API Replacement of Table 5 11 Thinning Damage Factors with Mathematical Model

Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011Scorecard Item: 581-2011-001Title: Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical Model Date: March 17, 2011Contact: Name: Mike Conley & Lynne Kaley Company: Lloyds Register & Trinity Bridge Phone: 720-346-4990 (Mike) 713-458-0098 (Lynne) E-mail: Mike Conley: [email protected] Lynne Kaley: [email protected] Purpose: To address concerns over limitations of current methodology surrounding Table 5.11 (Art table). Source: 581 Action list Revision: 0 Impact: Replace Art table with the reliability model originally developed in the BRD project for the purpose of creating the table. Little impact on software currently using the Art Table 5.11 in RP581 2nd Edition. Changes to the Thinning Factor are discussed in this proposal. Rationale: The model described here was developed during the Base Resource Document development in order to produce the “ar/t” table in the BRD. That table was not intended to replace the model, although it has for reasons that do not need reiteration here. The model has been in use for about 18 years and is fully ready for immediate insertion into any RBI software with appropriate changes to update it to reflect the changes to the “generic” failure frequencies. The current table 5.11 is a revision of the “ar/t” table that is known to produce inaccurate results, and has no supporting documentation in API 581 2nd Edition. This proposal addresses these issues.Table of Contents 1. Summary...... 3 2. Background...... 3 3. Step by Step Summary Calculation of the Probability of Failure...... 7 4. Known Issues Related to the Proposed Reliability Model...... 10 4.1. Discontinuities under conditions of high uncertainty...... 10 4.2. Limitations of Mean Value First Order Reliability Method (MVFORM)...... 11 5. Proposed Thinning Model - Use of Bayes’ Theorem and Reliability Index Method Integrated to Determine Impact of Thinning and Inspection for Thinning on PoF...... 12 5.1. Reliability Index Method to Determine Impact of Thinning on PoF of a Cylindrical Shape...... 12 5.2. User Inputs...... 13 5.3. Outputs...... 15 6. Appendix A Excel VB Function Module Code for Thinning Factor or POF Calculation (Bayesian Updating, Miscellaneous)...... 16Mike Conley and Lynne Kaley Page 1 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 6.1. Excel VB Module Code to Calculate POF (Spherical) via MVFORM...... 19 6.2. Excel VB Module Code to Calculate POF (Cylinder) via MVFORM...... 20 6.3. Excel VB Module Code to Calculate POF (ASME Head) via MVFORM...... 21 6.4. Excel VB Module Code to Calculate POF (Cladding) via MVFORM...... 22 7. Appendix B Guidance on Use of Table 3, Prior (to Inspection) Probability of Predicted Damage Rate...... 23 7.1. Determine the Confidence Level in the Damage Rate...... 23 8. Appendix C Example of Bayes’ Theorem for Inspection...... 26 8.1. Another view of Bayes’ Theorem with URL for More...... 28 9. Appendix D References...... 29 10. Appendix E On Moving Past the Art Table 5.11, by Michael J. Conley...... 29 10.1. Introduction...... 29 10.2. Background Material...... 30 10.3. Will the Damage Factors Change, and by How Much?...... 30 10.4. “Calibration” of the Thinning Model – A Caution...... 31 10.5. Is There Any Logic Available To Justify The Values Used For Variances? 32 10.6. Review Of The “Calibration” Results And The Model Results In General. .34 10.6.1. Model Results for Thick Wall Cylinder...... 34 10.6.2. Model Results for Thin Wall Cylinder (1” Sch 40 Pipe)...... 35 10.6.3. Model Results for Average Wall Cylinder (ar/t Base Case)...... 37 10.6.4. Model Results for ASME Head...... 39 10.6.5. Model Results for Hemispherical Heads and Spheres...... 40 10.6.6. Model Results for NEW Cladding Model...... 41 10.7. On “Special” Uses of the Art Table 5.11 in RBI, e.g. CUI, & Thinning of the Base Metal in Lined or Clad Equipment...... 43 10.8. Final Note on Moving Past the Art Table 5.11...... 43Table of Tables Table 1 Representing API RP 581 2nd Edition Table 5.11 – Thinning Damage Factors...... 3 Table 2 Impact of Thinning on PoF of a Cylindrical Shape...... 12 Table 3 Prior (to Inspection) Probability of Predicted Damage Rate...... 13 Table 4: Conditional Probability of Inspection (i.e. the “Inspection Effectiveness” probabilities)...... 13Table of Figures Figure 1 Discontinuities under conditions of high uncertainty...... 9Figure 2 Comparison of reliability indices calculated using FORM FORM and MVFORM,MV...... 10 Figure E.1 Model Results for Thick Wall Cylinder...... 34 Figure E.2 Model Results for Thin Wall Cylinder (1” Sch. 40 Pipe)...... 36 Figure E.3 Model Results for Average Wall Cylinder (ar/t Base Case)...... 37 Figure E.4 POF Model Results for “Typical” Wall Cylinder (ar/t Base Case)...... 38 Figure E.5 Model Results for ASME Head...... 39 Figure E.6 Model Results for Hemispherical Heads and Spheres...... 40 Figure E.7 Model Results for NEW Cladding Model...... 42Mike Conley and Lynne Kaley Page 2 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 20111. Summary nd This submittal addresses known problems with Art Table (API RBI RP 581 2 Edition Table 5.11 Thinning Damage Factors) by replacing the table with the mathematical model that was originally used to generate the table. The table was generated as a simplified version of the original model for use as a look-up table. For most RBI approaches using API RBI as a basis for risk calculations, replacing the look-up table steps of a damage factor from the table with example code in Appendix A can be used. These changes do not necessarily require any changes to work practices for data gathering. 2. Background As defined in the original project scope of work, a Risk-based approach for prioritization of equipment for inspection was developed in the early 1990’s. No software for the calculation of risk was envisioned at the beginning of the project development. The “Art” table was generated as a simplified version of the original reliability model to provide an easy look-up table for use in equipment risk determination. Later is the project it was determined that software was desired to efficiently perform risk calculations and facilitate inspection planning. Table 1, representing Table 5.11 (API RBI RP 581 2nd Edition), is used to evaluate the probability of failure due to thinning mechanisms such as corrosion, erosion, and CUI. Art is a factor related to the fraction of wall loss. The modification was an attempt to improve the table results. This submittal will demonstrate that these types of adjustments do not address more fundamental issues with the table. As more inspections are performed and accounting for the effectiveness of the inspections (moving to the right across the table from the Art value), the thinning factor (which is directly proportional to the probability of failure) becomes smaller. Note that at an Art of exactly 0.25, the number at the far right becomes exactly 1. This far right column indicates a number and effectiveness of inspections that effectively eliminates the uncertainty in the corrosion rate, or at least makes it very small. The table was calibrated to produce this result with the idea that a damage factor of 1 would become the “action point” indicating that the minimum wall had been reached, or that due to uncertainty in the corrosion rate with fewer inspections, the minimum wall might be reached.The table was developed as a way to visualize and report the impact of inspection on the probability of failure as the vessel becoming thinner with time, as originally developed as part of the Base Resource Document (BRD). The table was developed using a structural reliability model integrated with a method based on Bayes’ Theorem for including the impact of the number and type of inspections performed on the probability of failure and risk. The model itself is described in the BRD and in API RP 581 1st Edition, in sufficient detail so that persons experienced and skilled in structural reliability could see the basis for the table. Mike Conley and Lynne Kaley Page 3 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 Table 1 Representing API RP 581 2nd Edition Table 5.11 – Thinning Damage FactorsMike Conley and Lynne Kaley Page 4 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011Table 5.11 – Thinning Damage FactorsInspection EffectivenessArt 1 Inspection 2 Inspections 3 Inspections E D C B A D C B A D C B A 0.02 1 1 1 1 1 1 1 1 1 1 1 1 1 0.04 1 1 1 1 1 1 1 1 1 1 1 1 1 0.06 1 1 1 1 1 1 1 1 1 1 1 1 1 0.08 1 1 1 1 1 1 1 1 1 1 1 1 1 0.10 2 2 1 1 1 1 1 1 1 1 1 1 1 0.12 6 5 3 2 1 4 2 1 1 3 1 1 1 0.14 20 17 10 6 1 13 6 1 1 10 3 1 1 0.16 90 70 50 20 3 50 20 4 1 40 10 1 1 0.18 250 200 130 70 7 170 70 10 1 130 35 3 1 0.20 400 300 210 110 15 290 120 20 1 260 60 5 1 0.25 520 450 290 150 20 350 170 30 2 240 80 6 1 0.30 650 550 400 200 30 400 200 40 4 320 110 9 2 0.35 750 650 550 300 80 600 300 80 10 540 150 20 5 0.40 900 800 700 400 130 700 400 120 30 600 200 50 10 0.45 1050 900 810 500 200 800 500 160 40 700 270 60 20 0.50 1200 1100 970 600 270 1000 600 200 60 900 360 80 40 0.55 1350 1200 1130 700 350 1100 750 300 100 1000 500 130 90 0.60 1500 1400 1250 850 500 1300 900 400 230 1200 620 250 210 0.65 1900 1700 1400 1000 700 1600 1105 670 530 1300 880 550 500 Inspection Effectiveness A 4 Inspections 5 Inspections 6 Inspections rt E D C B A D C B A D C B A 0.02 1 1 1 1 1 1 1 1 1 1 1 1 1 0.04 1 1 1 1 1 1 1 1 1 1 1 1 1 0.06 1 1 1 1 1 1 1 1 1 1 1 1 1 0.08 1 1 1 1 1 1 1 1 1 1 1 1 1 0.10 2 1 1 1 1 1 1 1 1 1 1 1 1 0.12 6 2 1 1 1 2 1 1 1 1 1 1 1 0.14 20 7 2 1 1 5 1 1 1 4 1 1 1 0.16 90 30 5 1 1 20 2 1 1 14 1 1 1 0.18 250 100 15 1 1 70 7 1 1 50 3 1 1 0.20 400 180 20 2 1 120 10 1 1 100 6 1 1 0.25 520 200 30 2 1 150 15 2 1 120 7 1 1 0.30 650 240 50 4 2 180 25 3 2 150 10 2 2 0.35 750 440 90 10 4 350 70 6 4 280 40 5 4 0.40 900 500 140 20 8 400 110 10 8 350 90 9 8 0.45 1050 600 