Device and method for measuring liquid level in well based on sound wave principle
By using acoustic ranging technology in the well, the propagation characteristics of acoustic waves in the wellbore are used to solve the problems of vulnerability, high cost and inaccurate measurement of probes in traditional liquid level measurement technology, and high-precision, low-cost and convenient liquid level measurement are achieved, suitable for various well depths and well conditions.
Patent Information
- Application Number
- CN202510066434.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-16
- Publication Date
- 2025-03-04
- Estimated Expiration
- 2045-01-16
AI Technical Summary
Traditional well level measurement technology has problems such as vulnerability to probes and cables, high cost, short life, difficulty in long-term dynamic monitoring, and inaccurate measurements in complex well conditions.
Using methods and equipment based on the principle of sonic distance measurement, a two-way probe is set at the wellhead, and the propagation characteristics of sound waves in the wellbore is used to measure the sound wave time difference and calculate the liquid level depth, achieving convenient, fast, accurate and low-cost liquid level measurement.
This method is suitable for all well depths and complex well conditions, achieving high-precision liquid level measurement, reducing equipment costs and maintenance risks, and is suitable for applications of one machine, one well and one machine, and supports long-term dynamic monitoring and remote measurement and control.
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Figure CN119554016A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the field of acoustic wave ranging and dynamic monitoring in a well, and particularly relates to a well liquid level measurement technology and device. Background Art
[0002] The traditional technology of measuring the liquid level in a well based on pressure sensing is to install the pressure sensing probe at a fixed depth below the liquid surface in the well, determine the installation depth of the probe by the length of the signal transmission cable connected to the probe or the length of the pipe column of the fixed cable, fix the signal transmission cable in sections on the pipe in the well or hang it in the well, seal it at the wellhead with a cable sealing device, and connect the cable to the ground display after leaving the well; when measuring, the depth of the liquid surface from the probe measured by the probe is subtracted from the depth of the probe (pressure-depth conversion is performed using a water density of 1 gram / cubic centimeter), which is the depth of the liquid surface from the wellhead.
[0003] This method faces many difficulties in measuring the liquid level in the well.
[0004] First, the insulation, sealing and fixing process of the probe and the cable is complicated. In actual operation, the equipment is easily damaged when it is lowered into or pulled out of the well. For example, the lifting and lowering operation can cause the cable to rub against the well wall, or be subjected to other mechanical forces, resulting in damage to the outer skin, which affects the accuracy of the measurement and the stability of the equipment.
[0005] Secondly, the continuous strong vibrations generated by the water pumps and water pipes in the well will cause serious damage to the probes and cables. Under long-term vibration conditions, the precision components inside the probes are prone to displacement or damage, and the cable connections will also loosen, causing equipment failure. Once a failure occurs, the entire set of equipment often needs to be replaced, which not only increases maintenance costs but also interrupts production.
[0006] Third, traditional level gauges require one set per well, which is expensive and short-lived, making it difficult to meet long-term dynamic monitoring needs. In many cases, the dynamic liquid level in a well without a level gauge cannot be monitored in real time, causing many inconveniences and safety hazards to production activities, such as unstable material supply in industrial production, prone to pump accidents, and possible flooding accidents in mine environments.
[0007] Fourth, with the development of modern industry and the increase in well depth, the requirements for liquid level measurement technology are increasing. Existing liquid level measurement technology has shortcomings in terms of convenience, speed, labor intensity, operating cost, reliability and adaptability. In deep well environments, the measurement accuracy of traditional liquid level meters decreases, the signal transmission cable is inaccurate in measuring depth, and the difficulty of installation and maintenance increases.
[0008] Fifth, under special well conditions, such as when the formation water in the wellbore contains complex gases, mineral particles, large temperature changes or other interference factors, the measurement results of traditional level meters will have large deviations. When the well contains corrosive fluids, higher requirements are placed on the corrosion resistance and service life of the equipment.
