Multi-Physics Modeling of Above-Ground Electromagnetic Inspection on Underground Pipeline

Oil spills and gas leaks can result in catastrophic environmental damages, substantial financial losses, and potential human fatalities, highlighting the critical importance of maintaining the integrity of underground pipelines in the oil and gas industry. To monitor the underground pipelines and address such potential risks, various Non-Destructive Evaluation (NDE) methods are currently employed to detect pipeline defects, due to reasons such as cracks and corrosion.

One of the most widely used NDE techniques is In-Line Inspection (ILI), which employs “PIGs” (Pipeline Integrity Gauges). These devices are equipped with sensors that travel through the pipeline to assess the condition of its walls. Despite its widespread use, ILI has significant drawbacks. Implementing ILI requires specialized launching and receiving mechanisms within the pipeline infrastructure, which can be costly and complex. The design of pigs must be tailored to specific pipeline diameters, and their movement can be obstructed by pipeline geometries or internal features. Additionally, the production and deployment of smart pigs are expensive, and retrieving a stuck pig can lead to significant downtime and financial loss [1, 2].

Due to these limitations, ILI is not always feasible for inspecting many pipeline sections. Alternative NDE methods for external inspection, such as ultrasonic guided waves, eddy current and magnetic methods, have been explored. Ultrasonic guided waves, for instance, have an effective inspection range often limited to several meters from the transducer position. This range can be affected by factors such as pipe material, diameter, wall thickness, and the presence of bends or welds. The method is biased towards detecting certain types of defects, such as those oriented perpendicular to the wave propagation direction. Defects that are parallel to the wave propagation may be less detectable. Additionally, ultrasonic waves can attenuate and disperse as they travel along the pipeline, reducing the amplitude and making it more challenging to identify small defects at longer distances. Moreover, the transducers typically need to be directly attached to the pipe’s surface, which requires excavation [3, 4].

Magnetic Particle Inspection (MPI) and Magnetic Flux Leakage (MFL) are commonly used magnetic Non-Destructive Evaluation (NDE) techniques, but they exhibit several limitations. MPI is effective only for detecting surface-breaking and near-surface cracks, as it requires bare metal for visual inspection using fluorescent magnetic particles. This restricts its applicability in coated or insulated materials. Furthermore, the pipe needs to be extracted, and the surface must be adequately prepared before inspection, which adds additional complexity and cost to the evaluation process. Brondel et al. [5]. MFL, on the other hand, is capable of detecting subsurface defects by applying a continuous magnetic field. When defects are present, the magnetic flux leaks, and sensors detect these leaks to identify and locate the issues. However, its sensitivity decreases in thick-walled pipes due to challenges in achieving magnetic saturation. Moreover, axially oriented defects require orthogonal flux rotation, complicating the inspection process. Both techniques are most effective when used on circumferentially oriented defects, but defect characterization and sizing require model comparison, which is often unreliable in industrial conditions [6]. While articulated In-Line Inspection (ILI) tools for unpiggable pipelines using MFL have been proposed, they remain unproven in industry [7]. Pulsed MFL, using discretize magnetic field pulses which offers greater tolerance to standoff distances, is still in research stages, and further development is necessary before it can be widely adopted [8]. These challenges limit the effectiveness of MPI and MFL in certain pipeline inspection applications, particularly for complex geometries and thick-walled pipes. Additionally, both methods require contact or very low standoff distances, making them impractical for inspecting buried pipelines.

Eddy-current testing (ECT) is one of the most widely used electromagnetic NDE techniques, yet it comes with several limitations. Near-field eddy current testing works by inducing alternating magnetic fields from a coil, generating eddy currents in the material. Discontinuities like cracks or corrosion disrupt these currents, altering the electromagnetic field, which is detected as impedance changes to identify defects. This method is effective for surface defects but struggles with deeper ones. The skin effect, a phenomenon in which alternating current (AC) tends to flow near the surface of a conductor, limits sensitivity to subsurface flaws due to the use of high frequency current [9]. Pulsed eddy current testing improves depth sensitivity by using multiple frequency pulsed current but is challenged by signal attenuation and difficulty in cladded or coated pipes [10]. Remote-field eddy current testing, which use low frequency current, is suitable for long pipeline segments, but it lacks sensitivity to axial cracks and requires high power, making it less efficient [11]. Moreover, methods like Saturated Low-Frequency Eddy-Current (SLOFEC), which uses direct current (DC) magnetic field to magnetically saturate the pipe allowing induced eddy currents to penetrate deep into the material, and Rotating Permanent Magnetic Inspection (RPMT), which uses a rotating permanent magnet to induce eddy currents within the pipe wall and measure disturbances in the induced magnetic field with an array of Hall-effect sensors, offer potential, but their complexity and high power requirements limit their practical application [12, 13]. These drawbacks highlight the need for further development in eddy-current testing techniques to ensure effective and reliable inspection of pipelines, especially in challenging conditions such as unpiggable pipelines. Eddy-Current Testing is primarily used for internal inspections, with external applications facing challenges due to low sensitivity and complications from coated or ferromagnetic materials.

