# A Sensitivity Analysis of a Computer Model-Based Leak Detection System for Oil Pipelines
## 1 Introduction
These uncertainties cause discrepancies between the modelled and measured pipeline states even when there is no leak. The impact of uncertainties on hydraulic modelling and leak detection has been extensively studied for water distribution systems. For example, [PERSON] [10] noted that the accuracy in predicting pipe pressure using a hydraulic model was affected by the uncertainty in pipe roughness, and to a greater extent by the water tank level (i.e., boundary condition of the hydraulic model). [PERSON] [11] evaluated the performance of a leak detection system which incorporates a water hammer hydraulic model and a leak detection algorithm based on leak-induced damping in the frequency domain. It was concluded that the uncertainties in wave speed and pressure measurements had a significant impact on leak detectability. Research on the effectiveness of real-time transient model-based leak detection systems in liquid energy pipelines is very limited. A report by the American Petroleum Institute (API) 1149 [12] is the most relevant publication. Initially published in 1993, the report discussed various sources of uncertainty including pipeline system characteristics, fluid properties, and data noise. The leak detection system developed by [PERSON] [7] was utilized to evaluate the impact of uncertainties on leak detectability. A similitude parameter \(R\) (\(=\frac{V_{0}Lf}{2 aD}\)), comprised of five variables including initial velocity (\(V_{0}\)), friction factor (\(f\)), wave speed (\(a\)), pipe length (\(L\)) and diameter (\(D\)), was developed for the purpose of characterizing the pipelines and simplifying the uncertainty analysis. Pipelines with identical \(R\) values were found to have the same hydraulic behavior. Uncertainties in the variables that are components of \(R\) factor were shown to have equal impact on leak detectability. Pipeline systems with low \(R\) values can generally tolerate higher uncertainties compared to those with high \(R\) values. [PERSON] and [PERSON] [13] compared two solution techniques of the water hammer equations and found that the Cauchy algorithm can tolerate more uncertainty in \(R\) factor compared to the time-marching algorithm. As these findings were based on pattern recognition, their applicability to other prevailing leak detection algorithms needs further investigation. API 1149 was updated in 2015 [14] and provided a framework to assess the effect of uncertainties on a full range of computational pipeline monitoringmethods currently in use. The uncertainties associated with SCADA systems were also included, but the impact on leak detectability was evaluated with a simple mass balance method which may not be applicable to the more sophisticated real-time transient model-based leak detection systems. The objective of this research was to provide a better understanding of the effects of real-world uncertainties on the performance of a widely used real-time transient model-based leak detection method. The evaluated system was built upon the broadly applied Synergi pipeline simulator (SPS) Statefinder software [15]. Uncertainties of various sources were introduced into the leak detection system, and the changes in leak detectability were quantified using simulated leaks under various operating conditions.