In the field of pressure vessel inspection, particularly during periodic assessments, the accurate quantification of weld defects is paramount for ensuring structural integrity and operational safety. Among various flaws, slag inclusion defects pose a significant challenge due to their irregular morphology and potential to act as stress concentrators, leading to crack initiation and propagation. This article delves into a comprehensive study on the detection and sizing of a slag inclusion defect discovered in the longitudinal weld of an esterification reactor during its first in-service inspection. We employ a multi-faceted approach, combining simulation studies with practical ultrasonic testing methods, to evaluate the effectiveness of different techniques in measuring the defect’s length and, more critically, its self-height. The self-height of a slag inclusion defect is a key parameter in safety assessment codes, as it directly influences the defect’s severity rating and the subsequent decision for repair or continued service. Our work aims to bridge the gap between theoretical simulation and field application, providing insights into optimal non-destructive testing (NDT) strategies for such defects.
The core of our investigation revolves around a specific slag inclusion defect found in a reactor vessel. We begin by outlining the equipment’s specifications and the defect’s context. Following that, we utilize CIVA simulation software to model the acoustic response of the slag inclusion defect under different ultrasonic inspection modalities, specifically focusing on the Total Focusing Method (TFM) and Time-of-Flight Diffraction (TOFD). These simulations help predict the detectability and sizing accuracy before physical testing. Subsequently, we conduct actual inspections using four distinct ultrasonic methods: Conventional Ultrasonic Testing (UT), Phased Array Ultrasonic Testing (PAUT), TFM, and TOFD. A comparative analysis of the results from these methods is presented, with emphasis on the measurement of the defect’s self-height. Finally, we discuss the findings in light of relevant safety standards and the outcomes from the defect’s repair and physical dissection, which served as a ground truth for validation.
Equipment Overview and Defect Context
The subject of this study is an esterification reactor, designated as R-1102, which is a common pressure vessel in fine chemical processes. It facilitates the reversible reaction between acids and alcohols in the presence of a catalyst to produce esters and water. The reactor had been in service for three years prior to its first periodic inspection. Key design and operational parameters are summarized in the table below. A notable feature is the internal cladding of a 3mm thick titanium layer, which is bonded to the carbon steel base material (Q345R) to enhance corrosion resistance. This bi-metallic structure introduces complexities for ultrasonic inspection due to the acoustic impedance mismatch at the interface.
| Parameter | Value |
|---|---|
| Shell Material | Q345R |
| Shell Thickness | 30 mm (base) + 3 mm (Ti cladding) |
| Head Material | Q345R |
| Head Thickness | 30 mm (base) + 3 mm (Ti cladding) |
| Design Pressure | 2.32 MPa |
| Design Temperature | 130 °C |
| Operating Pressure | 2.13 MPa |
| Operating Temperature | 70–110 °C |
| Service Duration | 3 years |
| Working Medium | C4 mixture, acetic acid mixed esters, water |
The weld joint where the slag inclusion defect was located is a butt weld. The presence of the titanium cladding layer means the ultrasound must traverse this interface before interacting with defects in the base metal weld. During routine ultrasonic inspection, a subsurface indication was identified in a longitudinal seam. Initial assessment suggested it was a slag inclusion defect. According to safety regulations like TSG 21-2016 (Fixed Pressure Vessel Safety Technical Supervision Regulation), the classification of a linear slag inclusion defect into a safety level depends on its length (L) and its self-height (H). While length measurement is relatively straightforward with ultrasound, accurately determining the self-height of a slag inclusion defect is notoriously difficult. The self-height refers to the through-thickness dimension of the flaw. Inaccurate height measurement can lead to incorrect safety ratings—either unnecessary repairs or, more dangerously, the acceptance of a critical defect. This forms the motivation for our detailed study.
Simulation Study of Slag Inclusion Defect Response
To theoretically analyze the detection and sizing capability for the slag inclusion defect, we performed simulations using the CIVA NDT simulation platform. CIVA allows for the modeling of complex inspection scenarios, including probe characteristics, beam propagation in multi-layered media, and interaction with various defect types. We constructed a model representing the reactor’s wall: a 30 mm thick Q345R steel base with a 3 mm titanium layer on the inner surface. Within the weld metal, we introduced a slag inclusion defect. Based on the initial UT indications, we modeled this slag inclusion defect as an aggregate of three smaller, closely spaced slag inclusions to mimic a realistic cluster. The defect parameters in the simulation were as follows:
- Defect F1: A linear slag inclusion, height = 1.5 mm.
