Editor's Note: This article is an overview, distilled from a detailed technical report. The detailed technical report, with explanations and equations, may be accessed at http://www.trinity-bridge.com/sites/default/files/publications/API-581_3rd_Thinning_Example_2.pdf. Please note that this article and the referenced technical paper are focused on thinning. The term “base case” is used throughout this article. It always refers to the data basis that was used to establish thinning damage factors in the rst two editions of the API RP 581 technical basis.
A Joint Industry Project for Risk-Based Inspection (API RBI JIP) for the refining and petrochemical industry was initiated by the American Petroleum Institute in 1993. The project was conducted in three phases:
- Methodology development Sponsor Group resulting in the publication of the Base Resource Document on Risk-Based Inspection in October 1996.
- Methodology improvements documentation and software development User Group resulting in the publication of API RP 581 Second Edition in September 2008. API Software User Group split from methodology development through the creation of an API 581 task group in November 2008. The document is now managed in an API task group under the oversight of the API Sub-Committee on Inspection instead of the former JIP structure.
- Methodology improvements documentation resulting in the publication of API RP 581 Third Edition in April 2016.
The work from the JIP resulted in two publications: API 580 Risk-Based Inspection, released in 2002 and API 581 Base Resource Document – Risk-Based Inspection, originally released in 1996. The concept behind these publications was for API 580 to introduce the principles and present minimum general guidelines for implementing and maintaining a risk-based inspection (RBI) program while API 581 was to provide specific quantitative RBI methods for calculating risk. The API RBI JIP made improvements to the technology since the original publication of these documents and released API RP 581, Second Edition in September 2008. Since the release of the Second Edition, the API 581 task group has been improving the methodology and revising the document for the Third Edition release in 2016.
Like the Second Edition, the Third Edition is a three volume set, Part 1: Inspection Planning Methodology, Part 2: Probability of Failure Methodology, and Part 3: Consequence of Failure Methodology.
Among the changes incorporated into the Third Edition of API RP 581 is a significant modification to the thinning Probability of Failure (POF) calculation. The methodology documented in the Third Edition provides the basis for the original Art table approach it will replace. This paper provides the background for the technology behind the Third Edition thinning model as well as step-by-step worked examples demonstrating the methodology for thinning in this new edition of API RP 581. This paper is a revision to a previous publication: API RP 581 Risk-Based Inspection Methodology – Basis for Thinning Probability of Failure Calculations published in November 2013.
The project started in May 1993 as a JIP to develop practical methods for implementing RBI, the API RP 581 methodology focuses inspection efforts on process equipment with the highest risk. This sponsor group was organized and administered by API and included the following members at project initiation: Amoco, ARCO, Ashland, BP, Chevron, CITGO, Conoco, Dow Chemical, DNO Heather, DSM Services, Equistar, Exxon, Fina, Koch, Marathon, Mobil, Petro-Canada, Phillips, Saudi Aramco, Shell, Sun, Texaco, and UNOCAL.
The stated objective of the project was to develop a Base Resource Document (BRD) with methods “aimed at inspectors and plant engineers experienced in the inspection and design of pressure-containing equipment.” The BRD was specifically not intended to become “a comprehensive reference on the technology of Quantitative Risk Assessment (QRA).” For failure rate estimations, the project was to develop “methodologies to modify generic equipment item failure rates” via “modification factors.” The approach that was developed involved specialized expertise from members of the API Committee on Refinery Equipment through working groups comprised of sponsor members. Safety, monetary loss, and environmental impact were included for consequence calculations using algorithms from the American Institute of Chemical Engineers (AIChE) Chemical Process Quantitative Risk Assessment (CPQRA) guidelines. The results of the API RBI JIP and subsequent development were simplified methods for estimating failure rates and consequences of pressure boundary failures. The methods were aimed at persons who are not expert in probability and statistical methods for Probability of Failure (POF) calculations and detailed QRA analysis.
Perceived Issues with POF Calculation
The POF calculation is based on the parameter Art (known as “ar over t”) that estimates the percentage of wall loss and is used with inspection histories to determine a Damage Factor (DF). The basis for the Art table (Table 1) was to use structural reliability for load and strength of the equipment to calculate a POF based on equipment failure by plastic collapse. The Art factor is the product of the age and the corrosion rate of the vessel, divided by the furnished thickness, not including the corrosion allowance. A dimensionless DF is calculated based on the number and thoroughness of inspection.
