57.3.3.1 Performance Measures

The performance of any ILI technologies can be measured with the following four parameters: probability of detection (POD), probability of identification (POI), probability of false call (POFC), and sizing tolerance, in accordance with the procedures recommended by API 1163 ILI [21] and using the binomial probability distribution methods [22–24]. The following are their definitions:

• POD (probability of detection): A probability (or certainty), e.g., 80% of time, that the number of anomalies (e.g., dents) is successfully detected by the ILI tool in terms of the total number of anomalies of the same type (dents) on the pipeline. Usually, the pipeline industry adopts POD = 80% (of the time) with a confidence level of 95%, indicating that the probability of detection is satisfied.
  
• POI (probability of identification): A probability (or, certainty) that the number of anomalies (e.g., gouge) is correctly classified by the ILI tool from the anomalies having similar ILI characteristics (e.g., corrosion and cracks) on the pipeline. Usually, POI = 80% (of the time) at a confidence level of 95% is adopted by the pipeline industry.
  
• POFC (probability of false call) is a closely associated measure against POD, which is the frequency that the tool falsely reports an anomaly where no anomaly existed. The probability of false call is defined as a probability (or the certainty) of a nonexisting feature being reported as a feature by the ILI tool at 95 confidence level. A confidence level of 95% indicates the confidence with which the certainty level is satisfied.
  
• Sizing tolerance is a measure of an ILI technology’s ability to predict an anomaly’s dimensions, typically, the depth, length, and width. API 1163 indicates that the sizing accuracy shall include the following three parameters when using a small sample size of excavation for tool performance validation:
  
  
  
  • A tolerance, e.g., within ±10% of wall thickness.
    
  • A certainty, i.e., the probability, e.g., 80% of time, that a reported anomaly depth is within the specified tolerance.
    
  • A confidence level indicating the confidence, e.g., 95%, with which the tolerance and certainty levels are satisfied.

The method used for calculating POD, POI, POFC, and sizing tolerance are the binomial probability distribution and confidence interval methods in accordance with API 1163 [21]. For confidence interval methods, the Clopper–Pearson method known as the “Exact” confidence interval for binomial probability distribution is preferred because this confidence interval method provides the most conservative intervals, PL and P_U, i.e., the lower and upper ends of the interval, respectively, for a given confidence level. The details of the binomial distribution analysis and Clopper–Pearson confidence interval methods are given elsewhere [22–24].

In the following section, the performance of current ILI technologies for characterization of dents and dents with metal loss in terms of POD, POI, POFC, and sizing tolerance is summarized and reviewed [10, 11, 20].

57.3.3.2 Dent: POD, POI, POFC, and Sizing Performance

It is known that the probabilities of detection and identification of dents for the depth greater than 2.0% OD in pipelines are very high, and the probability of false call is very low for all types of generic technologies listed in Table 57.4. POD, POI, and POFC were not the concerns. Only the sizing performance was evaluated and reported [10, 23].

For dent sizing, geometry sensing technologies (calipers) are generally regarded as providing the most accurate results for sizing dents at specified detection thresholds because they directly measure the deviation from the circular form of the pipe wall. Other technologies, e.g., MFL and UT/EMAT, alone are not capable of sizing dents with industry-expected certainty and confidence, except tri-axial MFL.

Two data sources have been used for evaluation of the depth sizing performance: one from ILI vendors and the other from pipeline operators. Some of the data from ILI vendors were obtained from pull-through tests without errors from rebounding and rerounding of dents, where “rebound” refers to the reduction in the dent depth and change in shape due to elastic unloading that occurs when the indenter is removed from the pipe and “rerounding” refers to the change in dent depth and shape due to change in internal pressure. Therefore, the vendors’ data represent the sizing accuracy that can be achieved by the ILI tools, while the data from operators were affected by the conditions of ILI run and re-rounding and rebounding due to excavation and pressure reduction, in particular, for the bottom side of constrained dents. Another source of large error in the operator’s data was due to variability in the in-ditch protocol for dent measurement. However, the operators’ data represent the current level of tool performance influenced by various conditions in addition to the error from the ILI tool itself.

56.6.2 Dent Sizing Performance: Operators’ Data

A total of 359 data points were collected from pipeline operators. Overall, the data scatters are larger and consequently the tolerance larger than that of vendors. The results are summarized in Table 57.5, for dent depth, and in Table 57.6, for dent length and width.

Among the 359 data points, 103 data points were collected in 2006, (i.e., Phase I in the table), and the other 256 data points were collected in 2009 (i.e., Phase II) [10, 23]. During the earlier time of the study (2006), the data collected from operators showed significant scatter compared with the validation populations obtained from the vendors. The depth tolerance is in the range between ±1.6 and ±4.48% OD. Progress was made in reducing the data scatter during the later time (Phase II, 2009) due to the better quality and more complete information of the data gathered, which allowed filtering the top-side and bottom-side dents from the total populations. For the bottom-side dents, attempts have been made to apply corrections for rerounding and rebounding using Equation (57.1) recommended by European Pipeline Research Group [25]:

(57.1)

where D= pipe diameter, H_r = residual dent depth measured upon excavation at reduced pressure and unrestrained condition, H_p = maximum dent depth during indentation as measured by ILI under restrained conditions, and is expressed in %.

Technologies for Dents		Data Source	# of Dent Features Evaluated			Mid-range Size Caliper Specifications		Validation %D
						LOD, %D	Depth Tolerance	Binomial Distribution Method	C-P Confidence Interval Method
1	DAMC(EM)	Phase I			28	0.5	±1.00	±1.60	±1.60
2	Caliper (EM) + MFL combo	Phase I			58	0.5	±1.00	±4.48	±4.65
3	Caliper + MFL combo	Phase I			17	1.0	±0.50	±1.63	1.63
4	Caliper + MFL combo	Phase II	All	135	Dents	1.00	±0.50	±1.07	±1.08
			Top side	25	Dents	1.00	±0.50	±1.00	±1.20
			Bottom side	110	Dents, uncorrected	2.00	±0.50	±1.10	±1.10
			Bottom side	110	Dents, correcteda	2.00	±0.50	±1.32	±1.32
5	MFL (3 axis)	Phase II	All	26	Dents	0.50	±1.00	±2.40	±2.88
			Top side	6	Insufficient for analysis	0.50	±1.00	NA	NA
			Bottom side	20	Uncorrected	0.50	±1.00	±2.88	±3.00
			Bottom side	20	Correcteda	0.50	±1.00	±0.95	±1.00
6	Caliper + MFL	Phase II	All	95	Dents	0.60	±0.80	±5.30	±5.34
			Top side	1	Insufficient for analysis	0.60	±0.80	NA	NA
			Bottom side	94	Uncorrected	0.60	±0.80	±5.34	±5.34
			Bottom side	94	Correcteda	0.60	±0.8	±1.51	±1.52

^a Depth corrected for spring back using EPRG recommended equation [25].

