Accepted: August 14, 2023 | Published Online: August 16, 2023

Citation: Aliev T, Guluyev G, Rzayev A, Pashayev F (2023) Intelligent Correlation System for Identification of the Technical Condition of Oil Wells. Int J Signal Process Anal 7:009.

Copyright: © 2023 Aliev T, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Abstract

An intelligent correlation system of control and identification of technical condition of sucker rod pumping units (SRPU) is proposed. It is shown that by storing the reference curves of the dynamometer chart of typical faults $g_e(i\Delta t)$ and successively comparing them with the load curves of current dynamometer charts $g_j(i\Delta t)$ by the number of the reference dynamometer chart, at which the estimate of the correlation factor $r_{je}$ takes the maximum value, the current faults of the sucker rod pumping units can be identified.

The introduction of this technology in oil production using inexpensive technical means allows for considerable increase in the profitability of oil wells by saving energy and increasing the overhaul period. At present, SRPU is widely used in oil production and solving the problem of eliminating the difficulty of automation identification of its technical condition and practical application is a priority.

Keywords

Oil well, Sucker rod pumping unit, Dynamometer chart, Fault, control, Identification, Correlation, Intelligent technology

Introduction

The use of sucker rod pumping units (SRPU) is known to be the primary method in artificial lift. Sucker rod pumping is widespread in the world oil production practice at present, covering over 85% of the total active wells stock in the USA [1]. The popularity of the method is due to its simplicity, reliability and applicability in a wide variety of operating conditions.

However, everyday with the decreasing oil reserves, increased reservoir flooding and well shutdowns caused by the inadequate identification of the technical condition of equipment, the profitability of oil production by SRPU decreases considerably. Therefore, improved adequacy of identification of the technical condition of SRPU is the main issue in ensuring profitability of oilfields in long-term operation. By resolving this issue, we can manage SRPU in real time, which can ensure the necessary stabilization of oil production. To increase the overhaul period and create the most favorable conditions for oil production management, various methods and tools of control of technical condition and management of SRPU have been proposed over the last several decades [2-8]. The results of these studies showed that the load in the rod suspension point contains the comprehensive and least distorted data on the condition of the underground pumping equipment. Therefore, dynamometry, i.e. reading and analysis of the curve of the load $U_p(t)$ received from the load cell in the rod suspension point $P(S)$ is considered the common way to control the technical condition of SRPU. In [2,4-6], detailed description is given of the results of numerous studies, which have been carried out in this field over many years. Some or other identification methods have been used at different SRPU control stations at real-life oilfields for a long time. The scientific foundations have been formed on the basis of these works and various systems for SRPU control and management by means of dynamometer charts obtained at the well head.

On the basis on the results of operation of those systems, dynamometer chart based identification methods have been categorized as follows [2]:

- Identification based directly on the characteristics of the ground dynamometer chart:

- Identification based on the secondary characteristics of the ground dynamometer chart (spectral characteristics: variance, correlation and regression of the signal of the load cell, coefficients of Fourier series expansion for the dynamometer chart, etc.);

- Identification based on the typical characteristics of the shape of the ground dynamometer chart:

- Identification by comparison of the shape of the dynamometer chart under investigation with the reference one taken immediately after the repair of the well and stored in the device memory.

- Identification based on the characteristics of the plunger dynamometer chart calculated from the data of the ground dynamometer chart and well design:

- Identification based on the typical characteristics of the shape of the plunger dynamometer chart.