A statistical distribution is applied to a thinning corrosion rate over time, accounting for the variability of the actual thinning corrosion rate which can be greater than the rate assigned. The amount of uncertainty in the corrosion rate or equipment damage state is determined by the number and effectiveness of inspection and the on-line monitoring that has been performed. Confidence that the assigned corrosion rate is the rate that is experienced in-service increases with more thorough inspection, a greater number of inspections, and/or more relevant information gathered through on-line monitoring. The DF is updated based on increased confidence in the measured corrosion rate provided by using Bayes Theorem and the improved knowledge of the component condition.
The Art table contains DFs created by using a base case piece of equipment to modify the generic equipment item failure rates to calculate a final POF. The Art table has been used successfully since 1995 to generate DFs for plant equipment and POF for risk prioritization of inspection. The perceived issues that have been noted during almost 20 years of use are:
- Use of three thinning damage states introduced non-uniform transitions in DFs vs. Art, leading to confusion during inspection planning and the methods for smoothing the data to eliminate the “humps” were undocumented.
- Use of Mean Value First Order Reliability Method (MVFORM) is less accurate for calculating POF over other, more accurate statistical methods such as First Order Reliability Method (FORM) or Weibull analysis.
- Results for specific equipment studied could be significantly different from the base case equipment used due to different properties:
- Component geometric shapes used a cylindrical shape equation (not applicable for a semi-hemispherical, spherical or other shapes).
- Material of construction tensile strength, TS, and yield strength, YS, values may not be representative for all materials of construction used in service.
- Design temperature and pressure values may not be representative for all design and operating conditions used in service.
- The 25% corrosion allowance assumption of furnished thickness at the time of installation may not be representative for all equipment condition.
- The Art approach does not reference back to a design minimum thickness, tmin, value.
- Statistical values for confidence and Coefficients of Variance (COV) are not representative of all equipment experience.
- The uncertainty in corrosion rate is double counted by using three damage states in addition to a thinning COV of 0.1.
- A POF limit of 0.5 for each damage state limits the maximum DF to 3,210.
- Rounding DFs to integers limits the minimum DF to 1.
This article addresses the perceived issues and shows the modified POF approach to address the stated limitations, as applicable. While some of the perceived issues in reality have little significance in the final calculated results, use of the model outlined in this article in high level terms addresses all of the above limitations. In addition, two worked examples are provided in the technical report to:
- Validate the step-by-step calculations representing the DFs values in the modified methodology.
- Provide examples using results from Table 1 and the modified methodology. In these examples, using Table 1 produces a non-conservative DF and POF.
The methodology and worked examples are presented in the technical report referenced in the editor’s note. The worked examples follow the step-by-step methods for calculation of the thinning DF as outlined in API RP 581, Third Edition April 2016. A major part of the POF calculation and increase over time is due to general or local thinning (both internal and external). The background for the original basis of the thinning DF determination and POF is also provided in the technical report. Figure 1 shows the decision tree in determining the thinning DF.
Original Basis for Thinning Damage Factor and Table
Background of Art Table
The DF methodology, developed in the early 1990’s as a part of the API RBI JIP development project, used probabilistic structural mechanics and inspection updating. Probabilistic analysis methods normally used for evaluating single equipment were simplified for use as a risk prioritization methodology. Table 1 was created as a part of the original API RBI JIP project to provide an easy look-up table for use in risk determination for multiple equipment items.
Table 1 (Table 5.11 in API RP 581 Second Edition, Part 2) was developed using a flow stress approach to evaluate the probability of failure due to thinning mechanisms such as corrosion, erosion, and corrosion under insulation (CUI). Flow stress is the minimum stress required to progress plastic deformation of a pressure-containing envelope to failure and provides conservative POF estimates. Art is a factor related to the fraction of wall loss at any point in time in the life of operating equipment. Table 1 was developed as a way to evaluate the impact of inspection on POF as equipment wall becomes thinner with time. The Art factor was developed using a structural reliability model integrated with a method based on Bayes’ Theorem to allow credit for the number and type of inspections performed on the POF and risk. The model was outlined in the API RBI JIP project and documented in API RP 581 First Edition in sufficient detail for skilled and experienced structural reliability specialists to understand the basis for the factors in Table 1.
