Comparative Study between Degradation Analysis and First Order Reliability Method for Assessing Piping Reliability for Risk-Based Inspection

Transcription

1 International Journal o Engineering & Technology IJET-IJENS Vol:09 No:10 77 Comparative Study between Degradation Analysis and First Order Reliability Method or Assessing Piping Reliability or Risk-Based Inspection Ainul Akmar Mokhtar*, Mokhtar Che Ismail, and Masdi Muhammad Abstract Piping systems in reineries and petrochemical plants are exposed to corrosive environment causing various types o degradation mechanisms. One o the damage mechanisms experienced is gradual wall thinning that causes the pipe to leak. Since the piping systems carry hydrocarbons or other process luids, the presence o small leak may lead to a hazardous situation. Thereore, proper inspection and maintenance o these systems is essential or maintaining a sae and continuous operation. Risk-based inspection (RBI) strategy has been adopted to establish the inspection strategy or piping systems where the strategy is based on risk calculated. Risk is deined as the product o the probability o ailure and its consequences o ailure. Assessing the ailure probability or piping systems in RBI approach typically ollows the guideline by American Petroleum Institute (API 581) where the method is deterministic. This study explores the available probabilistic analysis techniques in estimating the piping ailure probability, namely, degradation analysis and irst-order reliability method (FORM). The objective o this paper is to estimate the pipes ailure probability using these two techniques where both models require dierent input data. Degradation analysis only uses the pipe wall thickness data that are usually being collected during inspection or pipes subject to wall thinning. Conversely, FORM model requires data on material properties and physical geometric o the piping system to estimate the ailure probability. The ailure probability estimated by these two techniques are then compared and discussed. The results showed that the degradation analysis is more conservative compared to FORM. Index Term Piping Reliability, Degradation Analysis, First- Order Reliability Method, Risk-based Inspection I. INTRODUCTION ONE o the most important structural elements in reineries and petrochemical plants is piping systems. According to the statistics, the highest percentage o structural elements in those plants is piping systems when compared to other equipment [7]. In general, piping systems in reineries and petrochemical plants are exposed to corrosive environment due to the presence o water, minerals and the stress concentration and this usually leads to various types o degradation mechanisms. Guidelines on the damage mechanisms that aect ixed equipment and piping systems in reineries were issued by American Petroleum Institute, API 571 []. One o the most common damage mechanisms experienced by piping systems is wall thinning which can be due to many reasons, including low-accelerated corrosion [13, 6] and erosion-corrosion [5]. Gradual wall thinning can cause the pipe to leak or in the worst scenario, the pipe may rupture. Since the piping systems carry hydrocarbons or other process luids, the presence o small leak or rupture in lines may lead to a hazardous situation. Hence, to maintain a sae and continuous operation, proper inspection and maintenance o these piping systems is crucial. Unortunately, regulatory requirements on piping saety and inspection interval is lacking when compared to pressure vessels where the inspection interval requirement is clearly documented. American Petroleum Institute does provide a guideline on the inspection interval o three categories o piping systems based on luid content in piping or the hal remaining lie [3]. However, this is generally insuicient as the actual conditions o the piping are not considered and thus, the possible ailure o the piping is usually not quantiied. According to Giribone and Valette [1], ailure probability is the main driver or scheduling periodical inspections in riskbased inspection (RBI) approach. The traditional method to quantitatively assess the ailure probability is through statistical analysis o ailure data rom which a lietime distribution is developed. This is applicable i there are enough ailure data available which is rarely the case or piping ailures. What usually available is a collection o degradation data which is the measurements o equipment wear taken during inspection. This measurement data is used to assess damage beore any catastrophic ailure occurs. For piping systems that are susceptible to wall thinning degradation mechanism, the wall thickness measurements are usually collected. In this case, degradation analysis is useul or the analysis o ailure time distributions in reliability studies [4, 0]. Another technique to assess the ailure probability is using irst-order reliability method (FORM), a computational method or structural reliability. Unlike degradation analysis that uses only the actual condition data o the piping system where in this study, the wall thickness are considered, FORM model requires more data such as material properties and physical geometric o the piping system to estimate the ailure probability. This study aims to model the pipe ailure probability using degradation analysis and FORM, to be urther used in RBI strategy in establishing the inspection interval or piping system. The guideline by American Petroleum Institute, API 581, provides the method to assess the ailure probability [1]; IJET-IJENS December 009 IJENS

