Abstrakt

The dissertation concerns the issue of modeling the pipeline flow process under incompressible and isothermal conditions, with a target application to the leak detection and isolation systems. First, an introduction to the model-based process diagnostics is provided, where its basic terminology, tools, and methods are described. In the following chapter, a review of the state of the art in the field of leak detection and isolation is provided. Thereafter, the derivation of the continuous-time partial differential equations governing the flow process in transmission pipelines is presented, which is further discretized and presented as a reference discrete base model. Three models, developed on the basis of the diagonal approximation, the Thomas method and the solution of the partial differential equations for steady-state conditions, respectively, are presented. The subsequent chapter contains an analysis of the numerical stability of the discrete-time algorithms, where an approximate formula for determining the optimal Courant number is proposed. In the following part, the comparison of the derived models in terms of their computational complexity and dissimilarity of the steady state vectors, is provided. An experiment that examines the models' ability to simulate complex pipeline geometries is conducted and discussed. Afterward, the analytical steady-state model is related to the Darcy-Weisbach equation, and the difference between the models is examined. A new explicit formula for calculating the friction factor is proposed. Further, the models are compared in terms of applicability to the leak detection and isolation task, where the quality of the diagnostic estimators corresponding to the analyzed models is assessed and compared. The main thesis stating that the commonly used base model is neither optimal numerically, nor functionally, is proven on the basis of the obtained results. The dissertation is finalized with conclusions, relations to the theses and enumeration of the author's original contributions.

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