Mathematical models for transient gas flow are described by partial differential equations or a system of such equations. Depending on the degree of simplification with respect to the set of basic equations, the equations may be linear or quite generally non-linear. They may be parabolic or hyperbolic of the 1st or 2nd order. With respect to the transport of gas in pipelines, there are two technically relevant special cases of pipe flow:
flow without heat exchange with the ground outside; adiabatic and, more especially, isentropic flow;
flow with complete heat exchange with the ground outside, which is regarded as being a heat storage unit of infinite capacity with constant temperature; isotermal flow.
Numerical solution of the partial differential equations which characterize a dynamic model of network takes much computation time. The problem is to find for given mathematical model of a pipeline a numerical method which meets the criteria of accuracy and relatively small computation time. The main goal of this paper is to characterized different transient models and existing numerical techniques to solve the transient equations.
It is a well established fact that flow in gas pipelines is unsteady. Conditions are always changing with time, no matter how small some of the changes may be. When modelling systems, however, it is sometimes convenient to make the simplifying assumption that flow is steady. Under many conditions, this assumption produces adequate engineering results. On the other hand, there are many situations where an assumption of steady flow and its attendant ramifications produce unacceptable results. The steady state in a gas network is described by system of algebraic nonlinear equations. In steady-state problems, loads and supplies are not functions of time; the system variables nodal pressures and branches flows) do not change with time. The steady-state model is widely used as the basis of many traditional design methods because it is usually relatively simple to solve and is conceptually easier to understand. However, in some systems the dynamics cannot be neglected without gross error and we must use a dynamic model. Dynamic models are just a particular class of differential equation model in which time derivatives are present. A good example of the use of steady-state and dynamic models is found in gas networks: in low pressure networks the dynamics are very rapid and can be ignored for most practical purpose and steady-state models are used. In high pressure networks the dynamics are much slower because of the large amount of gas stored in the pipes and cannot be neglected. Transients are initiated in gas systems by the time variant nature of the load at distribution points and from adjustments made by the system operator in reacting to the demands of the system. As larger loads are placed on existing systems, the ability to supply gas at contract pressures during periods of peak customer demand is decreased. To cope with this situation a larger variation of the supply system input capacity must be provided.