2 International Journal o Engineering & Technology IJET-IJENS Vol:09 No:10 78 however, the assessment is deterministic and does not incorporate the uncertainties in the values o the parameter. The objective o this paper is to estimate the pipes ailure probability using the abovementioned probabilistic techniques, degradation analysis and FORM. The ailure probability approximated by these two techniques are compared and discussed. A brie description o both methods will also be discussed. II. RISK-BASED INSPECTION Over the past ew decades, the strategies in inspection and maintenance have progressed rom the primitive breakdown maintenance to the more sophisticated strategies like condition monitoring and reliability centered maintenance. One o the reasons or the paradigm shit was motivated by the need to implement new maintenance strategies which would increase the eectiveness and proitability o the business. Another link in this chain o progress has been recently added by the introduction o a risk-based approach to inspection and maintenance. Risk-based approach to inspection and maintenance has been suggested as a new vision or asset integrity management [15, 16, 17]. RBI has been an industry standard or prioritizing inspection o static equipments aiming at identiying, characterizing, quantiying and evaluating the likelihood o the loss caused as a result o the occurrence o a speciic event. In RBI strategy, risk is used as a criterion to prioritize inspection tasks or the systems. Risk is deined as the product o the probability o ailure and its consequence o ailure. The methods to assess risk range rom qualitative to quantitative where qualitative approaches are based primarily on expert judgment and speciic plant experience and quantitative approaches are based on statistical calculations using large historical databases. The techniques to estimate probability o ailure also varies rom qualitative to quantitative. In qualitative ailure probability assessment, the probability o ailure is primarily based on engineering judgments made by experts. The ailure probability is described using terms such as very unlikely, unlikely, possible, probable or highly probable where subjective scores are assigned to dierent actors which are thought to inluence the probability o ailure [8, 9, 10]. In a ully quantitative ailure probability assessment, the most straightorward approach is to obtain statistical estimates o equipment ailure rates based on data collected such as ailure data [11, 16, 1, 5]. The main problem with statistical analysis is that it is oten diicult to collect enough data to estimate the parameters o the statistical distribution. Another diiculty is to obtain an appropriate statistical distribution o the data and to justiy the underlying assumptions o the selected distribution. When such assessments are undertaken, justiication o the relevance o the underlying data and chosen model is usually necessary. Reliability assessment based on ailure data is oten hindered by the lack o observed or recorded ailures. In this case, inspection data is typically collected. Inspection data are a collection o degradation data which is the measurements o equipment wear usually taken during the inspection period. For piping systems that are susceptible to wall thinning degradation mechanism, the wall thickness measurements are usually collected. In this case, degradation analysis is useul or the analysis o ailure time distributions in reliability studies [4, 0]. III. DEGRADATION ANAYSIS Degradation analysis involves the measurement and extrapolation o degradation data that can be directly related to the presumed ailure []. A level o degradation at which a ailure is said to have occurred needs to be deined irst. The use o the term ailure in this context is deined as when the wall thickness reaches the minimum wall thickness allowed. To perorm degradation analysis, the extrapolation can be done using the one o the ollowing models: inear model y ax b Exponential model Power model a y bx ax y be ogarithmic model y a ln x b where y represents the degradation, x represents time and a and b are model parameters to be solved or. Once the model parameters have been estimated or each sample i, a time x can be extrapolated, which corresponds to the deined level o ailure y. The computed x i can now be used to as the mean time-to-ailure data or the lie data analysis. ie data analysis is one o the well-known engineering tools or analyzing ailure data and becomes the