Pipeline network problems balancing flows

In principle, the steady-state pipeline network problems can always be solved by the transient solution methods after allowing sufficient time steps for the solution to reach steady state. This possibility was discussed by Nahavandi and Catanzaro (Nl) who made a comparison of a transient solution method with the Cross method of balancing flows (R4). For the particular 35-node and 45-branch hydraulic network problem tested, the transient solution method took 108 seconds as compared with the 134 seconds required by the Hardy-Cross method. (See also Section V,A,2.)... 

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... 

A more complicated problem is met in the multi-product case where batches of products have to be routed through the pipeline (network) whereby a batch may also be split into sub-batches at pipeline forks. In the oases of multiple sources, additionally a coordinated pumping planning is required under consideration of the pumping capacity, the due dates of the batches, and the segment-wise flow balances. 

Of special relevance among these types are the one-to-many and many-to-many networks as these show the most challenging planning problems. In the single product case, the main problem is to keep the flow in balance along the pipeline or pipeline segments such that inflow and outflow are equal at any time. 

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