The two-dimensional Table 1 was generated using a base case equipment approach, as outlined in Section 2.2 of the technical report and listed below. This base case approach provided a limited number of variables available to determine the DF and limited the user’s ability to enter actual values or change assumptions for different equipment design cases. Using the modified methodology outlined in Section 4.0 with actual data for physical dimensions, materials properties and operating conditions to calculate POF and DF will result in a more accurate POF and risk results and improve discrimination between equipment risk and risk ranking.
Base Case for Art Table Development
The fixed variables and assumptions used to develop Table 1 were:
- Cylindrical shape
- Corrosion rate used to determine POF at 1x, 2x and 4x the expected rate
- Diameter of 60 inches
- Thickness of 0.5 inches
- Corrosion allowance of 0.125 inches (25% of thickness)
- Design Pressure of 187.5 psig
- Tensile strength of 60,000 psi
- Yield strength of 35,000 psi
- Allowable Stress of 15,000 psi
- Weld Joint Efficiency of 1.0
- Failure frequency adjustment factor of 1.56E-04Maximum POF of 0.5 imposed for all each of the three damage states, limiting the maximum damage factor to 3,205 (or )
- DF table values calculated up to Art = 0.65 and linearly extrapolated to Art = 1.0
- COV for variables of pressure = 0.050, flow stress = 0.200, thinning = 0.100
Categories and values of prior probabilities using low confidence values from Table 1 was based on the equipment dimensions and properties outlined above and applied to all general plant fixed equipment. It was considered sufficiently applicable for other equipment geometries, dimensions, and materials for the purposes of equipment inspection prioritization.
Methodology Used for Development of the Thinning Damage Factor
Damage States and Data Uncertainty
Three damage states were used to account for corrosion rates higher than expected or measured that could result in undesirable consequences to generate the Art in Table 1. The three damage states used in the methodology were:
- Damage State 1 – Damage is no worse than expected or a factor of 1 is applied to the expected corrosion rate
- Damage State 2 – Damage is worse than expected where a factor of 2 is applied to the expected corrosion rate
- Damage State 3 – Damage is worse than expected where a factor of 4 is applied to the expected corrosion rate
General corrosion rates are rarely more than four times the expected rate, while localized corrosion can be more variable. The default values provided here are expected to apply to many plant processes. Note that the uncertainty in the corrosion rate varies, depending on the source and quality of the corrosion rate data. The result of using the three discrete damage states creates a POF curve with humps for the low confidence (no inspection) case. As more inspections are performed, less uncertainty in the corrosion rate results and the POF curve is smoothed due to higher confidence in the equipment condition. The DFs in Table 1 were rounded and visually smoothed to eliminate these abrupt changes causing damage state changes.
As confidence in the current state of the equipment is improved through effective inspection, the influence of damage states 2 and 3 are reduced and the curve is smooth.
It is important to note that the humps only occur in inherently high uncertainty situations and are not noticeable in the practical application of the methodology for inspection planning. As thinning continues over time, the DF will increase until an inspection is performed. After inspection, the DF is recalculated based on the new inspection effectiveness case. While the DF is not increasing at a constant rate in the low confidence inspection curves, the changes in the rate are unnoticeable in the practical application. Changing the coefficient of variance for thickness, , value from 0.100 to 0.200 results in a smoother curve, as demonstrated in the examples in Sections 4.0 and shown in Figure 5 of the technical report. When using the modified methodology outlined in Section 4.0, the user may also redefine the three damage state definitions as well as the confidence probability values in Table 4 of the technical report for specific situations.
Corrosion Rate Uncertainty
Since the future corrosion or damage rate in process equipment is not known with certainty, the methodology applies uncertainty when the assigned corrosion rate is a discrete random variable with three possible damage states (based on 1x, 2x, and 4x the corrosion rate). The ability to state the corrosion rate precisely is limited by equipment complexity, process and metallurgical variations, inaccessibility for inspection, and limitations of inspection and test methods. The best information comes from inspection results for the current equipment process operating conditions. Other sources of information include databases of plant experience or reliance on a knowledgeable corrosion specialist.