[0009] Therefore, the industry urgently needs more accurate, reliable and convenient modern liquid level measurement technology to improve production efficiency, obtain complete and accurate liquid level data, reduce costs and ensure production safety. Summary of the invention
[0010] The present invention aims to provide a method and device for measuring the liquid level in a well at a long distance and without contact at the wellhead based on the principle of acoustic ranging. The method overcomes the problems of the fragility of probes and cables, high cost, short life, difficulty in long-term dynamic monitoring, and inaccurate measurement under complex well conditions in traditional liquid level measurement technology. By utilizing the propagation characteristics of sound waves in the wellbore, convenient, fast, accurate and low-cost liquid level measurement can be achieved, the adaptability and accuracy of liquid level measurement technology under different well conditions can be improved, and the demand for liquid level measurement in the development of the industry can be met.
[0011] One of the technical solutions adopted by the present invention is: a well liquid level measurement device based on the acoustic wave principle, comprising: an excitation device, a receiving device;
[0012] The excitation device is arranged at the wellhead and sends a continuous acoustic wave up-frequency scanning signal toward the wellhead;
[0013] The receiving device includes two probes facing opposite directions and a main acquisition board installed at the upper part of the well, one of which faces the downhole liquid surface and the other faces the excitation device;
[0014] The two probes facing opposite directions are connected to a main acquisition board, and the main acquisition board calculates the liquid level depth in the well according to the sound signals collected by the two probes.
[0015] The second technical solution adopted by the present invention is: a method for measuring the liquid level in a well based on the principle of sound waves, which calculates the depth position of the liquid surface in the well according to the time difference of sound waves collected by two probes facing opposite directions and the transmission speed of sound waves in the well.
[0016] The specific steps include:
[0017] S1, exciting a continuous acoustic up-conversion scanning signal at the wellhead;
[0018] S2, the probe facing the excitation device is recorded as probe A, and the probe facing the downhole liquid surface is recorded as probe B; the scanning signal of step S1 is recorded by probe A and probe B in turn;
[0019] S3, the scanning signal in step S1 propagates downward along the wellbore in an acoustic waveguide manner, generates total reflection when propagating to the liquid surface, and the total reflection signal returns upward to the wellhead and is recorded by probe B and probe A in turn;
[0020] The signal obtained by probe A is recorded as signal A, and the signal obtained by probe B is recorded as signal B;
[0021] S4, perform autocorrelation on signal A, and perform cross-correlation processing on signal A and signal B, the first peak (based on the autocorrelation data of signal A) is the system start time 0, and the second peak (based on the cross-correlation data of signals A and B) is the time when the liquid surface reaches the probe after total reflection; read the time difference between the second peak and the first peak to obtain the round-trip time difference of the sound wave from the wellhead to the liquid surface;
[0022] S5. Based on the acoustic wave round-trip time difference calculated in step S4 and in combination with the acoustic wave velocity in the well, the depth position of the liquid level in the well is calculated.
[0023] Beneficial effects of the present invention: The present invention sets two bidirectional probes at the wellhead, utilizes the propagation characteristics of sound waves in the wellbore, measures the sound waves in two directions respectively, and combines the time difference of the sound waves measured by the two probes to achieve convenient, fast, accurate and low-cost liquid level measurement; the present invention has the following advantages:
[0024] 1) The present invention is applicable to high-precision measurement of liquid level in wells of all well depths and complex well conditions, filling the gap in measuring deep well liquid level at the wellhead;
[0025] 2) The present invention is applicable to one machine and one well, one machine and multiple wells, long-term dynamic monitoring and convenient remote measurement and control;
[0026] 3) The present invention collects data at the wellhead, eliminating the safety and equipment risks of downhole operations;
[0027] 4) The present invention is easy to operate, can instantly obtain liquid level data, and has low cost. BRIEF DESCRIPTION OF THE DRAWINGS
[0028] Figure 1 The schematic diagram of the well liquid level measuring device based on the acoustic wave principle of the present invention;
[0029] Figure 2 It is the structural principle diagram of the bidirectional probe in the present invention;
[0030] Figure 3 A three-dimensional diagram of a bidirectional probe installation frame in the present invention;
[0031] Figure 4 It is a schematic diagram of a cylindrical housing in the present invention;
[0032] Figure 5 It is a schematic diagram of the probe installation structure in the present invention. DETAILED DESCRIPTION
[0033] To facilitate those skilled in the art to understand the technical content of the present invention, the present invention is further explained below with reference to the accompanying drawings.
