1. Introduction
Pipelines conduct essential roles in transporting oil and gas across the nation, fueling the modern industry and way of life [
1,
2]. However, pipelines are claimed to suffer from internal corrosion due to the properties of the transported fluids, operating pressure, as well as the injected inhibitors [
3]. According to the released data from the Pipeline and Hazardous Materials Safety Administration (PHMSA), internal corrosion accounts for approximately 60% of all corrosion-related incidents in transmission and gathering pipelines [
4].
Internal corrosion poses many challenges to pipeline integrity, necessitating a comprehensive comprehension of its consequences. The gradual reduction in pipeline walls due to corrosion constitutes a primary concern, jeopardizing structural robustness and increasing susceptibility to leaks and ruptures. Such vulnerabilities, if left unchecked, can accumulate in catastrophic failures with severe implications for safety and environmental preservation. The financial toll of internal corrosion is equally substantial, encompassing the costs of repair, replacement, and lost productivity due to unscheduled downtime. Regulatory fines and penalties, coupled with the tarnishing of reputations, compound the financial ramifications. Furthermore, the accumulation of corrosion by-products can impede fluid flow, impacting operational efficiency and disrupting resource delivery to industries and households. By elucidating these challenges and potential risks, we underscore the pivotal significance of the proposed modeling strategy. This strategy’s ability to predict corrosion rates, identify vulnerable areas, and guide mitigation efforts resonates as a proactive solution to prevent corrosion-induced failures, ensuring safety, environmental protection, and financial stability within the pipeline industry.
The timely monitoring of internal corrosion in pipelines continues to pose significant challenges due to limited accessibility for regular inspection and maintenance. Moreover, internal corrosion often occurs discreetly and gradually at random locations along extensive pipeline networks, resulting in potentially severe consequences that may go unnoticed until significant damage has already occurred [
5,
6]. Also, additional environmental factors can exacerbate the impact of corrosion, leading to potentially catastrophic outcomes [
7,
8]. Thus, it is of paramount importance to locate corrosion events along the long-distance pipe system, in order to ultimately implement optimal corrosion control practices in Structural Health Monitoring (SHM) [
9].
The fluid flow in pipelines is essentially a mixture of crude oil, water, and dissolved gases such as CO
2 and H
2S. It is well established that the distribution of water and oil inside the pipeline has a significant impact on the corrosion rate of the pipe wall [
10]. To address the internal corrosion issues, oil-water two-phase flow is commonly employed to model the fluid behavior. On one hand, internal corrosion occurs when a free layer of the water phase comes in contact with the pipe wall. The flow patterns (i.e., water distribution) directly determine the phase for wetting on the inner wall of the pipeline. Considering that water and oil phases can exhibit different forms, such as emulsion (water-in-oil emulsions and oil-in-water emulsions), stratified, slug, or annular flow. It is necessary to model the fluid flow with consideration of the hydrodynamic parameters and geometric shape of the pipe that will impact the wetting conditions. On the other hand, the long distance of the pipeline network brings about difficulties in real-time corrosion detection and monitoring [
11]. A balance between the sensing coverage for corrosion locations and the total expense of the sensor layout is hence required in engineering applications [
12]. Based on this, a comprehensive strategy, which is capable of modeling oil and water phases with various flow characteristics and further predicting the corrosion rate accurately based on the flow-induced wall shear stress, is thus expected for the implementation of better corrosion practices.
Experimental measurements on pipeline internal corrosion are usually limited due to the uncertainty and difficulty in controlling the flow patterns [
13]. Computational Fluid Dynamics (CFD) have been commonly used to simulate the flow behavior of a crude oil and water mixture, which significantly facilitates the parametric study on different flow characteristics. Hu et al. [
14,
15] carried out CFD analysis on the oil-water two-phase flow containing dissolved CO
2. Importantly, a map of flow pattern was derived to demonstrate the potentials of corrosion under different conditionings with regard to water cut and flow velocity. The CFD analysis revealed that corrosion is prone to occur at the bottom part of the pipe when the flow pattern is stratified and dispersed. Particularly, when the water cut exceeds 80% and the flow velocity is greater than 1 m/s, the entire inner wall will be wetted with water. Additionally, the corrosion rates were also predicted using empirical models based on the shear stresses calculated from the CFD study. Results show good agreement with the actual measurements. Hassan et al. [
13] performed a CFD study on the internal corrosion of oil-water two-phase flow in straight pipelines, addressing an emphasis on the distribution of water and the types of wetting (i.e., water wetting and oil wetting) that could result in corrosion at the bottom of the pipe wall. Zhang et al. [
16] further investigated the bottom corrosion of the pipe wall in upward-inclined pipe fittings. The key parameters, such as the water cut, mixture velocity, oil viscosity, and inclination angle of the pipe, were analyzed. The simulation results show good coincidence with experimental measurements. Clearly, CFD simulation provides an efficient way to solve the complex fluid problems associated with sets of partial differential equations that describe the fluid flow.