- Defect F2: A circular slag inclusion, height = 1.0 mm.
- Defect F3: A linear slag inclusion, height = 2.0 mm.
The longitudinal separation between adjacent defects was set at 0.5 mm. Thus, the combined overall height of this slag inclusion defect cluster was 5.5 mm (1.5 + 0.5 + 1.0 + 0.5 + 2.0 = 5.5 mm, accounting for gaps). The total length was defined based on the aggregate.
First, we simulated inspection using the Total Focusing Method (TFM), an advanced phased array technique. TFM uses full matrix capture (FMC) data and synthesizes a focused beam at every point in the region of interest, providing superior resolution. The simulation setup involved a linear phased array probe with appropriate frequency and element count, placed on the outer steel surface. The simulated TFM image clearly resolved the three individual components (F1, F2, F3) of the slag inclusion defect. Using the 6 dB drop method (or endpoint diffraction technique) on the simulated image, the measured total height of the slag inclusion defect was 5.9 mm. This represents an error of 0.4 mm compared to the actual modeled height of 5.5 mm. The simulation demonstrated TFM’s potential for high-resolution imaging and accurate height measurement of clustered slag inclusion defects.
The signal amplitude from a point reflector in TFM can be related to the beamforming process. The synthetic focus at a point \( \vec{r} \) is achieved by summing the delayed signals from all transmitter-receiver pairs. The pressure field can be expressed as:
$$ P_{TFM}(\vec{r}) = \sum_{i=1}^{N} \sum_{j=1}^{N} w_i w_j s_{ij}(t_{ij}(\vec{r})) $$
where \( N \) is the number of array elements, \( w_i, w_j \) are weighting factors, \( s_{ij} \) is the signal from transmitter i and receiver j, and \( t_{ij}(\vec{r}) \) is the time delay for the path from element i to point \( \vec{r} \) and back to element j. For a slag inclusion defect, the scattering response \( s_{ij} \) depends on the defect’s geometry and orientation.
Next, we simulated the Time-of-Flight Diffraction (TOFD) technique for the same slag inclusion defect configuration. TOFD relies on the diffraction of ultrasound from the tips of a defect. It is renowned for accurate depth and height sizing. In the simulation, we used a typical TOFD setup with a transmitter-receiver pair separated by a specific offset. The simulated TOFD B-scan showed a clear diffraction signal from the defect. However, due to the close spacing, the individual components of the slag inclusion defect cluster were not distinctly resolved as separate tips; instead, they produced a combined diffraction pattern. Measuring the time difference between the upper and lower tip diffraction signals, and converting it to depth using the material sound velocity \( c \), yielded a defect height of 5.7 mm. The height measurement error was 0.2 mm, slightly better than the TFM simulation for this case. The diffraction signal arrival time is given by:
$$ \Delta t = \frac{2 \sqrt{d^2 + (H/2)^2}}{c} – \frac{2d}{c} $$
where \( d \) is the depth of the defect center, \( H \) is the defect height, and \( c \) is the shear wave velocity. For small \( H \) relative to \( d \), this approximates to \( \Delta t \approx \frac{H^2}{4dc} \), illustrating the sensitivity to height.
The simulation results confirmed that both TFM and TOFD are capable of providing accurate height measurements for the slag inclusion defect, with TOFD having a marginal edge in absolute accuracy for this specific model, but TFM offering superior defect characterization and resolution of individual features within the slag inclusion defect cluster. This preliminary analysis guided our subsequent experimental approach.
Comparative Ultrasonic Testing in Practice
Guided by the simulation insights, we proceeded to inspect the actual reactor weld containing the suspected slag inclusion defect. We employed four ultrasonic testing methods to independently measure the defect’s length and self-height. The inspection was conducted from the outer surface of the vessel. The titanium cladding layer was accounted for in calibration and sound path calculations. Below, we detail the setup, procedures, and results for each method.
