# A Sensitivity Analysis of a Computer Model-Based Leak Detection System for Oil Pipelines
## 1 Introduction  
Pipelines are an efficient and safe way of delivering large quantities of liquid oil over long distances. However, pipeline leaks cannot be completely eliminated even with extensive regulations in place and pipeline companies taking various measures to maintain and monitor their pipelines. As reported by the National Energy Board [1], there were a total of 59 leaks between 2008 and 2016, resulting in 1765.38 m\({}^{3}\) volumetric losses of liquid oil from Canada's international and interprovincial oil pipelines. Detecting all leaks is an ongoing challenge, and the pipeline industry is highly motivated to enhance the current leak detection technologies and develop new ones. There are currently a wide variety of leak detection techniques employed by the energy pipeline industry, and these can be categorized as external or internal systems. External systems use field sensors directly to physically detect a leak. For example, fiber optic sensing cable laid along the pipeline measures the temperature changes when the released substances come into contact with the cable; acoustic emission detectors installed on the outside of the pipe are used to detect the low frequency acoustic signals caused by a leak. The cost and associated retrofit challenges for existing pipelines, of cable-based external systems, is usually high, thus limiting their application to local high-risk areas [2]. Internal systems include inline inspection and various computational pipeline monitoring approaches. inline inspection involves running acoustic tools such as SmartBall throughthe pipeline as part of the integrity program. This method is very sensitive but is better suited to larger pipes and requires specialized deployment-retrieval equipment [3]. Computational pipeline monitoring is a recommended practice for federally regulated pipelines [4] and a mandatory practice for Alberta regulated pipelines [5] due to its advantage of being relatively non-invasive to the pipe and requiring no field installation. Computational pipeline monitoring approaches use field measurements of internal pipeline parameters and estimate new values via some kind of algorithmic computation. If the calculated new values exceed certain thresholds, an alarm is generated that may indicate a leak [6]. The real-time transient model-based leak detection method is the most sophisticated algorithm developed for computational pipeline monitoring. The occurrence of a leak creates a transient event that may be possible to detect by analyzing the hydraulic behavior of the pipeline system. The governing equations are solved by a computer model to calculate the hydraulic state (primarily pressure and flow rate) along the pipeline in real time. The pipeline state is indicated by the measurements from field sensors, provided to the leak detection system by the supervisory control and data acquisition (SCADA) system. A comparison of the computed and measured hydraulic states can indicate whether a leak is present. Various model-based leak detection methods have been developed in the past a few decades. For example, [PERSON] [7] developed a leak detection system combining a water hammer hydraulic model and a \"pattern recognition\" algorithm. The pipeline was assumed intact until a leak induced discrepancy pattern was detected. [PERSON] [8] developed a method that assumes a leak is present in the pipeline unless no evidence of a leak is found. Trial leaks were continuously imposed on the hydraulic model at different locations, and the leak that matches the actual leak would minimize the discrepancy between computed values and corresponding measurements. He et al. [9] developed a method that separates the entire leaking process into four stages based on the magnitude of the transient pressure variations and used three models to calculate the leak volume. The effectiveness of real-time transient model-based leak detection systems in practical applications is often challenged by real-world uncertainties.