As stated above, CFD-based numerical analysis allows dealing with a large number of variables impacting the corrosion rate of the pipeline. On the other hand, a variety of commercially available corrosion sensors have been developed to monitor the corrosion process from causes to consequences using different sensing principles [
16]. Numerous sensors serving different monitoring purposes are required to maintain the integrity of the corrosion inspection along pipelines, especially in large-scale infrastructures. Consequently, it brings about a large amount of investment in manufacturing and operating costs. Thus, the sensor optimization with regard to quantity and layout is hence essential to promise sensing efficiency and expense control. Upon this, data-driven approaches have been gaining increasing attention to solve complex (system) problems with typical characteristics in terms of high nonlinearity and stochasticity [
16]. Sensor placement optimization based on the pipeline corrosion associated with the correlated parameters of the fluid flow can thus take advantage of the strong mapping ability of AI algorithms to find out an optimal solution, with adjusting the parameters during the prediction process. Among various algorithms, Genetic Algorithm (GA), due to its global searching ability without getting trapped in local minimal, is widely adopted in SHM fields. Cheng et al. [
17] used GA to optimize the temperature and CO
2 sensor placement for thermal comfort and indoor air quality monitoring under limited field measurements. The coverage checking and accuracy checking were conducted, respectively, to demonstrate the applicability of GA in sensor placement optimization. The developed GA program shows quick convergence and high fitness over approximately 40 iterations, indicating good efficiency for the optimization. Kim et al. [
18] proposed an Adam-mutated GA approach to determine the optimal locations of sensors in the pipeline network for real-time monitoring. The evolutionary process in terms of mutation was further optimized by integrating a mutation operator to increase the robust ability to escape from the local minimal.
Motivated by the aforementioned sophisticated techniques, this study addresses efforts to integrate the strong nonlinear solving ability of CFD and the global stochastic searching ability of GA. The workflow of the hybrid modeling strategy using CFD and GA is exemplified in a step-by-step manner. The shear stresses of the pipe wall obtained from the CFD calculation are used to estimate the corrosion rate for different pipe fittings containing the oil-water two-phase flow. Importantly, the time steps divided in the CFD solving are recorded and thereafter used as the corresponding identification numbers of initial individuals in GA. The schemes of sensor placement for the U-shaped, upward-inclined, and downward-inclined pipes were optimized through the population evolutions of the GA to demonstrate the applicability of the developed strategy.
6. Conclusions and Future Work
This study introduced a hybrid modeling strategy using CFD and GA for optimization of the internal corrosion sensor placement, to achieve a good balance between economical cost and measurement accuracy. The methodology mainly consists of CFD analysis, corrosion rate prediction, and GA optimization. The complete workflow of the hybrid modeling was presented and illustrated through case studies involving three typical pipe fittings. Specifically, the conclusions can be drawn in the following:
The essence of the hybrid modeling is to utilize the strong fluid analysis ability of CFD to provide a rich database and the stochastic searching ability of GA to explore optimal solutions on a global level. The information binding of CFD and GA is realized by converting the grid elements and time steps into chromosome length and population size, respectively. Importantly, the fitness function involves the in-line corrosion induced by the oil-water phase flow and overall cost of sensors. Based on this, the population evolution keeps iterating until the target fitness is achieve. It is an efficient way to find out the optimal scheme of sensor placement, especially for decision-making in engineering projects;
The GA scheme used the field of corrosion rates as the original population input. Three typical pipe fittings were investigated, including the U-shaped, upward-inclined, and downward-inclined pipes. By adopting the suggested meshing strategy discussed in
Section 2.2.5, the appropriate number of elements for the three scenarios were determined to 13,192, 8841, and 8841, respectively. After the GA optimizations, the sensor layout schemes were suggested to be a total of 6, 9, and 8, respectively. The best fitness and average fitness values, surpassing 0.9, intimately align with the core objectives of sensor placement optimization. These fitness metrics directly quantify the success of the strategy in identifying optimal sensor locations. The best fitness value signifies exceptional performance, pinpointing prime positions for corrosion risk mitigation. The average fitness value reflects the overall quality of selected solutions. Their congruence with optimization objectives highlights the strategy’s efficacy in striking a vital equilibrium between measurement accuracy and economic feasibility. This achievement is pivotal, enabling industries to access precise corrosion data while minimizing costs linked to complex investigations and monitoring setups. The elevated fitness values affirm the strategy’s capability to comprehensively address corrosion risks, underscoring its practical significance in enhancing pipeline integrity management. Additionally, scenario studies of various oil fraction and fluid velocity reveal that the high fluid velocity significantly reduces the optimized sensor quantity, focusing on the critical locations with high corrosion rates.
In order to further utilize the robust mapping ability of artificial intelligence, cross-integration with other algorithms can be further investigated, such as the Artificial Neural Network (ANN) integrated with GA and Particle Swarm Optimization (PSO)-ANN. Such data-driven approaches have been reported to yield good convergence and high accuracy when applied in engineering projects. Cross-integration with algorithms like ANN and PSO augments the proposed modeling strategy’s robustness. Integrating ANN can harness its mapping ability to complement GA’s optimization, yielding more accurate sensor placements. This fusion could overcome challenges like local convergence and enhancing reliability. PSO’s global search capabilities can counter local optima, further refining the sensor layout. In scenarios requiring nonlinear relationships or intricate search spaces, ANN-PSO synergy could excel. These integrations address limitations, bolstering feasibility studies and providing comprehensive solutions for complex sensor placement challenges in pipeline corrosion monitoring. In addition, due to the fact that the literature lacks details in sensor placement and limitations in performing field testing as analyzed, the effectiveness of the developed sensor placement scheme was not compared with other methods in this study. In the future, experimental and field testing are needed to validate the developed method through comparisons with other methods available in the literature.