200 30 15 500 160 20 15 400 130 20 15 0.50 1200 800 270 50 40 700 210 40 40 600 180 40 40 0.55 1350 900 350 100 90 800 260 90 90 700 240 90 90 0.60 1500 1000 450 220 210 900 360 210 210 800 300 210 210 0.65 1900 1200 700 530 500 1100 640 500 500 1000 600 500 500 Since Table 5.11 is a two dimensional table, a limited number of variables can be represented. It would require multiple tables to approximate what can be calculated in the model used to produce the numbers in the table. Mike Conley and Lynne Kaley Page 5 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011  All variables not in the table must have fixed values, meaning the user has no ability to enter actual values or change assumptions. By using the model, the user has complete control over all of this. By using actual data for physical dimensions, materials properties, and operating conditions, the meaningfulness of the result will obviously be greatly enhanced. More importantly for RBI, the discrimination between equipment items based on their actual data will be enhanced hugely. These currently fixed variables and assumptions are: 1. Cylindrical shape 2. Corrosion rate could be exactly two times or four times the entered rate 3. Diameter = 60 inches 4. Thickness = 0.5 inches 5. Corrosion Allowance = 0.125 inches (25% of thickness) 6. Pressure = 187.5 psig 7. Tensile Strength = 60 ksi 8. Yield Strength = 35 ksi 9. Variances on stochastic variables (pressure, strengths, thinning) 10. Categories and values of “Prior” probabilities (Table 3)* 11. Values but not categories of “Inspection Effectiveness” probabilities (Table 4)*  Unless the equipment is equal to or close to the above, the table is not technically applicable (degree of applicability is not known)  Heads, spheres, pipes, high pressure, little or no CA, large CA, etc. are not handled at all * The whole topic of Tables 3 and 4 in Section 5.2 “User Inputs” is part of Bayes’ Theorem and is worthy of a separate session of the API RP581 committee for training in the actual method, followed by peer review of the probabilities used yet unexamined since 1993. This is beyond the scope of this proposal, since no changes to the methods originally developed are considered here. It is not proposed that any of the values of Tables 3 or 4 should actually be user inputs at this time. The categories of Tables 3 and 4 can be selected by the user in this proposal. See Appendix B.The Table 5.11 was based on the equipment dimensions and properties above and applied to general plant equipment. It was considered sufficiently applicable for other equipment geometries, dimensions, and materials for the purposes of equipment inspection prioritization. Note also that the damage factors represented in the table are based on an original generic failure frequency of a pressure vessel. The POF calculated by the model could be determined simply by multiplying the damage factor by the generic failure frequency of 1.56 X 10-4. Since creation of the table, the generic frequencies have been modified based on actual plant failure frequency experience. Use of the model allows the user to enter any GFF, or not use one at all. If a GFF of 1.0 is entered, the model simply returns the calculated POF. If a GFF is entered that has been obtained from any source or data, the function returns the Thinning Factor. Individual Mike Conley and Lynne Kaley Page 6 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 applicators of the model can decide if they want to use the POF itself (by entering a GFF of 1.0), or convert it to a Thinning Factor simply by entering the GFF they choose to use.Mike Conley and Lynne Kaley Page 7 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 20113. Step by Step Summary Calculation of the Probability of Failure The following procedure may be used to determine the probability of failure for a cylinder due to thinning. a) STEP 1 – Determine the number of inspections, I N and the corresponding inspection effectiveness category for all past inspections. Combination of the inspections to an “equivalent” number in one effectiveness category is not necessary in the proposed model b) STEP 2 – Determine the time in-service, age , associated with entered corrosion rate. The thickness entered should correspond to the nominal, measured (minimum measured) or estimated total initial thickness at start of Age (for example if Rate changes significantly during the equipment lifetime, Age starts over at the time the new rate is entered.) c) STEP 3 – Determine the corrosion rate for the base metal, Cr, bm , based on the material of construction and process environment. d) STEP 4 – Determine Prior Probabilities using damage rate reliability of data in Table 3. e) STEP 5 – Determine Conditional Probabilities using Table 4 for Inspection History credit. f) STEP 6 – Determine Posterior Probabilities using the following equations:IN I N I N Posterior1= (Prior 1创 Conditional 1 ) / ( Prior 1 Conditional 1 ) + ( Prior 2 Conditional 2 )IN + (Prior3 Conditional 3 )IN I N I N Posterior2= (Prior 2创 Conditional 2 ) / ( Prior 1 Conditional 1 ) + ( Prior 2 Conditional 2 )IN + (Prior3 Conditional 3 )IN I N I N Posterior3= (Prior 3创 Conditional 3 ) / ( Prior 1 Conditional 1 ) + ( Prior 2 Conditional 2 )IN + (Prior3 Conditional 3 ) g) STEP 7 – Determine Loss Thinning States using the following equations:LossState1 = Age Rat eLossState2= Age 创Rate Factor 1LossState3= Age 创Rate Factor 2 h) STEP 8 – Determine the Flow Stress using the following equation: FlowStress=(( YieldStrength + TensileStrength ) / 2 i) STEP 9 – Determine the Standard Deviations for Pressure, Flow Stress and Thinning using the following equations:Mike Conley and Lynne Kaley Page 8 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011PressureSD = Pressure× Pressure VarianceFlowStressSD = FlowStress FlowStressVarianceThinningSD = Thinning ThinningVarianceWhere PressureVariance = 0.05 FlowStressVariance = 0.170 ThinningVariance = 0.170 j) STEP 10 (Equations shown are for cylindrical shapes only.) – Determine Derivative Values for Pressure , Flow Stress and Thinning using the following equations: dg_Pressure_by_dPressure= - Diameter / (2 Thickness) dg_ by_ dFlowStress= ( 1 - ( Thinning / Thickness) dg_ by _ dThinning= - FlowStress / Thickness k) STEP 11 (Equations shown are for cylindrical shapes only.) – Determine Standard Deviation of the Limit State Function for three damage states using the following equation:2 ((PressureSD dg_by_dPressure/1000) 2 StdDev_ g= + ( FlowStressSD dg _ by _ dFlowStress ) 2 +(ThinningSD dg _ by _ dThinning ) )) l) STEP 12 (Equations shown are for cylindrical shapes only.) – Determine the Limit State Function for three damage states using the following equation: g=( FlowStress� ((1 - Thinning ) / Thickness )) 创 ( Pressure /1000 Diameter / (2 Thickness )) m) STEP 13 – Determine Beta for three damage states using the following equation: Beta= g/ StdDev _ g n) STEP 14 – Determine the Probability of Failure of three damage states for Thinning in a Cylinder using the following equation: APICylinderThinningPOF= ApplicationNormSDist( - Beta )Mike Conley and Lynne Kaley Page 9 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 o) STEP 15 – Determine the Probability of Failure using the following equation:POF= ( POF1� Posterior 1 ) � ( POF 2 Posterior 2 ) ( POF 3 Posterior 3 ) p) STEP 16 – If desired, the Thinning Damage Factor can be determined by using the following equation (note that if GenericPOF is 1.0, the overall POF is returned):Thinning Factor= ( POF1 / GenericPOF� Posterior 1 ) ( POF 2 / GenericPOF Posterior 2 )+ (POF3 / GenericPOF Posterior 3 )Mike Conley and Lynne Kaley Page 10 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 20114. Known Issues Related to the Proposed Reliability Model4.1. Discontinuities under conditions of high uncertaintyDamage Factor (=POF/1.56X10-4) vs. Thickness (Known Limitation of Reliability M odel) 700060005000 r o t c Damage Factor - a 4000 Low Confidence F e in Rate g a m 3000 a D Damage Factor - 2000 High Confidence in Rate10000 0.00 0.10 0.20 0.30 0.40 0.50 Wall Loss (inches)Figure 1 Discontinuities under conditions of high uncertaintyFigure 1 illustrates a known issue with the BRD model, which uses three discrete “states of nature” to hypothesize the possible existence of corrosion rates higher than expected, as is known to sometimes occur, and has lead to disastrous failures. In Table 5.11, these three states are: 1) the worst corrosion rate is equal to or less than the expected or measured rate, 2) the worst corrosion rate is as much as two times greater than the expected or measured rate, and 3) the worst corrosion rate is as much as four times greater than the expected or measured rate. NOTE: These are the state definitions used for Table 5.11. If the actual model is used, then of course these can be changed by the user to better suit a particular situation. The result of using discrete states is a POF curve with “humps” in it for the case of little or no inspection. For the case of many inspections, hence little uncertainty in the corrosion rate, a smooth curve results. Since the discontinuities only occur in what is an inherently a high uncertainty situation, this is not, in practical application of the model, an issue or even noticeable. Incorporation of continuous instead of discrete states presents daunting statistical and mathematical challenges*, but a solution may be found in a future generation of RP 581. * Use of continuous states involves development of a cumulative probability distribution function for the underlying statistical distribution (e.g. normal, lognormal, weibull, etc.) that best describes the distribution of corrosion rates for each environment plus all variables that affect that rate (material, temperature, velocity, etc.), for each piece of Mike Conley and Lynne Kaley Page 11 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 equipment considered. Such an approach