Technologies for Dents	Data Source	# of Dent Features Evaluated	Validation of Length and Width Tolerance, inch, at 80% Certainty and 95% confidence Level
			Binomial Distribution Method	Clopper-Pearson Confidence Interval Method
Length Assessment
Caliper + MFL	Phase II	28	±17.00″	±17.00″
MFL (3 axis)	Phase II	12a	±14.70″	NAa
Width Assessment
Caliper + MFL	Phase II	23	±15.00″	±21.00″
MFL (3 axis)	Phase II	12a	±20.00″	NAa

^a Note: for Clopper–Pearson 95% confidence interval method, the minimum required excavation number for validation is 14 for a certainty of 0.8. No tolerance values can be obtained for the validation excavation number 12 [23, 24].

The application of Equation (57.1) to the bottom-side dents could predict the residual dent depth upon excavation when the indenter would be removed. The calculated residual depth is then used to compare with the in-ditch validation measurements. As shown in Table 57.5, with this correction, the overall scatter bands are narrowed to the range between ±1 and ±1.5% OD.

56.7 Sizing Accuracy: Pull Test Data

It has long been recognized that the difficulties in validation of ILI sizing performance for dents are associated with multiple sources of error, mainly due to resolution (sensor spacing) of the ILI tool, rebounding, rerounding, and in-ditch measurement errors. The dent sizing correlations between ILI and in-ditch measurements collected from pipeline operators usually exhibit large scatters. Consequently, a laboratory pull test was performed with a high-resolution caliper and validated using the LaserScan 3D technology, an improved and more accurate method for in-field NDE measurement (see Section 57.4) [23]. The purpose of the pull test is not only to eliminate the errors resulting from rerounding and rebounding but also to minimize uncertainties in in-ditch direct measurements.

The pull test was conducted on a 30 in. OD × 0.342 in. wall × 10 ft long test piece that contained 10 dents with varying depths (0.5–6% nominal depth) made by Battelle Memorial Institute. Figure 57.9 shows a sketch of the 10 dents and the LaserScan image of the deformed pipe test piece.

The ILI tool used for the pull test was a high-resolution DAMC (EM) caliper with a total of 72 sensors (sensor spacing = 1.3 in.). This ILI tool was repeatedly pulled 12 times with a speed between 0.5 and 1.8 m/s with the majority of tests at 1 m/s to provide statistically significant sizing results. A total of 120 data points (12 data points/dent) were generated.

For direct measurement, a commercially available laser profilometer, Nvision 3D scanner, was used. The laser profilometry has a spatial resolution of 0.1 mm and a depth accuracy of 0.1 mm. This resolution is considered to be sufficient for dent profiling. The laser scans were done on the outer surface. A one-on-one comparison of ILI and LaserScan profile methods was used to determine the depth of the dent to avoid errors due to using different reference points for the depth measurement between ILI and laser. The dent depth is directly measured from the overlapped profiles with the same reference points. Figure 57.10 illustrates how the measurements and comparisons were made.

The evaluation was performed using the linear regression best fit against the laser profilometry validation measurements.

Figure 57.11 is the unity graph of the ILI dent depth prediction against LaserScan validation. From Figure 57.11, it is seen that the linear correlation between ILI and LaserScan data is extremely good with the R² value = 0.9889. The slope of the regression line is very close to 1 (0.9673), with only a small shift of the regression line from the unity line, indicating the ILI tool underestimates the dent depth by 0.20% OD. This systematical shift can be readily corrected. The reason for this shift is unclear. It may be partially attributed to the difference in measurements from external and internal surfaces and requires further investigation.

The linear regression analysis showed that the tool tolerance from the 12 sets of repeated test data is ±0.20% OD at 80% confidence level and ±0.31% OD at 95% confidence level. By comparing the vendor’s specification for this caliper technology, ±0.5% OD at 95% confidence level, the tool performance is justified.

The above results appear to be very promising. The data suggest that with the minimized error from field measurement and with no rerounding and rebounding involved, the tool’s “inherent capacity” can be evaluated. The evaluated results can serve as a basis for assessing errors of ILI prediction from various sources.

57.3.3.3 Dents with Metal Loss: POD, POI, POFC, and Sizing Performance

Since metal loss (such as corrosion, gouge, groove, and/or crack on the dent) causes stress concentration, one of the major threats to pipeline integrity, evaluation of the capabilities and performance of ILI technologies to detect and size metal loss and to discriminate between corrosion and scratch/gouge/crack is particularly important.

A total of 718 samples were used for evaluating the tool performance for characterization of dent metal loss (DML) [10, 20]. The results showed that the overall performance of the current technologies is POD = 83.5%, POI = 91.2%, and POFC = 29.5% at a 95% confidence level using the binomial distribution method and POD in the range of 83.4–89.9%, POI = 91.4–96.4%, and POFC = 36.6–44.3% using the Clopper–Pearson confidence interval method.

From the established overall performance of ILI tools, the capabilities of current ILI technologies for detecting and discriminating dents with metal loss are acceptable in accordance with the commonly accepted probability of detection (POD) and discrimination (POI), i.e., 80% time at 95% confidence level. The actual POI is higher, 91% time the same confidence level. However, the probability of false calls is high, 29.5%, which could have resulted in many unnecessary excavations. Tables 57.7–57.9 summarize the results as reported by the study [10, 20].

However, the capabilities for detection and identification of DML vary greatly with individual technologies. The POD can be as high as 94.7%, but at the same time, it can be as low as below 80%. The same pattern can be seen for POI; out of 10, 6 are higher than 80% and 4 are below 80% with the lowest 47.3%.

Since no detailed information is available about the conditions for ILI runs and excavations, it is not fair to make any conclusions about which technologies are better than the others. The only conclusion that can be made from the study is that high values of POD and POI have been achieved and potentially are achievable for all the technologies.

57.3.3.4 Closing Remarks

From the above review, a few remarks may be made on the overall performance of ILI tools as follows:

1. The capabilities of current ILI technologies for detecting and discriminating dents and dents with metal loss are acceptable. This is based on the commonly accepted POD and POI level of 80% at 95% confidence. However, the probability of false calls is high, i.e., 29.5%, which may have resulted in unnecessary excavations. Some ILI vendors stressed the importance of manual subject matter expert (SME) data interpretation in discriminating metal loss within dents as a significant factor affecting probability of false calls.
   
2. The capability for detecting and discriminating dents and dents with metal loss varies greatly with individual technologies. However, high values of POD and POI have been achieved by some of the current technologies, which imply that the same level of POD and POI are achievable by all technologies.
   
3. The ILI tool capability in discrimination of metal loss between corrosion and gouges was not evaluated because there were insufficient data to validate the vendors’ claims. However, one technology (MFL plus caliper type) claimed a success rate between 50 and 90% for identification of gouges was achieved, but as pointed out by those vendors, the capabilities are subject to limitations, suggesting that the confidence level is low. Additional research would be required to address this challenging issue.
   
4. There have been reported applications of ultrasonic sensor technologies, but the data for validation are not sufficient. Therefore, the capabilities of ultrasonic sensor technologies including EMAT for coincident metal loss and crack detection and discrimination are unknown and remain a subject for future study.
   
