Pipeline network elements

In this abstraction each edge corresponds to a pipeline network element and each vertex corresponds to a junction connecting two or more elements. It is often convenient to refer to the formal definition of a graph G as the sets... 

A pipeline network is a collection of elements such as pipes, compressors, pumps, valves, regulators, heaters, tanks, and reservoirs interconnected in a specific way. The behavior of the network is governed by two factors (i) the specific characteristics of the elements and (ii) how the elements are connected together. The first factor is determined by the physical laws and the second by the topology of the network. 

Although reservoirs and tanks are not network elements in the sense discussed above, they do enter into pipeline network calculations. For many types of calculations, the impact on the network behavior may be modeled by treating a reservoir or a tank as a constant pressure vertex. On the other hand, the storage field deliverability curve (S5) is sometimes represented by... 

We are now in a position to formulate the steady-state pipeline network problem based on the laws governing the behavior of the network and its elements. As it turns out, there is more than one way of formulating the problem, and since the computational efforts required for the solution are unequal, it behooves us to examine the ramifications of these formulations. 

In Section II,C we have deliberately chosen a simple set of problem specifications for our steady-state pipeline network formulation. The specification of the pressure at one vertex and a consistent set of inputs and outputs (satisfying the overall material balance) to the network seems intuitively reasonable. However, such a choice may not correspond to the engineering requirements in many applications. For instance, in analyzing an existing network we may wish to determine certain input and output flow rates from a knowledge of pressure distribution in the network, or to compute the parameters in the network element models on the basis of flow and pressure measurements. Clearly, the specified and the unknown variables will be different in these cases. For any pipeline network how many variables must be specified And what constitutes an admissible set of specifications in... 

In the treatment of steady-state pipeline network problems so far we have tacitly assumed that there is a unique solution for each problem. For certain types of networks the existence of a unique solution can indeed be rigorously established. The existence and uniqueness theorems for formulation C were proved by Duffin (DIO) and later extended by Warga (Wl). In Warga s derivation the governing relation for each network element assumes the form,... 

Each element of the branch in Fig. 12.10 contains numerical probability information related to technical and historical data for each segment of the complete pipeline network. In some cases, it was simpler to assume some probability values for an entire system. The probabilities of operating at maximum permitted pressure and the presence of electrolyte were both set at value unity in Fig. 12.10, therefore forcing the focus on worst case scenarios. Other more verifiable variables can be fully developed as is shown in Fig. 12.12... 

The capacity matrix C that provides information about capacity constraints of the network elements including input source nodes, demand nodes and information about connected pipeline capacities ... 

Inasmuch as the nature of pipeline elements sets these networks apart from electrical networks (more commonly referred to as electrical circuits) we shall review briefly the modeling of these elements. We shall, however, limit ourselves to the correlations developed for single-phase fluid flow the modeling of two-phase flow is a subject of sufficient diversity and complexity to merit a separate review. 

Pipeline design puts together and connects various elements. Line or network pipeline systans consist of... 

Table 1 shows types of nodes used in the test network. The virtual supersource node 1, virtual supersink sink node 47 and other virtual nodes (used for computational purposes only) are not shown in the Table 1. The test case network contains major elements of the gas transmission network. The network is supplied by pipelines and no ENG terminal is available. Table 2 shows maximum capacities of input supply nodes in millions of cubic meters (mcm) per day. It should be noted that maximum shown UGS supply capacity decreases with time.

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