Journal of Failure Analysis and Prevention

, Volume 15, Issue 6, pp 873–882

# Probability of Detection and False Detection for Subsea Leak Detection Systems: Model and Analysis

• Alireda Aljaroudi
• Faisal Khan
• Ayhan Akinturk
• Premkumar Thodi
Technical Article---Peer-Reviewed

## Abstract

Ensuring the integrity of subsea process components is one of the primary business objectives of the oil and gas industry. Leak detection system (LDS) is one type of system used to safeguard reliability of a pipeline. Different types of LDS use different technologies for detecting and locating leaks in pipelines. One technology, which is gaining wide acceptance by the industry, is the fiber optic-based LDS. This technology has great potential for subsea pipeline applications. It is the most suited for underwater applications due to the ease of installation and reliable sensing capabilities. Having pipelines underwater in the deep sea presents a great challenge and a potential threat to the environment and operation. Thus, there is a need to have a reliable and effective system to provide the assurances that the monitored subsea pipeline is safe and functioning as per operating conditions. Two important performance parameters that are of concern to operators are the probability of detection and probability of false alarm. This paper presents a probabilistic formulation of the probability of detection and probability of false detection for a fiber optic-based LDS.

## Keywords

Probability of detection (PD) Probability of false alarm (PFA) Leak detection system (LDS) Oil and gas pipeline

## Nomenclature

BSS

Brillouin-Stimulated scattering

CW

Continuous wave

LDS

Leak detection system

NP

Noise Power

PD

Probability of detection

PFA

Probability of false alarm

PMD

Probability of missed detection

SNR

Signal-to-noise ratio

c

Speed of light (Km/s)

d

Location of the temperature change

$${\raise0.7ex\hbox{{{\text{d}}P}} \!\mathord{\left/ {\vphantom {{{\text{d}}P} {{\text{d}}T}}}\right.\kern-0pt} \!\lower0.7ex\hbox{{{\text{d}}T}}}$$

Temperature coefficient (mW/°C)

$${\raise0.7ex\hbox{{{\text{d}}P}} \!\mathord{\left/ {\vphantom {{{\text{d}}P} {{\text{d}}\varepsilon }}}\right.\kern-0pt} \!\lower0.7ex\hbox{{{\text{d}}\varepsilon }}}$$

Strain coefficient (mW/µε)

n

Refractive index

Aeff

Effective area of the fiber

Leff

Effective length of the fiber

gB

Gain

$$P_{o}$$

Reference power

PB(measured)

Measured Brillouin power

PCW

Input probe power

PP

Pulse power

$$\alpha_{\varepsilon }$$

Strain coefficient expressed in MHz/με

$$\alpha_{T}$$

Temperature coefficient expressed in MHz/°C

$$\Delta \varepsilon$$

Strain change

$$\Delta T$$

Temperature change

$$\Delta T_{\text{measured}}$$

Measured temperature change

Δt

Minimum detectable temperature change

Va

Acoustic velocity

$$v_{\text{B}}$$

Brillouin frequency shift

$$\tau$$

Pulse width

λ

Wavelength of the incident light

$$v_{\text{o}}$$

Reference Brillouin frequency at no strain and at the ambient temperature (MHz)

Δt

Traveled time

Xth

Temperature change threshold

## Notes

### Acknowledgments

The authors gratefully acknowledge and appreciate the partial financial support provided by the Research & Development Corporation (RDC) of Newfoundland and Labrador, Canada. Likewise, the authors greatly appreciate and thank ASME’s permission to publish this paper in the Journal of Failure Analysis and Prevention.

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## Authors and Affiliations

• Alireda Aljaroudi
• 1
• Faisal Khan
• 1
• Ayhan Akinturk
• 2