sequence F_β(k) Frequency f of 1 times of the echo signal of the selected frequency domain_N1Then in the frequency domain_β(k) The frequency values of the echo signals of the selected frequency domain are respectively 2f_N、3f_N、4f_NAnd 5f_NSearching for the 2-time frequency f corresponding to the spectral line with the maximum energy between the left neighborhood and the right neighborhood_N23 times of the frequency f_N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5According to the formula

Calculating a frequency domain echo signal sequence F_β(k) The sound velocity v of the echo signal corresponding to the echo signal of the selected frequency domain_ε；

When f is_NminAnd f_NmaxThere is no spectral line with the maximum energy in between, the computer (4) looks for a spectral line at 2f_NminAnd 2f_NmaxThe frequency value corresponding to the spectral line with the maximum energy is the frequency domain echo signal sequence F_β(k) Frequency f of 2 times of the echo signal of the selected frequency domain_N2Then in the frequency domain_β(k) Wherein the frequency values of the echo signals of the selected frequency domain are respectively

And

searching for the frequency multiplication frequency f of 3 times corresponding to the spectral line with the maximum energy between the left neighborhood and the right neighborhood_N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5According to the formula

Calculating a frequency domain echo signal sequence F_β(k) The sound velocity v of the echo signal corresponding to the echo signal of the selected frequency domain_εWhere ε is the frequency domain echo signal sequence F_β(k) The number of the intermediate frequency domain echo signal is not less than epsilon and not more than beta;

according to the formula

Calculating the sound velocity v of the echo signal;

step 404, the computer (4) processes the frequency domain echo signal sequence F_γ(k) In each frequency domain echo signal, respectively carrying out echo signal sound velocity calculation, and a frequency domain echo signal sequence F_γ(k) The echo signal sound velocity calculation methods of each frequency domain echo signal are the same; computer (4) for frequency domain echo signal sequence F_γ(k) All the echo signals of any frequency domain have the frequency value f_NminBegin to find the frequency value f_NmaxFinding is at f_NminAnd f_NmaxNormalized frequency value corresponding to the spectral line having the greatest energy between, when f_NminAnd f_NmaxThe spectral line with the maximum energy exists between the two, and the normalized frequency value corresponding to the spectral line with the maximum energy is the normalized fundamental frequency f of the infrasonic wave on a single pipe joint_NThe normalized fundamental frequency f of the infrasonic wave on a single pipe section_NThe accurate value of is a frequency domain echo signal sequence F_γ(k) Frequency f of 1 times of the echo signal of the selected frequency domain_N1Then in the frequency domain_γ(k) The frequency values of the echo signals of the selected frequency domain are respectively 2f_N、3f_N、4f_NAnd 5f_NSearching for the 2-time frequency f corresponding to the spectral line with the maximum energy between the left neighborhood and the right neighborhood_N23 times of the frequency f_N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5According to the formula

Calculating a frequency domain echo signal sequence F_γ(k) The sound velocity v of the echo signal corresponding to the echo signal of the selected frequency domain_φ；

When f is_NminAnd f_NmaxThere is no spectral line with the maximum energy in between, the computer (4) looks for a spectral line at 2f_NminAnd 2f_NmaxThe frequency value corresponding to the spectral line with the maximum energy is the frequency domain echo signal sequence F_γ(k) Frequency f of 2 times of the echo signal of the selected frequency domain_N2Then in the frequency domain_γ(k) Wherein the frequency values of the echo signals of the selected frequency domain are respectively

And

searching for the frequency multiplication frequency f of 3 times corresponding to the spectral line with the maximum energy between the left neighborhood and the right neighborhood_N34 times of frequency multiplication frequency f_N4And 5 times the frequency f_N5According to the formula

Calculating a frequency domain echo signal sequence F_γ(k) The sound velocity v of the echo signal corresponding to the echo signal of the selected frequency domain_φWhere phi is the frequency domain echo signal sequence F_γ(k) The number of the intermediate frequency domain echo signals is phi less than or equal to gamma;

computer (4) for frequency domain echo signal sequence F_γ(k) Screening gamma echo signal sound velocities corresponding to the medium gamma frequency domain echo signals, screening 4 continuous sound velocity values with the minimum change rate, and solving the average value of the 4 sound velocity values as an echo signal sound velocity v;

step five, data return-to-zero processing of the echo sampling signals: the computer (4) extracts the amplitude eta (i) of each sampling point in the echo sampling signal s (i) according to a formula

Calculating the average amplitude of each sampling point

Wherein M is the total number of sample points in the echo sampling signal s (i);

according to the formula

Calculating the return-to-zero amplitude eta '(i) of each sampling point to obtain a return-to-zero echo sampling signal s' (i);

sixthly, filtering the return-to-zero echo sampling signal: estimating value Y according to working fluid level depth_hFiltering the return-to-zero echo sampling signal s' (i) when Y is_hWhen the depth is more than 600m, the oil well is regarded as a deep well, and step 601 is executed; when Y is_hWhen the distance is less than or equal to 600m, the oil well is regarded as a shallow well, and step 602 is executed;

step 601, the computer (4) sequentially adopts a first low-pass filter, a band-stop filter and a second low-pass filter to filter the return-to-zero echo sampling signal s' (i) to obtain a deep well return-to-zero echo filtering signal S (i), wherein the cut-off frequency of the first low-pass filter is 0.01Hz, the sidelobe attenuation of the first low-pass filter is 80dB, the stopband attenuation of the band-stop filter is 80dB, the cut-off frequency of the second low-pass filter is 0.02Hz, and the sidelobe attenuation of the second low-pass filter is 80 dB;