tool o choice or many reliability engineers. The technique has applications in a wide range o industries such as military, automotive, electronics, composites research, aerospace, electrical power, nuclear power, dental research and advertising. There are several lietime distribution models that have been successully served as population models or ailure data such as exponential, Weibull, lognormal, gamma and many other distributions. In this study, the mean time-to-ailure data is itted to the Weibull distribution. In lie data analysis, the mean lie is determined by analyzing time-to-ailure data. For the case o the piping reliability, the time-to-ailure data are extrapolated rom degradation analysis. The cumulative density unction or Weibull distribution is t Ft 1 exp where F represents the cumulative density unction o t time-to-ailure i.e. probability that a ailure occurs beore time t and t is the time-to-ailure. The distribution is characterized by two parameters, the scale parameter and the shape parameter. The value o the parameter identiies the mode o ailure rate. For example, < 1 means decreasing ailure rate, = 1 indicates random ailure (constant ailure rate) and > 1 describes wear-out ailure (increasing ailure rate). The scale parameter is deined as the lie at which 63.% o units will ail. Figure 1 depicts the degradation analysis ramework or assessing the ailure probability. i IJET-IJENS December 009 IJENS

3 International Journal o Engineering & Technology IJET-IJENS Vol:09 No:10 79 Selection o piping system Collection o wall thickness data M D t or or Fig. 1. Degradation analysis ramework or piping reliability estimation IV. FIRST-ORDER REIABIITY METHOD First-order reliability method (FORM) has been applied to assess the system reliability with corrosion deects, or example, in pipelines [14, 3, 4]. The ailure behavior o the structure is described by a ailure unction g (x), depending on basic random variables x x1,..., x n which denote applied loads and structural resistance parameters such as dimensions and material properties. By deinition, g (x) < 0 implies ailure, whereas no ailure occurs with g (x) > 0. g (x) = 0 deines the so-called ailure surace, a hyper-surace in the n -dimensional space o the basic variables. The ailure surace separates the ailure domain F (with g (x) < 0) and the sae domain ( g (x) > 0). The ailure probability P can be calculated as the probability content o the ailure domain F : P where i x i F x1... n xn d x1... dxn (1) 1 represents the probability densities o the respective basic variables x i, which or the sake o simplicity are assumed to be stochastically independent. In this study, the ailure unction is deined as the dierence between the pipe ailure pressure P and the pipe operating pressure P op as stated: g( x) P P op Degradation analysis Identiy the best curve it. Extrapolate the data to get the mean time-to-ailure data ie data analysis using mean time-toailure data Calculate probability o ailure or RBI Two ailure pressure models are used to determine the ailure probability namely modiied B31G [5] and Shell 9 [6]. The modiied B31G ailure pressure model is deined as d( ( YS 68.95) t P t D d( M t where The Shell 9 ailure pressure is deined as: d( 1 1.8UTSt P t D d( 1 1 M t where M d ( = depth o corrosion YS = Yield strength (MPa) UTS = Ultimate tensile strength (MPa) t = Thickness o the pipe (mm) D = Outer diameter o the pipe (mm) CR = Corrosion rate (mm/yr) P = Operating pressure (MPa) op T = Time o inspection (year) = Axial length o corrosion deect (mm) In this study, it is assumed that the depth o corrosion is d( 0. 0t CRT Figure represents the FORM ramework or assessing the ailure probability. Selection o piping system Collection o operating data Calculate ailure probability using FORM based on standard models or RBI Fig.. FORM ramework or piping reliability estimation V. CASE STUDY The pressurized heavy water reactor (PHWR) outlet eeder piping system is taken as a case study [5]. The 70-mm diameter eeder pipes are made o carbon steel A106GrB and are subjected erosion-corrosion damage mechanism. Wall thickness data were simulated based on the mean and standard deviation, as shown in Table I. Both parameters are assumed to ollow normal distribution. It is also assumed that the wall thickness data were taken at six dierent locations. T ABE I Pipe parameters [5] Parameters Mean Standard deviation Thickness o the pipe (mm) Corrosion rate (mm/yr) IJET-IJENS December 009 IJENS