is arguably more accurate, if the function uses the correct mean, variance and underlying distribution in each case. This may be beyond the reach of current RBI applications.4.2. Limitations of Mean Value First Order Reliability Method (MVFORM) (Reference: Madsen, H.O., Lind, N.C. and Krenk, S., Methods of Structural Safety, Prentice-Hall, Engelwood Cliffs, N.J. (1986)) MVFORM is known to be less accurate at estimating the POF at very small values (high reliability index, β), compared to other estimating methods (e.g. FORM, SORM, etc.), especially for highly nonlinear limit state equations. This issue was raised by reliability engineers at an early stage in the BRD development, and was addressed by the following excerpt from a paper. Figure 2 compares the reliability indices calculated by MVFORM with the more accurate FORM for the thinning limit state equation, which is linear. Comparison of MVFORM vs. FORM for other, nonlinear limit state equations has not been evaluated. Three different distribution types were investigated: normal, weibull, and lognormal over a range of mean and variance values. The results show that for reliability indices less than about =4 (POF = 310-5) the results are comparable. At larger ’s (lower POF) the results diverge. Since the primary goal of the POF calculation is to identify items that fail at a higher rate than the generic, the divergence of  estimates at larger  values is not very important.8.0 Normal Lognormal 6.0 Weibull4.02.00.0 0.0 2.0 4.0 6.0 8.0FORMFigure 2 Comparison of reliability indices calculated using FORM FORM and MVFORM,MV. In Figure 2, three different cases were investigated, input is all normal variables, input is all lognormal variables and input is all weibull random variables. A fairly wide range of variances and mean values was calculated. The plot above shows that for reliability indices below 4 (POF = 310-5) there is very little difference in the estimated .Mike Conley and Lynne Kaley Page 12 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 20115. Proposed Thinning Model - Use of Bayes’ Theorem and Reliability Index Method Integrated to Determine Impact of Thinning and Inspection for Thinning on PoF5.1. Reliability Index Method to Determine Impact of Thinning on PoF of a Cylindrical Shape Table 2 Impact of Thinning on PoF of a Cylindrical Shape Variable Description Variable Description sf Flow stress = (sy + st)/2 p Pressure D Diameter t Original wall thickness Δt Thinning Expression Description t  pD Limit state function. Use of pD/2t g = s f 1 -  - 1 2  t  2t requires that D >> t. Thus it would not be applicable in the case of extremely high pressure piping (e.g. as found in HDPE processes) where the pipe resembles a thick steel bar with a small hole in the middle. dg 2  t  Derivative of limit state function = 1 -  2 with respect to flow stress. d s f  t  dg s f Derivative of limit state function 2 = - 3 dt t with respect to thinning. dg D Derivative of limit state function 2 = - 4 dp 2t with respect to internal pressure. D First order approximation to the   t   p  g =  sf 1 -  - 5 mean of the limit state function.  t  2t2 2 2 First order approximation to the 2  dg   dg   dg   g =   p +   sf  +   t 6 variance of the limit state function.  dp   ds f   dt Mike Conley and Lynne Kaley Page 13 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 g Reliability index and probability of  = P f = - (- ) 7 failure.  () is the cumulative  g probability function of a normal random variable with a mean of 0 and standard deviation of 1. This is the standard method to convert a reliability index (regardless of its source) to a nominal probability of failure and is not unique to this method.5.2. User Inputs  Prior (to Inspection) State: User selects from one of the choices below. See Appendix B for guidance. Table 3 Prior (to Inspection) Probability of Predicted Damage Rate Actual Low Confidence Moderate High Confidence Damage Rate Data Confidence Data Data Range Predicted 0.5 0.7 0.8 "rate" or less Predicted 0.3 0.2 0.15 "rate" to two times "rate" Two to four 0.2 0.1 0.05 times predicted "rate" Table 4: Conditional Probability of Inspection (i.e. the “Inspection Effectiveness” probabilities) Conditional “E” None “D” “C” “B” “A” Probability or Poorly Fairly Usually Highly of Ineffective Effective Effective Effective Effective Inspection Predicted 0.4 0.5 0.9 "rate" or less 0.33 0.7 Predicted "rate" to two 0.33 0.33 0.3 0.2 0.09 times "rate" Two to four times 0.33 0.27 0.2 0.1 0.01 predicted "rate"Mike Conley and Lynne Kaley Page 14 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011  Shape, The geometry of the equipment or component being evaluated. Currently limited to: o - Cylinder o - ASME (Head) o - Spherical (Sphere or hemispherical head) o - Clad  Thickness (inches), Nominal, measured (minimum measured) or estimated total initial thickness corresponding to start of Age (for example if Rate changes significantly during the equipment lifetime, Age starts over at the time the new rate is entered..)  Pressure (psig), Should be the MAXIMUM anticipated operating pressure. Often the PRD set pressure unless maximum anticipated pressure is not that high.  Diameter (inches), Should be outside diameter.  Age (years), Age associated with entered rate. The thickness entered should correspond to the nominal, measured (minimum measured) or estimated total initial thickness at start of Age (for example if Rate changes significantly during the equipment lifetime, Age starts over at the time the new rate is entered.)  Tensile (ksi), The specified minimum tensile strength. Defaults to 60 ksi if 0 or not entered.  Yield (ksi), The specified minimum yield strength. Defaults to 35 ksi if 0 or not entered.  Rate (inches/year), Measured, estimated, or calculated thinning rate associated with time period of Age. May differ over equipment lifetime, (for example if Rate changes significantly during the equipment lifetime.)  Priors (0 to 3), Prior (to testing) probabilities of each state, o 1 = Low Confidence in rate o 2 = Moderate Confidence in rate o 3 = High Confidence in rate o Defaults to 1 if zero or blank.  NumberInsp Highly Effective [A] (Number), Enter all four NumberInsp values (value for each effectiveness) as 1X4 array.  NumberInsp Usually Effective [B] (Number), Enter all four NumberInsp values (value for each effectiveness) as 1X4 array.  NumberInsp Fairly Effective [C] (Number), Enter all four NumberInsp values (value for each effectiveness) as 1X4 array.  NumberInsp Poorly Effective [D] (Number), Enter all four NumberInsp values (value for each effectiveness) as 1X4 array.  GenericPOF (Failure/year) Enter chosen generic failure frequency, OR Enter 1 to return calculated POF.  Factor1 Multiplier times corrosion rate for State 2. Defaults to 2 if 0 or not entered.Mike Conley and Lynne Kaley Page 15 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 o State 1 always has a multiplier of 1.0 (corrosion rate = entered rate) and need not be entered. o State 2 has postulated corrosion rate of Factor1 times entered rate. o State 3 has postulated corrosion rate of Factor2 times entered rate.  Factor2 Multiplier times corrosion rate for State 3. Defaults to 4 if 0 or not entered. o State 1 always has a multiplier of 1.0 (corrosion rate = entered rate) and need not be entered. o State 2 has postulated corrosion rate of Factor1 times entered rate. o State 3 has postulated corrosion rate of Factor2 times entered rate.5.3. Outputs  ThinningFactor or Calculated POF (Output). Entering GFF value returns Thinning Factor, Entering 1 for GFF returns calculated POF.Mike Conley and Lynne Kaley Page 16 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 20116. Appendix A Excel VB Function Module Code for Thinning Factor or POF Calculation (Bayesian Updating, Miscellaneous)Function API581ThinningFactor (Shape, Thickness, Pressure, Diameter, Age, Tensile, _ Yield, Rate, Priors, NumberInsp, GenericPOF, _ Factor1, Factor2) As Double ' 1. Written By: ' 2. Date Started: ' 3. Date Last Modified: ' 4. Description of the Function or Subroutine: The first section is the Bayesian _ updating. The prior (to testing) probabilities of three damage states is set based on the _ variable "Priors". These probabilities are updated based on the number of _ inspections in four inspection categories. Inspection Category #1 is "Highly" _ effective. Inspection Category #2 is "Usually" effective. Inspection Category _ #3 is "Fairly" effective. Inspection Category #4 is "Poorly" effective. Next _ the Probability of Failure for each of the three damage states are calculated _ by calling Function API[Shape]ThinningPOF. Then _ the updated probabilities are used with the probabilities of failure to determine _ an overall Thinning Factor or POF, which is returned. ' 5. Example and Usage: Calculation of the Thinning Technical Module Factor. _ This is used by RBI to modify the "generic" failure frequency (Quantitative RBI) _ or to set the likelihood category (Semi-Quantitative RBI). Shape = Cylinder, ' Thickness = 0.5, Pressure = 187.5, Diameter = 60, Age = 25, Corrosion Rate = 0.005, No inspections, Defaults for others; Factor = 652.5754 ' 6. Measurement Units Involved: ' Thickness: inches (starting thickness of the equipment, default is original minimum shell thickness) ' Pressure: psig (evaluation pressure, default is operating pressure) ' Diameter: inches (preferably outside diameter, although this is not important. Should correspond to the shell thickness.) ' Age: years (the time period for the evaluation, default is equipment age.) ' Tensile: ksi (tensile strength, default is 60 ksi) ' Yield: ksi (yield strength, default is 35 ksi) ' Rate: inches/year (corrosion rate) ' Priors: 1, 2, or 3 (default is 1, used to indicate the prior (to testing) probabilities, i.e. the confidence in the "source" of information.) ' NumberInsp: integer array (the number of inspections in Category 1 to 4) ' GenericPOF: events/yr (the generic probability for the equipment, default is 0.000156/yr). Entering 1.0 causes the function to return the calculated POF. ' Factor1: integer (the increase of damage state 2 over damage state 1, default is 2, i.e. the corrosion rate is 2 times the estimate) ' Factor2: integer (the increase of damage state 3 over damage state 1, default is 4, i.e. the corrosion rate is 4 times the estimate) ' 7. Version: Version 1.0 ' 8. Modification Logs:Mike Conley and Lynne Kaley Page 17 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011Dim Prior1, Prior2, Prior3 As Double ' Prior probabilities Dim Conditional1, Conditional2, Conditional3 As Double ' Conditional probabilities (Inspection Effectiveness) Dim Posterior1, Posterior2, Posterior3 As Double ' Updated probabilities after (posterior to) inspecction Dim Loss1, Loss2, Loss3 As Double ' Wall loss corresponding to three states Dim POF1, POF2, POF3 As Double ' Probability of failure due to wall loss state Dim InspCat As Integer ' Set Prior Probabilities (See Table 3 Prior (to Inspection) Probability of Predicted Damage Rate) Select Case Priors Case 1, 0 ' Defaults to lowest Prior1 = 0.5 Prior2 = 0.3 Prior3 = 0.2 Case 2 Prior1 = 0.7 Prior2 = 0.2 Prior3 = 0.1 Case 3 Prior1 = 0.8 Prior2 = 0.15 Prior3 = 0.05 End SelectFor InspCat = 1 To 4 'Perform Bayesian updating Select Case InspCat ' Set Conditional probabilities (Inspection Effectiveness) Case 1 ‘Highly Effective Conditional1 = 0.9 Conditional2 = 0.09 Conditional3 = 0.01 Case 2 ‘Usually Effective Conditional1 = 0.7 Conditional2 = 0.2 Conditional3 = 0.1 Case 3 ‘Fairly Effective Conditional1 = 0.5 Conditional2 = 0.3 Conditional3 = 0.2 Case 4 ‘Poorly Effective Conditional1 = 0.4 Conditional2 = 0.33 Conditional3 = 0.27 End Select ' Calculate Posterior ProbabilitiesMike Conley and Lynne Kaley Page 18 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 Posterior1 = Prior1 * Conditional1 ^ NumberInsp(InspCat) / (Prior1 * Conditional1 ^ NumberInsp(InspCat) + Prior2 * Conditional2 ^ NumberInsp(InspCat) + Prior3 * Conditional3 ^ NumberInsp(InspCat)) Posterior2 = Prior2 * Conditional2 ^ NumberInsp(InspCat) / (Prior1 * Conditional1 ^ NumberInsp(InspCat) + Prior2 * Conditional2 ^ NumberInsp(InspCat) + Prior3 * Conditional3 ^ NumberInsp(InspCat)) Posterior3 = Prior3 * Conditional3 ^ NumberInsp(InspCat) / (Prior1 * Conditional1 ^ NumberInsp(InspCat) + Prior2 * Conditional2 ^ NumberInsp(InspCat) + Prior3 * Conditional3 ^ NumberInsp(InspCat)) Prior1 = Posterior1 Prior2 = Posterior2 Prior3 = Posterior3 Next InspCat' Calculate three thinning states If Factor1 = 0 Then Factor1 = 2 'default value If Factor2 = 0 Then Factor2 = 4 'default value Loss1 = Age * Rate 'State1 Loss2 = Age * Rate * Factor1 'State2 Loss3 = Age * Rate * Factor2 'State3 ' Calculate probability of failure If Shape = "Spherical" Then POF1 = APISphericalThinningPOF (Thinning:=Loss1, Thickness:=Thickness, Pressure:=Pressure, Diameter:=Diameter, Tensile:=Tensile, Yield:=Yield) POF2 = APISphericalThinningPOF (Thinning:=Loss2, Thickness:=Thickness, Pressure:=Pressure, Diameter:=Diameter, Tensile:=Tensile, Yield:=Yield) POF3 = APISphericalThinningPOF (Thinning:=Loss3, Thickness:=Thickness, Pressure:=Pressure, Diameter:=Diameter, Tensile:=Tensile, Yield:=Yield) End If If Shape = "Cylinder" Then POF1 = APICylinderThinningPOF (Thinning:=Loss1, Thickness:=Thickness, Pressure:=Pressure, Diameter:=Diameter, Tensile:=Tensile, Yield:=Yield) POF2 = APICylinderThinningPOF (Thinning:=Loss2, Thickness:=Thickness, Pressure:=Pressure, Diameter:=Diameter, Tensile:=Tensile, Yield:=Yield) POF3 = APICylinderThinningPOF (Thinning:=Loss3, Thickness:=Thickness, Pressure:=Pressure, Diameter:=Diameter, Tensile:=Tensile, Yield:=Yield) End If If Shape = "ASME" Then POF1 = APIASMEThinningPOF (Thinning:=Loss1, Thickness:=Thickness, Pressure:=Pressure, Diameter:=Diameter, Tensile:=Tensile, Yield:=Yield) POF2 = APIASMEThinningPOF (Thinning:=Loss2, Thickness:=Thickness, Pressure:=Pressure, Diameter:=Diameter, Tensile:=Tensile, Yield:=Yield) POF3 = APIASMEThinningPOF (Thinning:=Loss3, Thickness:=Thickness, Pressure:=Pressure, Diameter:=Diameter, Tensile:=Tensile, Yield:=Yield) End If If Shape = "Clad" ThenMike Conley and Lynne Kaley Page 19 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 POF1 = APICladThinningPOF (Thinning:=Loss1, Thickness:=Thickness) POF2 = APICladThinningPOF (Thinning:=Loss2, Thickness:=Thickness) POF3 = APICladThinningPOF (Thinning:=Loss3, Thickness:=Thickness) End If ' Calculate damage factor If GenericPOF = 0 Then GenericPOF = 0.0000306 'default to RP 581 2nd Edition API581ThinningFactor = ((POF1 / GenericPOF) * Posterior1) + ((POF2 / GenericPOF) * Posterior2) + ((POF3 / GenericPOF) * Posterior3) End Function6.1. Excel VB Module Code to Calculate POF (Spherical) via MVFORMFunction APISphericalThinningPOF (Thinning, Thickness, Pressure, Diameter, Tensile, Yield) As Double ' 1. Written By: ' 2. Date Started: ' 3. Date Last Modified: ' 4. Description of the Function or Subroutine: This function works with the API581ThinningFactor function. This function ' calculates the probability of failure due to thinning in spheres and hemispherical heads by evaluation of a limit state equation via mean value FORM. ' 5. Example and Usage: ' 6. Measurement Units Involved: ' Thinning: inches (the amount of thinning to be evaluated) ' Thickness: inches (starting thickness of the equipment, default is original minimum shell thickness) ' Pressure: psig (evaluation pressure, default is operating pressure) ' Diameter: inches (preferably outside diameter, although this is not important. Should correspond to the shell thickness.) ' Tensile: ksi (tensile strength, default is 60 ksi) ' Yield: ksi (yield strength, default is 35 ksi) ' 7. Version: Version 1.0 ' 8. Modification Logs: 'Dim PressureVar, FlowStressVar, ThinningVar As Double ' % Variation used to calc Std. Dev. Dim PressureSD, FlowStressSD, ThinningSD As Double ' Std. Deviations Dim dg_dPressure, dg_dFlowStress, dg_dThinning As Double ' Derivatives of limit state g Dim FlowStress, StdDev_g, g, Beta As Double ' Intermediate values ' Initial calcs PressureVar = 0.050 FlowStressVar = 0.170 ThinningVar = 0.170Mike Conley and Lynne Kaley Page 20 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 If Yield = 0 Then Yield = 35# 'default If Tensile = 0 Then Tensile = 60# 'default FlowStress = ((Yield + Tensile) / 2) ' Standard Deviations PressureSD = Pressure * PressureVar FlowStressSD = FlowStress * FlowStressVar ThinningSD = Thinning * ThinningVar ' Derivative values dg_dPressure = -Diameter / (4 * Thickness) dg_dFlowStress = (1 - (Thinning / Thickness)) dg_dThinning = -FlowStress / Thickness ' Calculations StdDev_g = ((PressureSD * dg_dPressure / 1000) ^ 2 + (FlowStressSD * dg_dFlowStress) ^ 2 + (ThinningSD * dg_dThinning) ^ 2)^0.5 g = (FlowStress * (1 - Thinning / Thickness)) - (Pressure / 1000 * Diameter / (4 * Thickness)) Beta = g / StdDev_g APISphericalThinningPOF = Application.NormSDist(-Beta)End Function6.2. Excel VB Module Code to Calculate POF (Cylinder) via MVFORMFunction APICylinderThinningPOF(Thinning, Thickness, Pressure, Diameter, Tensile, Yield) As Double ' 1. Written By: ' 2. Date Started: ' 3. Date Last Modified: ' 4. Description of the Function or Subroutine: This function works with the API581ThinningFactor function. This function ' calculates the probability of failure due to thinning in cylinders by evaluation of a limit state equation via mean value FORM. ' 5. Example and Usage: ' 6. Measurement Units Involved: ' Thinning: inches (the amount of thinning to be evaluated) ' Thickness: inches (starting thickness of the equipment, default is original minimum shell thickness) ' Pressure: psig (evaluation pressure, default is operating pressure) ' Diameter: inches (preferably outside diameter, although this is not important. Should correspond to the shell thickness.) ' Tensile: ksi (tensile strength, default is 60 ksi) ' Yield: ksi (yield strength, default is 35 ksi) ' 7. Version: Version 1.0 ' 8. Modification Logs: 'Mike Conley and Lynne Kaley Page 21 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 Dim PressureVar, FlowStressVar, ThinningVar As Double ' % Variation used to calc Std. Dev. Dim PressureSD, FlowStressSD, ThinningSD As Double ' Std. Deviations Dim dg_dPressure, dg_dFlowStress, dg_dThinning As Double ' Derivatives of limit state g Dim FlowStress, StdDev_g, g, Beta As Double ' Intermediate values ' Initial calcs PressureVar = 0.050 FlowStressVar = 0.170 ThinningVar = 0.170 If Yield = 0 Then Yield = 35# 'default If Tensile = 0 Then Tensile = 60# 'default FlowStress = ((Yield + Tensile) / 2) ' Standard Deviations PressureSD = Pressure * PressureVar FlowStressSD = FlowStress * FlowStressVar ThinningSD = Thinning * ThinningVar ' Derivative values dg_dPressure = -Diameter / (2 * Thickness) dg_dFlowStress = (1 - (Thinning / Thickness)) dg_dThinning = -FlowStress / Thickness ' Calculations StdDev_g = ((PressureSD * dg_dPressure / 1000) ^ 2 + (FlowStressSD * dg_dFlowStress) ^ 2 + (ThinningSD * dg_dThinning) ^ 2)^0.5 g = (FlowStress * (1 - Thinning / Thickness)) - (Pressure / 1000 * Diameter / (2 * Thickness)) Beta = g / StdDev_g APICylinderThinningPOF = Application.NormSDist(-Beta)End Function6.3. Excel VB Module Code to Calculate POF (ASME Head) via MVFORMFunction APIASMEThinningPOF (Thinning, Thickness, Pressure, Diameter, Tensile, Yield) As Double ' 1. Written By: ' 2. Date Started: ' 3. Date Last Modified: ' 4. Description of the Function or Subroutine: This function works with the API581ThinningFactor function. This function ' calculates the probability of failure due to thinning in ASME heads by evaluation of a limit state equation via mean value FORM. ' 5. Example and Usage: ' 6. Measurement Units Involved: ' Thinning: inches (the amount of thinning to be evaluated)Mike Conley and Lynne Kaley Page 22 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 ' Thickness: inches (starting thickness of the