[0034] First, the working principle of the present invention is described:
[0035] 1. Physical properties of sound waves of air in a circular tube
[0036] According to Maxwell's wave equation theory, in a two-dimensional structure with a large difference in wave impedance, the phenomenon in which the wave is constrained to propagate forward in the local space and its energy cannot penetrate the wave impedance interface is called a waveguide. The notable features of a waveguide are its slow wave attenuation, long propagation distance, and high transmission frequency. This structure is called a waveguide structure. In human social practice, the waveguide structures that are easy to realize are circular waveguide structures and rectangular waveguide structures.
[0037] The air and the wellbore wall in the wellbore form a typical circular waveguide structure. First, the circular tubular wellbore and the air inside the wellbore are typical two-dimensional structures. Second, the speed of sound waves in the air is about 340 meters per second and the density is negligible. The speed of sound waves in the steel pipe wellbore wall is about 5200 meters per second and the density is about 7.85 grams per cubic centimeter. The two form a huge difference in sound wave impedance, which meets the conditions for sound waveguide.
[0038] The sound of flutes in natural life, the transmission of sound through bamboo tubes in tunnel warfare, the traditional cylinder messaging on ships, etc., all belong to the category of sound wave guides; the sound of firecrackers propagating over a long distance in a river channel belongs to the semi-waveguide (slot wave) phenomenon.
[0039] Therefore, sound waves propagate above the liquid surface in the well and in the air in the casing. They have the characteristics of slow waveguide attenuation in the air in the well, long propagation distance (greater measurement depth), and high transmission frequency (high measurement accuracy), which provides a physical basis for high-precision sound wave measurement of deep well liquid level.
[0040] 2. Related energy-gathering properties of continuous controllable sound sources
[0041] In human social practice, the sound sources (vibration sources) for artificially exciting sound waves (elastic waves) are divided into two types: pulse sound sources and continuous sound sources. The methods for exciting pulse sound sources include explosives (gunpowder, firecrackers), air guns, electric sparks, and percussion vibration methods; the methods for exciting continuous sound sources include electromagnetic vibration speakers, piezoelectric speakers (horns), piezoelectric sonars (high frequency bands), and air compression vibration methods (hand-cranked alarms).
[0042] Pulse sound sources have the characteristics of large amplitude, short time (on the order of milliseconds to tens of milliseconds), and wide bandwidth, and their energy, frequency, and phase cannot be artificially controlled; continuous sound sources have the characteristics of small amplitude, long time (on the order of tens of seconds), and wide bandwidth, and their total energy, frequency, and phase can be artificially controlled.
[0043] With the progress of society, in the field of seismic exploration, traditional explosive excitation (pulse source) has been gradually replaced by controllable source (continuous source) excitation. Controllable source is to excite a long-term frequency scanning signal, and use this signal to do cross-correlation calculation (integral of amplitude energy) with the received formation signal to obtain the reflection information of the formation; its reflection information has the same kinematic physical properties as the reflection information obtained by explosive source excitation, and its dynamic properties have a higher signal-to-noise ratio and bandwidth than explosive source. Controllable source technology has become a mature industrial production technology.
[0044] Therefore, the continuous sound source correlation method is the most effective and high-precision industrial method to solve the sound source energy, frequency band, phase, environmental protection and achieve artificial modulation.
[0045] 3. Boundary Effect
[0046] The wall of the wellbore constrains the divergent path of the sound wave in the pipe. When the sound wave leaves the sound source, it is constrained by the huge difference between the acoustic impedance of the air and the acoustic impedance of the casing, and the sound wave undergoes a total reflection phenomenon. The comprehensive effect of this total reflection phenomenon is the acoustic wave waveguide effect of the sound wave in the wellbore. Since the total reflection path is larger than the straight ray path of the sound wave, the group velocity of the sound wave propagating in the well is slightly lower than the speed of straight-line propagation in the air. The sound wave velocity in the air on the ground is 340 meters per second, and the sound wave velocity in the circular pipe is about 338 meters per second. This is the core mechanism of the acoustic waveguide.
[0047] The application of acoustic ranging method in ground ranging: used to measure the location of short-distance targets (less than 20 meters), such as measuring the vibration of lathes, the water level of rivers, etc.; due to the short measurement distance, it has been basically replaced by laser ranging and microwave ranging. The main reason is that the generated pulse sound source has a short propagation distance and generates environmental noise.
