Modelling and simulation of transient gas flow
One of the objectives of this research was to develop mathematical models for transient flow in a gas transmission system. Models were developed from the continuity and the momentum equations. Different approximations in the equations result in the formulation of two different sets of partial differential equations, and these are the hyperbolic and the parabolic models. The Partial Differential Equations were numerically solved by an implicit finite difference technique. A Four Point Scheme was use to approximate the pressures, flows and their partial derivatives. With this scheme a second order accuracy for both spatial and time variables was achieved for both hyperbolic and parabolic models. The nonlinear equation sets from the finite differences discretization process are solved by using a Newton-Raphson iterative procedure. This procedure resulted in the formation of a sparse Jacobian Matrix. This large matrix was then compacted algebraically to reduce the time of the numerical solution. Although an implicit finite difference approximation was used in simulating the models, the important of the correct choice of the magnitude of the temporal and spatial steps should not be overlooked, particularly for high frequency disturbances 'Aliasing' problems will occur if temporal or spatial steps which are too large relative to the frequency of disturbance are used. Comparisons between the response of the hyperbolic and the parabolic models with different input boundary conditions were performed. As a result, recommendations are made on how the different models should be used in simulating real pipeline systems.