## Abstract

Corrosion under insulation (CUI) is a common cause of pipeline failure in the oil and gas industry. Its detection with conventional inspection techniques is challenging due to the presence of the insulation layer and a protective metallic cladding that prevent direct access to the pipe surface. Currently, several techniques are being developed to detect sections of wet insulation since water is a necessary precursor to corrosion. Among these, guided microwave testing (GMT) has been proposed as a cost-effective approach to screen an extended length of pipeline. The sensitivity of GMT is dependent on the strength of microwave reflections from wet volumes of insulation and has been demonstrated in the case of relatively abrupt transitions from dry to fully saturated insulation. This paper investigates the performance of GMT in the presence of saturation gradients characterizing more gradual transitions. Due to the lack of detailed field observations about realistic saturation paths, the paper proposes model experiments of saturation dynamics in a highly permeable material in a first attempt to determine saturation profiles resulting from capillary rise and seepage. The experimental observations reveal that the extent of the transition region is typically much smaller than the wavelength of the probing microwave signal and therefore has a limited effect on the amplitude of the reflected signal.

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## Acknowledgments

The authors are grateful to Prof. Peter B. Nagy for many stimulating discussions and for suggesting the use of the input impedance method for the numerical simulations.

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## Appendix: Simulation of Microwave Backscattering

### Appendix: Simulation of Microwave Backscattering

In order to determine the reflection coefficient from an arbitrary refractive index profile \(n_{eff}(z)\) the transition length, \(\Delta \), is divided into \(N-1\) small equal intervals of length \(\delta =\Delta /(N-1)\) according to Fig. 14. It is then assumed that the refractive index of the *k*th element centered at position \(z=z_k\) is constant and equal to \(n_{eff}(z_k)\). Under this assumption the transition region can be considered as a layered medium and the reflection coefficient estimated using the input impedance method outlined in [24] for a plane wave incident on a planar system of layers. Letting \(Z_{in}^{(N)}\) be the input impedance of the system of \(N-1\) layers the reflection coefficient is given by the well known expression

where \(Z_{dry}\) is the impedance of dry insulation. The impedance \(Z_{in}^{(N)}\) is calculated from the impedances of each layer, \(Z_k\), given by

through the recursive formula

where \(v_k=\omega n_{eff}(z_k) /c\) is the wavenumber inside the \(k\)-th layer. To obtain \(Z_{in}^{(N)}\), formula (A3) is applied \(N-1\) times starting from layer 2 with the initialization condition \(Z_{in}^{(1)}=Z_1\).

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Bejjavarapu, S.M., Simonetti, F. An Experimental Model for Guided Microwave Backscattering from Wet Insulation in Pipelines.
*J Nondestruct Eval* **33**, 583–596 (2014). https://doi.org/10.1007/s10921-014-0254-8

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DOI: https://doi.org/10.1007/s10921-014-0254-8

### Keywords

- CUI
- Pipelines
- Microwave
- Coaxial waveguides
- Saturation gradient