[0048] The present invention provides a measuring device, including an exciting device and a receiving device.
[0049] In this embodiment, the excitation device is a slender cylindrical digital speaker with a power of about 40 watts, which is basically suitable for all deep well conditions. The speaker opening size is less than 2 / 3 of the wellhead inner diameter (generally about 150 mm), leaving space for placing the receiving probe. According to the sinusoidal linear up-scan:
[0050] A(t)=sin(2pai(f1+(f2-f1) / T*t)*t)) (1)
[0051] Insert digital frequency sweep signal;
[0052] In formula (1), f1 is the scan start frequency, f2 is the scan end frequency, and T is the scan length.
[0053] The receiving device includes a main acquisition board and a probe. In this embodiment, the main acquisition board has a dual-channel 36-bit analog-to-digital conversion and a sampling rate greater than 8K (less than 1 / 8 millisecond). In this embodiment, the probe has a dynamic range greater than 80 decibels and a sensitivity less than 0.1 millivolt.
[0054] Probe integration: Figure 1 As shown, a dual-probe integrated structure is adopted, in which the probe that is aimed upward at the sound source to collect the downgoing wave field of the near-field sound source is recorded as the upward vector probe A; the probe that is aimed downward at the wellbore is recorded as the downward vector probe B, which collects the upgoing wave field reflected by the wellbore. The dual-probe integrated structure is installed at a depth greater than three apparent wavelengths from the sound source in the well to ensure the purity of the wellbore wave generated after the signal leaves the sound source. If the distance is too small, the signal is messy. In this embodiment, the installation position is at a depth of 1 meter vertically away from the excitation device in the well. Specifically, a hoisting installation method is adopted. After reaching the predetermined depth in the well, it is pushed against the well wall to ensure that the probe does not resonate during the collection process.
[0055] like Figure 2 As shown, the two probes are designed as cylindrical long bodies with back-to-back integrated structures, that is, the angle between the vector directions of the two probes is 180 degrees, and the vector direction is along the direction of sound wave transmission in the well. There is a layer of sound insulation board design between the two probes to avoid crosstalk, and the inner layer of the sound insulation board is filled with sound-absorbing rubber.
[0056] In practical applications, as long as the two probes are arranged on the same axis and have opposite vector directions, one probe is aimed upward at the sound source to collect the downgoing wave field of the near-field sound source, and the other probe is aimed downward at the liquid surface in the wellbore; Figure 3-5 The specific structure of the integrated probe shown is only one implementation of the probe appearance structure design. Those skilled in the art should know that the dual-probe design appearance structure of the present invention is not limited to Figure 3-5 This one is shown.
[0057] like Figure 3 As shown, the front of each probe has a conical sound receiving port structure design, which is used to provide a focusing reflection surface to facilitate signal focusing.
[0058] like Figure 4As shown, the probe specifically includes a cylindrical shell, and two probes in opposite directions are respectively installed at both ends of the cylindrical shell; a sound insulation board structure b is arranged in the middle of the cylindrical shell; the two probes are connected to the main acquisition board outside the wellbore through a data transmission channel a arranged on both sides of the cylindrical shell; a first fixed limiter c is also designed on the outside of the cylindrical shell, and the first fixed limiter c is used to install the probe in the wellbore.
[0059] like Figure 5 As shown, the two probes have the same structure, and a second fixed limiter f is arranged on the outer periphery of the conical sound receiving port e, which is used to fix the probe to the corresponding slot position in the cylindrical shell; it also includes a probe fixing position d, which is fixed to the corresponding matching slot in the cylindrical shell.
[0060] The present invention also provides a distance measurement method using the above-mentioned measuring device, which specifically includes the following process:
[0061] The excitation device excites a continuous acoustic up-conversion scanning signal at the wellhead, which is recorded by the near-source upward vector probe A; the scanning signal propagates downward in the wellbore in the form of an acoustic wave guide, generates total reflection when it reaches the liquid surface, and then returns upward to the wellhead to be recorded by the downward vector probe B.