Statistical and Reliability Methods and Modified Thinning Methodology
Limitations of Simplified Statistical Methods
Use of continuous states involves development of a cumulative probability distribution function that best describes the underlying statistical distribution of corrosion rates (e.g., normal, lognormal, Weibull, etc.). All variables that affect that corrosion rate (material, temperature, velocity, etc.) for each piece of equipment should be considered. This approach is more accurate if the function uses the correct mean, variance and underlying distribution in each case. More detailed statistical methods were considered during development of the DF approach, but were believed to add unnecessary complexity for use in risk-based inspection prioritization. An MVFORM was adopted for use in the DF calculation and is known to be overly conservative, particularly at very low POF values ().
Modified vs. Base Case Equipment Data Values
As outlined in the technical report, a base set of equipment data was initially used to generate the DF values in Table 1. If the modified methodology outlined in this paper is used in place of the base case data, equipment specific DF and POF will be calculated and the limitations discussed previously no longer apply.
Stress due to internal pressure varies with equipment geometry. The base case uses a cylindrical shape for the calculations. The modified approach described in Section 4.0 of the technical report allows for calculations of other geometric shapes. Non-circular equations can be substituted if additional geometries are desired (e.g., header boxes, pump and compressor casings, etc.). Testing indicated that component geometry did not significantly affect DFs since design typically accounts for the impact of geometry on applied stress.
Material of Construction Properties
The TS and YS values used in the base case apply to a large population of equipment in most applications. However, these assumed values may be non-conservative or overly conservative depending on the actual materials of construction used. For improved accuracy, the modified approach in Section 4.0 allows for use of the TS and YS values for the materials of construction.
The pressure, P, used in the base case is considered to be a high average condition for most applications, but may be non-conservative or overly conservative depending on the actual service. The modified approach in Section 4.0 allows for using a pressure chosen by the user for more accuracy.
It is important to note that the DF is not a direct indication of predicted equipment thickness to tmin, particularly if operating pressure is used for the calculation. The user should consider the impact of P used in the calculation compared to the design condition basis for tmin. If DF and POF are required to provide a closer match to tmin values (i.e., inspection is recommended and higher DF and POF are required), the user should consider using design pressure or a pressure relief device (PRD) set pressure.
The most significant potential impact in the base case used to generate the Art table is the assumption that the corrosion allowance, CA, is 25% of the furnished thickness. More importantly, this assumption is non-conservative in specific situations, i.e., when the actual CA<<25% (much less than 25%). Alternatively, the results are overly conservative when the CA>>25%.
The modified approach in Section 4.0 generates a DF and POF based on design and condition of the equipment without the need for the CA assumptions used in the base case. The result is an increased applicability and accuracy with direct application of the model.
Minimum Thickness, tmin
The Art factor equation does not use tmin directly to calculation the Thinning DF and POF. To address the desire to incorporate tmin in API RP 581, Second Edition, the Art factor equation was modified to incorporate tmin into the calculation. The equation modification eliminated an overly conservative DF result when t>>tmin+CA by assigning a DF of 0. However, if t=tmin+CA, there is no difference between the First and Second Edition equations.
Use of the above approach will reduce the non-conservative and overly conservative results when using the original Art table.
It was never the intent of the DF calculation using the Art approach to develop a methodology that was specifically tied to the equipment tmin. In fact, the intent was to develop a risk-based methodology that allowed for safe continued operation of very low consequence equipment at thicknesses below the tmin. In these very low consequence cases, a run to failure strategy might be acceptable and therefore, tmin may not be relevant as an indication of fitness for service. The use of this methodology does not imply that tmin is not important for risk-based inspection planning. In fact, it is considered important to calculate the future predicted thickness and corrosion allowance compared to DF and risk with time to develop the most appropriate inspection planning strategies for each situation.
Coefficient of Variances (COV) and Impact of inspection on Damage Uncertainty
The three possible damage states described API RP 581 Third Edition and the technical report are used by Bayes’ theorem with inspection measurements, prior knowledge and inspection effectiveness. Uncertainty in equipment thickness due to inspection measurements is also accounted for when the probability of three damage states are combined using a normal distribution with a =0.20. The COV is a measure of the measurement variation of thickness. The use of damage states and COV has a cumulative effect on the calculated POF due to the combined uncertainty of expected damage rates in the future combined with inspection measurement inaccuracy. If the combined conservativeness is not applicable for the specific application, the user may modify the damage state confidence values or adjust the to suit the situation using the modified methodology.
