An analysis of reliability of electric submersible centrifugal pumps

The average operating time before structural and technological failures of the submersible part of a typical ESP is 64.5–81.9% of the average operating time of new ESPs. Given that the set of typical ESPs includes a significant share of repaired and mixed (equipped with new and refurbished units) installations, this fact can be interpreted as evidence of poor quality of repair. The data obtained from Tatneft and Bashneft companies agree with this conclusion. The data provided by Nizhnevartovskneftegaz company do not contradict this conclusion. The high values of Ttkt obtained by Rosneft-Samaraneftegaz are a consequence of poor identification of the causes of ESP lifting during control operations, as a result of which some failures are treated as design and technological ones.


Introduction
A modern electric submersible pump (ESP) for oil production consists of a submersible part, including a centrifugal pump, an electric motor, a hydraulic protection (compensator and protector), a cable line, and a ground part, consisting of a control station and a transformer [1]. If any of the submersible units fails, it is necessary to perform underground repairs -silencing the well with process fluid, extracting the submersible part from the well, installing an arc submersible part, starting the installation, developing the well (removing process fluid from it) and putting the ESP into operation. The duration of underground repairs is several days, the cost is comparable to the cost of ESP, and losses from downtime significantly exceed it. Therefore, reliability of the submersible part of the ESP is crucial for consumers [2].

Materials and methods
After lifting, the failed submersible part is disassembled, and the units included in it are sent for inspection, and repair or write-off. The submersible part is never assembled from the units of which it consisted. Therefore, the level of reliability of the submersible part determined by the reliability of randomly selected units that have been repaired, does not depend on the level of reliability of the submersible part of the previous ESP. In this case, the failure rates can differ due to the different quality of repair, and the fact that each of them worked in different conditions and was audited in different states in previous operation periods [3].
Given the most important indicator of ESP failures, existing as a single assembly unit only during its descent into the well before the first failure, it is advisable to apply the average operating time before The set of operating ESPs can be divided into two groups: with submersible parts, equipped before the descent into the well with new units, and with submerged parts, a certain share of which are already operated units [4].
The When determining the operating time before failure based on the results of control operation, there were methodological difficulties since almost every set of operating time of submersible ESPs is a repeatedly truncated (centered) sample, as its variation series consists of arbitrarily mixed operating time before failure and before suspension (suspension means the end of an operation without a refusal). In these calculations, the operating time of a ESP was defined as termination (interruption) of monitoring or lifting the working submersible part to take geological and technical measures. The operating time of an ESP before failure for operational reasons was taken into account as the operating time before failure (when determining the average operating time of the ESP before operational failure) and before suspension (when determining the operating time before structural failure) [5].
The average operating time before structural and technical failures of the submersible part of a new ESP was determined as follows. It was assumed that the operating time before failures of the submersible parts is subject to the Weibull distribution law [6]. The values were determined from the values of b using the expression by the method of maximum probability for a repeatedly truncated sample [7]   where ti and tjoperating time of i and j of objects before failure and before suspension; G and J are the total number of objects. For each pair of b and a, the Pearson criterion χр 2 was determined, and the dependence χр 2 = f(b), which determines the minimum value of χр 2 min and the corresponding values of am and bm, was constructed. The value χр 2 min was compared with the maximum tabular value of the Pearson criterion, determined at a confidence level of γ = 0.9. If χр 2 min n exceeded the limit value of the criterion, the distribution law was discarded; if it did not exceed, it was taken for further calculations with the values of am and bm.
The average operating time before structural and technological failures of the submersible part of a new ESP was determined by formula [8] is the value of the gamma function.

Results and Discussion
The analysis was conducted on 22 samples of nine most common ESPs used by Tatneft The analysis of these six samples showed that in all cases the calculated minimum value of the Pearson criterion was less than its limit value, which indicates a satisfactory approximation of the distributions of workflows before failures of the Weibull distribution law with a rather narrow range of shape values (bm = 0.9 ÷ 1.1); in all cases, the values of bm for the distribution of these developments were: 1.1 -in Bashneft; 1 -in Tatneft; 0.9 -in Rosneft-Samaraneftegaz; this suggests that the values of bm depend on the location of control operations, and, therefore, it is possible to extend the obtained values to the whole set of samples. Due to the lack of samples sufficient for calculations in Nizhnevartovskneftegaz, the distribution of operating time before failures in all samples in this association was subject to the Weibull distribution law with an average static value of bm = 1, i.e. to the exponential distribution law.
As a calculation result for each new ESPs sample, the average operating time values TNKT before design and technological failures were determined. If the value of the average operating time before failures of the submersible part for four associations is 1, in Tatneft the average operating time is significantly higher (1.59-1.92), in Bashneft it is almost the same (0.89-1), in Rosneft-Samaraneftegaz it is 0.55-0.67, which indicates the influence of the location of a control operation.
The average operating time before the failure of the submersible part of a typical ESP (in days) is determined by formula [10] 365 M N К T э T  (4) where N is the average number of ESPs in operation; M is the annual failures number; Кo is the operation coefficient.
Substituting the number of total annual failures for design and technological reasons in this formula, we obtain the average operating time Ttkt before design and technological failures of the submersible part of a typical ESP; substituting the total annual number of failures (including failures for operational reasons) in the formula, we obtain the average operating time Ttd before any failure requiring underground repairs [11,12].
Taking the values of Tnkt in each of the associations equal to 100%, we obtain the following values of Tnkt and Ttd (in % of Tnkt). The data are presented in the table.
The set of units includes a significant share of repaired and mixed (equipped with new and refurbished units) installations, this fact can be interpreted as evidence of poor quality of repair. The data obtained from Tatneft and Bashneft fully agree with this conclusion. The data obtained from Nizhnevartovskneftegaz do not contradict this conclusion. The high values of Ttkt in Rosneft-Samaraneftegaz are a consequence of poor identification of causes of ESP lifting during control operation, as a result of which some failures caused by operational reasons are treated as failures caused by design and technological reasons.

Conclusion
On average, the share of Ttd in the four associations was 45.8-58.1% of Ttkt,; in Tatneft it was a slightly lower ratio, and in Rosneft-Samaraneftegaz it was slightly higher. It follows that under the influence of repair poor quality and submersible parts maintenance of ESPs (more failures for operational reasons) and wrong practice of equipping them with new and repaired units, the operating time before failure of a typical ESP can be reduced by almost half compared to the initial operating time before the failure of new (factory-made) ESPs. These data indicate that due to the elimination of these shortcomings in all associations, there are significant reserves to increase the actual operating time before the failure of the submersible parts of typical ESPs.