4 International Journal o Engineering & Technology IJET-IJENS Vol:09 No:10 80 A. Degradation Analysis Degradation analysis was perormed on the simulated data or each dierent location where a linear model is assumed to describe the relationship between the wall thickness and time. Using Regression in Microsot Excel Analysis Tools, the model parameters a, the slope or the corrosion rate and b, the intercept are established. Table shows the equation o the linear model or each location. All locations show a strong relationship between the two variables, time and wall thickness, with the R-squared is more than Using the linear model, the wall thickness data was extrapolated to the time when the presumed ailure may occur. Here, the ailure is deined as when the wall thickness reaches 50% o the wall thickness which is 3.50 mm. The time-to-ailure data or each location is also ound in Table II. T ABE II inear regression and time-to-ailure data ocation inear Equation R-squared Time-to-Failure (in year) 1 y 0.033x y 0.058x y 0.051x y 0.051x y 0.037x y 0.065x The next step is to construct a lietime distribution using Weibull distribution or the estimated time-to-ailure data with the assumption that all locations experienced the same conditions. The Weibull cumulative distribution unction or the data can be expressed as ollows: t F t 1 exp 8.9 where t time in years. The shape parameter and scale parameter or the Weibull distribution was ound to be and 8.9, respectively. This unction now can be used to predict the reliability o the piping system at any point time. B. First-Order Reliability Method To assess the ailure probability using FORM, the ollowing parameters are used as tabulated in Table III. T ABE III Parameter or limit-state unction with mean and coeicient o variance [5] Symbol Parameters Mean Variance YS Yield strength (MPa) UTS Ultimate tensile strength (MPa) t Thickness o the pipe (mm) D Outer diameter o the pipe (mm) CR Corrosion rate (mm/yr) P o Operating pressure (MPa) T Time o inspection (year) 30 (constant) Axial length o corrosion deect (mm) 300 (constant) Solver, with the objective unction to minimize the reliability index subject to the constraint that the limit-state unction, g(x) = 0. The probability o ailure is then calculated. VI. RESUTS AND DISCUSSIONS A case study o eeder piping system is analyzed. Note that or degradation analysis, inspection data in term o wall thickness were used or the analysis whereas or FORM method, the data on pipe material properties and operating parameter were used to assess the probability o ailure. The average corrosion rate in degradation analysis was mm/year which is comparable to mm/year used in FORM analysis. However, the variance o the corrosion rate or degradation analysis is very much smaller with compared to used in FORM. The dierence might be due to the method in estimation the corrosion rate where in FORM analysis, the corrosion rate was estimated using empirical model as explained in [5]. In FORM analysis, deect depth o 0% o wall thickness was assumed as the initial corrosion depth. A limit state unction was deined or a pipe subject to corrosion mechanism that causes wall thinning. The reliability index and the probability o ailure were evaluated or various values o inspection period. Based on the probability values, the categorization o ailure probability in severity classes has been ormulated. Table IV shows the range o ailure probabilities and their categories. T ABE IV Failure probability categories [1] ikelihood Category Range to Very high to High to Medium to ow < Very low The plots o the ailure probability and the reliability index against inspection time are presented, as shown in Figure 3 and 4, to draw the inerences. The graphs can be used as a guide in setting an eective inspection strategy. It is observed rom the ailure probability generated or the irst 10 years or both methods are almost the same. However, ater the irst 10 years, the probability o ailure or FORM model (both B31G and Shell 9) increases exponentially, whereas, or degradation analysis technique, the probability o ailure increases gradually at a slower rate. Since > 1 or Weibull distribution, the distribution has an increasing ailure rate or wear-out ailure. As expected, Shell 9 model gives higher probabilities o ailure when compared to the B31G model that gives the smaller estimate as mentioned in [5]. FORM model was built using Microsot Excel and Visual Basic or Application [18, 19, 7]. The reliability index was obtained by calling Excel s built-in optimization program, IJET-IJENS December 009 IJENS

5 Probability o ailure International Journal o Engineering & Technology IJET-IJENS Vol:09 No: it. For saety reasons, it would be wise or the pipe to be repaired or replaced. The FORM results are well comparable with the results available in the literature Time (in year) Degradation analysis Shell 9 B31G Fig.. Failure probability plot Fig. 3. Reliability index vs. exposure time The ailure probabilities and the likelihood categories were calculated at the end o the 30 years o service lie as shown in Table 5. The reliability index equations or each method are presented in Table V. T ABE V Reliability index equations METHOD Degradatio n Analysis FORM using B31G FORM using Shell 9 REIABIITY INDEX EQ UATION Β( AT 30 YEAR S FAIURE PROBABIIT Y AT 30 YEARS IKEIHOO D CATEGORY VII. CONCUSION In this paper, the ailure probability assessment models based on degradation model and irst-order reliability method were developed and applied to estimate the ailure probability o wall-thinned eeder piping systems. This study was needed to