Conductive heat transfer is studied in the complex geometries encountered with partial buried and fully buried pipes. Both geometries can be simplified with conformal mapping. Since Laplace's equation is preserved, an analytical steady state solution is obtained. Closed form solutions are also proposed that are practical for engineering applications. Transient heat transfer is considered when the conduction in the pipe wall is much higher than in the soil.

1.1 Application

In an offshore subsea environment, pipeline embedment into the seafloor is a reasonably common phenomenon. Resulting from the action of currents, sediment deposition, wave action or settling, embedment of a pipeline can significantly impact the thermal description of the pipeline system in steady state and transient situations. Incorrect modelling of such situations at the design stage can impact both production availability and pipeline integrity of the production system. Until recently no robust analytical solutions for the situation of partially or shallowly buried pipe have existed, and therefore engineering judgement has been used along with appropriate margins to ensure conservative designs. This is true for both steady state and transient applications, but the transient scenarios have received even less attention in the literature with little or no analytical work being done. This is surprising since even in the steady state case the result of such conservatism can lead to practical implications such as poor thermal performance of cooling spools, overly conservative designs, uncontrolled lateral bucking of pipelines, accelerated top of line corrosion rates and many other design related issues. In the transient realm the implications may be even greater with erroneous prediction of cooldown times, pipeline thermal response or operational philosophies. While the context discussed here is appropriate for the oil and gas industry the issue itself is the same across the entire engineering domain.

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