A complete pipeline model is governed by three differential equations, which come from conservation of mass, conservation of momentum, and conservation of energy. The simultaneous solution of these three equations gives the state of the fluid in the pipeline, which consists of values of the flow rate, pressure, and temperature. These equations can be solved numerically. There are various numerical approaches that can be used to solve the set of partial differential equations. In this paper comparative analysis of selected implicit finite difference schemes used in the solution of partial differential equations of hyperbolic type is conducted. The appropriateness of the schemes with respect to accuracy, programming effort, flexibility of the incorporation of nonpipe elements is evaluated. The main goal of the analysis is to choose the most effective scheme for transient simulation of large-scale fluid network with non-pipe elements. The numerical examples are provided and their results are analyzed based on mass/momentum/energy balance errors, number of discretization intervals, and number of iterations in the solution procedure
Transmission of natural gas through high pressure pipeline networks can be modeled by numerically solving the system of partial differential equations of hyperbolic type, i.e. the governing equations for one-dimensional compressible fluid flow. The flow model describing the transient behavior of the pipeline system should be accurate, but at the same time fast and efficient, enabling the dispatcher to promptly and automatically facilitate network operations.
An overview of different numerical techniques used to solve the governing flow equations can be found in literature (Thorley and Tiley (1987); Osiadacz (1987); (1996)). These include the method of characteristics, finite difference, finite volume and finite element methods. Finite difference methods have commonly been used to model the flow of natural gas through pipeline systems with implicit methods being preferred to explicit, as these are stable for any choice of time and spatial discretisation step (Wylie et al. (1974); Osiadacz, (1987); Kiuchi (1994); Abbaspour and Chapman (2008); Helgaker and Ytrehus (2011); Helgaker et al. (2014a); Wang et al. (2015)). In this paper comparative analysis of selected implicit finite difference schemes used in the solution of partial differential equations of hyperbolic type is presented. The main goal of the analysis is to choose the most effective scheme for transient simulation of large-scale fluid network with non-pipe elements.