1. Conventional Ultrasonic Testing (UT)
We used a standard pulse-echo ultrasonic flaw detector with a single-element, normal-incidence longitudinal wave probe of frequency 5 MHz. The probe was scanned manually along the weld. The defect produced a clear echo. Its length was measured by scanning the probe along the weld and noting the positions where the echo amplitude dropped by 50% (6 dB) from its maximum. The self-height of the slag inclusion defect was estimated using the echo amplitude comparison technique (DAC curve) and the 6 dB drop method across the defect’s depth extent. This method is known to have limitations, especially for irregular defects like slag inclusions, as it assumes a smooth, reflective surface. The measured dimensions were:
– Length (L_UT) = 29.5 mm
– Self-height (H_UT) = 9.2 mm
The relatively large measured height suggested a potentially severe slag inclusion defect.
2. Phased Array Ultrasonic Testing (PAUT)
We employed a linear phased array probe with 64 elements, frequency 5 MHz, and a 0.6 mm pitch. A sectorial scan (S-scan) was performed, covering an angular range from 40° to 70° with longitudinal waves. The PAUT system allows for electronic scanning and beam steering, providing a cross-sectional view of the weld. The image showed an indication consistent with a slag inclusion defect. The defect appeared as a cluster of reflectors but lacked the resolution to clearly separate individual components. The length and height were measured using the software’s sizing tools based on the sector scan image. The results were:
– Length (L_PAUT) = 28.7 mm
– Self-height (H_PAUT) = 6.6 mm
The height measurement was notably smaller than that from conventional UT, highlighting the improved sizing capability of phased array for this slag inclusion defect.
3. Total Focusing Method (TFM)
Using the same phased array probe, we acquired Full Matrix Capture (FMC) data. All possible transmit-receive element combinations were recorded. This data was then post-processed using the TFM algorithm to generate a high-resolution image of the inspection region. The TFM image remarkably revealed the internal structure of the slag inclusion defect. It clearly showed three distinct reflective regions, closely spaced, corresponding to the simulated F1, F2, F3 cluster. This level of detail was not visible in the standard PAUT S-scan. Furthermore, the echo from the titanium-steel interface was distinctly visible, demonstrating the method’s high resolution. Using the image analysis tools, we applied the 6 dB drop method to the top and bottom edges of the defect cluster to measure its height. The measured dimensions were:
– Length (L_TFM) = 26.8 mm
– Self-height (H_TFM) = 6.0 mm
The TFM result provided a more refined height measurement and confirmed the clustered nature of the slag inclusion defect.
4. Time-of-Flight Diffraction (TOFD)
A dedicated TOFD system was used with a pair of longitudinal wave probes (transmitter and receiver) operating at 5 MHz, with a specific separation (PCS) optimized for the weld thickness. The probes were scanned along the weld. The TOFD B-scan displayed the characteristic lateral wave, backwall echo, and diffraction signals from the defect tips. The diffraction signals from the upper and lower extremities of the slag inclusion defect were identified. The depth and height were calculated from the time differences between these signals. TOFD is considered one of the most accurate methods for height sizing. The measurements obtained were:
– Length (L_TOFD) = 27.5 mm (determined by the extent of the diffraction signals along the scan axis)
– Self-height (H_TOFD) = 5.8 mm
This height measurement was the smallest among all techniques and was very close to the expected value from simulations.
We summarize the comparative results from all four methods in the table below. The variation in measured height, particularly the large value from conventional UT, underscores the challenge of sizing slag inclusion defects accurately.
| Inspection Method | Measured Length (mm) | Measured Self-Height (mm) | Notes |
|---|---|---|---|
| Conventional UT | 29.5 | 9.2 | Largest height measurement, likely overestimation. |
| PAUT (S-scan) | 28.7 | 6.6 | Improved resolution over UT, but cluster details not clear. |
| TFM (FMC-based) | 26.8 | 6.0 | High-resolution image, revealed clustered structure of slag inclusion defect. |
| TOFD | 27.5 | 5.8 | Most accurate height measurement based on diffraction. |
Safety Assessment and Defect Repair Validation
Based on the inspection data, the slag inclusion defect required evaluation against the acceptance criteria of the applicable safety code, TSG 21-2016. For a linear slag inclusion defect, the safety level (ranging from 1 to 5, with 5 being the most severe) is determined by its length and self-height relative to the material thickness (t). The relevant clause states that for a level 3 rating, the self-height H must satisfy \( H \leq 0.2t \) and \( H \leq 4 \) mm, and the length L must satisfy \( L \leq 6t \), where t is the measured wall thickness (30 mm in this case).