establish inspection program or piping systems based on the quantitative risk assessment. Both models are compared and the ollowing key indings have been derived: Degradation analysis is conservative because it appears that the pipe might not ail or longer exposure time. Even i it appears that it has not ailed, it may not be sae to use ACKNOWEDGMENT The authors grateully acknowledge all reviewers or their valuable suggestions or enriching the quality o the paper. The support o Universiti Teknologi PETRONAS is greatly acknowledged. REFERENCES [1] American Petroleum Institute. (1996). Base Resource Document on Risk-Based Inspection. API Publication 581. [] American Petroleum Institute. (1997). Damage mechanisms that aect ixed equipment and piping systems in reineries. API Publication 571. [3] American Petroleum Institute. (001). Piping Inspection Code. API Publication 570. [4] Bae, S.J., Kuo, W. and Kvam, P.H. (007). Degradation models and implied lietime distributions. Reliability Engineering and Systems Saety, 9, [5] Caleyo, F., Velazquez, J.C., Valor, A. and Hallen, J.M. (009). Markov chain modeling o pitting corrosion in underground pipelines. Corrosion Science, doi: /j.corsci [6] Caleyo,F., Gonzalez, J.. and Hallen, J.M. (00). A study on the reliability assessment methodology or pipelines with active corrosion deects. International Journal o Pressure Vessels and Piping, 79, [7] Chang, M., Chang, R. Shu, C. and in, K. (005). Application o risk based inspection in reinery and processing piping. Journal o oss Prevention in the Process Industries, 18, [8] Dey, P. (001). A risk-based model or inspection and maintenance o cross-country petroleum pipeline. Journal o Quality in Maintenance Engineering, 7 (1), [9] Dey, P. (004). Decision support system or inspection and maintenance: A case study o oil pipelines. IEEE Transactions on Engineering Management, 51 (1), [10] Dey, P.K., Ogunlana, S.O. and Naksuksakul, S. (004). Risk-based maintenance model or oshore oil and gas pipelines: a case study. Journal o Quality in Maintenance Engineering, 10 (3), [11] Fleming, K. (004). Markov models or evaluating risk-inormed inservice inspection strategies or nuclear power plant piping systems. Reliability Engineering and System Saety, 83, [1] Giribone, R. and Valette, B. (004). Principles o ailure probability assessment (PoF). International Journal o Pressure Vessels and Piping, 81, [13] Hales, C., Stevens, K.J., Daniel, P.., Zamanzdeh, M. and Owens, A.D. (00). Boiler eedwater pipe ailure by low-assisted chelant corrosion. Engineering Failure Analysis, 9, [14] Juang, C. H., Fang, S. Y and Khor, E. H. (006). First -order reliability method or probabilistic liqueaction triggering analysis using CPT. Journal o Geotechnical and Geoenvironmental Engineering, 13 (3), [15] Khan, F.I. and Haddara, M.M. (003). Risk-based maintenance (RBM): a quantitative approach or maintenance /inspection scheduling and planning. Journal o oss Prevention in the Process Industries, 16, [16] Khan, F.I., Haddara, M.M. and Bhattacharya, S.K. (006). Risk-based integrity and inspection modelling (RBIMM) o process components/system. Risk Analysis, 6 (1), [17] Krishnasamy,.,Khan, F. and Haddarra, M. (005). Development o risk-based maintenance (RBM) strategy or a power-generating plant. Journal o oss Prevention in the Process Industries, 18, [18] ow, B. K. and Tang, W. H. (007). Eicient spreadsheet algorithm or irst-order reliability method. Journal o Engineering Mechanics, 133 (1), [19] ow, B. K. and Tang, W. H. (004). Reliability analysis using objectoriented constrained optimization. Structural Saety, 6, [0] Meeker and Escobar. (1998). Statistical methods or reliability data. New York: Wiley. [1] Podoillini,., Zio, E. and Vatn, J. (006). Risk-inormed optimisation o railway tracks inspection and maintenance procedures. Reliability Engineering and System Saety, 91, IJET-IJENS December 009 IJENS

6 International Journal o Engineering & Technology IJET-IJENS Vol:09 No:10 8 [] ReliaSot Corporation. (006). ie Data Analysis. Tucson, AZ: ReliaSot Publishing. [3] Santosh, Vinod, G., Shrivastava, O.P., Sara, R.K., Ghosh, A.K. and Kushwaha, H.S. (006). Reliability analysis o pipelines carrying HS or risk based inspection o heavy water plants. Reliability Engineering and System Saety, 91, [4] Teixeira, A. P., Soares, C. G., Netto, T. A. and Esteen, S. F. (008). Reliability o pipelines with corrosion deects. International Journal o Pressure Vessels and Piping, 85, [5] Vinod, G., Bidhar, S.K., Kushwaha, H.S., Verma, A.K. and Srividya, A. (003). A comprehensive ramework or evaluation o piping reliability due to erosion-corrosion or risk-inormed inservice inspection. Reliability Engineering and System Saety, 8, [6] Yuan, X. X., Pandey, M. D. and Bickel, G. A. (008). A probabilistic model o wall thinning in CANDU eeders due to low-accelerated corrosion. Nuclear Engineering and Design, 38 (1), [7] Zhao, Y. and Ono, T. (1999). A general procedure or irst/second-order reliability method (FORM/SORM). Structural Saety, IJET-IJENS December 009 IJENS