equipment, default is original minimum shell thickness) ' Pressure: psig (evaluation pressure, default is operating pressure) ' Diameter: inches (preferably outside diameter, although this is not important. Should correspond to the shell thickness.) ' Tensile: ksi (tensile strength, default is 60 ksi) ' Yield: ksi (yield strength, default is 35 ksi) ' 7. Version: Version 1.0 ' 8. Modification Logs: 'Dim PressureVar, FlowStressVar, ThinningVar As Double ' % Variation used to calc Std. Dev. Dim PressureSD, FlowStressSD, ThinningSD As Double ' Std. Deviations Dim dg_dPressure, dg_dFlowStress, dg_dThinning As Double ' Derivatives of limit state g Dim FlowStress, StdDev_g, g, Beta As Double ' Intermediate values ' Initial calcs PressureVar = 0.050 FlowStressVar = 0.170 ThinningVar = 0.170 If Yield = 0 Then Yield = 35# 'default If Tensile = 0 Then Tensile = 60# 'default FlowStress = ((Yield + Tensile) / 2) ' Standard Deviations PressureSD = Pressure * PressureVar FlowStressSD = FlowStress * FlowStressVar ThinningSD = Thinning * ThinningVar ' Derivative values dg_dPressure = -Diameter / (1.13 * Thickness) dg_dFlowStress = (1 - (Thinning / Thickness)) dg_dThinning = -FlowStress / Thickness ' Calculations StdDev_g = ((PressureSD * dg_dPressure / 1000) ^ 2 + (FlowStressSD * dg_dFlowStress) ^ 2 + (ThinningSD * dg_dThinning) ^ 2)^0.5 g = (FlowStress * (1 - Thinning / Thickness)) - (Pressure / 1000 * Diameter / (1.13 * Thickness)) Beta = g / StdDev_g APIASMEThinningPOF = Application.NormSDist(-Beta)End Function6.4. Excel VB Module Code to Calculate POF (Cladding) via MVFORMFunction APICladThinningPOF (Thinning, Thickness) As DoubleMike Conley and Lynne Kaley Page 23 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 ' 1. Written By: ' 2. Date Started: ' 3. Date Last Modified: ' 4. Description of the Function or Subroutine: This function works with the API581ThinningFactor function. This function ' calculates the probability of failure due to thinning of a cladding material (not the shell) by evaluation of a limit state equation via mean value FORM. ' 5. Example and Usage: ' 6. Measurement Units Involved: ' Thinning: inches (the amount of thinning to be evaluated) ' Thickness: inches (starting thickness of the cladding) ' 7. Version: Version 1.0 ' 8. Modification Logs: ' ' Dim ThinningVar As Double ' % Variation used to calc Std. Dev. Dim ThinningSD As Double ' Std. Deviations Dim dg_dThinning As Double ' Derivatives of limit state g Dim StdDev_g, g, Beta As Double ' Intermediate values ' Initial calcs ThinningVar = 0.17 ' Standard Deviations ThinningSD = Thinning * ThinningVar ' Derivative values dg_dThinning = -1 ' Calculations StdDev_g = ((ThinningSD * dg_dThinning) ^ 2) ^ 0.5 g = Thickness - Thinning Beta = g / StdDev_g APICladThinningPOF = Application.NormSDist(-Beta)End Function7. Appendix B Guidance on Use of Table 3, Prior (to Inspection) Probability of Predicted Damage Rate (Reference: “API Committee on Refinery Equipment BRD on Risk Based Inspection” February 1999 Revision 04 Page 8.24)7.1. Determine the Confidence Level in the Damage Rate The damage rate in process equipment is often not known with certainty. The ability to state the rate of damage precisely is limited by equipment complexity, process and metallurgical variations, inaccessibility for inspection, and limitations of inspection and test methods.The uncertainty in the expected damage rate can be determined from historical data on the frequency with which various damage rates occur. A realistic understanding of the uncertainty in expected damage rates will include consideration of case histories from aMike Conley and Lynne Kaley Page 24 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 variety of similar processes and equipment. The best information will come from operating experiences where the conditions that led to the observed damage rate could realistically be expected to occur in the equipment under consideration. Other sources of information could include databases of plant experience or reliance on expert opinion. The latter method is used most often, since plant databases, where they exist, usually do not contain sufficiently detailed information.Example: Economical equipment design often requires internal corrosion rates of less than five mils per year. However, higher rates are sometimes observed. It is not very unusual to observe corrosion rates twice what was expected or previously observed. Usually these higher rates are detected during inspections, but sometimes the occurrence of higher-than-expected corrosion rates is not detected until failure of the pressure boundary of the process occurs.Observed less frequently are corrosion rates as much as four times the expected rate. Rarely are corrosion rates for uniform corrosion more than four times the rate expected. (Although corrosion rates as much as tem times the expected rate have been observed and have lead to serious equipment failure.) The default values provided here are expected to apply to many plant processes. Notice that the uncertainty in the corrosion rate varies, depending on the source and quality of the corrosion rate data.For general internal corrosion, the reliability of the information sources used to establish a corrosion rate can be put into the following three categories:A. Low Confidence Information Sources for Corrosion Rates  Published data  Corrosion rate tables  "Default" values Although they are often used for design decisions, the actual corrosion rate that will be observed in a given process situation may significantly differ from the design value.B. Moderate Confidence Information Sources for Corrosion Rates  Laboratory testing with simulated process conditions  Limited in-situ corrosion coupon testingCorrosion rate data developed from sources that simulate the actual process conditions usually provide a higher level of confidence in the predicted corrosion rate.C. High Confidence Information Sources for Corrosion Rates  Extensive field data from thorough inspections  Coupon data, reflecting five or more years of experience with the process equipment (assuming no change in process conditions has occurred)Mike Conley and Lynne Kaley Page 25 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 If enough data are available from actual process experience, there is little likelihood that the actual corrosion rate will greatly exceed the expected value under normal operating conditions.Table B.2 (See Section 4.2) expresses the degree of confidence that the true damage rate falls into the listed damage rate ranges, based on the confidence of the damage rate data. Table B.2 Confidence in Predicted Damage RateActual Low Confidence Moderate High Confidence Damage Rate Data Confidence Data Data Range Predicted 0.5 0.7 0.8 "rate" or less Predicted 0.3 0.2 0.15 "rate" to two times "rate" Two to four 0.2 0.1 0.05 times predicted "rate"Mike Conley and Lynne Kaley Page 26 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 20118. Appendix C Example of Bayes’ Theorem for Inspection (Reference: Benjamin, J.R. and Cornell, A, Probability, Statistics and Decision for Civil Engineers, McGraw-Hill, New York (1970))Use of an accepted and systematic approach to determining the impact of inspection on POF is extremely valuable in making rational, justifiable decisions in the face of uncertainty and to lend credibility to the entire RBI process. A widely recognized method for just such problems is called Bayes' Rule or Bayes' Theorem. This rule is used in many civil engineering problems where uncertainty is inherent in the data that must be used. The rule is especially applicable to cases where an inspector or engineer has an existing understanding of the likely states of a structure or a material, and wants to perform a test to help confirm his expectations. In the deterministic approach, the test results are considered to be perfect, that is, the results confirm with 100% accuracy the state of the material. While this may be the case with certain very accurate tests performed under controlled conditions, in most "real" cases, the test can only indicate a tendency towards one state or another. Obviously, limited tests and inspections performed in the field on large structures would fall into the uncertain results category. A simple example of the application of the Bayesian method is:An engineer is assigned to survey an existing reinforced concrete building to determine its adequacy for future use. He has studied the construction records and examined the appearance of the concrete. Based on experience and previous studies, he decides that the concrete quality can be classified as 2000, 3000, or 4000 psi. Also, he decides that the concrete is most likely 3000 psi class, it may be 2000 psi class but he suspects that it is stronger than that, and he doubts that it is 4000 psi class although it is possible. He assigns the following relative likelihoods (the prior probabilities) to these states:Class Expected (experience based) likelihood of being in class 2000 psi class 0.3 3000 psi class 0.6 4000 psi class 0.1 1.0 (total)Concrete quality classification is determined by the "28-day cylinder" strength test. The engineer decides to cut some concrete cores and test them to help determine the true state. He knows that the test is reasonably reliable, but not conclusive. For one thing, cores from fully cured concrete will be stronger than a 28-day cylinder, so the results tend to overestimate the class. (From the rules for concrete design, the class is based only on the 28-day strength, not the final strength.) A result of 3500 tends to indicate the 3000 psi class, but sometimes higher and lower classes will give the Mike Conley and Lynne Kaley Page 27 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 same result. Previous studies of the test method (performed on concrete of known strength) have established some test reliability data (the inspection effectiveness probabilities):Core