The shortcoming of all these methods is that they do not allow performing automatic identification of a dynamometer chart in real-time mode with sufficient adequacy. For this reason, the identification of dynamometer charts in real life is mostly performed by interpreting it in the semi-automated mode, which eventually comes down to the visual analysis of the obtained dynamometer information by a technologist, who makes the final decision on the presence of a fault in SRPU. The results depend on the qualification of the technologist and the diagnostics of all wells takes rather a long time. Besides, even a highly qualified specialist sometimes cannot determine precisely the technical condition of a deep-well pump visually only from dynamometer charts, particularly for deep wells. Therefore, new technologies for real-time analysis and identification of dynamometer charts with the use of modern controllers have to be developed. In this case, it is appropriate to ensure the monitoring of changes in the technical condition of SRPU by identifying the signal of the load on the rod hanger per pumping cycle. Our research has demonstrated that one of the most efficient ways to solve this problem is to use a technology for identifying load signals combined with the methods of correlation analysis [6,7].

Problem Statement

In the known SRPU control systems, the dynamometer chart information comes from load cells and stroke sensors in the form of the electric signal of load $U_p(t)$ and stroke $U_S(t)$ via the communication channel. Using the combinations of these two variables $U_p(t)$ and $U_S(t)$, the dynamometer chart $U_p(t)\text{ = }f(U_S)$, whose form is described by a parallelogram, is formed. A specialist technologist determines more than 20 types of the technical condition of SRPU by visual analysis of distortions in different sections of its shape [1,2]. However, performing this operation for a hundred wells is challenging.

It should be noted that in case of hardware implementation of identification of facility's state there is no need to use $U_S(t)$ , since this can be accomplished by analyzing only the stress curve $U_p(t)$. However, when the correlation analysis technology is used for this purpose, the condition of robustness is not fulfilled, because the error of the obtained estimates of correlation functions caused by the effects of the noise ${\epsilon }_1(t)$ accompanying the useful load signal $U_p(t)$ under operation changes within quite a wide range. This is because the control object, i.e. SRPU, operates in the field environment (temperature, humidity extremes, etc.). Besides, during the pump operation, various faults also cause the formation of the noise ${\epsilon }_2(t)$ that correlates with the signal $U_p(t)$ [9]. Therefore, the noise $\epsilon (t)$ accompanying the load signal $U_p(t)$ forms under the influence of the following two factors:

$$\epsilon (t)\text{ = }{\epsilon }_1(t)+{\epsilon }_2(t)$$

${\epsilon }_1(t)$ forms due to the changes in the environment (temperature and humidity differences, etc.);

${\epsilon }_2(t)$ forms during the operation of the object due to the changes in the technical condition of the mechanical components of the pump, such as wear and tear, bends, cracks, fatigue, etc.

Thus, during the operation of objects, the signal contaminated with the noise comes to the input of the system instead of the signal $U_p(t)$. The analyzed signal in the analog form is as follows:

$$g(t)\text{ = }{U}_p(t)+\epsilon (t)$$

and in the digital form is as follows:

$$g(i\Delta t)\text{ = }{U}_p(i\Delta t)+\epsilon (i\Delta t)$$

Where i is the serial number of the measurement (of the signal's analog-to-digital conversions); $\Delta t$ is the sampling interval of the signal in the analog-to-digital conversion.

For these reasons, both the amplitude and the spectrum of the noise $\epsilon (i\Delta t)$ vary in quite a wide range. The errors of the obtained estimates of the correlation functions $R_{gg}(i\Delta t)$ of the measuring signal $g(i\Delta t)$ also vary in time in a wide range due to the above-mentioned reasons. Therefore, it becomes impossible to ensure the condition of robustness for the estimates of the correlation function in real time, i.e. to eliminate the dependence of the obtained results on the effects of the noise $\epsilon (i\Delta t)$ [3-7,9-15]. This, in turn, complicates solving the problem of identification of the dynamometer chart with the use of correlation methods. Consequently, ensuring the adequacy of identification requires that the conditions of robustness hold, i.e., that the effects of said factors on the error of the estimates $R_{gg}(i\Delta t)$ be eliminated.