Damage Factor Calculations
POF Extended to 1.0 for Three Damage States
In the Second Edition of API RP 581, the Art table was constructed using a maximum POF of 0.5 (or 50% failure rate). This POF limit produces maximum DFs of 3,205
(0.5/1.56E-0.5=3,205) for each of the three damage states. However, since the maximum Art factor in Table 1 was originally set to 0.65, the impact of the limitation was not obvious unless the Art table is extended through a POF of 1.0 (or 100% failure rate). The practical application of the methodology required setting Art=1.0 to a DF of 5,000(expected through-wall) and interpolating DFs between Art=0.65 and 1.0 in order to improve risk ranking discrimination between equipment nearing or at a failure thickness. The Third Edition methodology removes the POF limitation and calculates DF through an Art of 1.0.
DF Upper Limit
By removing the POF limit of 0.5, the maximum DF is increased to 6,410
(1.0/1.56E-0.5=6,410) and the DFs calculated through an Art value of 1.0 rather than using interpolation. The DF increase using this approach is most significant when Art>0.70 and where the DF>2,500(Category 5 POF).
An increase in thinning DF from 5,000 to 6,410 results in a maximum of 28% increase in DF. This increase is most significant at Art>0.70(Category 5 POF) when inspection is highly recommended regardless of consequence levels, unless a run to failure scenario is used.
DF Lower Limit
Table 1 rounded DFs to a minimum value 1 to prevent a POF<Gff. A minimum DF of is used to limit the final POF to an order of magnitude lower than Gff. The user may specify a different minimum or no minimum DF for individual cases, if desired.
Whether the thinning is expected to be localized wall loss or general and uniform in nature, this thinning type is used to define the inspection to be performed. Thinning type is assigned for each potential thinning mechanism. If multiple thinning mechanisms are possible and both general and localized thinning mechanisms are assigned, the localized thinning type should be used.
Localized corrosion in API RP 581 methodology is defined as non-uniform thinning occurring over < 10% of the equipment affected area such that spot thickness measurements would be highly unlikely to detect the localized behavior or even find the locally thinning areas. Localized thinning in this case is not intended to be a Fitness-For-Service (FFS) evaluation method for locally thin areas. For the localized thinning experienced, an area inspection method is required to achieve a high level of certainty in the inspection conducted.
Summary and Conclusions
The background and methodology for the thinning DF and POF determinations and perceived problems with the original Art approach has been discussed. The basis for the original Art table is a structural reliability equation for load and strength of the equipment to calculate a POF using a base case for data. A suggested modified approach has been outlined to address the limitations of the table values using the base case. While some of the perceived issues or limitations have little impact on the accuracy of the final calculated results, use of the model in API RP 581 Third Edition addresses all of the potential limitations identified during 20 years of practical application (with the exception of smoothing to eliminate the damage state step changes and the resulting humps). Two worked examples are available in the technical report and include: a validation of the step-by-step calculations compared to Art table values as well as an example that demonstrates more realistic results for non-conservative scenarios (low corrosion allowance) than were in the original table.
Use of the modified methodology will provide the following results:
- Three thinning damage states introduce non-uniform changes in DFs over time. The magnitude of the humps/transitions are reduced by using a =0.2. These humps occur in high uncertainty situations and are not noticeable in the practical application of the methodology for inspection planning. As thinning continues over time, the DF will increase until an inspection is performed. After inspection, the DF is recalculated based on the new inspection effectiveness case. In addition, the modified approach allows the user to tailor calculations to their actual experience by defining the damage states and corrosion rate confidence probabilities. Changing the coefficient of variance for thickness, , value from 0.100 to 0.200 results in a smoother curve. The user may define the three damage state definitions as well as the confidence probability values for the specific application.
- MVFORM for calculation of POF is less accurate and more conservative than other statistical methods if the variable is not normally distributed. This significantly affects reliability indices when β < 4 (POF > 3.00E−05). The primary goal of the POF calculation is to identify items at higher than generic failure rates and provide a risk ranking priority. For this reason, loss of accuracy at very low POF values is sufficiently accurate for risk prioritization and inspection planning practices.