sample test results 28-day cylinder class 2000 psi 3000 psi 4000 psi 2500 (favors 2000 psi 0.7 0.2 0.0 class) 3500 (favors 3000 psi 0.3 0.6 0.3 class) 4500 (favors 4000 psi 0.0 0.2 0.7 class) 1.0 1.0 1.0In the controlled experiments on the test technique, with concrete of true 3000 psi class, the test only indicated this class 60% of the time. The 40% margin for error was equally divided between the higher and the lower classes. Finally, the test is performed on a core sample, and the result was 2500 psi, tending to favor a true class of 2000 psi. How does the engineer now update his expectation of the building's concrete strength class? Bayes' Rule states:The probability that the true state is known, given the results of a test equals: {(the probability or expectation that the test result would occur, if the true state is known) times (the prior probability of the state)) divided by (the sum over all states of (the probability or expectation that the test result would occur, if the true state is known) times (the prior probability of the state))}. In mathematical terms:P[A| B j ]xP[ B j ] P[ B j | A] = i P[A| Bi ]xP[ Bi ]In light of the test's limitations, the engineer decides to take another test. The second test result is 3500 psi (favors true class of 3000 psi). The results are summarized below (the posterior or conditional (on the test result) probabilities): True class Likelihood of Likelihood of Likelihood of class (no tests) class (1 test, class (2 tests, results = result = 2500 2500 & 3500 psi) psi) 2000 psi 0.3 0.6 0.47 3000 psi 0.6 0.4 0.53 4000 psi 0.1 0.0 0.0 1.0 1.0 1.0It doesn't matter which result comes first. The method extends to any number of Mike Conley and Lynne Kaley Page 28 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 tests, and can include new information, for example, the engineer finds lab test results from test cylinders cast at the time of construction.This example is very similar to many of the practical problems faced by engineers assessing the safety of process vessels via RBI. 8.1. Another view of Bayes’ Theorem with URL for More (Reference http://en.wikipedia.org/wiki/Bayes'_theorem)From above URL, “In the Bayesian interpretation, probabilities are rationally coherent degrees of belief, or a degree of belief in a proposition given a body of well-specified information.[5] Bayes' theorem can then be understood as specifying how an ideally rational person responds to evidence.”[6] Put in another way, relevant to RBI, the Theorem can be expressed as: If you are uncertain about the physical state, (e.g. the thickness, the presence of cracks or other damage) of, e.g. a pressure vessel, you may perform one or more tests to learn more. However, the results of such tests may be in themselves uncertain (e.g. damage is not detected). Given an uncertain state before the test (the prior probability of the state) what can be logically concluded after an uncertain test result is obtained (the posterior probability of the state)? Bayes’ Theorem provides a scientifically and mathematically accepted method of answering such a question. The uncertainty involved in the test results is called in RBI the inspection effectiveness.Mike Conley and Lynne Kaley Page 29 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 20119. Appendix D References 1. Benjamin, J.R. and Cornell, A, Probability, Statistics and Decision for Civil Engineers, McGraw-Hill, New York (1970) 2. Madsen, H.O., Lind, N.C. and Krenk, S., Methods of Structural Safety, Prentice- Hall, Engelwood Cliffs, N.J. (1986) 3. “ API Committee on Refinery Equipment BRD on Risk Based Inspection” February 1999 Revision 04 4. API Recommended Practice 581, Second Edition, September 2008 5. Jaynes, Edwin T. (2003). Probability theory: the logic of science. Cambridge University Press. ISBN 9780521592710. 6. Howson, Colin; Peter Urbach (1993). Scientific Reasoning: The Bayesian Approach. Open Court. ISBN 9780812692341. 10. Appendix E On Moving Past the Art Table 5.11, by Michael J. Conley10.1. Introduction This is the only part of this proposal that bears the author’s name. The sole reason for this is that this Appendix necessitates that the inclusion of material that the author is solely responsible for, and some material that can only be considered to be the author’s opinions or requirements imposed by the attempt to minimize the impact of a change in methods. The validity of such opinions is left open for peer review. One such opinion is that the model presented herein is rendered necessary by competing and sometimes conflicting requirements of RBI: 1. It must provide an approach to predict the future condition of large numbers of equipment (100’s or 1,000’s) for the purpose of recommending inspection based on varying amounts of historical data available. 2. It must be simple enough to comprehend, in application, if not entirely with respect to some of the mathematical methods employed. 3. It must also be simple enough in data requirements, computational time, and needed support to be economical to use, whether it is by industry using one or more of the methods described in API RP 581 internally, or a service provider of software and technical assistance in implementation. 4. To strive, to the attempt possible, to make the methods both technically defensible to regulators and peers, and accurate to the degree to which probability of failure can ever be considered “accurate.” Acknowledgements: The following are gratefully acknowledged:  Lynne Kaley, Trinity Bridge, who wrote and clarified much of this proposal. Without her, this proposal might not have ever been submitted.  Dr. Andrew Tallin, who was the author’s mentor in all matters relating to Bayes’ Theorem and Structural Reliability methods. The author claims no great degree of knowledge with regards to either subject.  The original sponsors of the Base Resource Document (BRD) and the continued efforts by RP 581 committee members on behalf of the Mike Conley and Lynne Kaley Page 30 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 technology and application of Risk Based Inspection, still in its infancy in the author’s opinion compared to the holistic management tool it could become.  The people who revised, reorganized and basically rewrote the BRD in RP 581, 2nd Edition. As a significant contributor to the writing of the original BRD, this author knows that the resulting document basically wrote itself as new concepts were developed and modified, and as new insights came. The resulting document thus had the feel of what it was – “written by committee”, and desperately need the overhaul. Finally, this proposal has been made with sincere effort to promote only the continued improvement of RBI Technology in such a way that no individual or company can receive any competitive advantage based on the contents of this proposal in and of itself. Of course, RBI as a whole offers many opportunities for advantage for any industry or company applying or providing it, but only to the extent that the technology is applied cleverly and efficiently by experienced and well trained people. API RP 580, Risk Based Inspection provides necessary and ample guidance in the requirements for successful application of any RBI system.10.2. Background Material The model presented herein was originally developed by the necessity of producing the original “ar/t” table in the BRD. It has changed insignificantly over the ensuing period, except for some changes introduced in the writing of this proposal. The biggest change is the introduction of new “Generic Failure Frequencies” (GFF) in RP 581, 2nd Edition. The original model was “calibrated” to produce a Thinning Factor of approximately 1.0 when the approximately calculated corrosion allowance (CA) has been consumed. This was done by adjusting the variances on stochastic variables (pressure, flow strength, and thinning) to yield a calculated POF of roughly 1.56 X 10-4 at this amount of wall loss. In an effort to maintain this grounding in the proposed model, it was recalibrated to produce approximately the same results using the newer GFF of 3.06 X 10-5. This will assure that the Thinning Factor (TF) will remain in the same general range, in the case of well inspected equipment that is maintained within the usual Code limits with respect to thinning. The TF may vary considerably for cases of high uncertainty, but this variation will be in proportion to the damage that might be present weighted by the actual shape, dimensions, materials properties, operating conditions, etc. for each case. But that is the whole point of RBI.10.3. Will the Damage Factors Change, and by How Much? This question is surely on the minds of anyone who has already developed inspection plans based on the old methods (See also Section 10.6). The answer cannot be given for all possible combinations of “real” data that can be used in place of the “assumed” data behind the Art Table 5.11. This “assumed” data is presented in Section 2 and repeated here: 1. Cylindrical shape 2. Corrosion rate could be exactly two times or four times the entered rate 3. Diameter = 60 inches 4. Thickness = 0.5 inchesMike Conley and Lynne Kaley Page 31 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 5. Corrosion Allowance = 0.125 inches (25% of thickness) 6. Pressure = 187.5 psig 7. Tensile Strength = 60 ksi 8. Yield Strength = 35 ksi 9. Variances on stochastic variables (pressure, flow strength, and thinning) All of these variables can be entered using actual data for the equipment being evaluated. The Excel Visual Basic Code offered in Appendix A (Section 6) of this proposal provides for defaults for data numbers 2,7,8, and 9 (more on #9 later). The individual applicator of this model can accept the defaults, or provide for user entry of these. Thus it is not absolutely necessary for any software user interface to change, but it may be desirable to do so, especially for data numbers 2,7 and 8. The