Calculating the limits:
– \( 0.2t = 0.2 \times 30 = 6.0 \) mm.
– The absolute limit for H is 4 mm.
– \( 6t = 6 \times 30 = 180 \) mm.
All methods reported lengths well below 180 mm. However, for height:
– UT: H_UT = 9.2 mm > 4 mm and > 6.0 mm.
– PAUT: H_PAUT = 6.6 mm > 4 mm and > 6.0 mm.
– TFM: H_TFM = 6.0 mm > 4 mm but equal to 6.0 mm.
– TOFD: H_TOFD = 5.8 mm > 4 mm but less than 6.0 mm.
Since the height exceeded 4 mm according to all measurements (with UT being a clear outlier), the defect could not be assigned a safety level 3. According to the code, it would be classified as level 4 or 5, necessitating repair. The plant management decided to repair the weld section containing the slag inclusion defect. This provided a unique opportunity for physical dissection and validation.
After gouging out the weld metal around the defect, the slag inclusion was exposed. Careful physical measurement using precision tools yielded the actual dimensions of the slag inclusion defect:
– Actual Length (L_actual) = 27.0 mm
– Actual Self-Height (H_actual) = 5.5 mm
These values confirmed that the slag inclusion defect was indeed a cluster of smaller slag particles, with a total height of 5.5 mm. Comparing the actual dimensions with the NDT measurements allows us to calculate the percentage errors for each method. This is summarized in the table below.
| Method | Length Error (%) | Height Error (%) | Absolute Height Error (mm) |
|---|---|---|---|
| Conventional UT | +9.3% | +67.3% | +3.7 |
| PAUT | +6.3% | +20.0% | +1.1 |
| TFM | -0.7% | +9.1% | +0.5 |
| TOFD | +1.9% | +5.5% | +0.3 |
The analysis reveals several key points:
1. Length Measurement: All methods performed reasonably well for length, with errors under 10%. The TFM result was closest to the actual length.
2. Height Measurement: This is where significant differences emerge. Conventional UT grossly overestimated the height of the slag inclusion defect by 67%, which could lead to overly conservative and costly repairs. PAUT reduced the error to 20%, a substantial improvement. TFM and TOFD delivered the best performance, with height errors of 9.1% and 5.5%, respectively. The absolute error for TOFD was only 0.3 mm, demonstrating its precision for sizing the self-height of this slag inclusion defect.
3. Defect Characterization: TFM provided unparalleled insight into the morphology of the slag inclusion defect, successfully resolving its clustered nature. This information is valuable for understanding the defect’s origin and potential behavior under stress.
Theoretical Analysis and Formula Application
To further understand the ultrasonic response of slag inclusion defects, we can consider some fundamental principles. The reflection and diffraction of ultrasound depend on the defect’s size, shape, orientation, and acoustic impedance contrast with the base material. A slag inclusion defect typically consists of non-metallic oxides with lower density and sound velocity than steel. This impedance mismatch causes reflection.
The reflection coefficient \( R \) for normal incidence at an interface between two media with acoustic impedances \( Z_1 \) (steel) and \( Z_2 \) (slag) is:
$$ R = \frac{Z_2 – Z_1}{Z_2 + Z_1} $$
For slag, \( Z_2 \) is much smaller than \( Z_1 \) for steel, so \( R \) is negative and its magnitude is less than 1, indicating a partial reflection. The amplitude of the reflected signal from a planar slag inclusion defect of area \( A \) at a distance \( x \) can be modeled as:
$$ A_{reflect} = A_0 \cdot R \cdot \frac{A}{x} \cdot e^{-\alpha x} $$
where \( A_0 \) is the initial amplitude, and \( \alpha \) is the attenuation coefficient. For a distributed slag inclusion defect cluster, the signal is a superposition of reflections from individual facets.
For height measurement using diffraction (as in TOFD), the key is the arrival time difference \( \Delta t \) between the top and bottom tip signals. For a defect at depth \( d \) below the surface, with probe center separation \( 2S \), the travel time for a tip at depth \( z \) is:
$$ t(z) = \frac{\sqrt{S^2 + (z + \frac{H}{2})^2} + \sqrt{S^2 + (z – \frac{H}{2})^2}}{c} $$
where \( c \) is the sound velocity. The time difference \( \Delta t = t_{bottom} – t_{top} \) simplifies to the expression given earlier when \( z = d \). Accurate measurement of \( \Delta t \) allows precise calculation of \( H \), the self-height of the slag inclusion defect.