5. One of the sources for the scatters in pipeline operators’ data was the lack of appropriate in-ditch inspection tools and inconsistent protocols for dents and dents with metal loss depth measurement. Developing an improved in-ditch measurement technology and well-defined measurement protocol could be the accuracy of in-ditch measurements. This will be discussed in the next section.

57.4.1.1 Hardware: 3D LaserScanner

Figure 57.12 shows the overview of the LaserScanner system hardware. The system consists of a scanner with a built-in camera and a laptop computer and cables. The scanner is portable and lightweight, approximately two pounds.

Table 57.11 shows two specifications of the LaserScanner commercially available. The single point accuracy is 50 and 40 μm, and resolution is 0.1 mm (0.004 in.) or better, such as 0.05 mm (0.002 in.) depending on the model of the scanner.

The LaserScan has an auto-positioning stereo vision. The camera sees the patterns of the positioning targets that are applied on the surface to be scanned, and by triangulation, the scanner is able to determine its position relative to the targets (Figure 57.13).

The scanner can scan all nonshiny surfaces with minimal surface preparation. However, for shiny surfaces, the surface should be covered with an opaque powder. The positioning targets should be placed in and around the area of interest with a random distance of 3–4 in. from each other. Once the positioning targets are placed, the LaserScan can be used to scan the surface with the positioning targets.

The accuracy, reliability, and repeatability of the scanner tool were tested by measuring the step wedge with nominal dimensions of 0.1 in. per step. Figure 57.14 shows the step wedge and dimensions as measured using Model 1 LaserScanner (Table 57.11) by a specialist and a volunteer. The difference is in the order of a few mils, which is acceptable for in-ditch dent measurement. The specialist-measured step wedge is within the tool accuracy specification of 0.0016 in.

Figure 57.15 shows the pipe containing five dents, with one of them, Dent 1, containing a gouge.

57.4.1.2 Data Processing

Once the area of interest is scanned, the scanning system digitally resembles the original surface of the pipe and dents and associated defects. Figure 57.16 is the resembled pipe, showing the dents and dent with gouge (as shown in Figure 57.15), and a gouge closeup with the measured length, width, and depth.

These 3D image data are further processed with the system’s proprietary software, which extracts and converts each of the points on the scanned pipe surface into a cylindrical coordinate system. The figure next to the table in Figure 57.17 shows a Point P(r, θ, z) on the scanned pipe surface in the cylindrical coordinate system, where r and θ are the point P(r, θ, z) projection onto the polar-coordinate r–θ plane and z is the coordinate of the point on the z axis, i.e., the centerline of the pipe. The numbers inside the table in Figure 57.17 are the r values of the data points. For the undeformed pipe, r ₌ r_o, i.e., the radius of the pipe. In the deformed or dented area, the r value shows the change in r_o due to denting.

Once the scanned surface data are extracted and saved in the above cylindrical coordinate system format (Figure 57.17), the axial and circumferential profiles of a dent can be readily extracted and plotted for any given values of z and θ, respectively. Figure 57.18 shows 180 axial-profiles of a dent (i.e., Dent 1, Figure 57.16) around the circumference of the pipe from 0° to 360° with an increment of 2° from θ = 0° (reference). From the profile, it is seen that the deepest point of the dent is located at the axial distance of z = 146 mm at θ = 86°. The resolution of the profile is 2 mm (i.e., z = 2 mm increment for each point, Figure 57.17). As a common practice for both ILI and in-ditch manual measurement, this profile, i.e., the axial profile passing through the deepest point, is used to determine the depth and length of the dent.

It is noted that in the profile next to the deepest point at θ = 84°, there is a depression near the tip indicating the presence of a gouge near z = 126 mm, which is consistent with Dent 1 as described previously.

Similarly, one can also readily extract and plot any circumferential profile for any given z value. Figure 57.19a is a circumferential profile at z = 146 mm, which passes through the deepest point of the dent. This profile can be used to determine the circumferential angular span and width of the dent. Figure 57.19 (b-1) and (b-2) is the circumferential profile at z = 126 mm, which passes through the gouge in the dent. Again, the depression near the tip of the profile is noticeable due to the presence of the gouge.

Once the profile is generated, the axial and circumferential data can be used to quantify the dent depth, length, and width of the mechanical damage and calculate the deformation strains at each point in the deformation (dent) using the strain calculation models [18, 35, 36, 37, 17, 33–36].

57.4.2.1 Calibration of Depth-Based ILI Technologies for Mechanical Damage Evaluation [25]

Usually, ILI tools are calibrated for mechanical damage using pull-through tests. The tests use pipe samples with pre-made dents and performed at ambient pressure without the influence of re-bounding and rerounding errors. Calibration is generally limited to measuring the maximum depth of the deformation (dent) and associated metal loss such as gouge and corrosion, which are manually measured with the traditional bridging bar and profile gouge technologies. Since the improved 3D scan system can provide accurate (at least one order of magnitude higher than ILI) depth measurement, 3D information of deformation including axial and circumferential profiles, and less dependent on technician’s skill, it is an ideal tool.

It is known that the standard and high-resolution multiple-channel caliper tools can provide dent axial and circumferential profile data with the same format and the same cylindrical coordinate system as used by the 3D scanner. Therefore, this makes it possible to perform one-on-one comparison of the profiles between ILI and 3D-scanner data, which could provide the most accurate calibration for ILI tools. The data shown in Figures 57.5 and 57.6 are examples for the comparison. The tool tolerance can be accurately and reliably determined.

57.4.2.2 Better Evaluation of the Depth-Based Tool Performance for ILI Runs

For caliper and caliper-MFL tool ILI runs, evaluation of ILI sizing performance requires manually measuring the maximum depth of the dent and coincident metal loss such as corrosion and gouge. This is generally quite a difficult and tedious job, in particular for bottom-side dents in a very confined space. The errors from in-ditch measurement may be significant or less reliable, which add additional uncertainties for ILI sizing performance evaluation. With the aid of this improved technology, not only the intensive labor can be reduced, but also the in-ditch measurement errors could be minimized. Moreover, differentiation of the effect of re-rounding and re-bounding from tool performance itself becomes possible.

Figure 57.20 is a plot of 31 depth data points of bottom-side dents measured in-ditch with a 3D scanner against those reported by the ILI caliper tool again. In spite of the large error bands (R² = 0.51), the overall correlation looks good. The slope of the regression line is 1.08, close to 1. The shift of the regression line from the ideal 3D ILI 1:1 ratio line (i.e., the dashed line) is about 0.42% OD. This systematic error is mainly caused by dent rerounding and rebounding and can be corrected for integrity management of dents.

