Articles | Volume 10, issue 2
Research article
10 Oct 2017
Research article |  | 10 Oct 2017

Limitations of demand- and pressure-driven modeling for large deficient networks

Mathias Braun, Olivier Piller, Jochen Deuerlein, and Iraj Mortazavi

Abstract. The calculation of hydraulic state variables for a network is an important task in managing the distribution of potable water. Over the years the mathematical modeling process has been improved by numerous researchers for utilization in new computer applications and the more realistic modeling of water distribution networks. But, in spite of these continuous advances, there are still a number of physical phenomena that may not be tackled correctly by current models. This paper will take a closer look at the two modeling paradigms given by demand- and pressure-driven modeling. The basic equations are introduced and parallels are drawn with the optimization formulations from electrical engineering. These formulations guarantee the existence and uniqueness of the solution. One of the central questions of the French and German research project ResiWater is the investigation of the network resilience in the case of extreme events or disasters. Under such extraordinary conditions where models are pushed beyond their limits, we talk about deficient network models. Examples of deficient networks are given by highly regulated flow, leakage or pipe bursts and cases where pressure falls below the vapor pressure of water. These examples will be presented and analyzed on the solvability and physical correctness of the solution with respect to demand- and pressure-driven models.

Short summary
The article introduces a stable formulation of the model for water distribution systems that guarantees the existence of a unique solution. This is done regarding two modeling paradigms. First for models with customer demand as a fixed boundary condition and second for models that add a boundary condition on the minimum network pressure. The following discussion concludes that pressure-driven models are superior in modeling deficient networks, but still have to be improved.