EVALUATION OF THE INTER-REPAIR OPERATION PERIOD OF ELECTRIC SUBMERSIBLE PUMP UNITS

In recent years, in the oil and gas industry of Azerbaijan, the use of electric submersible pumps (SEP) as one of the effective way to increase the level of production of well products. Currently, electric centrifugal pumping units (ECPU) are widely used both on land and in offshore fields. Currently, a total of about 15 % of SOCAR’s oil wells are produced using electric submersible pumping units. ECPU effectiveness is largely determined by both the period of their operation and the frequency of repair and restoration work. It is established that the use of ECPUs contributes to an increase in the service life of equipment and the effectiveness of a mechanized method of oil production. To assess the benefits of the latter, the most important factor is the inter-repair period (Tir) of the equipment. Existing methods for determining the inter-repair period of oilfield equipment are accompanied by large errors, which significantly reduce their reliability. In this regard, the article is tasked with developing a more practical and reliable method for determining the inter-repair period, where the point of change in the nature of the failure rate is adopted as the determining parameter.


Introduction
Oil and gas sectors of Azerbaijan are the determining factors of the fuel and energy complex (FEC) of the republic. More than 60 % of the country's budget is formed here and therefore, issues related to improving the efficiency of technological processes and equipment resources used in this industry are relevant.
At present, in the republic's oil producing fields, along with fountain and rod-pumping methods, a production method using electric submersible pumping units is also used. About 15 % of SOCAR's oil wells produce oil using electric submersible pumps (ESP) [1].
Prediction of the time between ESP failures before launching into the well, as well as assessment of its residual life during operation, will determine the operating time to failure, plan repair measures and prevent the maximum wear of their components. One of the main parameters characterizing the performance of oil pumping equipment is their interrepair period.
The aim of research is development of a new solution in the determination of the inter-repair period (T ir ) of electric submersible pumps, using the point of change in the nature of the intensity of their failures.

Theoretical background of the problem
Field data on malfunctions and premature failure of parts and assemblies of ESPs shows that the nature of their occurrence varies in time and a sharp fracture occurs at a certain point (Fig. 1), which leads to dangerous failures [2].
Engineering In the main period of operation, the physics of failures contains elements of both wear-out and sudden failures, but with a large predominance of wear-out gradual failures with some characteristic increasing function of the failure rate ( ).
λ t In fact, if the pump element has almost no hidden defects, but it quickly is "aging", then the failure rate and the reliability function P(t), that is, the probability of failure-free operation, should be well approximated by Weibull law with a parameter of >1 or a normal law [6].
In the case when the consequences of failures can be the occurrence of dangerous situations and injuries of staff, existing in the theory of reliability methods for determining the inter-repair period (IRP), based on the analysis and minimization of operating losses, for example [3][4][5], become unacceptable.
The results of numerous experiments and analysis of the evaluation data for the operation of electric submersible pumps (ESP) allow to divide the nature of their intensity into two cases: before the point of intensity breakdown and after. In this work, the intensity tipping point t* is determined using the nonlinear corrosion-regression approximation of the empirical intensity functions ( ) ( ) 1 2 and λ λ e e t t, respectively, to the fracture point and after. The point t* obtained in [7] using a linear approximation of the above empirical functions is taken as the initial approximation.
After the fracture point, the failure rate increases sharply due to the physico-mechanical and physico-chemical processes occurring in the nodes and parts of the equipment. The frequency of these deviations is described as follows: where ( ) λ t -the failure rate; ( ) P t -the probability of failure-free operation associated with the distribution function ( ) F t and the distribution density ( ) f t of the time between failures by the ratios: The appearance of dangerous failures is considered to be possible [2], if the ratio of neighboring (at intervals) values of the empirical failure rate satisfies the relation Substituting the last least-squares equation , , let's reduce to the following formula [7]: Here ( )  (4) is taken in [8] as the value of the inter-repair period T ir .
The refinement of estimate (4) is achieved by smoothing the intensity curves for a given initial approximation 0 *, at the initial approximation 0 *, In particular, for the exponential distribution law with distribution density For a truncated normal distribution law with a distribution density is the distribution function of the standard normal law, the failure rate is determined by the formula for Weibull distribution with distribution density

Research results
In this case, statistics , ν = r N are used where r -the number of failed samples for the running time t of the N samples put to the test, and the probability of failure-free operation ( ) P t is related to ν by the ratio ( ) 1 .

= − ν P t
The reliability characteristic determined by the value ν is sufficient statistics [6]. This means that knowledge of any other statistics (that is, a random variable depending on the sampled data) does not add anything to the knowledge of probability ( ), P t obtained on the basis of statistics ν [10,13].
Statistical processing of volume data 12 = n from the last column of Table 1 shows that they obey the truncated normal distribution law (N)  This inequality can be rewritten in the form two-sided confidence boundaries for the parameter b of the Weibull distribution are: The failure rate, obeying the Weibull distribution c 2, > b tends to increase sharply. Since in our example the parameter , b according to (14) can have a value greater than 2, dangerous failures can occur.

Discussion of research results
Based on the experimental data, a series of failure values of submersible ESPs is constructed, which is presented below: As shown in [9], a number of developments (15) up to t=86 are rather well described by the normal distribution with parameters а 0 =0.636 and σ=0.336, and after t=86 -by the Weibull distribution with parameters 1.2969 ∧ = a and 1.9470.
Let's take the point t=86 or, which is the same thing, v=0.673 for the suspicious point of fracture of the failure rate. Let's assume that up to the point v * =0,673, the statistics v obeys the truncated normal law with parameters а 0 =0.636 and σ=0.336 and with intensity and after the point v * =0.673 -to the Weibull distribution with density ( ) with parameters 1.2969 ∧ = a and 1.9470 and intensity ( ) Regression equations for statistics v can be written as The function ( ) Φ x is calculated by the approximate formula [12] ( ) ( ) and not exceeding * v the value * , t determined by value (26) is taken as the value of the inter-repair period Т ir . Table 2 shows the data on the average (T av ) and maximum (T max ) inter-repair periods for the operation of ESP-type submersible units in various oil and gas production units for Azneft. As can be seen from the Table 2 experimental data on the average T av value of the inter-repair period for Azneft Production Association of the Azerbaijan Republic using ESP in difficult operating conditions, the T av is in the range 63 ... .100, which is consistent with our calculated value t*=90 days.

Table 2
Data on the average (T av ) and maximum (T max ) inter-repair period of operation of EDP-type submersible units in various oil and gas production units for Azneft