advantages of using actual data vs. the above it is hoped is readily apparent in increasing the meaningfulness of the results, the discrimination between equipment items that vary largely from the assumed values, and in the overall credibility and defensibility of the Thinning Factor technique.As mentioned, the expected POF or TF cannot be given for all possible combinations of “real” data that can be used. However, the maximum possible POF and TF are known. The maximum Thinning Factor (TF) obtainable by the proposed model can be readily determined by the equation: POFcalculated ThinningFactor = GFF Since the maximum POF is 1.0 by definition, the maximum TF using the old GFF of 1.56 X 10-4 is:1 ThinningFactor = @ 6,410 1.56E -04The maximum TF using the new GFF of is:1 ThinningFactor = @ 32,680 3.06E -05The two differ by the ratio of old to new GFFs, or almost exactly 5.1 (the new GFF is 5.1 times less frequent than the old GFF.) 10.4. “Calibration” of the Thinning Model – A Caution As explained in Section 10.2 above, an attempt has been made to “calibrate” the model to roughly yield a DF of 1.0 (calculated POF of 3.06 X 10-5). This result cannot be reproduced exactly using the same values in the POF calculations for all shapes and corrosion allowances expressed as a percentage of wall. It would make little sense to try to separately modify the POF calculation for a head, since it likely has similar variances as the cylindrical shell to which it is attached.At the last API RP581 committee meeting in Nashville, November 2010, this author gave a presentation on the background of the original “ar/t” table, which pointed out some Mike Conley and Lynne Kaley Page 32 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 problems of perception that resulted from the attempt at calibration based on Tmin. These points are raised again here, so that the mistakes of the past are not repeated. Especially important is point #5, which states that the Thinning Factor or calculated POF cannot be used to determine if the equipment under study actually meets the requirements of the deterministic design Code. This must be done separately, by whatever means have been used in the past for this purpose, or sometimes as a calculation included in RBI software. In the future, process equipment design Codes may move to a reliability basis, which could result in a unification of RBI with those Codes. The calibration effort: 1. Assured that calculated POF was at least in the same range as observed failure frequencies. 2. BUT, has in some cases given the misperception that POF is somehow related to Code required Tmin. 3. It must be recognized that the limit state is based on the physical description of failure (laws of physics), while Tmin is in a sense, a political decision (laws of man, changeable by man). 4. POF vs. thickness curve is smooth and continuous as the Tmin is passed (Tmin does not impact POF) 5. Therefore, Tmin calculations (deterministic) must be made separately from the determination of POF (probabilistic)10.5. Is There Any Logic Available To Justify The Values Used For Variances? There are basically two choices available: 1. Try to determine the “true” variances of pressure, flow strength, and thinning for each and every set of process variables, material specifications, and thinning mechanism(s) evaluated. This is a dubious undertaking (in this author’s opinion) if for no other reason than it violates the simplicity and economical RBI requirements #3 in Section 10.1 above. Also, the calculated POF is quite sensitive to the variances used, and if “true” variances are used for each case, there likely will be little apparent harmony in the Thinning Factors or POFs calculated from case to case, with few or no ways to practically resolve what the differences mean. 2. Apply variances that can be justified within the limits of the model as originally conceived, some of these limits being the same regardless of whether the model or the “ar/t” table is used. These limits are implied for each variance by looking at the input requirements of Section 5.2 in this proposal (See):  Input Pressure (psig): Should be the MAXIMUM. Often the PRD set pressure unless maximum anticipated pressure is not that high.  Implied Pressure Variance: The maximum anticipated operating pressure is used because if the higher rates of thinning are present to any extent, they will be there all the time as the pressure may vary. Thus the variance in maximum pressure is low compared to the (sometimes) highly variable actual operating pressure.  (Thinning) equals Age times Thinning Rate:  Input Age (years), Age associated with the entered rate. The thickness entered should correspond to the nominal, measured (minimum measured)Mike Conley and Lynne Kaley Page 33 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 or estimated total initial thickness at start of Age (for example if Rate changes significantly during the equipment lifetime, Age starts over at the time the new rate is entered.)  Input Thinning Rate (inches/year), Measured, estimated, or calculated thinning rate associated with time period of Age. May differ over equipment lifetime, (for example if Rate changes significantly during the equipment lifetime.)  Background to Thinning Variance: The Thinning model is based on using Bayes’ Theorem to handle Thinning Rates that are sometimes observed to be much higher in localized areas that may not be found with little or no inspection. The default ranges for the Thinning Rates are 2 to 4 times the expected or measured rate. Many case histories indicate localized rates as much as 8 to 10 times the measured rate. Thus the Thinning Variance considered by the model as a whole may be as much as 400% to 1000% (conceivably much more in rare cases.) One of the first obvious ways to handle this was to use high values of variance, and “reduce it by some amount as more inspections are performed”. This quickly ran into two problems: the POF methods used break down if the standard deviation exceeds the mean, as shown in Section 4, Step 9: Thinning= Thinning ThinningVariance SD Secondly, there seems to no way to logically decide what is meant by “reduce it [the variance] by some amount as more inspections are performed”. Bayes’ Theorem is designed to handle just this type of problems in a way that has been called “ideally rational”. Just how Bayes’ Theorem does this, by what is called in RBI the “Inspection Effectiveness” (actually a table of probabilities) is beyond the scope of this proposal, since no changes to the methods originally developed are considered here. The whole topic is worthy of a separate session of the API RP581 committee for training in the actual method, followed by peer review of the probabilities used yet unexamined since 1993. Effect of Thinning Variance: The thinning variance used in the original model, and modified somewhat in the “calibration” procedure to produce this proposal, is the “residual variance” in the corrosion rate after inspections have all but eliminated the possibility of higher thinning rates, and the rate used at this point is the user entered measured rate (or calculated, or estimated by other means in practice). In other words, thinning mechanisms result in inherently uneven surfaces and no matter how much inspection is performed, this unevenness cannot be fully quantified. This is of enormous practical importance in the case of relatively thin walled pipe, where the corrosion allowance may be a small percentage of the total wall thickness (indeed vanishingly so if Mike Conley and Lynne Kaley Page 34 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 only hoop stresses are considered. Thus, the Thinning Variance creates a “built in” protection that will not allow pipes to reach a dangerously thin level without the model generating an increasingly larger Thinning Factor or POF. This is why the “ar/t” table does not work well for small CA percentages of wall, and cannot do so. The table also does not handle large percentages of wall very well either, but as will be seen, the model does a reasonable job of both.  Input Flow Strength, actually input yield and tensile strengths, the average of which is the flow strength. This strength is often considered in structural engineering to be the point at which ductile yielding becomes so severe that the structure cannot be relied upon to perform its intended duties.  Implied Flow Strength Variance: Admittedly, there is little in the way of a logical assignment of this value, except that in the face of good reasons for setting the other two variances, this one is simply set to “what it has to be” in order to achieve the desired control over the model outputs. If there are suggested values that are in some way “typical” or “average” for broad classes of materials, other values can be used, although perhaps at a cost of “recalibrating” or doing away with calibration altogether.10.6. Review Of The “Calibration” Results And The Model Results In General (NOTE: This Section 10.6 can be considered to be optional reading. This Section is to complete the documentation regarding the outcomes of certain technical changes to the original model for “calibration” purposes. Skip to Section 10.7 unless this information is pertinent to your needs.)10.6.1. Model Results for Thick Wall CylinderBasis: Physical Data:YS, TS, T min, approximate, Thickness, Maximum Operating Diameter, OD, Geometric Shape ksi ksi inches inches Pressure, psig inchesCylinder 35 60 3.800 4.0 1900 60CA as % CA of Wall0.200 5%Basis: Technical InputsThinning Variance0.170Pressure VarianceMike Conley and Lynne Kaley Page 35 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 20110.050Flow Stress Variance0.170GFF3.06E-05Calibration Results Chart Figure E.1 shows that for a thick wall cylinder with the above inputs, the calibration came out very well. At exactly 5% wall loss (equal to the CA % of wall), the Thinning Factor is 1.03 with 10 Highly Effective Inspections. Figure E.1 Model Results for Thick Wall CylinderCylinder % Wall Loss vs. TF Thick Wall Vessel 60" / Wall 4" CA = 5.0%)10.00 5 - 0 1 X 6 0 . 