In TFM, the signal-to-noise ratio (SNR) enhancement is achieved through coherent summation. The SNR gain for a point target is proportional to \( N \), the number of array elements. For an extended defect like a slag inclusion defect, the focusing gain improves the separation of signals from nearby reflectors. The lateral resolution \( \delta_x \) and axial resolution \( \delta_z \) in TFM can be approximated by:
$$ \delta_x \approx \frac{\lambda F}{D}, \quad \delta_z \approx \frac{c}{2B} $$
where \( \lambda \) is the wavelength, \( F \) is the focal distance, \( D \) is the aperture size, and \( B \) is the bandwidth of the probe. High resolution is crucial for characterizing the intricate details of a clustered slag inclusion defect.
Discussion on Method Selection and Practical Implications
The comparative study clearly indicates that for critical sizing of slag inclusion defects, especially their self-height, advanced techniques like TFM and TOFD are superior to conventional methods. While conventional UT is widely available and useful for defect detection, its sizing accuracy, particularly for height, is often inadequate for precise code compliance assessment. This can result in unnecessary repairs or, in worse cases, missed critical defects. PAUT offers a good balance between speed and improved sizing, but for the highest accuracy in height measurement and defect characterization, TFM and TOFD are recommended.
In practice, the choice of method may depend on factors such as accessibility, equipment availability, time constraints, and the specific code requirements. For instance, TOFD is often mandated for critical welds due to its reliable height sizing. However, TOFD has a “dead zone” near the surface and may not provide detailed defect morphology. TFM, while computationally intensive and requiring specialized equipment, provides a comprehensive visual map of the defect, which is invaluable for engineering critical assessment (ECA). A combined approach using TOFD for accurate height measurement and TFM for defect characterization could offer the most complete evaluation of a slag inclusion defect.
Furthermore, the presence of cladding layers, as in this reactor, adds complexity. The titanium layer causes signal attenuation and mode conversion. Both simulation and practical inspection must account for this. Calibration on representative mock-ups with similar cladding is essential for accurate sizing. The success of TFM in clearly imaging the titanium interface in our test demonstrates its capability to handle such multi-layer structures.
The repeated focus on the term ‘slag inclusion defect’ throughout this analysis underscores its importance as a common yet challenging flaw in welded pressure equipment. Accurate NDT is the first line of defense against failure. Continuous improvement in ultrasonic techniques, supported by simulation tools like CIVA, enhances our ability to reliably size and assess these defects.
Conclusion
This detailed investigation into the ultrasonic detection and sizing of a slag inclusion defect in an esterification reactor weld has yielded significant insights. Through CIVA simulation, we predicted that both the Total Focusing Method (TFM) and Time-of-Flight Diffraction (TOFD) would provide accurate measurements of the defect’s self-height. Practical field inspection using four methods—Conventional UT, PAUT, TFM, and TOFD—confirmed these predictions. While all methods provided reasonably accurate length measurements for the slag inclusion defect, the height measurement accuracy varied dramatically. Conventional UT overestimated the height by over 67%, PAUT reduced the error to 20%, while TFM and TOFD achieved errors of about 9% and 5.5%, respectively. Physical dissection validated the TOFD measurement as the most accurate for height, and TFM as the best for revealing the clustered morphology of the slag inclusion defect.
From a safety assessment perspective, the accurate height measurement is crucial. Relying solely on conventional UT could have led to an incorrect safety rating—either an overly conservative repair decision or, if the error were in the opposite direction, a dangerous under-assessment. Therefore, for critical applications where slag inclusion defects are suspected, we strongly recommend the use of advanced ultrasonic techniques like TOFD for height sizing and TFM for comprehensive defect characterization. This multi-methodology approach, complemented by simulation-assisted procedure design, represents a robust framework for ensuring the integrity of pressure equipment containing such defects. Future work could involve extending this study to other defect types, different cladding materials, and automated data analysis algorithms to further improve inspection reliability and efficiency.
The mathematical models and error analysis presented here provide a quantitative basis for understanding the performance limits of various ultrasonic techniques when applied to slag inclusion defects. As NDT technology evolves, the integration of simulation, advanced imaging, and data analytics will continue to enhance our capability to safeguard industrial assets against the risks posed by welding flaws like slag inclusions.