# A Sensitivity Analysis of a Computer Model-Based Leak Detection System for Oil Pipelines
## 2 Methodology
### Study Pipeline  
API 1149 [12] demonstrated that pipeline systems with the same \(R\) value have the same hydraulic response. This means that a single pipeline configuration can be used to conduct tests which are representative of various operating conditions and pipeline configurations. In this study, a simple pipeline with one injection and one delivery was used. It was 150 km long, with a 762 mm outside diameter, 9.525 mm wall thickness, and 0.00254 mm pipe roughness. The pipeline was assumed to be horizontal to eliminate the effects of gravitational alignment. A single fluid with density of 858.6 kg/m\({}^{3}\), viscosity of 4.57 mPa-s, and bulk modulus of 1.45 GPa was carried by the pipeline. Flow rate and pressure measurements were assumed to be available at both the upstream and downstream ends of the pipeline (Figure 1).  
Pipelines typically have a pump station at the injection location and a control valve at the delivery location. This equipment was modelled indirectly by controlling pressure or flow rate rather than modelling the pump and valve curves directly. This method was shown to produce more accurate model results compared to direct modelling of the equipment [12]. Both steady state and transient operating conditions were studied as it has been observed that leak detectability tends to degrade during transient conditions (personal communication industry partner, 2013). For steady state, a constant flow rate was specified at the upstream end (US) and a constant delivery pressure was specified at the downstream end (DS). A flow increase transient was created to mimic a pump start at the injection location. The US flow was increased 50% over a time period of 5 s while the DS pressure was held constant. A flow decrease transient was used to mimic a valve closure at the delivery location. In this case the US pressure was held constant while the DS flow rate was decreased 50% over 5 s. Severe transient events in the real pipeline systems are often associated with the closure of a fast response pressure control valves which can be 95% closed within 3-5 s (personal communication industry partner, 2013). However, a flow decrease of more than 50% led to column separation in the study pipeline, i.e., pressure drops below the vapor pressure and gas vapor bubbles form in the oil. To eliminate this complexity introduced by two-phase flow, flow changes were limited to \(\pm\)50%. The transient events tested were considered comparable to relatively severe transient events that may occur in real pipeline systems.  
Systems with different \(R\) values were shown to have distinctly different hydraulic responses [12; 22]. Systems with high \(R\) values are friction dominated; thus, the transient signals caused by pipeline operations or leaks attenuate quicker compared to systems with low \(R\) values, which are inertia dominated. In this study, systems with two different \(R\) values were tested to observe how they were  
Figure 1: Schematic of the study pipeline with simulated leak.  
affected by uncertainties. A low \(R\) value of 0.49 and a high \(R\) value of 2.20 were obtained by changing the initial flow rate within the study pipeline.  
Leak flow rates equal to 2%, 5%, and 30% of the pipeline flow rate (prior to the leak) were tested. It was shown that the large leak (i.e., 30%) was minimally affected while the small leak (i.e., 2%) was often completely masked by uncertainties. Therefore, a 5% leak was used to quantify the performance of the leak detection system subjected to varying uncertainties. For each case, the Simulator model was used to simulate an 8 h time period with a leak located at the midpoint of the simulated pipeline starting at 4 h. For cases with transient operating conditions, the transient event was introduced at the same time as the leak, representing the worst-case scenario for leak detection [22].