Network theoretic concepts have been applied to the analysis and design of distribution network systems for sometime. Notable applications include the analysis of water distribution networks, electrical network systems and more recently systems in the gas distribution industry. Application of the technique to the simulation of natural gas field collection systems has been limited to the analysis of surface gathering configurations. This paper is an extension of tins concept to allow for the inclusion of gas reservoirs and production strings.
This matrix formulatiol1 of the problem is given. The application of the N-dimensional Newton-Raphson technique to the solution of the resulting system of equations is discussed, with an outline of it procedure that ensure convergence without the need for acceleration parameters.
The application of the resulting model to an evaluation of that performance of a gas reservoir is given. The treatment includes comprehensive evaluation of:
the effect of Hater influx on the performance and ultimate recovery from waterdrive gas reservoirs, and
the effect of liquid production on pressure drops and the design of gathering systems.
The increasing importance of natural gas in the energy supply spectrum demands comprehensive techniques for forecasting the future performance and deliverability of natural gas fields. It is a well known fact that the deliverability of natural gas fields is a function of three pressure drops. These occur in:
the production string, and
the surface facilities
Although it is possible to isolate each of these pressure drop segments for independent evaluation, the overall performance of the total system and consequent optimum exploitation plan for the natural gas field can best be ascertained through an evaluation that simultaneously considers the effect of all three. Network theory provides a comprehensive and elegant means of building this objective.
The application of the concepts of networks to the solution of flow distribution his been reported by various authors-notably, Shamir and forward. Stoner and more recently by Berard and Eliason.
This paper describes the development, testing and application of a gas gathering system simulator based on the concepts of network theory. The treatment includes the development of natural gas transmission network equation, the model to the evaluation of the parameters affecting gas deliverabilities under water drive conditions.
By definition aa directed network (see Figure 1) G = [N:A] consists of a collection of N elements X1, X2... . . Xn together with a subset A of the ordered pairs (1, X2) of elements taken form N. The elements N are variously called nodes vertices or junction point; members of A are referred to as aics, links, branches or edges.
Given such a network, as in Figure 1, a node-are incidence matrix, as shown in Figure 2 may he constructed. This incidence matrix contains all the information about the structure of the network.