Using the 1:1 ratio dashed line as a reference, 19 points are above the dashed line, indicating that the depths measured in-ditch by 3D Scanner are shallower than those reported by ILI. This is mainly caused by the effect on depth of rerounding and re-bounding by removing rocks underneath the dents. For the six points below the dashed line, the depths measured in-ditch by the 3D Scanner are deeper than those reported by ILI. This error is in the opposite direction of rerounding and rebounding, mainly caused by limited resolution of the ILI tool, which did not capture the deepest point of the dents, resulting in the depths measured in-ditch by the 3D scanner being deeper than those reported by ILI. For the five points on the dashed line, there might be a possibility that those dents were not constrained even though they are on the bottom side. Therefore, little of the rebounding effect would be expected.

It should the noted that ILI tool measures the inner surface, whereas the in-ditch 3D measures the outside surface of the pipeline; there may be an error between these two measurements; however, the contribution of this difference to the measurement error is relatively small in the order of wall thinning due the deformation.

57.4.2.3 Better Evaluation of Strain-Based Tool Performance for ILI Runs

The severity of dents has traditionally been defined by depth [4, 6, 17]. Practical experience showed that the use of depth alone can result in both unnecessary excavations due to many deep dents and ovalities that are not necessarily harmful and also potentially miss of moderate or shallow dents that are in fact severe due to their overall size and sharpness [4, 35, 38]. Since pipeline mechanical damage is related to strain, strain levels derived from the dent profile may offer another measure of dent severity [36]. Therefore, ASME B31.8 for gas pipelines affecting high-consequence areas offers an option to use strain-based assessment methods, including nonmandatory equations to estimate component and total strains. The nonmandatory equations use the dent geometrical parameters, namely, its axial and circumferential radius of curvature R1 and R2, and depth/length, to compute the bending and membrane strain components and total strain. Since some of the equations recommended by ASME 31.8 are incorrect, a major modification was made by Lukasiewicz et al. [33–35] and has been accepted for use [1, 2, 26, 27, 38]. A more detailed discussion is given in Section 57.5.3 of this chapter.

It is known that both ILI and the improved 3D LaserScan technology are able to provide dent 3D geometry and detailed axial and circumferential profiles, strains at each of the points in the dent can be calculated using the local deformation geometry at that point. The location and magnitude of the highest strain in the dent can be identified, which may not be the same as identified by the dent’s global geometry.

Since the improved 3D LaserScan technology provides much higher resolution than the ILI tool, the calculated strains would have higher accuracy than ILI. Therefore, the improved 3D LaserScan technology can be used as a calibration tool to evaluate strain-based ILI tool performance and establish a correct factor for strain-based integrity assessment of mechanical damage.

Proprietary software has been developed for computing strain components and total strain at every point of a dent using its local deformation geometry from axial and circumferential profiles [40]. The software first filters and smooths the raw displacement data with FFT low pass and Gaussian smooth filters to minimize both electronic noises and false readings from surface irregularities. The software then uses a piece-wise parametric cubic interpolating method to calculate the radius of curvature and bending strain components and finite difference in length before and after deformation to calculate the membrane strain components. It will be further discussed in Section 57.5.2 of this chapter.

Figure 57.21 is a comparison of the strain profile and maximum total strain reported by the standard ILI caliper and LaserScanner using the proprietary software, showing a factor of two differences between these two technologies. Because the caliper used for ILI is a low-resolution tool equipped with only 18 sensors for a 26-in. OD pipeline, the sensor spacing is about 4.5 in.; the difference in the computed strain value between ILI and LaserScan may be mainly attributed to the low resolution of the caliper tool. Statistical analysis showed that a 2.3 correction factor should be applied to the ILI strain data for integrity assessment of dent severity.

For a higher-resolution caliper, the difference in computed strain between the caliper and LaserScanner would be smaller. Figure 57.22 shows a correlation of 14 strain data points computed from ILI and LaserScan data. The ILI caliper has 48 sensors for a 24-in. OD pipeline; i.e., the sensor spacing is 1.75 in., which is about 2.9 times smaller (the sensor density is 2.9 times higher) than in the previous example. The correlation in strain between ILI and LaserScan appears to be good, with the correlation coefficient R² = 0.80.

With the correlation established in Figure 57.22, the following regression equation may be applied to the rest of the ILI reported dents for correction at the 95% confidence level:

(57.2)

The implication of the above examples is that because of the high resolution of the improved in-ditch technology, the LaserScan tool can used as a reference tool to evaluate the strain-based performance of the geometry ILI tool (caliper) and to establish a correlation between them for making corrections of ILI data for the purpose of dent severity ranking and prioritization of investigation. This is an example of one ILI tool correction. Such an approach can be adopted and utilized for strain modification and may improve integrity.

57.5.3.1 Static Strain Calculation Equations Recommended by ASME B31.8

So far, there are no standard methods for the calculation of dent strains under static loading and fully ductile conditions. Appendix R of ASME B31.8 (2003) and its newer edition (2018) provide the nonmandatory equations for computing three strain components, namely, two bending strains (longitudinal and circumferential) and one membrane strain (axial) using the dent’s global geometry. Then, the formulae for total strain calculation are provided using these three component strains. ASME 31.8 does not provide the formula for computing circumferential membrane strain and assumes it in compression.

The following are the six nonmandatory equations recommended by ASME B31.8 [36] for static strain calculation. Figure 57.23 defines the parameters used in the equations.

Circumferential bending strain (ε₁),

(57.3)

Longitudinal bending strain (ε₂),

(57.4)

Extensional strain (ε₃),

(57.5)

Total strain on the inside pipe surface (ε_i) and on outside pipe surface (ε_o) is

(57.6)

The overall maximum strain, ε_max, defined by the following equation, is then compared with acceptance/rejection criteria recommended by ASME B31.8 (2003):

(57.7)

The nomenclature in Equations (57.3–57.7) is that used in ASME B31.8:

• t = Wall thickness
  
• R_o = Initial pipe surface radius
  
• R₁ = Radius of curvature in the transverse plane, negative for reentrant dents
  
• R₂ = Radius of curvature in the longitudinal plane, negative for reentrant dents
  
• L = Dent length
  
• d = Dent depth

From Equation (57.6), the total effective strain on the pipe surface can be further deduced using ε_x = ± ε₂ + ε₃, ε_y = ± ε₁ [16, 53]:

(57.8)

where x and y refer to the longitudinal and circumferential axes of the pipe, as defined in Figure 57.23, and the positive and negative signs refer to the inner and outer wall surface, respectively. Again, Equation (57.7) is used to determine the overall maximum strain. The subscripts in Equation (57.8) refer to the strain directions shown in Figure 57.23.

Finally, the calculated maximum total strain is compared with the acceptance/rejection criteria to determine if the dent is acceptable for fitness-for-service (FFS). As described previously, 6% strain in pipe bodies and 4% strain in welds are acceptable for plain and rock dents.

It is noted that Equations (57.3–57.5) can be used to calculate strain components based on either global or local geometry using ILI and field inspection data [4, 52]. When using dent local deformation geometry, piecewise interpolation methods, such as Bessel cubic interpolation or fourth-order B-spline method [53, 54], should be used to approximate the local dent profile and to estimate the radius of curvature in both longitudinal and circumferential directions:

(57.9)

for a given θ (longitudinal) or z (circumferential) where r, θ, and z are the coordinates in the cylindrical coordinate system as defined in Figure 57.17.