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The Alternating Current Field Method (ACFM) is a non-contact technique developed to detect and size surface-breaking cracks by monitoring changes in the induced magnetic field caused by current deflection around defects [14‐16]. While it has certain advantages, such as not requiring the removal of coatings or paint and being capable of scanning and monitoring, ACFM presents several limitations, particularly when applied to unpiggable pipes outside of insulation. One major drawback is that the high frequency of the current (typically 20 kHz) limits the method’s to surface-breaking defects only, making it unsuitable for detecting subsurface or volumetric flaws [16]. Furthermore, thick insulation or coatings need to be removed to maintain sufficient sensitivity, reducing the practicality of the technique for field applications [17]. Geometric variations during inspection can also lead to false alarms, and the large size of the sensors complicates access to certain areas, particularly in constrained environments [16]. ACFM is typically used at low standoff distances, but this creates issues with accessibility and coverage, particularly in insulated or coated pipes. Additionally, despite advances in modeling and algorithms for better crack sizing, uncertainties still exist in the categorization of defects due to discrepancies between theoretical models and real-world conditions [9, 18]. These limitations restrict ACFM’s effectiveness in inspecting unpiggable pipelines, especially those with significant insulation or complex geometries. Another approach involves injecting low-frequency AC current into the pipe, with magnetic sensors measuring changes in the magnetic flux density caused by defects[19, 20]. Despite its effectiveness, the method faces several limitations, including high sensitivity of anisotropic magnetoresistive (AMR) sensors to environmental conditions, such as temperature fluctuations, which introduce noise and affect measurement accuracy. Additionally, achieving high detection sensitivity requires a dense sensor array, which increases complexity and costs. Moreover, factors such as material properties, variations in pipe geometry, and a lift-off distance over few millimeters further complicate the accuracy and consistency of the method, requiring complex compensatory techniques.

The NoPig method enhances the inspection of buried pipelines by utilizing an array of sensors to measure the magnetic field induced by a test current composed of multiple harmonic components. By analyzing the frequency-dependent deformation of magnetic field lines, this system effectively detects metal loss, offering a robust approach to pipeline monitoring [21]. A notable method in this field is the Above Ground Inspection Technique (AGIT) developed by EMPIT, which is a commercial implementation of the NoPig technique as shown in Fig. 1. EMPIT has built upon the multi-frequency above-ground magnetic field analysis approach and validated it through the development of the AGIT system, which has been successfully applied in various industrial contexts [22]. This system has been used extensively for pipeline diagnostics, capable of inspecting various types of pipelines and detecting numerous defects such as internal and external corrosion, dents, and mill defects at up to 2 meters above the pipe. Over 90% of the defects identified by AGIT have been verified through contact non-destructive testing, proving its reliability. The system is certified for pipelines ranging from 3” to 42” in diameter and can inspect both seamless and welded pipelines [22]. To contextualize the capabilities of the method, Table 1 provides a comparative overview of common NDE techniques used for pipeline inspection, highlighting differences in standoff capability, defect sensitivity, access requirements, and the need for pipeline pigging.

This comparison highlights the key advantages of the NoPig/AGIT method in terms of accessibility and long-range detection.

However, it is important to note that while some commercial companies claim to employ this method for pipeline inspection, very little publicly available experimental data, peer-reviewed validations, or third-party performance assessments have been released. The key motivation and scope of the present study is to numerically validate the capability of electromagnetic inspections applied in NDE technology, which aims to provide the first open-access, physics-based numerical evaluation of above-ground electromagnetic inspection methods in profiles/data quantifications. By rigorously modeling the physical phenomena behind such techniques, an independent study foundation is provided with sensitivity analysis based on different test/sensors variables, which could support future experimental validation and industrial deployment.