[0062] The record of probe A is processed by autocorrelation to read the peak value, and the time 0 of the system record is obtained; the record of probe A and the record of probe B are processed by cross-correlation to read the peak value, and the time of time 0 is subtracted to obtain the round-trip time difference of the liquid surface excited by the pseudo-pulse sound source at the wellhead returning to the wellhead. Combined with the sound wave velocity in the well, the following is calculated: Figure 1 The depth of the liquid level in the well is shown.
[0063] Based on the speed formula The formula for the depth of the liquid level in the well is derived:
[0064] Downhole liquid level
[0065] Δt=τ B2 -τ B1
[0066]
[0067] Among them, d 液面 Indicates the depth of the liquid surface from the wellhead, V 井 represents the speed of sound wave transmission in the wellbore, t 总 Indicates the time it takes for sound waves to travel in the wellbore.
[0068] Formula (2) is the calculation formula of the well liquid level expressed by phase velocity, ω is the angular frequency (obtained from the excitation spectrum), k z is the axial wave number (calculated from actual data), R is the wellbore radius (known), μ mnis the nth zero of the m-order Bessel function: τ B1 Indicated in the cross-correlation function R xy The time delay corresponding to the first peak in (t, τ) starting from the time 0 {τ0} determined by the autocorrelation (obtained from actual data); Indicates that from τ B1 The time delay corresponding to the next peak value searched afterwards (obtained from actual data); is the cross-correlation function, x A (t) is the signal recorded by probe A, x B (t) is the signal recorded by probe B.
[0069] Considering that probe A will record the signal reflected from the liquid surface, probe B will also record the sound source signal sent from the excitation device; before performing autocorrelation and cross-correlation processing, the present invention cuts off the data after the sound source scanning time recorded by probe A, retains the signal within the sound source scanning time recorded by probe A, and removes the subsequent liquid surface reflection signal outside the scanning time; the purity of the sound source sub-wave of A autocorrelation (no interference), the precise determination of the 0 time of the system, and the reading accuracy of the liquid surface reflection data after the cross-correlation of probes A and B are guaranteed.
[0070] In order to ensure the accuracy of the liquid level depth calculation result, the present invention also provides the following processing method:
[0071] (1) Determine the signal source based on energy: the maximum autocorrelation energy between A and A comes from the wellhead sound source signal (used to determine the system's zero time); the maximum cross-correlation energy between A and B comes from the total reflection signal from the downhole liquid surface (used to determine the reflection time);
[0072] (2) The signal source is determined based on the positive or negative value of the correlation peak: the positive value of the autocorrelation between A and A comes from the wellhead sound source, and the negative value comes from the reflection of the downhole liquid surface; the positive value of the cross-correlation between A and B comes from the reflection of the downhole liquid surface, and the negative value comes from the wellhead sound source.
[0073] (3) In actual operation, it is very simple. The computer automatically identifies the maximum positive peak of the autocorrelation between A and A as the system's zero moment (the same time is a small negative peak in the cross-correlation record between A and B), and automatically identifies the maximum positive peak of the cross-correlation between A and B as the liquid surface reflection moment (the same time is a small negative peak in the autocorrelation record between A and A).
[0074] Those skilled in the art should know that the measurement accuracy of conventional pressure sensors is 1 / 100 of the depth of the probe in water. For example, if the probe is 200 meters below the water surface, the depth measurement error (accuracy) is 2 meters. The measurement accuracy of the method of the present invention is independent of the liquid surface depth and the water depth.
[0075] The depth accuracy measured by the method of the present invention depends on the main frequency of the excited sound wave. Taking the excitation of 1000 Hz main frequency (the loudspeaker can easily excite 1-2000 Hz sound waves) and 8K sampling as an example, a 1000 Hz sound wave cycle is 1 millisecond, propagates about 0.34 meters in the wellbore (the sound wave speed is calculated at 340 meters / second), and has 8 digital sampling points; half a cycle (positive part or negative part) propagates 0.17 meters and has 4 digital sampling points.
[0076] Using the whole digits of the digital record to find the wave peak, the depth error (accuracy) is 0.17 / 4=0.0425 meters=4.25 centimeters.
