The object of the research were bends of steam pipelines 10CrMo9-10, in which the highest frequency of failures caused by material cracks occurs. The forecast of pipeline operation time was determined on the basis of results Rm. Applying the principles of statistical inference to forecast the trouble-free operation time of steam pipelines, mathematical models were selected that in a highly statistically significant way most reflect the actual reduction in Rm over time and determine the limit value of material exhaustion to avoid failure

A. Mesjasz

B. Gajdzik

J. Piątkowski

English

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581METALURGIJA 59 (2020) 4, 581-584J. PIĄTKOWSKI, B. GAJDZIK, A. MESJASZUSE OF ECONOMETRIC MODELS FOR PREDICTING THE LIFETIME OF STEAM PIPELINES IN THE POWER INDUSTRY Received – Primljeno: 2020-01-21Accepted – Prihvaćeno: 2020-05-30Review Paper – Pregledni radJ. Piątkowski, B. Gajdzik, e-mail: jaroslaw.piatkowski @polsl.pl, Sile-sian University of Technology, Faculty of Materials Science, Katowice, Poland; A. Mesjasz, Tauron, Jaworzno, Poland.The object of the research were bends of steam pipelines 10CrMo9-10, in which the highest frequency of failures caused by material cracks occurs. The forecast of pipeline operation time was determined on the basis of results Rm. Applying the principles of statistical inference to forecast the trouble-free operation time of steam pipelines, math-ematical models were selected that in a highly statistically significant way most reflect the actual reduction in Rm over time and determine the limit value of material exhaustion to avoid failure. Keywords: power engineering, 10CrMo9-10 steel, pipeline, tensile strength, econometric modelsINTRODUCTIONSteel 10CrMo9-10 is a typical construction material for heating installation. The functioning of the energy and heating sector is a strategy for the economy in many countries. It is an industry sector supplying electricity and heating for industrial and domestic purposes. To en-sure safe operation of heating installations (steam pipe-lines) and the required level of heat energy production, it is necessary to diagnose the installation to determine and assess the degree of degradation of the structure of materials used for pressure elements. The service life of the steam pipeline depends on many usability features of the construction material, and in particular its mate-rial durability, which includes [1 - 4]: •strength reserve, as a difference between the critical stress at which the failure occurs (e.g. yield strength or elasticity, fatigue, loss of stability) and the design stress, typical of a physical phenomenon that may be the cause or one of the causes of a failure, •permanent deformation or displacement of a pipe-line element (elbows, tees), •amount of looseness on joined elements or degra-dation of connections e.g. welds, •total fatigue and other damage typical of working conditions. Steel used in power engineering is exposed to ad-verse stress caused by pipeline operation. The useful-ness of pipelines is influenced by: material fatigue, creep, friction wear, exceeding of short-term strength, work in critical parameters, inter-crystalline and opera-tional cracking, corrosion, erosion, internal material de-fects, etc. [5, 6], which worsen the technical condition of the element in the considered its fragment, e.g. cross-section, connection point, narrowing, etc. ISSN 0543-5846METABK 59(4) 581-584 (2020)UDC – UDK 621.82.312: 669.15.26.28: 621.181.021:539.42:330.15=111METHODOLOGYThe object of research were secondary superheated steam pipelines made of 10CrMo9-10 steel. The scope of research included knee bends due to the high failure rate of these elements during their operation. Static ten-sile samples were cut from the knees (according to PN-EN ISO 6892-1 [7] and the tensile strength was deter-mined Rm [MPa] - as an input variable. All samples were cut from pipelines made of the same steel at differ-ent periods of operation (from 150 000 to 250 000 hours and longer). To assess the pipeline operation time, econometric models were used, which by means of equations repre-sent quantitative relationships between the phenomena studied. The research used a model of specific func-tions, e.g. exponential, power. It was a model of the form: y = Rm. Model parameters were estimated using statistical methods based on empirical data [8-9]. Esti-mation of the tensile strength index (Rm) was deter-mined for a group of samples taken with the known form of the random variable of time distribution of the object’s ability and based on the estimation of the reli-ability value from the random sample representing the examined population. Statistical verification of the models was made on the basis of the degree of match-ing the model to empirical data (R2) and establishing the statistical significance of model parameters. The distribution of changes was described using econo-metric models Rm of 10CrMo9-10 steel in time and time prediction for the failure to occur in a given time horizon [10]. Trends of the studied phenomenon with forecast simulation are presented using a standard graph (one-dimensional time series), in which the ob-ject’s abscissa (X) is the lifetime of the object (thou-sands of hours), and on the ordinate (Y) - tensile strength (Rm) [10-11]. 