step 602, the computer (4) adopts a second low-pass filter to filter the return-to-zero echo sampling signal S '(i) to obtain a shallow well return-to-zero echo filtering signal S' (i);

step seven, searching the abrupt peak value of the position of the working fluid level and the sampling point of the position of the working fluid level: the computer (4) determines the working fluid level depth searching range according to the depth of the oil well and determines the projection of the working fluid level position in the working fluid level depth searching rangeSampling points of variable peak values and dynamic liquid level positions, wherein the deep wells are divided into a first deep well, a second deep well and a third deep well, and the dynamic liquid level depth estimated value Y of the first deep well_hSatisfies the following conditions: y is more than 600m_h< 1100 m; the working fluid level depth estimated value Y of the second deep well_hSatisfies the following conditions: y is more than or equal to 1100m_hLess than or equal to 1800 m; the working fluid level depth estimated value Y of the third deep well_hSatisfies the following conditions: y is_h＞1800m；

When the oil well is a shallow well, the working fluid level depth search range is 0.7Y_h～1.2Y_hComputer (4) at 0.7Y_h～1.2Y_hCollecting each peak value in the shallow-well return-to-zero echo filtering signal S' (i) in the corresponding sampling point

When it is, will h_jThe abrupt peak value h of the working fluid level position is regarded as the abrupt peak value of the working fluid level position_jThe corresponding sampling point j is regarded as the sampling point of the position of the working fluid level, wherein h-and h₊Respectively, the sudden change peak value h of the working fluid level_jLeft and right adjacent peak values;

when the oil well is the first deep well, the working fluid level depth searching range is 0.4Y_h～1.3Y_hComputer (4) at 0.4Y_h～1.3Y_hAcquiring each peak value in the deep well return-to-zero echo filter signal S (i) in a corresponding sampling point, wherein the acquisition modes of the sudden change peak value of the working fluid level position of the first deep well and the sampling point of the working fluid level position are the same as the acquisition modes of the sudden change peak value of the working fluid level position of the shallow well and the sampling point of the working fluid level position of the shallow well;

when the oil well is the second deep well, the working fluid level depth searching range is 0.5Y_h～1.3Y_hComputer (4) at 0.5Y_h～1.3Y_hCollecting each peak value in the return-to-zero echo filtering signal S (i) of the deep well in a corresponding sampling point, wherein the acquisition modes of the sudden change peak value of the working fluid level position of the second deep well and the sampling point of the working fluid level position are the same as the acquisition modes of the sudden change peak value of the working fluid level position of the shallow well and the sampling point of the working fluid level position;

when the oil well is the third deep well, the working fluid level depth is searchedIn the range of 0.6Y_h～1.2Y_hComputer (4) at 0.6Y_h～1.2Y_hCollecting each peak value in the deep well return-to-zero echo filter signal S (i) in a corresponding sampling point, wherein the acquisition modes of the sudden change peak value of the working fluid level position of the third deep well and the sampling point of the working fluid level position are the same as the acquisition modes of the sudden change peak value of the working fluid level position of the shallow well and the sampling point of the working fluid level position of the shallow well;

step eight, acquiring the sampling time of the working fluid level position: the computer (4) respectively searches a sampling point j-1 and a sampling point j +1 at the left side and the right side of the sampling point j of the position of the working fluid level, and the corresponding amplitude of the sampling point j-1 is h_j-1The corresponding amplitude of the sampling point j +1 is h_j+1Using (j-1, h)_j-1)、(j,h_j) And (j +1, h)_j+1) Three points are used to obtain a quadratic function y ═ ax using sampling point as variable x and amplitude as function value y²+ bx + c, wherein a, b, and c are constants; obtaining a quadratic function y ═ ax²The extreme point coordinate of + bx + c

According to the formula

Calculating the sampling time t of the position of the working fluid level;

step nine, identifying the actual depth of the working fluid level: according to the formula

Calculating the actual depth Y of the working fluid level_s。

2. The method for identifying the working fluid level of an oil well according to claim 1, wherein: the sound wave generator (1) is an implosion type sound wave generator or an external explosion type sound wave generator, and when the sound wave generator (1) is the implosion type sound wave generator, the abrupt change peak value h of the working fluid level position in the step seven_jTaking a positive peak value; when the sound wave generator (1) is an external explosion type sound wave generator, the abrupt change peak value h of the working fluid level position in the step seven_jTaking the negative peak value.

3. The method for identifying the working fluid level of an oil well according to claim 1, wherein: the sampling frequency f of the dynamic liquid level measuring instrument (3)_sIs 470 Hz.

4. The method for identifying the working fluid level of an oil well according to claim 1, wherein: minimum sound velocity v of infrasonic wave propagating in annular space formed between oil pipe (5) and casing (7) in step 201_min220m/s, the maximum sound velocity v of the infrasonic wave propagating in the annular space formed between the oil pipe (5) and the casing (7)_maxIs 400 m/s.

5. The method for identifying the working fluid level of an oil well according to claim 1, wherein: the spectral line with the maximum energy represents that the spectral amplitude corresponding to the frequency is not less than 2 times of the spectral amplitude corresponding to the frequency in the neighborhood around the frequency.

6. The method for identifying the working fluid level of an oil well according to claim 1, wherein: abscissa of the extreme point coordinates

Satisfies the following conditions:

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