[0077] The actual peak position is not necessarily on the integer digit of the digital record. The current human-computer interactive graphic digitization technology can increase the sampling point of picking up the peak by at least 8 times. Calculated at 4 times, the depth error is 0.0425 / 4=0.016 meters=1.6 centimeters.
[0078] Therefore, the depth positioning accuracy of the method of the present invention can be accurate to the centimeter level; compared with the existing pressure sensing liquid level measurement technology, the measurement accuracy is significantly improved.
[0079] As a further improvement, by connecting a network data transmission terminal to the acquisition host, the present invention can also achieve the technical effects of remote measurement and control and real-time monitoring.
[0080] In addition, after a set of equipment of the present invention measures a well, the integrated probe hoisted in the well can be taken out to re-measure other wells, thereby achieving the effect of measuring multiple wells with one set of equipment.
[0081] Compared with traditional measurement, the purchase cost of the entire system equipment of the present invention is about 3,000 yuan, while the cost of a set of traditional conventional wired liquid level meters is about 20,000 yuan, and the equipment cost is lower.
[0082] Furthermore, the present invention does not require underground installation operations. Compared with traditional measurements that require underground installation operations, the installation of the present invention is cost-free.
[0083] The measurement method of the present invention takes no more than 2 minutes from collection to output of results, that is, scanning time. Two people can complete a well operation within half an hour, and the operation cost is lower than that of existing traditional measurement methods.
[0084] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. For those skilled in the art, the present invention may have various changes and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of the claims of the present invention.
Claims
1. A well liquid level measuring device based on the principle of acoustic waves, characterized in that: include: Excitation equipment, receiving equipment; The excitation device is arranged at the wellhead and sends a continuous acoustic wave up-frequency scanning signal toward the wellhead; The receiving device includes a probe body installed in the well and a main acquisition board arranged outside the wellbore, and the probe body includes two probes facing opposite directions, one of which faces the downhole liquid surface and the other faces the excitation device; The two probes facing opposite directions are connected to a main acquisition board, and the main acquisition board calculates the liquid level depth in the well according to the sound signals collected by the two probes.
2. The well liquid level measuring device based on the acoustic wave principle according to claim 1 is characterized in that: The probe body adopts a cylindrical shell, and two probes facing opposite directions are installed at two ends of the cylindrical shell.
3. The well liquid level measuring device based on the acoustic wave principle according to claim 2 is characterized in that: A sound insulation board structure is arranged in the middle of the cylindrical shell between the two probes.
4. A method for measuring the liquid level in a well based on the principle of acoustic waves, characterized in that: A well liquid level measuring device based on the acoustic wave principle as described in any one of claims 1-3 calculates the depth position of the liquid surface in the well according to the time difference of the acoustic waves collected by two probes facing opposite directions and the acoustic wave transmission speed in the well.
5. The method for measuring the liquid level in a well based on the acoustic wave principle according to claim 4, characterized in that: The calculation process of the acoustic wave time difference is: A1. The probe facing the excitation device is recorded as probe A, and the probe facing the downhole liquid surface is recorded as probe B; The signal obtained by probe A is recorded as signal A, and the signal obtained by probe B is recorded as signal B; A2, perform autocorrelation processing on signal A, and take the time corresponding to the first positive peak as time 0; A3. Perform cross-correlation processing on signal A and signal B. The time corresponding to the second positive peak is the time when the liquid surface reaches the probe after total reflection; A4. Subtract the time 0 obtained in step A2 from the time when the liquid surface reaches the probe after total reflection to obtain the round-trip time difference of the sound wave from the probe body to the liquid surface.
6. A method for measuring the liquid level in a well based on the acoustic wave principle according to claim 5, characterized in that: The distance from the probe body to the liquid surface is calculated based on the round-trip time difference of the sound wave from the probe body to the liquid surface and the sound wave transmission speed in the well. Then the installation position of the probe body in the well is added to the distance from the probe body to the liquid surface to obtain the distance from the wellhead to the liquid surface, that is, the depth position of the liquid surface in the well.
7. A method for measuring the liquid level in a well based on the acoustic wave principle according to claim 6, characterized in that: The calculation formula for the acoustic wave velocity in the well is: Where ω is the angular frequency, k z is the axial wave number, R is the wellbore radius, μ mn is the nth zero of the m-th order Bessel function.
Citation Information
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