582J. PIĄTKOWSKI et al.: USE OF ECONOMETRIC MODELS FOR PREDICTING THE LIFETIME OF STEAM PIPELINES... METALURGIJA 59 (2020) 4, 581-584HYPOTHESIS OF RESEARCH The paper hypothesizes that the operating condi-tions of the examined object from 150 000 to 250 000 hours and longer change as a function of time (chrono-logical time series). This change occurs under the influ-ence of the reheated steam factor and has an impact on the tensile strength of the construction material which is 10CrMo9-10 steel, from which the bend of the steam pipeline is made. EQUIPMENT AND RESOURCES FOR RESEARCHThe tests were carried out in the conditions of real operation of the facility. The distribution of material properties was determined based on the results of tensile strength Rm measurements. The input database consisted of from 10 to 20 samples taken from pipelines operating in various operating periods. Used empirical data were presented in Table 1. Samples were picked on an Instron 3382 testing machine using a 20: 1 gear ratio and a con-stant tensile speed of 5mm / min. In accordance with PN-75 / H-84024, the lower tolerance limit Lower Specifica-tion Limit (LSL) was determined to assess the change in Rm as a function of operating time, which is 440 MPa for reheated steam. Figure 1 shows the place of sampling for Rm tests from the knee arch (designations: sample 1 and sample 2). The choice of the place of sampling corre-sponded to the places where the damage occurred, the occurrence of which is shown in Figure 2. Table 1 Empirical data – an example [10]a) for Sample 1Exploration work time/thousand hoursRm/MPa0 551,50 551,5174 496,3174 496,3174 496,3174 496,3189 488,1189 488,1189 488,1190 487,5190 487,5190 487,5214 472,5214 472,5214 472,5215 471,8215 471,8215 471,8260 436,4260 436,4260 436,4280 417,2280 417,2280 417,2b) for Sample 2Exploration work time /thousand hoursRm/MPa0 548,10 548,1174 489,0174 489,0174 489,0174 489,0174 489,0174 489,0190 478,1190 478,1214 458,9214 458,9214 458,9214 458,9214 458,9214 458,9214 458,9215 458,1215 458,1215 458,1260 409,8260 409,8260 409,8280 382,0Figure 1  Diagram of the knee and places where strength samples are taken [10]Figure 2 Examples of steam pipeline arc cracks [10] 583J. PIĄTKOWSKI et al.: USE OF ECONOMETRIC MODELS FOR PREDICTING THE LIFETIME OF STEAM PIPELINES...METALURGIJA 59 (2020) 4, 581-584RESULTS OF RESEARCHThe graphical course of the function of changes Rm during the use of a knee arch made of tested steel is shown in Figure 3. By analyzing the distribution of points on the graph as a function of time, the following econometric models were tested based on their time se-ries: model based on exponential function, model based on quadratic function and hyperbolic model. Using econometric tests to assess the significance of models, the hyperbolic model was rejected. The correct models are shown below:•model based on exponential function:  y = 579 – e0,00633x+3,313 (1)  R2 = 0,7923•model based on quadratic function:  y = – 0,0016 x2 + 0,0013 x + 541,07 (2) R2 = 0,8910Both models describe in a statistically significant way the course of the Rm change depending on the oper-ating time of the steam pipe knee arc. The course of functions of the quadratic and exponential models for samples (1) is shown in Figure 3. Based on the econo-metric models obtained, it was found that the operation of the tested knee arch above 256 000 - 258 000 hours may lead to a decrease in the Rm value below 440 MPa. The same models were used to assess knee arch strength for samples (2). In this case, the hyperbolic model turned out to be the largest degree of matching empiri-cal data to functions. The results are shown in Figure 4. Capability analysis, (cp > 1), confirmed that the vari-ation limits have a smaller range from Upper to Lower Specification Limit (ULS÷LSL). The improved index of cpk capacity is equal to the index cpl, which indicates a significant decrease in Rm as the steam pipeline’s op-erating time increases, going far beyond the Lower Specification Limit (LSL) tolerance on the left. The val-ues of all prognostic models for the change in Rm as a function of operating time are presented in Table 2. Table 2 Obtained econometric models [10] a) for Sample 1Model y = Rm R2 F T/thousand hoursy = -0,0016x2 + 0,0013x + 546,01 0,891 256,2÷258,3y = 579 - e 0,00633x+3,313 0,792y = (607,2x -204319,1)/(x -375,06) 0,997 