This chapter examines the problem of modeling and parameterization of the transmission pipeline flow process. First, the base model for discrete time is presented, which is a reference for other developed models. Then, the diagonal approximation (AMDA) method is proposed, in which the tridiagonal sub-matrices of the recombination matrix are approximated by their diagonal counterparts, which allows for a simple determination of...

W pracy zastosowano standardowš korelację wrzenia w przepływie (wyprowadzonš dla rur o konwencjonalnych wymiarach) do przypadków wrzenia w rurach o małych rednicach. Porównanie wyników z danymi literaturowymi wykazało nieużytecznoć tej korelacji. Wykazano zatem potrzebę prowadzenia badań podstawowych celem uzyskania korelacji pozwalajšcej umiejętnie przewidywać warunki wymiany ciepła w kanałach o małych rednicach.

The paper addresses the issue of modeling the flow process in transmission pipelines. A base model used for numerical simulation is introduced. Under certain assumptions concerning steady state analysis, the differential equations describing the process are solved analytically for two cases: zero and nonzero inclination angle α. These equations describe a constant flow rate and a corresponding distribution of the pressure along...

The paper addresses the problem of computational efficiency of the pipe-flow model used in leak detection and identification systems. Analysis of the model brings attention to its specific structure, where all matrices are sparse. With certain rearrangements, the model can be reduced to a set of equations with tridiagonal matrices. Such equations can be solved using the Thomas algorithm. This method provides almost the same values...

the paper deals with the problem of early leak detection in transmission pipelines. First we present the derivation of state-space equations of the flow process in the pipelines. This description is then aggregated in order to obtain a principal model. Next, the problem of process model parameterization is addressed, taking into account the maximization of a model stability margin. The location of the maximum is determined using...