At first glance, the effects of the errors on the results of identification of dynamometer charts can be eliminated by filtration of the noise accompanying the useful signal $U_p(i\Delta t)$. If the noise spectrum is stable, the use of filtration usually produces satisfactory results. However, in the field conditions, the spectrum of the noise changes in a wide range due to the abrupt change of the factors of its formation. Besides, the variance of the spectrum of the noise that forms due to mechanical processes in SRPU changes in a wide range as well, frequently overlapping the range of the useful signal spectrum. For these reasons, we cannot achieve the desired effect by using the technology for filtering the load signal.

Therefore, solving of the problem under consideration first of all requires developing the technologies for calculating such estimates of correlation characteristics that practically cannot be affected by changes in said noises. Considering the above, in [6,7] the technology of calculation of robust normalized correlation functions of the signal from the load cell of the sucker-rod string on the sucker rod pumping unit suspension, by means of which sets of combinations of informative attributes are formed, each corresponding to one of its technical conditions.

Analysis of the results of introduction of identification technology using normalized correlation functions has shown that despite a number of advantages of this method, it should be improved with the use of intelligent correlation technologies.

Intelligent Correlation System for the Identification of the Technical Condition of SRPU

Figure 1 below shows a block diagram of one of the possible variants of intelligent correlation systems, which operates with five modules.

1- Module for analog-to-digital conversion of dynamometer charts into digital code.

2- Module storing the load signal curve of reference dynamometer charts of typical faults of SRPU.

3- Module for successive determining of the correlation coefficient $r_{je}$ between the current values of the dynamometer chart $g_j(i\Delta t)$ and the curves of the reference dynamometer charts $g_e(i\Delta t)$, which are previously formed experimentally with the corresponding typical faults and stored in the memory of module 2.

4- Module for determining the number of the reference dynamometer chart $g_e(i\Delta t)$, at which the estimate of the correlation coefficient $r_{je}$ takes the maximum value compared to the current load curve.

5- Module for SRPU fault identification by the number of the found load curve of the reference dynamometer chart.

During the operation of the intelligent correlation system (ICS), the input of module 1, i.e., the input of the analog-digital converter receives the load curve voltage of the current dynamometer chart g_j(t) from the load cell, where it is converted into the digital code $g_j(i\Delta t)$, which goes to the input of module 3, where between the current and the reference dynamometer charts alternately by the formula

$$r_{je}\text{ = }\frac{\frac{1}{N}{\displaystyle \sum _{j=1}^n{g}_j(i\Delta t)g_e(i\Delta t)}}{\frac{1}{N}{\displaystyle \sum _{i=1}^n{g}_j^2(i\Delta t)}}$$

The estimates of the correlation coefficient $r_{je}$ are determined, where j is the number of current typical faults, e is the number of the reference of typical faults, $r_{je}$ is the estimate of the normalized cross-correlation function between $g_j(i\Delta t)$ and $g_e(i\Delta t)$ .

By successively comparing the obtained estimates of the correlation coefficients between the current and reference curves of dynamometer charts in module 4, the number of the fault is determined, at which the obtained estimates $r_{je}$ has the maximum value. Thus, the presence of reference signals of typical faults through the use of ICS allows one to register the technical state of the SRPU at the current time. Due to this, during the operation of the SRPU, the obtained results of the ICS allow real-time identification of a malfunction and the formation of information about it.

Possibility of Using the Intelligent Correlation System as a Part of the SRPU Control and Management Complex

In the following, we show the possibility of using the proposed equipment for the identification of the technical condition of SRPU as part of the SRPU control and management complex in real time.

They have been used in the complex of control, diagnostics and management for oil wells operated by sucker-rod pumping units at Bibi-Heybat Oil and Gas Production Facility [8,9].

The simplicity of operation of the proposed system made it possible to implement the proposed identification technology by means of inexpensive modern industrial controllers (in our case, LPC 2148 FBD64 controller was used).

Figure 2 and Figure 3 show the block diagram of the SRPU management system that consists of three levels:

1. The level of the deep-well pumping unit consisting of plunger pump 1; plunger 2; tubing 3; rods 4; polished rod 5; horse head 6; walking beam 7; pitman 8; crank counterweight 9; reductor 10; multiple V-belt drive 11; electric motor 12; beam equalizer 13; load cell 14; wellhead pressure sensor 15; rotation angle sensor 16; crank of the beam-pumping unit 17.