This research aims to thoroughly evaluate the effectiveness of the AGIT system for the non-destructive evaluation (NDE) of underground pipelines. Specifically, it focuses on detecting corrosion and other structural defects on an underground pipeline through above-ground measurements, a significant advancement in pipeline inspection technologies. The primary goal of this study is to address the limitations of traditional NDE methods by applying a novel approach based on electromagnetic field perturbations induced by alternating current (AC) signals. These perturbations provide critical information about the presence and nature of defects in pipeline walls, offering a more efficient and cost-effective solution for pipeline integrity assessment. The above-ground inspection technique involves inducing an alternating current in the buried pipeline, which generates an external magnetic field. Above-ground sensors then measure the resulting electromagnetic field perturbations at various frequencies, and the data is analyzed to identify potential defects such as metal loss or corrosion.

By utilizing multi-physics modeling, this study not only aims to overcome the physical and logistical limitations of ILI and other contact-based inspection methods but also to contribute to improving overall pipeline safety and operational efficiency in the oil and gas sector. In order to investigate the various factors that influence the distribution of the induced magnetic field around a conductor containing a defect, a model must be developed. Previous researchers have derived models to calculate magnetic perturbations caused by current deflection around different defect geometries by analytically solving Maxwell’s equations. However, these models rely on thin-skin assumptions that only account for surface current flow, limiting their application to high-frequency scenarios and simple geometries [23‐25]. For more complex, irregular geometries that more closely resemble real-world defects, no closed-form analytical solutions to Maxwell’s equations exist. However, recent advances in computational efficiency allow for the creation of 3D numerical models that discretize the geometry into small “finite elements” [8, 9, 13, 14, 19, 20]. In these models, Maxwell’s equations are expressed as partial differential equations, and approximate solutions are found at discrete node points (the vertices of the finite elements) by minimizing an error function.

Finite Element Analysis (FEA) simulations, conducted using ANSYS Electronics Desktop, were employed to create a detailed model of the electromagnetic field around pipelines, both with and without defects. The simulations were designed to capture the interaction between the electromagnetic field and the pipeline under different conditions, enabling a precise analysis of how defects affect the magnetic field. The results demonstrated that above-ground sensors are capable of detecting magnetic field perturbations caused by corrosion defects from a distance of up to one meter above the pipeline surface. This characteristic distance was selected based on the common burial depth of underground pipelines, making it a practical parameter for real-world applications [26]. Furthermore, this study investigated the sensitivity of the system to sensor displacement, acknowledging that sensor movement during inspection can introduce measurement errors and false positives.

To address these potential errors, the Low-High Frequency Method was introduced as a means to reduce the likelihood of false positives. This method leverages the frequency-dependent behavior of the induced electromagnetic field, particularly the skin effect, which causes current to concentrate near the surface of the pipeline at higher frequencies. By comparing electromagnetic field measurements at both low and high frequencies, it becomes possible to differentiate between true defects and spurious signals caused by sensor displacement or other environmental factors. The implementation of this method marks a significant advancement in ensuring the reliability of above-ground electromagnetic inspections for pipelines.

The paper is structured as follows: Section 2 details the methodology, including the modeling approach and simulation setup. Section 3 presents the validation study of the electromagnetic simulations. Section 4 discusses the results, including the detectability of the induced magnetic field, sensitivity to sensor movement, and the effectiveness of the Low-High Frequency Method. Finally, Section 5 concludes the study and suggests directions for future research.

The above-ground electromagnetic inspection method, also named NoPig method [21], focuses on above-ground measurements of the magnetic field induced by a sinusoidal alternating current (AC) passed through the buried pipeline. The AC contains multiple harmonic components with frequencies ranging from a few Hertz to several hundred Hertz. This current creates an outer magnetic field around the pipe. Due to the skin effect, the current density with lower frequency components penetrates the entire wall thickness, while higher frequencies are confined to a thin layer near the outer surface of the pipe. The distribution of current density in the pipeline wall is frequency-dependent [21], and intends to induce different features for the external magnetic field.

This skin effect is quantified by the skin depth, \(\delta \), given by:where \(\sigma \) represents the electrical conductivity of the pipeline metal material, \(\mu \) the magnetic permeability of the pipeline material, and f is the frequency of the current [27]. For a pipe without defects, the magnetic field lines are circular in any cross-sectional planes that are perpendicular to the pipe axis, and their intensity are frequency-independent. However, the presence of a defect, either on the inner or outer surface, alters these magnetic field lines because unbalanced perturbations would be induced due to the circumferential asymmetry of the current density distribution caused by the skin effect on wall defects [21]. Figure 2 provides a comparison of the current density distributions in the cross-section of a defected pipe when the applied AC frequency varies. The results are obtained using finite element modeling. At low frequencies, the current penetrates more deeply into the pipe, allowing for greater interaction with the defect and resulting in more pronounced deformation of the magnetic field lines (see Fig. 2a).