The local axial membrane strain may be estimated using the local finite difference in length before and after deformation [53]:

(57.10)

where L_s,i is the local deformed length and L_o,i is its original length in the longitudinal direction at point i (coordinates r, θ, and z) in the dent.

By using Equations (57.9) and (57.10), the total strain at each point of the dent can be computed using the dent profile as reported by caliper ILI, and the location and magnitude of the maximum strain in the dent can be identified. The accuracy of the computed results depends on the resolution of the ILI tool. High-resolution tools yield better accuracy, whereas low-resolution tools result in large errors. This localized computing method has been called a “Point-to-Point” method for convenience [1, 2, 26, 35].

The bending component Equations (57.3) and (57.4) were developed considering strain in thin plate and shell theory [55]. However, the global axial membrane strain, Equation (57.5), was empirically established against a limited number of finite element analyses [17]. For the total effective strains, Equation (57.6), there are no documented explanations in the public domain regarding how they were established. Baker [16] indicated that Equation (57.6) can be seen to be either the effective strain for a plane strain condition where e₁ = ε₁, e₂ =ε₂ + ε₃, e₃ = 0 without having a preceded constant 2/3, or can be thought of as analogous to von Mises stress for a plane stress condition, where σ₃ = 0.

As noted by various authors [32–37, 39], the assumption made by ASME that the radial strain e₃ = 0 for the thin-walled pipe is incorrect because both the stress and strain in the radial direction cannot be 0 [34, 56]. It is also incorrect to assume that the formula of von Mises strain for the thin-walled pipe is analogous to the von Meses stress for a plain stress condition because it is not supported by plastic strain theory [56].

Lukasiewicz et al. [33, 58] further indicated that the ASME B31.8 code offers a simplistic Equation (57.5) for estimation of global longitudinal membrane strain; the accuracy of Equation (57.5) is extremely poor. A more rigorous derivation showed that Equation (57.5) underestimates axial membrane strain by a factor of 4; the correct equation should be [35].

Lukasiewicz et al. [33] also indicated that ASME 31.8 (2003) calculates only longitudinal membrane strain, which neglects the circumferential membrane and shear strains. The finite element method (FEM) analysis of actual dents has shown that these strain components can have a similar magnitude to the longitudinal strain [57].

In the following section, the improved equations for computing dent strains are discussed.

57.5.3.2 Improved Static Strain Calculation Methods

Lukasiewicz Method

Lukasiewicz et al. [33] and Czyz et al. [34] proposed an alternative method that combines mathematical algorithms and FEA tool for dent strain calculation. The authors indicate that strains in a pipe wall consist of two main components: longitudinal and circumferential, each of which can be further separated into bending and membrane strains. The membrane strain is constant through the wall, while the bending component changes linearly from the inner to outer surface. Figure 57.24 shows these strain components in a pipe wall.

The respective longitudinal and circumferential bending strain, i.e., and , can then be calculated from the curvature of the radial displacement w in the axial x and circumferential y directions (see Figure 57.25).

(57.11)

The bending strain becomes maximum on the pipe surface, i.e., z = ±t/2, where t is the pipe wall thickness. The strains at the outer surface are

(57.12)

On the inner surface, they have an opposite sign.

These authors [33, 34] further indicated that calculation of the bending components is fairly straightforward, directly from the dent displacement measured by the in-line high-resolution caliper tool. The in-line caliper measures the pipe wall deflection w in the Z(x, y) direction. A fourth-order B-splines approach may be employed with FEM simulation to calculate the curvature of dents from caliper data, which was demonstrated by Noronha et al. [54].

The main difficulty in strain-based methods is in determining membrane strains in the dented region. At present, no exact (analytical) solutions are available for calculation of membrane strains of the dented region in the pipe [33]. However, the membrane strains may be calculated using the relationships between membrane strain and displacement for large deformations of a cylindrical shell [57]:

(57.13)

where

• and are the membrane strains in the axial (x) direction and the circumferential (y) direction, respectively.
  
• γ_xy is the shear strain in the plane x, y
  
• R is the mean radius of the pipe
  
• and are the initial strains due to the pressure in the pipe, thermal expansion, etc.

These equations are solved numerically for the unknown displacements u and v (See Figure 57.25) using a two-dimensional FEA method. The normal displacement w is the only measured parameter, preferably a high-resolution geometry tool, on the dent geometry.

These strains can be superimposed with the bending components, thereby producing maximum values of strain in the axial and circumferential directions:

where the positive and negative signs refer to the outer and inner wall surface, respectively.

The maximum equivalent strain (both on the inner and outer surface) in the dented area of the pipe is then given by

(57.14)

Or, more precisely,

(57.15)

Equations (57.14) and (57.15) are derived directly on the basis of the plastic strain theory [56], with an incompressibility condition in the plastic regime ε_x + ε_y + ε_z = 0. Note that ε_z cannot be assumed to be identically 0. The pipe wall behaves as a thin shell, and therefore it is a plane stress, not a plane strain, condition. The through-thickness strain is in fact the sum of the two in-plane components. Equation (57.14) is a simplified version of Equation (57.15) by neglecting shear strain γ_xy that is generally small and insignificant.

This combined mathematical algorithm and two-dimensional FEA model allows the calculation of all the strain components based on the measurement of the radial deformation of a pipe with a high-resolution geometry in-line tool. The proposed method is likely to provide a practical tool for assessment of strain in dents. However, it still requires incorporating a 2-D FAE model. For most of the pipeline operators, this is still difficult, if not impossible.

There are two major differences between Equation (57.8) (ASME B31.8-recommended) and Equation (57.14) (Lukasiewicz et al. suggested): (1) a preceding constant (), and (2) a sign difference in the mid-term ε_xε_y. These differences could result in a significant discrepancy in the calculated effective strain value. Czyz et al. [34] demonstrated that the difference in effective strain can be more than 50% with the assumption that = 0. Further comparison [34] was made using the three-case data provided by Baker [17]. Again, the comparison assumes γ_xy = 0. The results showed that ASME B31.8 Equation (57.8) underestimates the effective strain by a factor of up to 1.8 and 2 for external and inner surfaces, respectively, which is significant.

57.5.4.1 Static Dent Strain-Severity-Based Criterion

A dent indicates permanent damage to a pipeline by local plastic deformation. Dent severity and its susceptibility to cracking can be assessed using a plastic damage criterion. Dents with high strain could be potentially associated with cracks.

For the proposed approach, ductile failure damage indicator (DFDI) is adopted as the severity criterion for identifying candidate dents that may contain cracks/gouges for further investigation. DFDI indicates the susceptibility of a dent, using local strains and stresses, to incipient cracking. The detailed discussion of DFDI can be found in References [60–63] and in Section 57.6.1.1 of this chapter. For the present study, a simplified upper bound DFDI equation is used:

(57.17)

where ε_eq is the equivalent strain calculated using the ILI dent profile and ε_o is the critical strain of the material. The critical strain (true strain) of the pipe material is measured from material testing and usually in the range of 0.3–0.5.