2. The level of RMS consisting of the controller for data acquisition from load cells 14; well-head pressure sensor 15 and rotation angle sensor 16; frequency converter for controlling the speed of the electric motor; a wireless modem equipped with an antenna to provide data exchange via MODBUS-RTU protocol between RMS and the centralized control station.

3. The level of the centralized control station of the oil field, which serves up to 200 wells and consists of an industrial computer and a wireless modem with an antenna.

As it was mentioned above, to ensure effective operation of oil wells it is necessary to carry out continuous real-time control and identification of the technical condition of SRPU.

The use of the proposed intelligent correlation system was tested in the SRPU management system. For its practical implementation, the sampling interval of the signal was determined first, on the basis of the duration of the pumping cycle $T_{ST}$. For most oil wells, the duration of $T_{ST}$ varies within the range of 5÷20 seconds. We have deduced from experiments that to obtain the sought-for estimates with the required accuracy, it is sufficient to sample the load signal at the frequency $f\text{ = }500-100Hz$ . Our experiments have established that any minute change in the technical condition of SRPU during the pumping cycle affects the load signal $g(i\Delta t)$, which, in turn, affects the estimate of the obtained informative attributes. As a result of SRPU operation, corresponding results were formed and saved for various technical conditions of SRPU. Our experiments have shown that they allow for reliable identification of the technical condition of SRPU in real time. The identification of the technical condition of SRPU here comes down to comparing the current load curve to the respective reference curves.

Results of Experimental Application of ICS at Real Oil Production Facilities

In the conducted experiments, load curves of reference dynamometer charts were selected for the 10 typical SRPU faults, which are shown in Figure 4. They were used in the experimental identification of the technical condition for several facilities at Bibi-Heybat Oil and Gas Production Facility [3,4,7,8]. The nature of tasks at hand made it possible to implement the proposed technology by means of inexpensive modern industrial controllers (in our case, LPC 2148 FBD64 controller was used). The sampling interval of the signal was determined first, on the basis of the duration of the pumping cycle. For most oil wells, the duration of $T_{ST}$ varies within the range of 5÷20 seconds. It was experimentally established that to obtain the sought-for estimates with the required accuracy, it is sufficient to sample the load signal at the frequency $f\text{ = }500-100Hz$ . It was also established that any minute change in the technical condition of SRPU during the pumping cycle affects the load curve $g(i\Delta t)$ of the dynamometer chart. Thanks to this, during the operation of the SRPU, it is easy to form and store the corresponding load curves of the reference dynamometer charts. Numerous experiments have confirmed that the use of ICS allows for reliable identification of SRPU faults in real time. This process practically comes down to determining the number of the load curve of the reference dynamometer chart $g_e(i\Delta t)$ , at which the desired estimate of the cross-correlation function $r_{je}$ takes on the maximum value compared to all other reference signals. This makes visual interpretation of the dynamometer chart unnecessary for determining the current technical condition of SRPU. To illustrate the possibilities of the considered identification option in real industrial practice, Figure 4 below gives 10 most common reference fault curves.

Numerous experiments have confirmed that using the number of the force curve of the reference dynamometer chart $g_e(i\Delta t)$, at which the estimate of the normalized cross-correlation functions with the curve of the current dynamometer chart $g_j(i\Delta t)$ takes the maximum value, it is possible to unambiguously determine the number of the typical SRPU fault. The advantage of using ICS to identify a dynamometer chart is that it does not require the involvement of a technologist. They are easily implemented on modern inexpensive controllers. The ease of implementation of these technologies allows one to build simple, reliable and inexpensive equipment. Experiments on various wells of the Bibi-Heybat field in Baku and on wells of other fields showed the feasibility of the practical application of these systems. At the same time, due to early diagnostics and control of SRPU, current malfunctions are eliminated in an easy and timely manner and operation of the well is ensured in a profitable mode and due to saving electric energy and shortening the overhaul period, their profitability is significantly increased.

