In the realm of pressure vessel integrity management, particularly during periodic in-service inspections, the accurate detection and precise sizing of welding defects are paramount for safety assessment and remaining life evaluation. Among various flaw types, slag inclusions are a common imperfection arising from the entrapment of non-metallic residues within the weld metal during solidification. While often benign if sufficiently small and isolated, clusters or elongated slag inclusions can act as stress concentrators, potentially initiating cracks under cyclic loading or aggressive environments. The critical task for inspectors is not only to locate these slag inclusions but, more importantly, to measure their planar dimensions—length and, crucially, their through-wall height—with high accuracy. Traditional ultrasonic testing (UT) methods, while reliable for detection and length sizing, have historically shown significant limitations and variability in determining the exact through-wall extent or “self-height” of planar flaws like slag inclusions. This uncertainty can directly impact the fitness-for-service assessment, potentially leading to overly conservative decisions (unnecessary repairs) or, worse, non-conservative ones (underestimation of risk). This study, conducted from a first-person engineering perspective, details a comprehensive investigation into the quantitative sizing of a specific cluster of slag inclusions discovered in a longitudinal weld seam of a critical esterification reactor. We employed a multi-faceted approach, beginning with advanced simulation to understand acoustic responses, followed by a practical comparative assessment using four distinct ultrasonic techniques: Conventional Ultrasonic Testing (UT), Phased Array Ultrasonic Testing (PAUT), Total Focusing Method (TFM), and Time-of-Flight Diffraction (TOFD). Our goal was to benchmark the performance of these methods, with a special focus on the challenging measurement of defect self-height.
The subject of this investigation was a first-inspection esterification reactor (designated R-1102) operating in a chemical plant. The vessel’s primary duty involved facilitating reversible reactions between acids and alcohols. Its construction featured a Q345R steel shell with a 3mm thick explosively bonded titanium cladding on the internal surface, a common design for corrosion resistance in aggressive process environments. Key design and operational parameters are summarized in the table below.
| Component | Parameter | Value |
|---|---|---|
| Shell | Material | Q345R + TA2 Clad |
| Thickness | 30 mm (Steel) + 3 mm (Titanium) | |
| Design | Pressure | 2.32 MPa |
| Temperature | 130 °C | |
| Operation | Pressure | 2.13 MPa |
| Temperature | 70 – 110 °C | |
| Service Life at Inspection | 3 years | |
During the routine volumetric examination, a conventional ultrasonic scan indicated the presence of an indictable linear indication within a longitudinal weld. The weld joint configuration was a standard double-V preparation. Initial UT evaluation suggested a cluster of slag inclusions. According to the governing safety code (analogous to TSG 21-2016), the classification of such linear defects into safety rating levels (e.g., Level 3, 4, or 5) hinges precisely on the measured length (L) and the self-height (H). The acceptance criteria often follow a relationship such as:
$$ H \leq \min(0.2t, 4 \text{ mm}) \quad \text{and} \quad L \leq 6t $$
where \( t \) is the material thickness. While length measurement is relatively straightforward, height measurement is the principal source of uncertainty. Literature suggests that height measurement errors using conventional ultrasonic amplitude-based techniques (like the 6dB drop method) can average over 40%. Therefore, accurately determining the ‘H’ value for these slag inclusions was the central challenge of this inspection.
To strategically plan the inspection and predict the capabilities of different methods, we first turned to numerical simulation using the CIVA nondestructive evaluation platform. CIVA allows for the modeling of ultrasonic wave propagation and interaction with defects in complex geometries. We constructed a 2D model representing the reactor’s clad wall and created a defect cluster to mimic the suspected slag inclusions. The cluster was modeled as three separate, closely spaced planar slag inclusions:
- Flaw F1: Height = 1.5 mm
- Flaw F2: Height = 1.0 mm (circular shape was simplified for 2D simulation)
- Flaw F3: Height = 2.0 mm
The longitudinal separation between adjacent flaws was set at 0.5 mm. Thus, the cumulative through-wall height of the cluster was 5.5 mm. We simulated two advanced techniques: the Total Focusing Method (TFM) and Time-of-Flight Diffraction (TOFD).