- Calculations use specific equipment data rather than a base case. Equipment designed and operating differently than the base case data used for the Art table generates more accurate results for risk and prioritization:
- The modified approach allows the user to model the calculations for other shapes and non-circular shapes (such as header boxes, pump and compressor casings, et al). While testing indicates that calculation of DF and POF is not very sensitive to component geometry, it is recommended that the user should tailor calculations to address varying geometric shapes realistically.
- While the material of construction tensile strength, TS, and yield strength, YS, are representative of a large population of in-service equipment, the base case values may be non-conservative or overly conservative depending on the actual materials of construction used. It is recommended that the user tailor calculations for actual TS and YS to improve accuracy for DF, POF, and risk prioritization determinations.
- While the pressure, P, used in the base case is considered to be a high average condition for most applications, it may be non-conservative or overly conservative depending on the actual service. It is recommended that the user tailor calculations for actual P to improve accuracy for DF, POF, and risk prioritization determinations.
- It is important to note that the DF is not a direct indication of predicted equipment thickness and tmin, particularly if operating pressure is used for the calculation. The user should consider the impact of the basis used for in the calculation compared to the design condition basis for tmin. If DF and POF are required to provide a closer correlation to tmin (i.e., inspection is recommended and higher DF and POF are required), the user should consider using design pressure or a PRD set pressure.
- The most significant potential impact in the original base case used to generate the Art table is the assumption that the corrosion allowance, CA, is 25% of the furnished thickness. This assumption is non-conservative when the actual CA<<25% and overly conservative when the when the CA>>25%. The modified methodology generates a POF based on design and measured thickness of the equipment without the need for CA assumptions. The result is an increased applicability and accuracy with direct application of the model.
- Corrosion rate uncertainty is introduced by using three damage states based on inspection measurements, prior knowledge and inspection effectiveness using Bayes’ theorem. Uncertainty in measured equipment thickness accounted for when the probability of the damage states are combined using a normal distribution with a = 0.200. This approach has a cumulative effect on the calculated POF due to the combined uncertainty of expected damage rates in the future combined with inspection measurement inaccuracy. It is recommended that the user tailor calculations for damage state confidence values or adjust the to improve accuracy for DF, POF, and risk prioritization determinations.
- Uncertainty is applied to P measurements and flow stress, reflected by TS and YS measurements for material of construction. It is recommended that the COVP and be tailored by the user for the actual application.
- A was assigned to reflect uncertainty in thickness measurements through inspection. Uncertainty of corrosion rate in predicting the future equipment condition is assigned by using three possible damage states. It is recommended that the user tailor calculations for damage states and thinning COV to improve accuracy for DF, POF, and risk prioritization determinations.
- The original Art table included artificial constraints to DF and POF. The Art maximum was set to 0.65 and the POF for each damage state was limited to 0.5 (setting a maximum DF of 3,210). As a result, interpolation between 0.65 and 1.0 (with DF set to 5,000) was required for an Art > 0.65. Removing the POF limit of 0.5 allows calculation of a damage factor to Art = 1.0 at DF = 6,420 (modeling a possible through wall failure) without the need for interpolation. An increased DF using the modified approach is most significant when Art > 0.70 and where the DF > 2,500 (Category 5 POF). The maximum DF increase of 5,000 to 6,410 reflects a possible 28% increase in DF and POF at the highest probabilities. This increase is most significant at Art > 0.70 (Category 5 POF) when inspection is highly recommended regardless of consequence levels, unless a run to failure scenario is used.
- The Art minimum DF values were originally set to 1, preventing a POF < Gff. The modified approach allows a minimum DF of 0.1, allowing a final POF less than the Gff with very low or no in-service damage potential. The user may specify a different minimum DF or minimum POF, if desired.
The modified DF and POF methodology discussed and examples presented provides a simplified approach for DF and POF calculations specifically developed for the purpose of equipment risk prioritization and inspection planning. While more quantitative methods are available to improve accuracy, the methodology presented avoids unnecessary statistical and probabilistic complexities that add little value for the purpose of fixed equipment inspection planning.
Those wishing to obtain a copy of the technical report visit the website http://www.trinity-bridge.com/sites/default/files/publications/API-581_3rd_Thinning_Example_2.pdf. The report contains worked examples using realistic field data, expands on the material contained in this article and many calculations from API RP 581 Third Edition, April 2016 as well as comparison graphs and charts.
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