In general, dents are susceptible to cracking when DFDI ≥ 1. For conservatism and screening purposes, a conservative DFDI value of 0.6, i.e., DFDI ≥ 0.6, is suggested as the severity criterion to determine if the MFL criterion should be applied for the dent of interest. A summary of a case study is shown in Table 57.16; when the simplified upper bound DFDI is greater than 0.6 there was a tendency to cracking.

57.5.4.2 MFL-Signal-Criterion

The second criterion of the combined approach is to review and characterize the associated MFL signals, particularly the tri-axial MFL signals, for the respective candidate dents.

It is known that the MFL ILI technology is capable of detecting crack signal(s) from the dent [8, 64, 65]. However, when the signal(s) is below the reportable threshold, the dent may be reported as a plain dent. In other cases, signals are reportable, yet the ILI tool is incapable of differentiating or discriminating cracking/gouging from corrosion according to signal(s) alone; therefore, ILI vendors commonly report them as metal loss. Sometimes, due to lack of experience, data analysts may ignore or dismiss the signals even though they are visible or reportable.

Whenever a dent is found to be associated with metal loss, a careful review of the MFL signal characteristics is required. There are a few steps involved in the MFL signal criterion to differentiate the metal loss between cracks, gouges, and corrosion:

• Determine how many metal loss features are within the dent region, only one isolated metal loss signal or many clustered features.
  
• If only a single strong MFL signal is found and located at the dent apex or highest strain spot in the dent, then the metal loss feature is most likely to be a crack.
  
• If a strong metal loss signal is located at the dent apex or highest strain spot but surrounded with general shallower metal loss features, then it is probably either a gouge or crack.
  
• If there is a strong metal loss feature signal oriented circumferentially and located at the dent apex or highest strain spot, then it is probably associated with the gouge.
  
• If many general metal loss signals clustered within the dent area are found, then it is most likely to be corrosion.

Although the above criterion appears to be quite simple and straightforward, it requires integrity engineers having good experience or working together with an MFL analyst in analyzing and discriminating the MFL signal data.

57.5.4.3 Illustration of the Effectiveness of the Approach: Case Study

A case study was reported to evaluate the effectiveness of the approach utilizing three in-line inspections with the MFL/Caliper combo tool. The inspection reported a total of 6361 dents. First, a quick screening was performed based on the strain value of the dent, which identifies 150 dents with high strain values. Then, upper-bound DFDI values were calculated for these dents and ranked in the descending order. A DFDI limit was set to 0.6 values to identify those dents that require a detailed review of the MFL signal. This limit was chosen based on the conservative material critical strain and will be finetuned in the future based on the future excavation and feedback. Finally, a total of 15 dents were identified for careful examination of the MFL signal. In addition, other dents reported by ILI as dent metal loss were also checked with the MFL criterion. At the end, seven dents were predicted to be associated with crack/gouge. Another eight dents were predicted not to be associated with crack/gouge. All these fifteen dents were excavated, verified in-ditch, and mitigated with appropriate methods as specified in the industry code. Table 57.16 is a summary of the 15 cases studied. The excavation results show an excellent agreement between the predictions and in-ditch findings with a 100% success rate. Even though the approach is still in the development stage, its effectiveness is obvious. This approach will eventually become a powerful tool for developing a safe and cost-effective integrity management of mechanical damage.

57.5.5.1 Rate and Temperature-Dependent Damage Criteria

As indicated by TC Energy, in the FEA software such as Abaqus/Explicit, damage criteria specifically for the loading rate and temperature-dependent material model can be incorporated to predict the onset of ductile fracture. The criteria can generally be classified in three categories:

1. Johnson–Cook damage criteria based on equivalent plastic strain,
   
2. Cumulative/progressive damage with defined fracture initiation rule such as Marciniak– Kuczynski criteria and
   
3. Tensile failure based on hydrostatic press stress.

Alternatively, calculated total strain and stress triaxiality can be extracted and compared with predefined damage criteria during postprocessing. The Johnson–Cook damage model in Equation (57.18) might be one of the most practical ways to account for rate-dependent fracture strain during a high loading rate dent formation process. Failure is predicted when total damage ω exceeds 1:

(57.18)

where is equivalent plastic strain in each increment and is rate-dependent failure strain, as defined in Equation (57.19):

(57.19)

where d₁–d₅ are material failure parameters, ε^̇₀ reference strain (typically equals 1/s), is plastic strain rate, and σ_m/σ^eq is stress triaxiality.

Comparing Equation (57.19) and the failure strain determination using the static-strain-based DFDI method, the reference fracture strain is defined in Equation (57.20):

(57.20)

Additional loading, (strain) rate- and temperature-dependency is included. To estimate strain damage under a high loading rate, a dynamic FEA for the dent formation process is currently the most practical method.

57.5.5.2 Dynamic Versus Static FEA for Dent Formation

In the static analysis, the Ramberg Osgood isotropic hardening law was used to model the material. The indenter was pushed into the pipe body with displacement boundary condition equal to the dent depth. In the dynamic explicit analysis, the pipe material was modeled with Johnson–Cook hardening; an initial velocity of 5 m/s was predefined for 100 kg reference mass. The displacement profiles in the longitudinal direction at same dent depth (9.5 mm or 1.3%OD) for both models are compared in Figure 57.26. In the static analysis, a point contact was created during the indentation process. The pipe was bent to a larger radius and did not conform to the same shape as the indenter. Under dynamic loading, the material generally follows the shape of the indenter and formed a sharp dent in the pipe.

Maximum in-plane principal plastic strain is compared in Figure 57.27. Due to the sharpness of the dent formed in the dynamic model, the strain level is much greater than in the static model.

57.5.5.3 A Multi-Element Dent Assessment Approach

Assuming all dents form under worst-case loading scenarios is a conservative approach but is not practical in integrity management of many dents since it could potentially lead to an unfavorable number of investigative digs. However, to temporarily fill gaps in current dent integrity management and minimize risks associated with dent cracks, TC energy recommended a multielement assessment approach that is described here:

1. Curvature-based dent strain assessment:
   
   
   
   1. If exceeds failure strain established based on static loading and conservative assumptions as described in Section 57.6.1, perform combined approach assessment or Level 3 continuum FEA study (see item #4).
      
   2. If not, proceed to 2.
   
   
2. ILI Reporting-Based Screening
   
   
   
   1. Screening dents in the heavy-walled pipe.
      
   2. Screening reported local metal loss interacting with dents.
   
   
3. Perform additional review for local metal loss, gouge, opened cracks—Caliper, MFL, AFD combined approach on selected list by 2) to identify high-risk dents:
   
   
   
   1. Screening dents with minor or no ovality.
      
   2. If characterized MFL and AFD signals observed proceed to remediation or 4) Level 3 continuum FEA study.
   
   
4. Level 3 continuum FEA study on high-risk dents:
   
   
   
   1. Iterate loading parameters to replicate the deformation profile.
      
   2. If deformation shape cannot be replicated under static loading and isotropic hardening, the dynamic model with rate- and temperature-dependent material model and damage criteria must be checked for remediation.

