User Case Study: Maple Used to Model Static Electromagnetic Fields of Underwater Pipelines

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The problem

Pipelines can reduce the costs of transporting oil and gas over long distances considerably. However, their presence in the earth’s magnetic field and in a conducting medium such as the earth or ocean generates detectable magnetic and electric fields. Quantifying the strength of these disturbances requires the creation of complicated electromagnetic models. When Defence Research & Development Canada – Atlantic (DRDC Atlantic) was contracted to quantify the magnetic and electric fields created by a long undersea pipeline, there was growing concern that a regular iron pipeline would interfere with equipment near the pipeline and would, hence, need to be replaced.

Induced magnetic field of a long pipeline

Prior to the analysis, it had been recommended that a stainless steel pipeline be used to reduce the impact of the interference, but this would require additional time and resources, and would increase the cost of the pipeline by a factor of ten.

Analytical solution to the rescue

The calculations of the electric and magnetic fields created when a steel structure with a set dimension is placed in a magnetic field and in a conducting medium are usually analyzed using modern finite element (FE) and boundary element (BE) procedures. Such solutions, however, have limitations, particularly when dealing with objects that run over long distances and have large cross-sectional shapes. Analytical solutions, on the other hand, are obtainable for only a limited set of shapes but can be structured from the outset to deal with large objects. The electric and magnetic fields existing around a long submerged pipeline represents a case in which analytical solutions can be derived.

“After starting the contract we quickly realized that our FE and BE commercial software would not be capable of generating the required solutions because we could not fit the large geometry into the computer’s memory,” said Troy Richards, Senior Defence Scientist at DRDC Atlantic. “That’s when I turned to Maple™ to help me solve the problem analytically. Maple’s vector calculus library significantly eases the algebraic burden required for the derivations.”

Details about the pipeline model

Corrosion-related Electric and Magnetic Fields along the Pipeline

Analytical expressions for the static electromagnetic fields due to a pipeline were derived for the permanent and induced magnetic fields, as well as for the corrosion-related electric and magnetic fields. A comparison of the three magnetic fields showed that the permanent field dominated close to the pipeline but that the induced field was largest at distances far from the pipeline. The development of this corrosion-related magnetic model represented a significant advancement in the static electromagnetic modeling of pipelines. By lifting some of the constraints from this model, a more complex model - which could have applications in the corrosion related magnetic modeling of other structures, such as a ship - can be generated.

Significant cost and time savings

The team at DRDC Atlantic confirmed that the electric and magnetic fields created by a standard iron pipeline would not interfere with nearby equipment. The findings meant that the pipeline need not be built using stainless steel, resulting in large cost savings.

Richards is pleased with Maple’s contribution. “Using Maple, we were able to solve very complex problems, including those that typically require about 20 pages of algebra,” he said. “It would have been extremely difficult, if not impossible, had I attempted it without Maple. Not only did Maple save me a lot of time, it also contributed significantly to my own knowledge base.” Richards later derived models that included the boundary effects of the water and seafloor, and presented the results at MARELEC, a biannual international conference that addresses work related to underwater electromagnetics.