At high frequencies, the current is confined to the surface of the pipe, resulting in less interaction with the defect and less deformation of the magnetic field lines (see Fig. 2b).

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By measuring and comparing the magnetic field outside the pipe at different frequencies, it is possible to differentiate between “metal loss” and “no metal loss” scenarios. This principle underpins the above-ground electromagnetic inspection method.

Finite Element Analysis (FEA) was conducted using ANSYS Electronics Desktop to simulate the electromagnetic field induced by frequency-dependent AC currents in the pipeline. The pipeline was modeled as an isotropic uniform carbon steel pipe with a square-shaped metal loss defect with constant depth. The multi-physics simulation software solved the electromagnetic field partial differential equations (PDEs) described by Maxwell’s equations, employing a fine mesh near the defect. Various scenarios, including different defect locations, AC frequencies, and sensor position, were considered in the FE modeling.

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A pipeline with specific material, geometrical, and electric-magnetic properties was modeled in 3D using ANSYS simulation. The pipeline section considered was 2 meters long, with an outer diameter of 10 inches and a wall thickness of 0.5 inches. A 16-ampere peak-value sinusoidal AC input was applied at the extremities of the pipe to study the electromagnetic effects under various frequencies. This current level was selected based on the EMPIT implementation of the AGIT system [22], which uses a similar excitation to produce detectable magnetic field perturbations at a 1-meter standoff. It ensures that the induced field remains within the sensitivity range of commercially available sub-nanotesla magnetometers, while also maintaining safe and practical operating conditions. Sensitivity analysis on numerical mesh convergence was performed, leading to the use of an adaptive mesh with a maximum initial length of 5 cm in ANSYS to balance simulation accuracy and computational solution time. A 20% refinement per pass was applied during the meshing process to ensure convergence. The average energy over time was calculated using the following formula:where: \(\textbf{B}\) is the magnetic flux density, \(\textbf{H}\) is the magnetic field, \(\textbf{E}\) is the electric field, \(\textbf{D}\) is the electric displacement, \(\text {Re}\) is the real part operation, the superscript \(*\) denotes complex conjugate, and the symbol \(\cdot \) is the dot product. This calculation method is based on the approach detailed in the ANSYS Maxwell documentation [28]. The fundamental defining equation that provides an error evaluation for the solved fields is:When the field solution is returned to this equation, an error term is obtained:The energy produced by these error terms (these errors act in a sense like sources) is computed in the entire solution volume. This is then compared with the total energy calculated to produce the energy error percentage:Additionally, delta energy is computed as:The convergence criteria were monitored and set so that the energy error and delta energy reached a value below \(10^{-5}\). In this context, energy error percentage refers to the percentage of the calculated energy error relative to the total energy in the system, serving as an indicator of the accuracy of the solution. Delta energy, on the other hand, measures the change in energy between successive iterations, helping to assess the stability and convergence of the solution. Both metrics are crucial in ensuring that the numerical solution accurately represents the physical behavior of the system being modeled. To accurately represent the environment around the pipeline, the simulation domain was configured as a vacuum cylinder with a radius and length of 2 meters. Boundary conditions were set for the electromagnetic field to simulate an infinite space: using insulation at the vacuum extremities base to simulate an infinite pipe. Using insulation boundary conditions at the ends of the pipe ensures that the normal component of the magnetic field is zero at those boundaries, effectively preventing any magnetic flux from crossing them. This approach minimizes the influence of edge effects, allowing for a more accurate focus on the magnetic field within the region of interest. In addition, a radiation boundary condition was applied to the outer surface of the simulation domain. The radiation boundary allows electromagnetic waves to exit the domain without reflecting back, effectively simulating an infinite surrounding space. This is crucial for ensuring that the magnetic field measured within the domain is not artificially influenced by reflections from the domain boundaries, which would otherwise distort the results. By using a radiation boundary, the simulation can accurately represent the behavior of the electromagnetic field as it would occur in an open, unbounded environment.

A defect was then introduced into the pipeline section. This setup enabled comprehensive parametric analysis of the electromagnetic field and its interactions with the pipeline in the presence of a geometrically defined defect. Positioned at the center of the pipe length, the defect was modeled in a square shape, measuring 6 cm by 6 cm, with a constant depth of 50% of the pipe’s wall thickness, selected based on defect detection benchmarks reported by AGIT systems. According to Krivoi et al. [22], defects of 50 mm \(\times \) 50 mm \(\times \) 50% wall thickness can be reliably detected with a probability of detection (POD) exceeding 96%, providing a realistic and industry-relevant reference geometry for this study. Figure 3 shows the finite element mesh of the pipe, including the surface defect region. The model comprises approximately 7 million tetrahedral elements, providing high spatial resolution for accurate field simulation. Figure 4 presents the full simulation domain, indicating the applied sinusoidal AC excitation at the pipe ends, the boundary conditions, and the sensor placement location used to measure the magnetic field response.