57.5.5.4 Closing Remarks

TC Energy identified and filled in a significant gap in strain-based dent severity assessment. Review of the present study shows that the scientific basis for the recommended approach and assessment methods is correct and feasible,

The only missing parts of the work by TC Energy are the metallurgical and operational conditions in the case studies, including fracture surface characterization of the ID cracks (fracture mode(s) and zone(s) of cracking, the time of ILI inspection, and excavations to support the findings).

57.5.6.1 Level 1 Assessment: Dent Geometry Severity Ranking Approach

The Level 1 assessment approach developed by BMT/PRCI uses geometry-based shape factors and shape parameter criterion to assess the relative severity of plain, single-peak dent features. The relative severity helps in the prioritization of dent features, allowing operators to allocate repair or remediation resources effectively to mitigate the effect of cyclic internal pressure on the fatigue life of the dented pipeline segment. The data required for a Level 1 assessment includes detailed ILI geometric data and some knowledge of the pipeline operational pressure spectrum (dominant mean pressure and pressure range combination).

Based upon a wide range of numerical simulations, an empirical equation-based approach to understanding the severity of dent shapes and their response was developed. This approach considers the nonlinear dent response to internal pressure to evaluate dent fatigue.

In Level 1 assessment, the dent geometrical parameters are used to estimate the fatigue life of the dented pipeline by

(57.21)

where N is the estimated fatigue life of the dented pipe in cycles, SP is the dent shape parameter, and A and B are geometrical coefficient and exponent, respectively.

Depending on the dent restraint condition, the shape parameter, SP, is defined by Equations (57.22) and (57.23):

(57.22)

(57.23)

In Equations (57.22) and (57.23), R is a dimensionless fitting parameter used to account for the pressure range and mean pressure and GSF is a dimensionless scale factor used to account for the effect of pipe material grade. The fitting parameter R has a linear correlation with the pressure factor, PF as shown in Equation (57.24)

(57.24)

The pressure factor, PF, is a function of the mean pressure and pressure range of the cyclic pressure for which the fatigue life is to be calculated by Equation (57.25):

(57.25)

P_mean and ΔP are defined in Equations (57.26–54.28) below:

(57.26)

(57.27)

(57.28)

where P_max and P_min are the maximum and minimum pressure values of the given pressure cycle, respectively; t and OD are the pipe wall thickness and outer diameter, respectively; and σ_SMYS is the specified minimum yield strength of the pipe steel grade.

The dimensionless grade scale factor GSF is defined by Equation (57.29):

(57.29)

where:

The shape factors xH and xL have been determined based on the best fit between the shape parameter and fatigue life for the highest pressure range (i.e., 10–80% PSMYS) and the lowest pressure range (i.e., 10–20% PSMYS), respectively. The shape factors depend on the dent type and whether the dent is a restrained or unrestrained dent. These factors are a function of several axial and transverse dent characteristic lengths and areas.

For deep restrained dents, the shape factors are given in Equation (57.30)

(57.30)

For unrestrained dents, the shape factors are given in Equation (57.31)

(57.31)

For unrestrained dents, Equation (57.31), λ_L and λ_H are scaling factors, which consider the change in the unrestrained dent profile with pipe internal pressure. These scaling factors depend on the pressure that the dent profile was measured and on the mean pressure of the cyclic pressure for which the fatigue life calculation shall be carried out. Appendix F in API RP 1183 2020 provides the tabulated data for the scale factors, λ_L and λ_H.

The issues and concerns with the shape parameter-based dent severity assessment for cyclic fatigue loading are discussed in the public domain since API RP published in November 2020 [43–49]. Recently, a detailed verification study of fatigue-based methods in API RP 1183 was performed by Zhu [46]. This is the most comprehensive study. Zhu convincedly indicated that for the BMT/PRCI shape-based assessment, it is a great challenge for users to calculate fatigue life for a plain dent because a set of extremely complicated curve fitting equations need to be used for determining the shape parameter, shape factor, pressure factor, grade scale factor, scaling factor, and others.

57.5.6.2 Level 2 Assessment

There are two approaches recommended by API PR 1183: namely, BMT/PRCI Approach and EPRG/API 579 Approach for Single Peak Plain Dent fatigue life prediction. In the following sections, each of the approaches is presented.

57.5.6.3 Review of the Scientific Basis of the EPRG 2000 Model

EPRG 2000 was a semi-empirical fatigue model; however, it developed based on the fundamental understanding of the commonly used S-N fatigue life in the form of the Basquin equation but reversed its independent variable (A) and dependent variable (N). In a logarithmic scale, the Basquin equation renders itself as a straight line, usually referred to as the S-N curve:

(57.32)

where A is the material- and stress-related independent variable; N is cycles to failure which is the dependent variable, and c and m are the coefficients and index of the Basquin equation. The c and m are constants for a specific material.

In other words, because the development of the model is based on the scientific understanding of the factors that equates the fatigue life to a function that includes material strength, pipe geometry, dent depth, and dent profile [7, 17]. The formulations are shown in Equations (57.33) through (57.38) that show the independent variable “A” is a function of material ultimate tensile strength (UTS), cyclic loading condition σ_A, and stress concentration factor K_d due to the presence of the plain dent:

(57.33)

(57.34)

(57.35)

(57.36)

(57.37)

(57.38)

Where:

• SF = Safety Factor = 10 for API 579
  
• σ_uts = Ultimate Tensile Strength, MPa
  
• σ_A = Stress amplitude at mean stress correction using the Gerber model or equivalent nominal fatigue stress range, MPa
  
• σ_a = Stress amplitude, MPa
  
• σ_max = Maximum stress, MPa
  
• σ_min = Minimum stress, MPa
  
• K_d = Stress concentration factor due to the dent
  
• K_g = Stress enhancement factor for gauge = 1.0 when the gauge is not present.
  
• d_g = Maximum depth of the gauge, mm = 0 (assumed).
  
• H_o = Dent depth when not pressurized, mm
  
• C_s = Dent shape factor, 2.0 for smooth dent (r_d ≥ 5t) and 1.0 for sharp dent (r_d < 5t)
  
• t = pipe wall thickness, mm
  
• D_o = pipe outside diameter, mm
  
• r_d = radius at the base of dent, mm

However, even though the EPRG 2000 model is built on the scientific understanding of the factors affecting S-N fatigue life for the unconstrained plain dent, the establishment of the EEPRG 2000 model is not analytical but semi-empirical. The model adopted the S-N equation from DIN 2413-1:1993-10 part 1, resulting in extreme conservativism. DIN 2413-1:1993-10 part 1 is a German standard for the design of steel pressure pipes and is now withdrawn [71–73]. A detailed review of the EPRG 2000 methodology and its development revealed that some unnecessary factors are involved in the method [73]. An attempt has been made in this study to develop a more realistic estimation of dent fatigue lives, which is presented in the following section.

