## Abstract

**Significance:** During the transport of oil and hydrocarbons, dissolved hydrogen can penetrate into the walls of pipelines, frequently causing delaminating of the metal. Hydrogen accumulates inside the cracks of metal creating pressure which eventually leads to damage of the pipeline. The excessive pressure can be especially dangerous when the metal surface is coated by a protective material where small-scale delaminations occur more commonly. In time, these delaminations spread, damaging the coating and allowing moisture access to the metal, resulting in the external corrosive fracture of the pipeline and its premature replacement.

**Summary of the Results:** The focus of this study is modeling how the radius of delamination grows with respect to time. First, we derived the integral equation describing crack and delamination growth using the i*deal *gas equation. However, with time, the pressure becomes higher as more gas accumulates into the cracks. Eventually, when the gas pressure becomes high enough, we use the *real* gas equation to calculate the crack and delamination growth rate. Even though, the equation for real gas is much more complicated compared to ideal gas equation, analytical solutions of delamination growth rate for both cases are obtained.

**Broad Impact:** Hydrogen embrittlement in metals is the major cause of a sudden rupture of pipelines, which is a very devastating phenomenon. A common feature of Hydrogen Induced Cracking (HIC) in pipes, as observed and reviewed by Gonzalez et al*.* (1997), is that the fractures propagate in the direction parallel to the pipe wall at a very small constant rate, which we managed to obtain in analytical form. In this paper, our goal is to provide estimates for the lifetime of pipes in a form suitable for simple analytical calculations. Specific calculations with real data are conducted to illustrate the capability of the developed model and possible implications for the pipeline lifetime estimates.

Key words: Hydrogen Embrittlement, Rate of Delamination Growth, Ideal Gas Equation, Real Gas Equation, Integral Equations.

## Files

This is a metadata-only record.

## Metadata

- Subject
Mathematics

- Institution
Dahlonega

- Event location
Library Technology Center 3rd Floor Common Area

- Event date
24 March 2017

- Date submitted
19 July 2022

- Additional information
*Acknowledgements:*A.V. Balueva