The TFM simulation, using a virtual phased array probe, produced a high-resolution image. The algorithm synthetically focuses at every pixel in the region of interest, dramatically improving signal-to-noise ratio and spatial resolution. The simulated TFM image clearly resolved the three individual slag inclusions (F1, F2, F3) within the cluster. Using the 6dB drop method (simulated) on the TFM image, the measured total height was 5.9 mm, representing a small overestimation of 0.4 mm (7.3% error). The formula for the amplitude-based sizing in the simulation can be related to the pixel intensity \( I(x,z) \):
$$ H_{\text{TFM}} = z_{\text{bottom}}(I = 0.5 \cdot I_{\text{max}}) – z_{\text{top}}(I = 0.5 \cdot I_{\text{max}}) $$
where \( z_{\text{top}} \) and \( z_{\text{bottom}} \) are the depth coordinates at the -6dB points.
Subsequently, a TOFD simulation was performed. TOFD relies on the diffraction of ultrasonic waves from the tips of a defect. The depth (\( d \)) of a diffractor is calculated from the time-of-flight (\( t \)) of the diffracted signal, the probe separation (2S), and the material sound velocity (\( c \)):
$$ d = \sqrt{\left( \frac{ct}{2} \right)^2 – S^2} $$
The self-height \( H \) is then the difference between the depths of the top and bottom tip diffractions: \( H = d_{\text{bottom}} – d_{\text{top}} \). The TOFD simulation successfully identified the defect cluster. However, due to the close proximity of the individual slag inclusions, their diffracted signals merged, making it impossible to distinguish them individually—a key difference from TFM imaging. The measured height from the simulated TOFD A-scan data was 5.7 mm, an error of only 0.2 mm (3.6% error). This simulation phase provided strong theoretical evidence that both TFM and TOFD offered superior height-sizing accuracy for these slag inclusions compared to the known limitations of conventional UT, with TFM providing superior defect characterization (shape, multiplicity).
Guided by the simulation results, we proceeded with the physical inspection using all four techniques on the actual reactor. The inspection procedures were calibrated on reference blocks matching the clad material thickness and curvature.
1. Conventional Ultrasonic Testing (UT):
A standard single-element, angle-beam probe (e.g., 45°, 5 MHz) was used. The length was determined by scanning the probe along the weld and marking the points where the echo amplitude dropped to 50% of its maximum (the 6dB drop method). The height was estimated using the same amplitude-drop technique in the vertical direction by maximizing the signal and moving the probe to find the amplitude fall-off points above and below the defect. This method yielded: \( L_{UT} = 29.5 \) mm, \( H_{UT} = 9.2 \) mm. The significant overestimation of height (9.2 mm vs. the later verified ~5.5 mm) is characteristic of the poor vertical resolution of conventional angle-beam probes and the influence of defect orientation and surface roughness on echo amplitude.
2. Phased Array Ultrasonic Testing (PAUT – S-Scan):
A linear phased array probe and scanner were employed. The electronic sweeping of beams (S-scan) provided a cross-sectional, real-time image of the weld. The PAUT S-scan clearly showed a single, elongated response zone suggesting a cluster of slag inclusions. While it indicated the defect was likely not a single entity, the individual reflectors were not distinctly resolved. Sizing was performed using software tools on the focused S-scan image. Results: \( L_{PAUT} = 28.7 \) mm, \( H_{PAUT} = 6.6 \) mm. This was a marked improvement over conventional UT, reducing the height error significantly.
3. Total Focusing Method (TFM):
Using the same phased array probe, a Full Matrix Capture (FMC) dataset was acquired. Here, every element in the array acts sequentially as a transmitter, and all elements record the reflected signals. This \( N \times N \) matrix of A-scans is then processed offline using the TFM algorithm, which focuses computationally on every point in the image. The resulting TFM image was strikingly clear. It definitively showed the defect as a cluster of three distinct, bright reflectors aligned vertically, closely matching our initial CIVA simulation model. The 3mm titanium clad interface was also sharply imaged. Measurement on this high-resolution image gave: \( L_{TFM} = 26.8 \) mm, \( H_{TFM} = 6.0 \) mm. The height measurement was now much closer to the expected value from simulation.