3 = F F G- s i s a 1.00 B( 5.0%; 1.03 r o t c a F g n i n n i h T0.10 0.0% 5.0% 10.0% % Wall Loss10.6.2. Model Results for Thin Wall Cylinder (1” Sch 40 Pipe)Basis: Physical Data:Maximum T min, Geometric Thickness, Operating Diameter, YS, ksi TS, ksi approximate, Shape inches Pressure, OD, inches inches psigMike Conley and Lynne Kaley Page 36 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 Cylinder 35 60 0.005 0.133 120 1.315CA CA as % of Wall (Hoop Stress Basis)0.128 96.0%Basis: Technical InputsThinning Variance0.170Pressure Variance0.050Flow Stress Variance0.170GFF3.06E-05Calibration Results Chart As can be seen above, the CA as % of wall for this pipe is 96%. It is unreasonable to expect any thinning mechanism to remove 96% of the wall without penetration, due to the inherently uneven nature of even general corrosion, and due to the presence of external loads in piping systems. The model has “built in” protection against this, due to the Thinning Variance (See Section 10.4 under “Effect of Thinning Variance” for more discussion.) Since it is not possible to know for any given pipe just what CA the piping designer may have used in the Pipe Specification, a commonly used rule of thumb in the absence of original Pipe Specifications is to assume that 50% of the wall is a safe minimum (at least for carbon steel pipe). Thus the “calibration” for piping is targeted at 50% of wall removal to yield a Thinning Factor of 1.0. Figure E.2 shows that for a thin wall cylinder (Sch. 40 Pipe) with the above inputs, the calibration came out very well. At 51.1% wall loss, the Thinning Factor is 1.22 with10 Highly Effective Inspections.Mike Conley and Lynne Kaley Page 37 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 Figure E.2 Model Results for Thin Wall Cylinder (1” Sch. 40 Pipe)Cylinder % Wall Loss vs. TF Thin Wall (Pipe 1-4" Sch. 40)10.0 5 - 0 1 X 6 0 . 3 = F F G- s 51.1%; 1.22 i s a 1.0 B ( r o t c a F g n i n n i h T0.1 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% % Wall Loss10.6.3. Model Results for Average Wall Cylinder (ar/t Base Case)Basis: Physical Data:T min, Maximum Geometric Thickness, Diameter, YS, ksi TS, ksi approximate, Operating Pressure, Shape inches OD, inches inches psigCylinder 35 60 0.375 0.5 187.5 60CA CA as % of Wall0.125 25.0%Basis: Technical InputsThinning Variance0.170Pressure Variance0.050Flow Stress VarianceMike Conley and Lynne Kaley Page 38 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 20110.170GFF3.06E-05Calibration Results Chart Figure E.3 shows that for a “typical” wall cylinder (”ar/t” Base Case) with the above inputs, the calibration came out fairly well. At 25% wall loss, the Thinning Factor is 2.33, meaning that the model calibration led to slightly conservative results in this case. At 20% wall loss, the Thinning Factor is 1.02 with 10 Highly Effective Inspections.Figure E.3 Model Results for Average Wall Cylinder (ar/t Base Case)Cylinder % Wall Loss vs. TF ar/t Base Case10.0 5 - 0 1 X 6 0 . 25.0%; 3 =F 2.33E+00 F G- s i s a 1.0 B (20.0%; r o t 1.02E+00 c a F g n i n n i h T0.1 0% 5% 10% 15% 20% 25% 30% 35% 40% % Wall LossFigure E.4 shows the same data, but expressed as POF (GFF = 1.0) instead of TF for full range of calculated POF. The same two points are highlighted as in Figure E.3, but showing corresponding POF values.Mike Conley and Lynne Kaley Page 39 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 Figure E.4 POF Model Results for “Typical” Wall Cylinder (ar/t Base Case)Cylinder % Wall Loss vs. POF ar/t Base Case1.0E+00- s i s 1.0E-01 a B ( e 1.0E-02 ) r 0 u . l i 1 a = FF 1.0E-03 f F oG y t 1.0E-04 i l i 25.0%; 7.13E-05 b a 20.0%; 3.13E-05 b 1.0E-05 o r P 1.0E-06 0% 20% 40% 60% 80% 100% 120% % Wall Loss10.6.4. Model Results for ASME HeadBasis: Physical Data:YS, TS, T min, approximate, Thickness, Maximum Operating Diameter, OD, Geometric Shape ksi ksi inches inches Pressure, psig inchesASME 35 60 0.664 0.789 187.50 60.00CA as % CA of Wall0.125 16%Basis: Technical InputsThinning Variance0.170Pressure Variance0.050Flow Stress Variance0.170GFF3.06E-05Mike Conley and Lynne Kaley Page 40 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 Calibration Results Chart Figure E.5 shows that for an ASME head with the above inputs, the calibration came out slightly nonconservative. At 22% wall loss, the Thinning Factor is 1.22. The actual CA expressed as % of wall is 16% in this case with 10 Highly Effective Inspections.Figure E.5 Model Results for ASME HeadASME % Wall Loss vs. DF10.0 5 - 0 1 X 6 0 . 3 = F F G- s 22%; 1.22 i s a 1.0 B ( r o t c a F g n i n n i h T0.1 0% 10% 20% 30% 40% % Wall Loss10.6.5. Model Results for Hemispherical Heads and SpheresBasis: Physical Data:T min, Maximum Geometric TS, Thickness, Diameter, YS, ksi approximate, Operating Shape ksi inches OD, inches inches Pressure, psig Spherical 35 60 2.063 2.188 187.50 660.00CA as % of CA Wall0.125 6%Basis: Technical InputsThinning Variance0.170Mike Conley and Lynne Kaley Page 41 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011Pressure Variance0.050Flow Stress Variance0.170GFF3.06E-05Calibration Results Chart Figure E.6 shows that for an hemispherical heads and spheres, with the above inputs, the calibration came out very well. At 6% wall loss, the Thinning Factor is 1.05. The actual CA expressed as % of wall is 6% in this case with 10 Highly Effective Inspections.Figure E.6 Model Results for Hemispherical Heads and SpheresSpherical % Wall Loss vs. DF10.0 5 - 0 1 X 6 0 . 3 = F F G- s i s 1.0 a 6%; 1.057 B ( r o t c a F g n i n n i h T0.1 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% % Wall Loss10.6.6. Model Results for NEW Cladding ModelBasis: Limit State FunctionThe cladding model is based on the assumption that the cladding itself plays no structural role. Since the cladding is well bonded to the base metal, it sees some of the same stresses as the structural shell beneath. Mike Conley and Lynne Kaley Page 42 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 However, since it cannot move or fail separately from the shell, all it can do to fail is be penetrated by thinning. The Limit State Function is then very simple: g= Thickness - Thinning dg = -1 dThinning As with all Limit State functions, failure results when g<0.Basis: Physical Data: Note that for this module, the defaults of 2 to 4 (200% to 400%) times the measured corrosion rate are almost certainly too high. Factors of 25% and 50% higher than the measured rate were chosen for this example.Geometric Clad Thickness, Damage State 2 Damage State 3 Shape inches Factor Factor Clad 0.125 1.25 1.50Basis: Technical Inputs Note that there are no variables for Flow Stress or Pressure in the Limit State, so the only variance on the only stochastic variable is Thinning. Note also there is no GFF, thus no Thinning Factor, only POF.Thinning Variance0.170Calibration Results Chart Figure E.7 shows a cladding 1/8” thick, At 100% wall loss, the Thinning POF is 0.709. This may seem a bit counterintuitive, but it is correct for the Limit State equation shown. Figure E.7 is the only graph in this Appendix based on no inspections. If many highly effective inspections were performed, then at 100% cladding loss, the limit state g would be 0, so β is 0, and POF = NORMSDIST(0) = 0.50Mike Conley and Lynne Kaley Page 43 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 Figure E.7 Model Results for NEW Cladding Model0.125" Clad % Thinning vs. POF1.2001.0000.800 100%; 0.709 FO 0.600 P0.4000.2000.000 0% 25% 50% 75% 100% 125% 150% 175% 200% % Clad Loss10.7. On “Special” Uses of the Art Table 5.11 in RBI, e.g. CUI, & Thinning of the Base Metal in Lined or Clad Equipment This proposal substitutes a mathematical model to replace the Art Table 5.11 in API RP581. Thus the model described herein may be substituted for lookup of factors from that table, where ever it may occur. Issues related to such special uses of the Thinning Model are beyond the scope of this proposal, except for the actual determination of the Thinning Factor (calculated herein, lookup from the Table in current applications). There are at least two cases in RBI where the Art Table 5.11 is used for special applications which may arise in practical situations. These two are: 1. For determining a Thinning Factor due to corrosion under insulation or other external corrosion with or without internal thinning at the same time. How this is handled with respect to combining Thinning Factors for cases in which the internal or external corrosion may be localized is beyond the scope of this proposal. 2. For determining a Thinning Factor for such equipment which may be lined or clad upon failure of the lining or cladding, thus exposing the base metal to a thinning mechanism.10.8. Final Note on Moving Past the Art Table 5.11 At least one developer of RBI software intends to install this model (if it is approved) in parallel with the existing Art Table 5.11 method. Since there will be some changes in the results, this will provide a way of tracking and managing the changes in the best way possible: using real databases with real data and many thousands of items to be planned. It is anticipated that a gradual transition will Mike Conley and Lynne Kaley Page 44 of 45 Replacement of RP 581 Table 5.11 “Thinning Damage Factors” with Mathematical ModelProposal to API RP 581 Committee March 17, 2011 take place, so that impending plans that are already budgeted will not be impacted.Mike Conley and Lynne Kaley Page 45 of 45

API Replacement of Table 5 11 Thinning Damage Factors with Mathematical Model

Details

Download

Copyright

We respect the copyrights and intellectual property rights of all users. All uploaded documents are either original works of the uploader or authorized works of the rightful owners.

Support