Prediction of Gas Transport through Ground and Atmosphere to Determine the Ability of Airborne Leak Detection Methods to Detect Pin-hole Leaks from Buried Gas Pipelines

New technologies for airborne detection of gas pipeline leaks have been introduced to the pipeline industry and have undergone several field-testing attempts. These technologies are based on an airborne detection device mounted on a small aircraft flying along the right of way (ROW) of the pipeline. It is proposed that during initial commissioning of the pipeline, leak testing is performed by first pressurizing the pipeline section with natural gas, and then launching an airborne leak detection aircraft to fly along the ROW in multiple passes. A delay between the completion of the pipe section pressurization and the launching of the leak detection aircraft is required in order to establish a discernable concentration of methane in the atmosphere. This 'wait time' includes the time required for the leak to penetrate upwards through the backfill to the ground surface and to subsequently diffuse into the atmosphere. Accuracy and reliability of these technologies clearly depend on the leak rate (i.e. leak hole size and line pressure), the depth and properties of the backfill, atmospheric conditions, prevailing wind speed and direction, and the properties of air including diffusion parameters of natural gas into air. Additionally, the accuracy of these airborne methods also depends on the altitude at which the aircraft is flying along the pipeline ROW and the degree of offset of the flight path from the centerline of the ROW. The present paper outlines the fundamental governing equations and solution techniques to predict the temporal-spatial-dependent diffusion of gas leakage from a pinhole into the ground. The mechanism of the gas transport through the ground, whether it is advective or diffusive, is dependent on the Peclet number, which is predominantly driven by the leak rate. Likewise, the fundamental governing equations along with solution techniques to predict the diffusion of the breakthrough flux of gas at the ground level into the atmosphere are formulated. Results of the time for the gas to break through at ground level, the concentration and gas flux at ground level, and the vertical and lateral concentration profiles of the gas in the atmosphere are all presented to facilitate assessment of the sensitivity of the airborne leak detection methods to the different ground and atmospheric parameters for a given leak rate at a given source depth.