It should be noted that based on the experience of operating the above systems, it was found that by determining the combinations of the force curves of the reference dynamometer charts with the corresponding characteristic faults for one well, they can be used in SRPU control systems of other wells of the same depths. Considering that in most cases each old field is characterized by approximately the same pump descent depths, it becomes obvious that the formation of one reference dynamometer curves for all SRPU will be sufficient. However, different well depths require experimental formation of reference curves corresponding to the dynamometer chart is required.

This makes visual interpretation of the dynamometer chart unnecessary for determining the current technical condition of SRPU. To illustrate the possibilities of the considered identification option in real industrial practice, Table 1 below gives the results of the experiment for 10 most common faults.

The curves of the reference dynamometer charts of all ten typical faults were used in the experiments. First, the estimate of the correlation coefficient $r_1{e}_1$ between the curve of the first reference dynamometer chart with the first current curve $r_{1e_1}$ was determined, then the estimate $r_{j_1{e}_1}$ between the first reference curve and the second current curve $j\text{ = 2}$ was determined, then $r_{j,e_1}$ between the third and the first, and so on. Finally, between tenth and first, $r_{j_{10}{e}_1}$ . After that, this process was repeated for the curve of the second reference dynamometer chart. To do this, we first determined the estimate $r_{j_1{e}_2}$, then $r_{j_2{e}_2}$, then $r_{j_3{e}_2},\mathrm{...},r_{j_{10}{e}_2}$ . This process was repeated for all curves of the reference dynamometer charts, and finally, for the curve of the tenth reference dynamometer chart, $r_{j_{10}{e}_1},r_{j_{10}{e}_2},r_{j_{10}{e}_3},\mathrm{...},r_{j_{10}{e}_{10}}$ were determined. This process was completed by analyzing the comparison of the results of all possible combinations between the reference and current dynamometer chart curves. As can be seen from the table, only one estimate $r_{d_j{e}_i}$ in each control cycle takes the maximum value and the number of the current fault is determined by its number, i.e., by the number of the curve of the reference dynamometer chart, at which the estimate $r_{je}$ takes on the maximum values. As can be seen from Table 1, in each row only in one column the estimate $r_{je}$ takes the maximum value, e.g., in the 5 ^th row the estimate $r_{j_5{e}_5}$ in comparison with other estimates of this column, has a maximum value, which corresponds to the 5 ^th typical fault.

 

8. Conclusion

Numerous experiments on real-life facilities have confirmed that the use of ICS allows for reliable registration of the beginning of SRPU faults in real time. This process practically comes down to determining the number of the load curve of the reference dynamometer chart $g_e\left(i\Delta t\right)$, at which the desired estimate of the cross-correlation function $r_{je}$ takes on the maximum value compared to all other reference signals. This makes visual interpretation of the dynamometer chart unnecessary for determining the current technical condition of SRPU.

It has been established on the basis of the operational experience of these systems that determining combinations of the load curves of reference dynamometer charts for corresponding typical faults for one well, they can be used in SRPU management systems of other wells of equal depth. Considering that the pump is placed approximately at the same depth at most old deposits, it becomes obvious that the formation of only reference dynamometer chart curves for all SRPU management systems will be sufficient.

Simplicity of implementation of the technology of ICS makes it possible to create a simple, reliable and inexpensive technical means. Experiments on various wells of Bibi-Heybat oil field in Baku and on wells of other fields have shown the advisability of practical application of these systems everywhere. At the same time, due to the early diagnostics and control of SRPU, current faults are eliminated in an easy and timely manner, the profitable operation of the well is ensured, electric power is saved and the overhaul interval is considerably increased.

The simplicity of operation of the proposed system makes it possible to implement the proposed identification technology using inexpensive modern industrial controllers.

---