Pipelines networks

A system for distribution of fluids such as cooling water in a process plant consists of many interconnecting pipes in series, parallel, or branches. For purposes of analysis, a point at which several lines meet is called a node and each is assigned a number as on the figure of Example 6.6. A flow rate from node i to node j is designated as Qij-, the same subscript notation is used for other characteristics of the line such as / L, D, and Aae. 

Three principles are applicable to establishing flow rates, pressures, and dimensions throughout the network  

A material balance is preserved at each node total flow in equals total flow out, or net flow equals zero. 

In the usual network problem, the terminal pressures, line lengths, and line diameters are specified and the flow rates throughout are required to be found. The solution can be generalized, however, to determine other unknown quantities equal in number to the number of independent friction equations that describe the network. The procedure is illustrated with the network of Example 6.6. 

The three lines in parallel between nodes 2 and 5 have the same pressure drop Py - P5. In series lines such as 37 and 76 the flow rate is the same and a single equation represents friction in the series  

The friction equation P,-Pj = ( p/gcn 2)fjLljQl/Dfj applies to the line connecting node i with 

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The Gulf Central Pipeline system (78) contains 3220 km of 152 mm, 203 mm, and 254 mm pipe and has a pumping capacity of 2545 metric tons per day and supporting terminal storage fackities. The Tampa Bay Pipeline network services several ammonia plants along a 133 km route. 

The requirements derived in Eq. (10-5) are relevant in the cathodic protection of distribution networks for low and as uniform as possible values of resistance and leakage loading. The second requirement is often not fulfilled with old pipeline networks on account of their different ages and the type of pipe coating. When setting up cathodic protection, a distinction must be made between old and new steel distribution networks. 

LNG—consisting of ethane, propane, butane, and natural gasoline (condensate)—arrives at the plant for upgrading before it is sent to petrochemical plants and refineries as feedstock. Residue gas is sold to the interstate and intrastate pipeline network. MESA, one of the world s major crude helium producers, also delivers helium to a pipeline operated by the U.S. Bureau of Mines. 

This analysis is far from exact since it assumes a remote groundbed, uniform soil resistivity and uniform defect density in the coating. At best it demonstrates that attenuation is likely to follow an exponential decay and that it will be less severe for larger diameter pipes than for smaller. The problem is more difficult to solve for more complex structures (e.g. congested pipeline networks) and especially so for marine installations where the development of the calcareous deposit introduces the possibility of temporal variations in attenuation. 

Richard S. H. Mah and Mordechai Shacham, Pipeline Network Design and Synthesis J. Robert Selman and Charles W. Tobias, Mass-Transfer Measurements by the Limiting-Current Technique... 

II. Steady-State Pipeline Network Problems Formulation.127... 

Some typical questions raised in pipeline network design and analysis are... 

In this review the status of the relevant technology will be assessed with particular reference to formulation of problems and methods of solution. We shall, for the most part, be concerned with the technical literature of the last ten years. Since that period corresponds to the total eclipse of analog simulation which had been previously used, to some extent, in modeling pipeline networks (R3), we shall focus exclusively on digital computation methods. However, we shall not be content with a mere catalog of the different... 

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. 

The mathematical abstraction of the topology of a pipeline network is called a graph which consists of a set of vertices (sometimes also referred to as nodes, junctions, or points)... 

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... 

To have a better appreciation of the utility of these representations let us first consider the laws that govern flow rates and pressure drops in a pipeline network. These are the counterparts to KirchofTs laws for electrical circuits, namely, (i) the algebraic sum of flows at each vertex must be zero (ii) the algebraic sum of pressure drops around any cyclic path must be zero. For a connected network with N vertices and P edges there will be (N — 1) independent equations corresponding to the first law (KirchofTs current... 

Equations (16) and (17) show the important link between fundamental cycles and cut-sets of a graph. Thus, a spanning tree provides a convenient starting point for formulating a consistent set of governing equations for steady-state pipeline network problems. 

Because Eq. (22) is implicit in /, an iterative method of solution must be employed. However, the convergence of this iteration usually presents no difficulty (B5, D2). Bending and Hutchison (B5) noted that in pipeline network calculations it was not necessary to calculate exact friction factors for each overall network iteration. In their experience the problem could be solved satisfactorily with single updating of factors for each overall iteration. This truncation results in significant reduction of computing time. In all... 

Valves and regulators are used in pipeline networks to perform a variety of functions. Isolating valves are used to interrupt flows and to shut off... 

Regulators have interesting implications for pipeline network calculations, which will be explored in Section III,C. 

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 our treatment so far we have dwelt on the description, formulation, and specification of steady-state pipeline network problems. As we stated at the... 

Under all but laminar flow conditions, the steady-state pipeline network problems are described by mixed sets of linear and nonlinear equations regardless of the choice of formulations. Since these equations cannot be solved directly, an iterative procedure is usually employed. For ease of reference let us represent the steady-state equations as... 

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