The traditional solution of a gas distribution network consists in the determination of the pressures in the nodes starting from the actual load and a knowledge of the morphology (topology and pipe characteristics). This procedure nevertheless, has been improved upon since the time when Shamir and Howard gave a more general approach to the problem developing a calculating algorithm in which the unknowns are not necessarily the pressures.
With this new approach it is now possible to solve directly many important problems which before required the trial-and-error method. Among the approachs many advantages are: the direct solution of design problems, and the determination of maximum loads.
The first consists in determining the diameters of certain pipes (in this case unknowns), so that the pressures have predetermined values.
In the second problem, pressure values are set at minimums which guarantee a good service level, determining the highest allowable flows.
As we can see, any combination of unknowns is valid provided that the number of unknowns coincides with the number of equations, and that the resulting system is compatible. All of this has been covered in a previous paper (See Ref. (7)) and is summarized in section (2).
Nevertheless, the main point of this article concerns the mathematical adjustment and (the consequent) modeling of a gas network. Its usefulness is fully justified in practice, especially when old networks are involved, since in long-installed networks line parameters are not known with precision: diameters and roughness levels are affected by aging, corrosion, wear, etc. We must therefore a priori estimate such parameters in order to approach the network solution.
Normally the results derived from this first analysis do not coincide with the measured values. This discrepancy is due to the uncertainty of the initial data. A subsequent, adequate readjustment of the original data will bring the new model data closer to those of the actual measurements. When a reasonable agreement between the two sets of values is obtained, we shall have solved the adjustment problem.
The use of sensitivity-analysis techniques allows us to calculate what effect variation in the pipe parameters and/or the consumptions will have on the pressures derived from a theoretical calculation. These techniques make possible the direct determination of the adjustments to be made on the initial data in order to obtain the desired level of agreement.
The algorithm developed for the application of sensitivity-analysis to the problem of network adjustment is based on the nodal formulation of the continuity equations in each node.