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The FEM analysis in ANSYS incorporated the evaluation of two components of the electromagnetic field: the normal and the tangential components. The normal component represents the flux in the radial direction, while the tangential component is the projection of the magnetic flux density vector in the circumferential direction, perpendicular to the normal component. Analyzing these components separately was essential for a comprehensive understanding of the electromagnetic field distribution around the pipeline and the detection capability of the electromagnetic inspection technique. The simulations provided detailed insights into the electromagnetic field’s interaction with the pipe’s structure under varying electrical input conditions.

Before the parametric study of the electromagnetic inspection method, the electromagnetic FE modeling method to be used in this study was validated for the magnetic field predictions in the 3D space around AC-induced conductors. The corresponding numerical simulation results were then compared to the analytical solutions and to the FE estimation in previously published literature.

First, the detailed comparison between the simulated results and the analytical calculations of the magnetic fields induced by an AC was conducted in two conductors: an infinite-length wire and an infinite-length pipe. This comparison aimed to ensure that the FE modeling method adheres to fundamental electromagnetic principles, validating their accuracy. The AC in this validation study was set to be 16 A, which is the same as the electromagnetic inspection simulation.

The magnetic flux density around the wire is calculated as:where \(\mu _0\) is the permeability of free space, I is the current intensity, and R is the radial distance from the center of the wire [29].

The magnetic flux density around an infinite-length pipe is analytically provided by:where b is the inner radius of the pipe, c is the outer radius of the pipe, and R is the radial distance from the centerline of the pipe [30].

The analytical calculation and the numerical modeling results for the magnetic flux density at various distances from an infinite-length wire (with a radius of 3 mm) and an infinite-length intact pipe (with an outer diameter of 10 inches and a thickness of 0.5 inches) are shown in Tables 2 and 3, demonstrating a close match with the simulated results shown in Table 2 third column and Table 3 third column, respectively.

Subsequently, further validation studies through comparisons with previously published results and experiments were also performed. The ANSYS model was developed under the same conditions and was compared with the published research results on magnetic flux density predictions [15, 19]. The numerical modeling demonstrated a good prediction with minimal deviation compared to the reported magnetic flux density in both published results with less than 3% percentage error. Through these validations, the project demonstrated the accuracy and reliability of its numerical modeling methods, grounded in both theoretical and empirical evidence.

This study has indicated the potential effectiveness of above-ground electromagnetic-based non-destructive testing for underground pipeline inspection to identify surface defects associated with metal loss. For this technology, an AC current is supplied through the underground pipeline with frequency sweep, and its resultant magnetic field will be measured by an above-ground sensor. The deviation in measured magnetic flux density across the low and the high AC supply frequencies would suggest a surface defect with metal loss on the underground pipeline. Key to the success of this method is the utilization of highly sensitive electromagnetic sensors with sub-nanotesla resolution, which enables the detection of extremely subtle magnetic field perturbations with precision. The presented multi-physics modeling and simulation results underscored the ability of high-resolution measurements to detect discrepancies in the magnetic field from distances up to one meter above the pipeline. Furthermore, the sensitivity of perturbations to the sensor movement was examined and quantified in the numerical simulation, which suggested that the fixed-frequency detection with a moving sensor might not be practical because a small disturbance on the sensor-pipe relative location could bring in significant noise in magnetic flux measurement, with potential to cause false positives in the defect detection. Therefore, a Low-High Frequency Method in relation to the skin effect, which uses various frequencies when examining the same pipe section, could be used to identify the pipeline surface defect when disruptions or discrepancies of the magnetic field from different frequencies are observed with a fixed sensor location. It could be used as an alternative and effective method for pipeline inspection.

While this work is simulation-based, it serves as a foundational step toward experimental validation. Due to the lack of openly accessible experimental data on AGIT and similar systems, our results provide an independent and numerical–based assessment of the physical feasibility of above-ground electromagnetic inspection, with sensitivity analysis upon both sensor variables and data quantifications. Future research will focus on developing a controlled experimental setup to benchmark the simulation results. Such validation is essential to bridge the gap between numerical feasibility and field applicability.

These presented results provide a step towards the validation of the precision and practicality of the electromagnetic inspection techniques, contributing towards advancing pipeline safety and operational efficiency in the oil and gas sector.