231,2÷235,0y = -0,0024x2 + 0,0921x + 546,62 0,939y = 567 - e 0,00815x+2,393 0,939b) for Sample 2y = -0,0022x2 + 0,1883x + 518,23 0,817 236y = 528 - e 0,0115x+1,757 0,823y = (554,7x -158158,3)/(x -307,76) 0,986 193,4÷198,2y = -0,0027x2 + 0,1334x + 515,13 0,962y = 525 - e 0,0119x+2,111 0,921Where F Forecast of exploration work timeThe trends of obtained prognostic charts Rm for the best model (which was the exponential model) is shown in Figure 5. CONCLUSIONThe motive for undertaking the research was dictat-ed by the need to maintain proper operation of steam Figure 3  Examples of models describing the course of the Rm change as a function of operating time for the knee arch for samples (1) (place 1) [10]Figure 4  Examples of models describing the course of the Rm change as a function of operating time for the knee arch for samples (2) (place 2) [10] Figure 5  Summary statement of the Rm change forecast as a function of elongation time of the secondary superheated steam pipe [10] 584J. PIĄTKOWSKI et al.: USE OF ECONOMETRIC MODELS FOR PREDICTING THE LIFETIME OF STEAM PIPELINES... METALURGIJA 59 (2020) 4, 581-584pipelines that operate above the critical temperature and ensure their safe use for subsequent years. This problem is very important because it concerns about 90 % of the power units used in Poland.The obtained models y = Rm (models of the function of the elbow of the steam superheated steam pipeline for 10CrMo9-10 steel) indicate that in all cases exceed-ing the pipeline’s operating time (200 000 hours) in-creases the risk of structural damage. Based on the re-sults of tensile strength, it can be assumed that the pre-dicted trouble-free operation of steam pipeline compo-nents is: about 231 200 - 258 300 hours for samples taken from the so-called “curvature” of the knee arch (samples 1), about 193 400 - 236 000 hours for samples taken from the so-called “straight” knee bends (samples 2).From the results it can be concluded that after ex-ceeding the above threshold time, the tensile strength reaches a value below the lower tolerance limit (440 MPa). In such cases, more frequent diagnostic tests should be recommended, as the pipeline “enters” the potentially emergency area, causing the need to replace the elbow in the pipeline installation. The presented methodology of statistical tests can be used to estimate the forecast of material durability, as a derivative of the reliability of operation of pressure installation compo-nents, in particular steam pipe elbows, which confirmed the assumed research thesis. The proposed statistical forecasting time operation of the pipeline should be considered as a tool to support decision-making pro-cess, which complement traditional studies to assess the degradation of the structure of materials, which are made knee steam pipelines. The analysis of forecasting models should be supplemented by a methodology based on the calculation of the theoretical degree of ma-terial depletion for a given pipeline life cycle divided into time intervals required for diagnostic services [12], and development of scenarios of possible events, in this case for operated devices energy industry (e.g. pipe-lines).AcknowledgeThe Article is part of Disertation [10]. REFERENCES[1] Bucior J.: Fundamentals of reliability theory and engineer-ing. Publishing House, Rzeszów 2004. [2] Będkowski L., Dąbrowski T.: Basic sof operation. WAT, Warsaw, 2006. [3] Słowiński B.: Basic of research and reliability assessment of technical objects. Koszalin 2002. [4] Szopa T.: Reliability and safety. Warsav University of Technology Publisher, Warsaw 2009. [5] UDT no 1/2015: Principles of diagnostics and assessment of service life of boiler components operating in creep con-ditions. Warsaw 2015. [6] Dobrzański J.: Material science interpretacion of steel du-rability for the Power industry. Open Access Library, (3), 2011. [7] PN-EN ISO 6892-1 Metals. Tensile test. PKN, Warsaw 2010. [8] Pawłowski Z.: Mathematical statistics. PWN, Warsaw 1980. [9] Szkutnik W., Balcerowicz-Szkutnik M.: Introduction to econometric methods. College of Management Gen. J. Ziętek, Katowice 2006. [10] Mesjasz A.: Dissertation: Application of statistical meth-ods of decision support for estimation material durability of steam pipelines. Promoter: Piątkowski J., Silesian Uni-versity of Technology, Gliwice, 2018. [11] Pilch R., Szybka J., Broniec Z.: Determining the sernice life of the heat pipeline based on the identification of limit states. Operation and reliability 14/3, (2012), 23-29. [12] Grzybowska K., Gajdzik B.: Optimisation of equipment setup process in enterprises, Metalurgija, 51 (2012) 4, 555-558. Note: The responsible for English language J. Jamrozik, Poland.

Use of econometric models for predicting the lifetime of steam pipelines in the power industry

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