57.5.6.4 Improvement of the EPRG 2000 Equation and Validation

For improvement of the EPRG 2000 equation, the following approach is used:

• Based on the understanding of the scientific basis, the EPRG 2000 formula, Equation (57.39) remains unchanged for the refinement:
  
  (57.39)
  
  
• Instead of selecting c and m from any existing dent-free S-N curves, the least squares linear regression in logarithmic scale (the above equation renders itself as a straight line) is used to determine c and m utilizing the PRCI MD 4-2 full-scale fatigue testing data for the improvement.
  
• σ_UTS and σ_A are the same as the data points given in the MD 4-2 report [74].
  
  
  
  • K_d is a function of OD (the pipe outer diameter), wt (the pipe wall thickness), Ho (the dent depth at zero pressure), and Cs (the dent shape factor),
    
  • Finally, additional refinement of c and m is made to improve predictions:

Using the above approach, the refined EPRG model, Equation (57.40), is obtained:

(57.40)

The improved EPRG equation is further validated using PRCI MD 4-11, 4-14, and 4-15 full-scale testing data. The results are shown in Figure 57.28.

Figure 57.29 shows that all the lab test data, MD 4-2 [74], MD 4-11 [75], and MD 4-14 [76], MD 4-15 [77], are above SF = 2 line except for three out of eleven test data of field dents, MD 4-15 data [77], that are below. However, and more importantly, all the data points (MD 4-2 to MD 4-15) are well above the SF = 5 line, indicating that the improved model satisfies the PHMSA MEGA rule [78].

The scatter band for field dent test results is slightly higher than the test results on lab-fabricated dents. The higher scatter band for field dents compared to the lab-fabricated dents is expected [77], considering that the lab-fabricated dents were in controlled conditions. The field dents tested were all removed from former in-service pipelines donated by different pipeline operators and formed under different operating conditions.

57.5.6.5 Execution of the Modified EPRG Model: Excel Based Software

Execution of the improved EPRG equation can be simply accomplished by using an EXCEL-BASED SOFTWARE. The software requires seven inputs: dent depth under pressure H_t, outer diameter OD and wall thickness wt of the pipe, ultimate strength σ_UTS, maximum and minimum cyclic pressures Pmax, Pmin, and the dent shape factor Cs. Two outputs for the model predictions of cycles to failure: one for the modified EPRG and the other for the original EPRG 2000. In addition, the software allows for the operator to select the safety factor for each model based on the operator’s integrity management plans or PHMSA’s rule. Figure 57.30 is a screenshot of the software.

From the above results, it may be concluded that, the improved EPRG equation is built on the scientific understanding of the factors that contributed to the single-peak plain dent. The model is simple and can be executed with Excel-based software.

57.5.6.6 Level 3 Dent Fatigue Life Assessment

The Level 3 assessment employs a detailed nonlinear finite element analysis (FEA) model that has been validated against full-scale dented pipeline fatigue trial data. This model provides a fatigue life assessment for mechanical damage features and forms the basis for the development of the Level 1 and 2 approaches. The detailed finite element model is intended to be used in fitness for purpose assessments of high-consequence dent features and/or for undertaking the assessment of dent features that at present cannot be assessed using the Level 1 or Level 2 assessment approaches. The Level 3 assessment based on FE modeling provides a more accurate method, where the crack growth can be simulated by nonlinear numerical analysis.

The responses of the dented pipe segment to internal pressure fluctuations defined by the pressure range and mean pressure histogram are used to define the dent fatigue life. The finite element models employed are complex and should be developed to consider material and structural nonlinearity as well as indenter contact and forming process. The models should be validated to demonstrate that they agree with full-scale trial data and comply with the Level 3 modeling requirements of API 579.

The concept of a dent being treated as a stress concentrating feature, with a single value regardless of internal pressure, should be used carefully because the ratio of pressure to maximum dent stress will change in a nonlinear fashion as the dent shape changes.

The concept of treating a dent as a stress concentration and applying a single stress concentration factor that linearly relates the internal pressure to the dent stress condition should be considered an engineering approximation that should be managed carefully to ensure conservatism. This is supported by the API 579 Fitness-For-Service, PART 12 (12.4.4.2) [79], Assessment of Dents, Gouges, and Dent-Gouge Combinations which states that, “The numerical stress analysis should be performed considering the material as well as geometric non-linearity in order to account for the effect of pressure stiffening on the dent and re-rounding of the shell that occurs under pressure loading”.

FE modeling approaches that ignore dent formation history are simple and computationally quicker as compared to the iterative approaches that include the dent formation stage that matches the stabilized dent shape at the inspection pressure. Although the Level 3 approach is an accurate and reliable way of assessing dent severity, it is desirable to have simplified approaches that do not require FE modeling and can be used to rapidly rank dent severity based on the given dent geometry and pipeline pressure spectrum.

57.5.6.7 Comparison of the Improved EPRG Equation with BS 7608 Class D and FEA Model for Fatigue Life Prediction

API RP 1183 adopted BS 7608 [46] Class D stress-range Sr-based S-N correlation, Equation (57.41), for unconstrained single-peak plain dent fatigue life prediction:

(57.41)

In the equation, S_r is the stress range in any one cycle (in N/mm²), which is the only variable in the equation and so far is thought that it can be determined only by using FEA for each dent. The stress range S_r distribution for each of the unconstrained plain dents from MD-4-2 and 4-11 was determined by FEA and is shown in (1) of Figure 57.31. The maximum S_r is extracted and used for fatigue life predictions using Equation (57.41), the BS 7608 Class D S-N Design equation [80]. The FEA model predicted fatigue life for unrestrained plain dent prediction is shown in (2) of Figure 57.31. In the plot, the Y-axis is stress range, Sr, and the X-axis is the number of cycles to failure.

It is noted in the improved EPRG equation plot. The Y-axis is the dependent variable, i.e., cycles to failure N, while the X-axis is the independent variable, i.e., which is the opposite used by the API RP 1183 plot. In addition, the API RP 1183 plot only includes two sets of test data, i.e., M 4-2 and MD 4-11 data with two lines: model prediction and model prediction minus one standard deviation (1 st dev). Therefore, two changes are made to the modified EPRG plots for comparison, accordingly.

Figure 57.32 shows plots of two models: (1) the improved EPRG model and (2) API RP 1183 Level 3 model. In the figure, the dashed lines are the model predictions, and the solid lines are the model predictions minus one standard deviation. Because the data points above and between the model prediction and minus one standard deviation are nearly the same, it suggests that both models are equivalent.

A comparison of the improved EPRG model and API RP 1183 Level 3 FE approaches has clearly demonstrated that the improved EPRG model is indeed the simplified Level 3 that API RP 1183 is looking for. As indicated previously, execution of the improved EPRG equation can be simply accomplished by using Excel-based software for less than 1 h for ILI or field excavation data.