We design a leak detection system consisting of an adaptive Luenbergertype observer based on a set of two coupled one dimensional first order nonlinear hyperbolic partial differential equations governing the flow dynamics. It is assumed that measurements are only available at the inlet and outlet of the pipe, and output injection is applied in the form of boundary conditions. Heuristic update laws for adaptation of the friction coefficient and leak parameters are given, and simulations demonstrate their ability to detect, quantify and locate leaks. Particular attention is given to time-varying boundary conditions, such as during pipeline shut-down. A scenario consisting of leak detection followed by pipeline shut-down during which the leak is accurately quantified and located is successfully simulated for both liquid and gas systems.
Summary An adaptive Luenberger-type estimator for the purpose of monitoring flow conditions and locating and quantifying leakages in petroleum pipelines is presented. The estimator only needs measurements of velocity, pressure, and temperature at the inlet and velocity and pressure at the outlet to function. The measurements are used to form a special set of boundary conditions for the estimator that ensures fast convergence of the estimation error. Depending only on measurements from inlet and outlet makes it possible to use OLGA, which is a state-of-the-art computational fluid dynamics simulator, to govern the one-phase fluid flow of the estimator. The estimator is tested with both a straight, horizontal pipeline and an actual, long pipeline with inclinations, and both simulations with oil and gas are carried out. In order to cope with modeling errors and biased measurements, estimation of roughness in the monitored pipeline is introduced. Introduction The benefits of a leak-detection system capable of locating the position of the leak are obviously of an environmental kind. But the economical aspect of it is also important. Leak detection based on dynamic modeling is a propitious approach in the special field of leak quantification and location. There have been numerous studies on model-based leak detection. We mention here the most relevant ones with regard to our work. Based on a discretized pipe flow model, Billmann and Isermann (1987) designed an estimator with friction adaptation. In the event of a leak, the outputs from the estimator differ from the measurements, and this is exploited in a correlation technique that detects, quantifies and locates the leak. Verde (2001) used a bank of estimators, computed by the method for fault detection and isolation developed by Hou and Müller (1994). The underlying model is a linearized, discretized pipe flow model on a grid of N nodes. The estimators are designed in such a way that all but one will react to a leak. Which one of the N estimators that does not react to the leak depends on the position of the leak, and this is the mechanism by which the leak is located. The outputs of the remaining estimators are used for quantifying the leak. The bank of estimators are computed using the recursive numerical procedure suggested by Hou and Müller (1994); however, it was shown in Salvesen (2005) that because of the simple structure of the discretized model, the estimators may be written explicitly. This is important, because it removes the need for recomputing the bank of estimators when the operating point of the pipeline is changed. Verde (2004) also proposed a nonlinear version, using an extremely coarse discretization grid. Several companies offer commercial solutions to pipeline monitoring with leak detection. Fantoft (2005) uses a transient model approach in conjunction with the commercial pipeline simulator OLGA2000, while EFA Technologies (1987, 1990, 1991) uses an event detection method that looks for signatures of no-leak to leak transitions in the measurements. The detection method of Verde (2001) using a bank of estimators can potentially detect multiple leaks. However, multiple simultaneous leaks is an unlikely event, so the complex structure of a bank of N estimators seems unnecessary. Aamo et al. (2006) instead employed ideas from adaptive control, treating the mass rate and location of a single point leak as constant unknown parameters in an adaptive Luenberger-type estimator based on a set of two coupled 1D first-order nonlinear hyperbolic partial differential equations. Heuristic update laws for adaptation of the friction coefficient, mass rate of the leak, and position of the leak were suggested. The method was developed further by Hauge et al. (2007) who remodeled the leak as a pressure- and density-dependent function, thereby improving the leak-detection capability during transient flow such as for instance pipeline shut-down. In this paper, we continue the development by employing the state-of-the-art multiphase flow simulator OLGA? as the underlying flow model, enabling more accurate flow predictions for complex pipeline conditions and thereby further improving the leak detection capability of our approach. The simulator is manipulated through MATLAB to work as an adaptive Luenberger-type estimator using measurements from the supervised pipeline. Because the only measurements fed into the estimator are velocity and pressure from the outlet and velocity, pressure, and temperature from the inlet, which in most cases already are available, the method can be used with most existing pipelines without additional instrumentation. Also, the OLGA simulator, which is the backbone of the estimator, is widely used in the petroleum industry. Our approach allows for easily turning an existing OLGA model of a real pipeline into a monitoring system, including leak-detection capabilities.
The main objective of this work is to study the dynamic behavior of gas expansion in marine risers. The term 'riser equilibrium' is used to provide a more rational explanation of gas expansion and its relation to riser unloading. While handling a gas kick situation with the blowout preventer closed, the gas within the riser expands until its pressure equals the hydrostatic pressure of the mud column above, plus any applied back pressure. Buoyancy or slip will cause the gas to migrate, which in turn will cause further expansion, if allowed to, or an increase in pressure. But after a certain point, termed as 'Riser Equilibrium Point', any small decrease in the hydrostatic pressure would trigger the gas to expand rapidly until enough back pressure is applied or the top of the gas reaches surface. This could cause an explosive unloading. Complete dissolution of gas in oil based muds and the relative delay in noticing any surface indications for the gas influx makes influx detection more complicated with oil based mud as opposed to water based mud. Estimation of various parameters to study these phenomena and their correlation to the gas expansion is studied through an analytical and iterative approach. All schemes are implemented in Matlab and give a basic understanding of the severity of the situation. Calculation of the riser equilibrium point is beneficial to understand the risks related to riser unloading and riser collapse through proper estimation of collapse load. Since the conventional 'free gas' approach to calculate surface volume of gas during kill operations tend to overestimate the risks involved, this study is expected to provide a more comprehensive understanding of the situation providing a safer operational conditions to handle gas in risers.
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