4. Time-of-Flight Diffraction (TOFD):
A dedicated TOFD system with a matched pair of longitudinal wave probes (transmitter and receiver) was set up straddling the weld. The A-scan data, displayed as a grayscale B-scan, showed characteristic hyperbolic arcs from the top and bottom edges of the defect. The lateral wave and backwall echo provided clear reference lines. The depth of the defect tips was calculated directly from the time difference between the lateral wave and the diffracted signals using the formula mentioned earlier. The distance between the probes (2S) was a critical, precisely measured parameter. The TOFD analysis provided: \( L_{TOFD} = 27.5 \) mm, \( H_{TOFD} = 5.8 \) mm.
The results from all four methods, along with the subsequent verification, are consolidated in the table below. The vessel owner, presented with the consistent data from TFM and TOFD indicating a defect height exceeding the code’s threshold for a Level 3 rating, authorized a local excavation (repair) of the weld section. This allowed for physical verification of the defect’s true dimensions.
| Inspection Method | Measured Length, L (mm) | Measured Self-Height, H (mm) | Error in H vs. Actual (mm) | Key Observation |
|---|---|---|---|---|
| Conventional UT (6dB drop) | 29.5 | 9.2 | +3.7 | Severe overestimation; poor vertical resolution. |
| PAUT (S-scan) | 28.7 | 6.6 | +1.1 | Improved; indicates clustering but low resolution. |
| TFM (FMC processed) | 26.8 | 6.0 | +0.5 | Excellent resolution; clearly shows 3 distinct slag inclusions. |
| TOFD | 27.5 | 5.8 | +0.3 | High precision for height; diffracted signals merged for cluster. |
| Actual (After Excavation) | ~27.0 | ~5.5 | 0 | Cluster of three slag inclusions confirmed. |
The analysis of the comparative data leads to several critical conclusions regarding the quantitative assessment of slag inclusions:
1. Defect Length Measurement: All four ultrasonic methods provided reasonably consistent and accurate length measurements for the cluster of slag inclusions. The maximum deviation from the actual length was less than 2.5 mm (under 10% error), which is generally acceptable for fitness-for-service evaluations against length-based criteria. The consistency stems from the fact that length sizing primarily relies on lateral scanning, which is a strength of even basic ultrasonic methods.
2. Defect Self-Height Measurement – The Core Challenge: This is where the methods diverged significantly. The performance can be ranked as follows:
- TOFD and TFM demonstrated superior accuracy, with errors of +0.3 mm and +0.5 mm, respectively. Their underlying physics—diffraction timing and synthetic aperture focusing—provide direct or highly resolved depth information that is largely amplitude-invariant.
- PAUT (S-scan) offered a substantial improvement over conventional UT but still overestimated the height by 1.1 mm (20% error). Its electronic focusing improves resolution but is still subject to some amplitude-based sizing uncertainties.
- Conventional UT performed poorly, overestimating the height by 67% (3.7 mm). This level of inaccuracy could directly lead to a non-conservative assessment if the defect were near a critical threshold, or to an overly conservative and costly repair decision.
The error in conventional UT can be modeled conceptually. The measured height \( H_{m} \) is often a function of the beam width \( W \), defect tilt angle \( \theta \), and the true height \( H_t \): $$ H_{m} \approx \frac{H_t}{\cos \theta} + W \cdot \sin \theta $$ This shows how beam spread and orientation inflate the measurement.
3. Defect Characterization and Resolution: Beyond mere sizing, understanding the defect’s nature is valuable. TFM provided unparalleled insight, clearly resolving the individual slag inclusions within the cluster. This information—knowing the flaw is a cluster of small, separated slag inclusions rather than a single large one—can be critical for a more nuanced engineering critical assessment (ECA), potentially affecting crack initiation and growth predictions. PAUT gave a hint of this clustering, while TOFD and conventional UT treated the cluster as a single entity.
From a practical engineering and inspection standpoint, this case study strongly advocates for the adoption of advanced ultrasonic imaging techniques, specifically TFM and TOFD, for the precise quantitative analysis of planar defects like slag inclusions in critical welds. While conventional UT remains a valuable and efficient screening tool, its limitations in height sizing are clear and potentially consequential. A combined approach, perhaps using PAUT/TOFD for rapid scanning and TFM for detailed characterization of significant indications, represents a robust strategy. This multi-method validation framework ensures high-integrity data for fitness-for-service evaluations, enabling plant owners to make informed, optimized decisions regarding repair, re-rating, or continued operation, thereby ensuring both safety and economic efficiency. The accurate quantification of slag inclusions is not merely a technical exercise but a fundamental pillar of reliable asset integrity management.